1,1,1022,0,1.390887," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{5} \, A b^{3} d g^{3} i x^{5} + \frac{1}{4} \, A b^{3} c g^{3} i x^{4} + \frac{3}{4} \, A a b^{2} d g^{3} i x^{4} + A a b^{2} c g^{3} i x^{3} + A a^{2} b d g^{3} i x^{3} + \frac{3}{2} \, A a^{2} b c g^{3} i x^{2} + \frac{1}{2} \, A a^{3} d g^{3} i x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a^{3} c g^{3} i + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{2} b c g^{3} i + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a b^{2} c g^{3} i + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B b^{3} c g^{3} i + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{3} d g^{3} i + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a^{2} b d g^{3} i + \frac{1}{8} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a b^{2} d g^{3} i + \frac{1}{60} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B b^{3} d g^{3} i + A a^{3} c g^{3} i x"," ",0,"1/5*A*b^3*d*g^3*i*x^5 + 1/4*A*b^3*c*g^3*i*x^4 + 3/4*A*a*b^2*d*g^3*i*x^4 + A*a*b^2*c*g^3*i*x^3 + A*a^2*b*d*g^3*i*x^3 + 3/2*A*a^2*b*c*g^3*i*x^2 + 1/2*A*a^3*d*g^3*i*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a^3*c*g^3*i + 3/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^2*b*c*g^3*i + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a*b^2*c*g^3*i + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*b^3*c*g^3*i + 1/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^3*d*g^3*i + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a^2*b*d*g^3*i + 1/8*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a*b^2*d*g^3*i + 1/60*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*b^3*d*g^3*i + A*a^3*c*g^3*i*x","B",0
2,1,671,0,1.231723," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{4} \, A b^{2} d g^{2} i x^{4} + \frac{1}{3} \, A b^{2} c g^{2} i x^{3} + \frac{2}{3} \, A a b d g^{2} i x^{3} + A a b c g^{2} i x^{2} + \frac{1}{2} \, A a^{2} d g^{2} i x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a^{2} c g^{2} i + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a b c g^{2} i + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B b^{2} c g^{2} i + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{2} d g^{2} i + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a b d g^{2} i + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B b^{2} d g^{2} i + A a^{2} c g^{2} i x"," ",0,"1/4*A*b^2*d*g^2*i*x^4 + 1/3*A*b^2*c*g^2*i*x^3 + 2/3*A*a*b*d*g^2*i*x^3 + A*a*b*c*g^2*i*x^2 + 1/2*A*a^2*d*g^2*i*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a^2*c*g^2*i + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a*b*c*g^2*i + 1/6*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*b^2*c*g^2*i + 1/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^2*d*g^2*i + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a*b*d*g^2*i + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*b^2*d*g^2*i + A*a^2*c*g^2*i*x","B",0
3,1,361,0,1.196459," ","integrate((b*g*x+a*g)*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{3} \, A b d g i x^{3} + \frac{1}{2} \, A b c g i x^{2} + \frac{1}{2} \, A a d g i x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a c g i + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B b c g i + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a d g i + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B b d g i + A a c g i x"," ",0,"1/3*A*b*d*g*i*x^3 + 1/2*A*b*c*g*i*x^2 + 1/2*A*a*d*g*i*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a*c*g*i + 1/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*b*c*g*i + 1/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a*d*g*i + 1/6*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*b*d*g*i + A*a*c*g*i*x","B",0
4,1,144,0,1.099090," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{2} \, A d i x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B c i + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B d i + A c i x"," ",0,"1/2*A*d*i*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*c*i + 1/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*d*i + A*c*i*x","A",0
5,1,241,0,1.840155," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g),x, algorithm=""maxima"")","A d i {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} + \frac{A c i \log\left(b g x + a g\right)}{b g} - \frac{B c i \log\left(d x + c\right)}{b g} + \frac{{\left(b c i - a d i\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{2} g} + \frac{2 \, B b d i x \log\left(e\right) + {\left(b c i - a d i\right)} B \log\left(b x + a\right)^{2} + 2 \, {\left(B b d i x + {\left(b c i \log\left(e\right) - {\left(i \log\left(e\right) - i\right)} a d\right)} B\right)} \log\left(b x + a\right) - 2 \, {\left(B b d i x + {\left(b c i - a d i\right)} B \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b^{2} g}"," ",0,"A*d*i*(x/(b*g) - a*log(b*x + a)/(b^2*g)) + A*c*i*log(b*g*x + a*g)/(b*g) - B*c*i*log(d*x + c)/(b*g) + (b*c*i - a*d*i)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^2*g) + 1/2*(2*B*b*d*i*x*log(e) + (b*c*i - a*d*i)*B*log(b*x + a)^2 + 2*(B*b*d*i*x + (b*c*i*log(e) - (i*log(e) - i)*a*d)*B)*log(b*x + a) - 2*(B*b*d*i*x + (b*c*i - a*d*i)*B*log(b*x + a))*log(d*x + c))/(b^2*g)","A",0
6,0,0,0,0.000000," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B d i {\left(\frac{{\left({\left(b x + a\right)} \log\left(b x + a\right) + a\right)} \log\left(d x + c\right)}{b^{3} g^{2} x + a b^{2} g^{2}} - \int \frac{b^{2} d x^{2} \log\left(e\right) + a^{2} d + {\left(b^{2} c \log\left(e\right) + a b d\right)} x + {\left(2 \, b^{2} d x^{2} + a^{2} d + {\left(b^{2} c + 2 \, a b d\right)} x\right)} \log\left(b x + a\right)}{b^{4} d g^{2} x^{3} + a^{2} b^{2} c g^{2} + {\left(b^{4} c g^{2} + 2 \, a b^{3} d g^{2}\right)} x^{2} + {\left(2 \, a b^{3} c g^{2} + a^{2} b^{2} d g^{2}\right)} x}\,{d x}\right)} + A d i {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - B c i {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{2} g^{2} x + a b g^{2}} + \frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{A c i}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-B*d*i*(((b*x + a)*log(b*x + a) + a)*log(d*x + c)/(b^3*g^2*x + a*b^2*g^2) - integrate((b^2*d*x^2*log(e) + a^2*d + (b^2*c*log(e) + a*b*d)*x + (2*b^2*d*x^2 + a^2*d + (b^2*c + 2*a*b*d)*x)*log(b*x + a))/(b^4*d*g^2*x^3 + a^2*b^2*c*g^2 + (b^4*c*g^2 + 2*a*b^3*d*g^2)*x^2 + (2*a*b^3*c*g^2 + a^2*b^2*d*g^2)*x), x)) + A*d*i*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - B*c*i*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^2*g^2*x + a*b*g^2) + 1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A*c*i/(b^2*g^2*x + a*b*g^2)","F",0
7,1,570,0,1.316168," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, B d i {\left(\frac{2 \, {\left(2 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} + \frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{4} \, B c i {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{{\left(2 \, b x + a\right)} A d i}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{A c i}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"-1/4*B*d*i*(2*(2*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) + (3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/4*B*c*i*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - 1/2*(2*b*x + a)*A*d*i/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*A*c*i/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
8,1,933,0,1.376492," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{36} \, B d i {\left(\frac{6 \, {\left(3 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}} + \frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{1}{18} \, B c i {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{{\left(3 \, b x + a\right)} A d i}{6 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{A c i}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/36*B*d*i*(6*(3*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) + (5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/18*B*c*i*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/6*(3*b*x + a)*A*d*i/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*A*c*i/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","B",0
9,1,1386,0,1.796544," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{1}{144} \, B d i {\left(\frac{12 \, {\left(4 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}} + \frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} + \frac{1}{48} \, B c i {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} - \frac{12 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{{\left(4 \, b x + a\right)} A d i}{12 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{A c i}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"-1/144*B*d*i*(12*(4*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) + (7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) + 1/48*B*c*i*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) - 12*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/12*(4*b*x + a)*A*d*i/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/4*A*c*i/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
10,1,1789,0,1.686209," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{6} \, A b^{3} d^{2} g^{3} i^{2} x^{6} + \frac{2}{5} \, A b^{3} c d g^{3} i^{2} x^{5} + \frac{3}{5} \, A a b^{2} d^{2} g^{3} i^{2} x^{5} + \frac{1}{4} \, A b^{3} c^{2} g^{3} i^{2} x^{4} + \frac{3}{2} \, A a b^{2} c d g^{3} i^{2} x^{4} + \frac{3}{4} \, A a^{2} b d^{2} g^{3} i^{2} x^{4} + A a b^{2} c^{2} g^{3} i^{2} x^{3} + 2 \, A a^{2} b c d g^{3} i^{2} x^{3} + \frac{1}{3} \, A a^{3} d^{2} g^{3} i^{2} x^{3} + \frac{3}{2} \, A a^{2} b c^{2} g^{3} i^{2} x^{2} + A a^{3} c d g^{3} i^{2} x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a^{3} c^{2} g^{3} i^{2} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{2} b c^{2} g^{3} i^{2} + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a b^{2} c^{2} g^{3} i^{2} + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B b^{3} c^{2} g^{3} i^{2} + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{3} c d g^{3} i^{2} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a^{2} b c d g^{3} i^{2} + \frac{1}{4} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a b^{2} c d g^{3} i^{2} + \frac{1}{30} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B b^{3} c d g^{3} i^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a^{3} d^{2} g^{3} i^{2} + \frac{1}{8} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a^{2} b d^{2} g^{3} i^{2} + \frac{1}{20} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B a b^{2} d^{2} g^{3} i^{2} + \frac{1}{360} \, {\left(60 \, x^{6} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} + \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} - \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} B b^{3} d^{2} g^{3} i^{2} + A a^{3} c^{2} g^{3} i^{2} x"," ",0,"1/6*A*b^3*d^2*g^3*i^2*x^6 + 2/5*A*b^3*c*d*g^3*i^2*x^5 + 3/5*A*a*b^2*d^2*g^3*i^2*x^5 + 1/4*A*b^3*c^2*g^3*i^2*x^4 + 3/2*A*a*b^2*c*d*g^3*i^2*x^4 + 3/4*A*a^2*b*d^2*g^3*i^2*x^4 + A*a*b^2*c^2*g^3*i^2*x^3 + 2*A*a^2*b*c*d*g^3*i^2*x^3 + 1/3*A*a^3*d^2*g^3*i^2*x^3 + 3/2*A*a^2*b*c^2*g^3*i^2*x^2 + A*a^3*c*d*g^3*i^2*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a^3*c^2*g^3*i^2 + 3/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^2*b*c^2*g^3*i^2 + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a*b^2*c^2*g^3*i^2 + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*b^3*c^2*g^3*i^2 + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^3*c*d*g^3*i^2 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a^2*b*c*d*g^3*i^2 + 1/4*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a*b^2*c*d*g^3*i^2 + 1/30*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*b^3*c*d*g^3*i^2 + 1/6*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a^3*d^2*g^3*i^2 + 1/8*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a^2*b*d^2*g^3*i^2 + 1/20*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*a*b^2*d^2*g^3*i^2 + 1/360*(60*x^6*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 60*a^6*log(b*x + a)/b^6 + 60*c^6*log(d*x + c)/d^6 - (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5))*B*b^3*d^2*g^3*i^2 + A*a^3*c^2*g^3*i^2*x","B",0
11,1,1200,0,1.473906," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{5} \, A b^{2} d^{2} g^{2} i^{2} x^{5} + \frac{1}{2} \, A b^{2} c d g^{2} i^{2} x^{4} + \frac{1}{2} \, A a b d^{2} g^{2} i^{2} x^{4} + \frac{1}{3} \, A b^{2} c^{2} g^{2} i^{2} x^{3} + \frac{4}{3} \, A a b c d g^{2} i^{2} x^{3} + \frac{1}{3} \, A a^{2} d^{2} g^{2} i^{2} x^{3} + A a b c^{2} g^{2} i^{2} x^{2} + A a^{2} c d g^{2} i^{2} x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a^{2} c^{2} g^{2} i^{2} + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a b c^{2} g^{2} i^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B b^{2} c^{2} g^{2} i^{2} + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{2} c d g^{2} i^{2} + \frac{2}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a b c d g^{2} i^{2} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B b^{2} c d g^{2} i^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a^{2} d^{2} g^{2} i^{2} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a b d^{2} g^{2} i^{2} + \frac{1}{60} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B b^{2} d^{2} g^{2} i^{2} + A a^{2} c^{2} g^{2} i^{2} x"," ",0,"1/5*A*b^2*d^2*g^2*i^2*x^5 + 1/2*A*b^2*c*d*g^2*i^2*x^4 + 1/2*A*a*b*d^2*g^2*i^2*x^4 + 1/3*A*b^2*c^2*g^2*i^2*x^3 + 4/3*A*a*b*c*d*g^2*i^2*x^3 + 1/3*A*a^2*d^2*g^2*i^2*x^3 + A*a*b*c^2*g^2*i^2*x^2 + A*a^2*c*d*g^2*i^2*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a^2*c^2*g^2*i^2 + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a*b*c^2*g^2*i^2 + 1/6*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*b^2*c^2*g^2*i^2 + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^2*c*d*g^2*i^2 + 2/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a*b*c*d*g^2*i^2 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*b^2*c*d*g^2*i^2 + 1/6*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a^2*d^2*g^2*i^2 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a*b*d^2*g^2*i^2 + 1/60*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*b^2*d^2*g^2*i^2 + A*a^2*c^2*g^2*i^2*x","B",0
12,1,671,0,1.254435," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{4} \, A b d^{2} g i^{2} x^{4} + \frac{2}{3} \, A b c d g i^{2} x^{3} + \frac{1}{3} \, A a d^{2} g i^{2} x^{3} + \frac{1}{2} \, A b c^{2} g i^{2} x^{2} + A a c d g i^{2} x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a c^{2} g i^{2} + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B b c^{2} g i^{2} + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a c d g i^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B b c d g i^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a d^{2} g i^{2} + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B b d^{2} g i^{2} + A a c^{2} g i^{2} x"," ",0,"1/4*A*b*d^2*g*i^2*x^4 + 2/3*A*b*c*d*g*i^2*x^3 + 1/3*A*a*d^2*g*i^2*x^3 + 1/2*A*b*c^2*g*i^2*x^2 + A*a*c*d*g*i^2*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a*c^2*g*i^2 + 1/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*b*c^2*g*i^2 + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a*c*d*g*i^2 + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*b*c*d*g*i^2 + 1/6*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a*d^2*g*i^2 + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*b*d^2*g*i^2 + A*a*c^2*g*i^2*x","B",0
13,1,280,0,1.101837," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{3} \, A d^{2} i^{2} x^{3} + A c d i^{2} x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B c^{2} i^{2} + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B c d i^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B d^{2} i^{2} + A c^{2} i^{2} x"," ",0,"1/3*A*d^2*i^2*x^3 + A*c*d*i^2*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*c^2*i^2 + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*c*d*i^2 + 1/6*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*d^2*i^2 + A*c^2*i^2*x","B",0
14,1,518,0,1.798525," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g),x, algorithm=""maxima"")","2 \, A c d i^{2} {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} + \frac{1}{2} \, A d^{2} i^{2} {\left(\frac{2 \, a^{2} \log\left(b x + a\right)}{b^{3} g} + \frac{b x^{2} - 2 \, a x}{b^{2} g}\right)} + \frac{A c^{2} i^{2} \log\left(b g x + a g\right)}{b g} - \frac{{\left(3 \, b c^{2} i^{2} - 2 \, a c d i^{2}\right)} B \log\left(d x + c\right)}{2 \, b^{2} g} + \frac{{\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{3} g} + \frac{B b^{2} d^{2} i^{2} x^{2} \log\left(e\right) + {\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} B \log\left(b x + a\right)^{2} + {\left({\left(4 \, i^{2} \log\left(e\right) - i^{2}\right)} b^{2} c d - {\left(2 \, i^{2} \log\left(e\right) - i^{2}\right)} a b d^{2}\right)} B x + {\left(B b^{2} d^{2} i^{2} x^{2} + 2 \, {\left(2 \, b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B x + {\left(2 \, b^{2} c^{2} i^{2} \log\left(e\right) - 4 \, {\left(i^{2} \log\left(e\right) - i^{2}\right)} a b c d + {\left(2 \, i^{2} \log\left(e\right) - 3 \, i^{2}\right)} a^{2} d^{2}\right)} B\right)} \log\left(b x + a\right) - {\left(B b^{2} d^{2} i^{2} x^{2} + 2 \, {\left(2 \, b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B x + 2 \, {\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} B \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b^{3} g}"," ",0,"2*A*c*d*i^2*(x/(b*g) - a*log(b*x + a)/(b^2*g)) + 1/2*A*d^2*i^2*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2*g)) + A*c^2*i^2*log(b*g*x + a*g)/(b*g) - 1/2*(3*b*c^2*i^2 - 2*a*c*d*i^2)*B*log(d*x + c)/(b^2*g) + (b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^3*g) + 1/2*(B*b^2*d^2*i^2*x^2*log(e) + (b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*B*log(b*x + a)^2 + ((4*i^2*log(e) - i^2)*b^2*c*d - (2*i^2*log(e) - i^2)*a*b*d^2)*B*x + (B*b^2*d^2*i^2*x^2 + 2*(2*b^2*c*d*i^2 - a*b*d^2*i^2)*B*x + (2*b^2*c^2*i^2*log(e) - 4*(i^2*log(e) - i^2)*a*b*c*d + (2*i^2*log(e) - 3*i^2)*a^2*d^2)*B)*log(b*x + a) - (B*b^2*d^2*i^2*x^2 + 2*(2*b^2*c*d*i^2 - a*b*d^2*i^2)*B*x + 2*(b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*B*log(b*x + a))*log(d*x + c))/(b^3*g)","A",0
15,1,992,0,1.908610," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-A {\left(\frac{a^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \frac{x}{b^{2} g^{2}} + \frac{2 \, a \log\left(b x + a\right)}{b^{3} g^{2}}\right)} d^{2} i^{2} + 2 \, A c d i^{2} {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - B c^{2} i^{2} {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{2} g^{2} x + a b g^{2}} + \frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{A c^{2} i^{2}}{b^{2} g^{2} x + a b g^{2}} - \frac{{\left(b^{2} c^{2} d i^{2} + a b c d^{2} i^{2} - a^{2} d^{3} i^{2}\right)} B \log\left(d x + c\right)}{b^{4} c g^{2} - a b^{3} d g^{2}} + \frac{{\left(b^{3} c d^{2} i^{2} \log\left(e\right) - a b^{2} d^{3} i^{2} \log\left(e\right)\right)} B x^{2} + {\left(a b^{2} c d^{2} i^{2} \log\left(e\right) - a^{2} b d^{3} i^{2} \log\left(e\right)\right)} B x + {\left({\left(b^{3} c^{2} d i^{2} - 2 \, a b^{2} c d^{2} i^{2} + a^{2} b d^{3} i^{2}\right)} B x + {\left(a b^{2} c^{2} d i^{2} - 2 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B\right)} \log\left(b x + a\right)^{2} + {\left(2 \, {\left(i^{2} \log\left(e\right) + i^{2}\right)} a b^{2} c^{2} d - 3 \, {\left(i^{2} \log\left(e\right) + i^{2}\right)} a^{2} b c d^{2} + {\left(i^{2} \log\left(e\right) + i^{2}\right)} a^{3} d^{3}\right)} B + {\left({\left(b^{3} c d^{2} i^{2} - a b^{2} d^{3} i^{2}\right)} B x^{2} + {\left(2 \, b^{3} c^{2} d i^{2} \log\left(e\right) - 4 \, {\left(i^{2} \log\left(e\right) - i^{2}\right)} a b^{2} c d^{2} + {\left(2 \, i^{2} \log\left(e\right) - 3 \, i^{2}\right)} a^{2} b d^{3}\right)} B x - {\left(4 \, a^{2} b c d^{2} i^{2} \log\left(e\right) - 2 \, {\left(i^{2} \log\left(e\right) + i^{2}\right)} a b^{2} c^{2} d - {\left(2 \, i^{2} \log\left(e\right) - i^{2}\right)} a^{3} d^{3}\right)} B\right)} \log\left(b x + a\right) - {\left({\left(b^{3} c d^{2} i^{2} - a b^{2} d^{3} i^{2}\right)} B x^{2} + {\left(a b^{2} c d^{2} i^{2} - a^{2} b d^{3} i^{2}\right)} B x + {\left(2 \, a b^{2} c^{2} d i^{2} - 3 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B + 2 \, {\left({\left(b^{3} c^{2} d i^{2} - 2 \, a b^{2} c d^{2} i^{2} + a^{2} b d^{3} i^{2}\right)} B x + {\left(a b^{2} c^{2} d i^{2} - 2 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a b^{4} c g^{2} - a^{2} b^{3} d g^{2} + {\left(b^{5} c g^{2} - a b^{4} d g^{2}\right)} x} + \frac{2 \, {\left(b c d i^{2} - a d^{2} i^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{3} g^{2}}"," ",0,"-A*(a^2/(b^4*g^2*x + a*b^3*g^2) - x/(b^2*g^2) + 2*a*log(b*x + a)/(b^3*g^2))*d^2*i^2 + 2*A*c*d*i^2*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - B*c^2*i^2*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^2*g^2*x + a*b*g^2) + 1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A*c^2*i^2/(b^2*g^2*x + a*b*g^2) - (b^2*c^2*d*i^2 + a*b*c*d^2*i^2 - a^2*d^3*i^2)*B*log(d*x + c)/(b^4*c*g^2 - a*b^3*d*g^2) + ((b^3*c*d^2*i^2*log(e) - a*b^2*d^3*i^2*log(e))*B*x^2 + (a*b^2*c*d^2*i^2*log(e) - a^2*b*d^3*i^2*log(e))*B*x + ((b^3*c^2*d*i^2 - 2*a*b^2*c*d^2*i^2 + a^2*b*d^3*i^2)*B*x + (a*b^2*c^2*d*i^2 - 2*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B)*log(b*x + a)^2 + (2*(i^2*log(e) + i^2)*a*b^2*c^2*d - 3*(i^2*log(e) + i^2)*a^2*b*c*d^2 + (i^2*log(e) + i^2)*a^3*d^3)*B + ((b^3*c*d^2*i^2 - a*b^2*d^3*i^2)*B*x^2 + (2*b^3*c^2*d*i^2*log(e) - 4*(i^2*log(e) - i^2)*a*b^2*c*d^2 + (2*i^2*log(e) - 3*i^2)*a^2*b*d^3)*B*x - (4*a^2*b*c*d^2*i^2*log(e) - 2*(i^2*log(e) + i^2)*a*b^2*c^2*d - (2*i^2*log(e) - i^2)*a^3*d^3)*B)*log(b*x + a) - ((b^3*c*d^2*i^2 - a*b^2*d^3*i^2)*B*x^2 + (a*b^2*c*d^2*i^2 - a^2*b*d^3*i^2)*B*x + (2*a*b^2*c^2*d*i^2 - 3*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B + 2*((b^3*c^2*d*i^2 - 2*a*b^2*c*d^2*i^2 + a^2*b*d^3*i^2)*B*x + (a*b^2*c^2*d*i^2 - 2*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B)*log(b*x + a))*log(d*x + c))/(a*b^4*c*g^2 - a^2*b^3*d*g^2 + (b^5*c*g^2 - a*b^4*d*g^2)*x) + 2*(b*c*d*i^2 - a*d^2*i^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^3*g^2)","B",0
16,0,0,0,0.000000," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B d^{2} i^{2} {\left(\frac{{\left(4 \, a b x + 3 \, a^{2} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} - 2 \, \int \frac{2 \, b^{3} d x^{3} \log\left(e\right) + 7 \, a^{2} b d x + 3 \, a^{3} d + 2 \, {\left(b^{3} c \log\left(e\right) + 2 \, a b^{2} d\right)} x^{2} + 2 \, {\left(2 \, b^{3} d x^{3} + 3 \, a^{2} b d x + a^{3} d + {\left(b^{3} c + 3 \, a b^{2} d\right)} x^{2}\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} d g^{3} x^{4} + a^{3} b^{3} c g^{3} + {\left(b^{6} c g^{3} + 3 \, a b^{5} d g^{3}\right)} x^{3} + 3 \, {\left(a b^{5} c g^{3} + a^{2} b^{4} d g^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{4} c g^{3} + a^{3} b^{3} d g^{3}\right)} x\right)}}\,{d x}\right)} - \frac{1}{2} \, B c d i^{2} {\left(\frac{2 \, {\left(2 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} + \frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{2} \, A d^{2} i^{2} {\left(\frac{4 \, a b x + 3 \, a^{2}}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + \frac{2 \, \log\left(b x + a\right)}{b^{3} g^{3}}\right)} + \frac{1}{4} \, B c^{2} i^{2} {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{{\left(2 \, b x + a\right)} A c d i^{2}}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} - \frac{A c^{2} i^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"-1/2*B*d^2*i^2*((4*a*b*x + 3*a^2 + 2*(b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a))*log(d*x + c)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) - 2*integrate(1/2*(2*b^3*d*x^3*log(e) + 7*a^2*b*d*x + 3*a^3*d + 2*(b^3*c*log(e) + 2*a*b^2*d)*x^2 + 2*(2*b^3*d*x^3 + 3*a^2*b*d*x + a^3*d + (b^3*c + 3*a*b^2*d)*x^2)*log(b*x + a))/(b^6*d*g^3*x^4 + a^3*b^3*c*g^3 + (b^6*c*g^3 + 3*a*b^5*d*g^3)*x^3 + 3*(a*b^5*c*g^3 + a^2*b^4*d*g^3)*x^2 + (3*a^2*b^4*c*g^3 + a^3*b^3*d*g^3)*x), x)) - 1/2*B*c*d*i^2*(2*(2*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) + (3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/2*A*d^2*i^2*((4*a*b*x + 3*a^2)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*log(b*x + a)/(b^3*g^3)) + 1/4*B*c^2*i^2*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - (2*b*x + a)*A*c*d*i^2/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*A*c^2*i^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","F",0
17,1,1515,0,1.633189," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{18} \, B d^{2} i^{2} {\left(\frac{6 \, {\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}} + \frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} - \frac{1}{18} \, B c d i^{2} {\left(\frac{6 \, {\left(3 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}} + \frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{1}{18} \, B c^{2} i^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{{\left(3 \, b x + a\right)} A c d i^{2}}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A d^{2} i^{2}}{3 \, {\left(b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}\right)}} - \frac{A c^{2} i^{2}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/18*B*d^2*i^2*(6*(3*b^2*x^2 + 3*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) + (11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4)) - 1/18*B*c*d*i^2*(6*(3*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) + (5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/18*B*c^2*i^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/3*(3*b*x + a)*A*c*d*i^2/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*(3*b^2*x^2 + 3*a*b*x + a^2)*A*d^2*i^2/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/3*A*c^2*i^2/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","B",0
18,1,2218,0,2.266388," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{1}{144} \, B d^{2} i^{2} {\left(\frac{12 \, {\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}} + \frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} - \frac{1}{72} \, B c d i^{2} {\left(\frac{12 \, {\left(4 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}} + \frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} + \frac{1}{48} \, B c^{2} i^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} - \frac{12 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{{\left(4 \, b x + a\right)} A c d i^{2}}{6 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} A d^{2} i^{2}}{12 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{A c^{2} i^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"-1/144*B*d^2*i^2*(12*(6*b^2*x^2 + 4*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) + (13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5)) - 1/72*B*c*d*i^2*(12*(4*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) + (7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) + 1/48*B*c^2*i^2*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) - 12*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/6*(4*b*x + a)*A*c*d*i^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/12*(6*b^2*x^2 + 4*a*b*x + a^2)*A*d^2*i^2/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/4*A*c^2*i^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
19,1,3029,0,3.036423," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^6,x, algorithm=""maxima"")","-\frac{1}{1800} \, B d^{2} i^{2} {\left(\frac{60 \, {\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}} + \frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} - \frac{1}{600} \, B c d i^{2} {\left(\frac{60 \, {\left(5 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}} + \frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} - \frac{1}{300} \, B c^{2} i^{2} {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} - \frac{{\left(5 \, b x + a\right)} A c d i^{2}}{10 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} A d^{2} i^{2}}{30 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{A c^{2} i^{2}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}}"," ",0,"-1/1800*B*d^2*i^2*(60*(10*b^2*x^2 + 5*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) + (47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6)) - 1/600*B*c*d*i^2*(60*(5*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) + (27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6)) - 1/300*B*c^2*i^2*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6)) - 1/10*(5*b*x + a)*A*c*d*i^2/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/30*(10*b^2*x^2 + 5*a*b*x + a^2)*A*d^2*i^2/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/5*A*c^2*i^2/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6)","B",0
20,1,2637,0,1.840113," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{7} \, A b^{3} d^{3} g^{3} i^{3} x^{7} + \frac{1}{2} \, A b^{3} c d^{2} g^{3} i^{3} x^{6} + \frac{1}{2} \, A a b^{2} d^{3} g^{3} i^{3} x^{6} + \frac{3}{5} \, A b^{3} c^{2} d g^{3} i^{3} x^{5} + \frac{9}{5} \, A a b^{2} c d^{2} g^{3} i^{3} x^{5} + \frac{3}{5} \, A a^{2} b d^{3} g^{3} i^{3} x^{5} + \frac{1}{4} \, A b^{3} c^{3} g^{3} i^{3} x^{4} + \frac{9}{4} \, A a b^{2} c^{2} d g^{3} i^{3} x^{4} + \frac{9}{4} \, A a^{2} b c d^{2} g^{3} i^{3} x^{4} + \frac{1}{4} \, A a^{3} d^{3} g^{3} i^{3} x^{4} + A a b^{2} c^{3} g^{3} i^{3} x^{3} + 3 \, A a^{2} b c^{2} d g^{3} i^{3} x^{3} + A a^{3} c d^{2} g^{3} i^{3} x^{3} + \frac{3}{2} \, A a^{2} b c^{3} g^{3} i^{3} x^{2} + \frac{3}{2} \, A a^{3} c^{2} d g^{3} i^{3} x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a^{3} c^{3} g^{3} i^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{2} b c^{3} g^{3} i^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a b^{2} c^{3} g^{3} i^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B b^{3} c^{3} g^{3} i^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{3} c^{2} d g^{3} i^{3} + \frac{3}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a^{2} b c^{2} d g^{3} i^{3} + \frac{3}{8} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a b^{2} c^{2} d g^{3} i^{3} + \frac{1}{20} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B b^{3} c^{2} d g^{3} i^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a^{3} c d^{2} g^{3} i^{3} + \frac{3}{8} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a^{2} b c d^{2} g^{3} i^{3} + \frac{3}{20} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B a b^{2} c d^{2} g^{3} i^{3} + \frac{1}{120} \, {\left(60 \, x^{6} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} + \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} - \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} B b^{3} c d^{2} g^{3} i^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a^{3} d^{3} g^{3} i^{3} + \frac{1}{20} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B a^{2} b d^{3} g^{3} i^{3} + \frac{1}{120} \, {\left(60 \, x^{6} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} + \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} - \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} B a b^{2} d^{3} g^{3} i^{3} + \frac{1}{420} \, {\left(60 \, x^{7} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{60 \, a^{7} \log\left(b x + a\right)}{b^{7}} - \frac{60 \, c^{7} \log\left(d x + c\right)}{d^{7}} - \frac{10 \, {\left(b^{6} c d^{5} - a b^{5} d^{6}\right)} x^{6} - 12 \, {\left(b^{6} c^{2} d^{4} - a^{2} b^{4} d^{6}\right)} x^{5} + 15 \, {\left(b^{6} c^{3} d^{3} - a^{3} b^{3} d^{6}\right)} x^{4} - 20 \, {\left(b^{6} c^{4} d^{2} - a^{4} b^{2} d^{6}\right)} x^{3} + 30 \, {\left(b^{6} c^{5} d - a^{5} b d^{6}\right)} x^{2} - 60 \, {\left(b^{6} c^{6} - a^{6} d^{6}\right)} x}{b^{6} d^{6}}\right)} B b^{3} d^{3} g^{3} i^{3} + A a^{3} c^{3} g^{3} i^{3} x"," ",0,"1/7*A*b^3*d^3*g^3*i^3*x^7 + 1/2*A*b^3*c*d^2*g^3*i^3*x^6 + 1/2*A*a*b^2*d^3*g^3*i^3*x^6 + 3/5*A*b^3*c^2*d*g^3*i^3*x^5 + 9/5*A*a*b^2*c*d^2*g^3*i^3*x^5 + 3/5*A*a^2*b*d^3*g^3*i^3*x^5 + 1/4*A*b^3*c^3*g^3*i^3*x^4 + 9/4*A*a*b^2*c^2*d*g^3*i^3*x^4 + 9/4*A*a^2*b*c*d^2*g^3*i^3*x^4 + 1/4*A*a^3*d^3*g^3*i^3*x^4 + A*a*b^2*c^3*g^3*i^3*x^3 + 3*A*a^2*b*c^2*d*g^3*i^3*x^3 + A*a^3*c*d^2*g^3*i^3*x^3 + 3/2*A*a^2*b*c^3*g^3*i^3*x^2 + 3/2*A*a^3*c^2*d*g^3*i^3*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a^3*c^3*g^3*i^3 + 3/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^2*b*c^3*g^3*i^3 + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a*b^2*c^3*g^3*i^3 + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*b^3*c^3*g^3*i^3 + 3/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^3*c^2*d*g^3*i^3 + 3/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a^2*b*c^2*d*g^3*i^3 + 3/8*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a*b^2*c^2*d*g^3*i^3 + 1/20*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*b^3*c^2*d*g^3*i^3 + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a^3*c*d^2*g^3*i^3 + 3/8*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a^2*b*c*d^2*g^3*i^3 + 3/20*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*a*b^2*c*d^2*g^3*i^3 + 1/120*(60*x^6*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 60*a^6*log(b*x + a)/b^6 + 60*c^6*log(d*x + c)/d^6 - (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5))*B*b^3*c*d^2*g^3*i^3 + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a^3*d^3*g^3*i^3 + 1/20*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*a^2*b*d^3*g^3*i^3 + 1/120*(60*x^6*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 60*a^6*log(b*x + a)/b^6 + 60*c^6*log(d*x + c)/d^6 - (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5))*B*a*b^2*d^3*g^3*i^3 + 1/420*(60*x^7*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 60*a^7*log(b*x + a)/b^7 - 60*c^7*log(d*x + c)/d^7 - (10*(b^6*c*d^5 - a*b^5*d^6)*x^6 - 12*(b^6*c^2*d^4 - a^2*b^4*d^6)*x^5 + 15*(b^6*c^3*d^3 - a^3*b^3*d^6)*x^4 - 20*(b^6*c^4*d^2 - a^4*b^2*d^6)*x^3 + 30*(b^6*c^5*d - a^5*b*d^6)*x^2 - 60*(b^6*c^6 - a^6*d^6)*x)/(b^6*d^6))*B*b^3*d^3*g^3*i^3 + A*a^3*c^3*g^3*i^3*x","B",0
21,1,1789,0,1.513167," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{6} \, A b^{2} d^{3} g^{2} i^{3} x^{6} + \frac{3}{5} \, A b^{2} c d^{2} g^{2} i^{3} x^{5} + \frac{2}{5} \, A a b d^{3} g^{2} i^{3} x^{5} + \frac{3}{4} \, A b^{2} c^{2} d g^{2} i^{3} x^{4} + \frac{3}{2} \, A a b c d^{2} g^{2} i^{3} x^{4} + \frac{1}{4} \, A a^{2} d^{3} g^{2} i^{3} x^{4} + \frac{1}{3} \, A b^{2} c^{3} g^{2} i^{3} x^{3} + 2 \, A a b c^{2} d g^{2} i^{3} x^{3} + A a^{2} c d^{2} g^{2} i^{3} x^{3} + A a b c^{3} g^{2} i^{3} x^{2} + \frac{3}{2} \, A a^{2} c^{2} d g^{2} i^{3} x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a^{2} c^{3} g^{2} i^{3} + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a b c^{3} g^{2} i^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B b^{2} c^{3} g^{2} i^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a^{2} c^{2} d g^{2} i^{3} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a b c^{2} d g^{2} i^{3} + \frac{1}{8} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B b^{2} c^{2} d g^{2} i^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a^{2} c d^{2} g^{2} i^{3} + \frac{1}{4} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a b c d^{2} g^{2} i^{3} + \frac{1}{20} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B b^{2} c d^{2} g^{2} i^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a^{2} d^{3} g^{2} i^{3} + \frac{1}{30} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B a b d^{3} g^{2} i^{3} + \frac{1}{360} \, {\left(60 \, x^{6} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} + \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} - \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} B b^{2} d^{3} g^{2} i^{3} + A a^{2} c^{3} g^{2} i^{3} x"," ",0,"1/6*A*b^2*d^3*g^2*i^3*x^6 + 3/5*A*b^2*c*d^2*g^2*i^3*x^5 + 2/5*A*a*b*d^3*g^2*i^3*x^5 + 3/4*A*b^2*c^2*d*g^2*i^3*x^4 + 3/2*A*a*b*c*d^2*g^2*i^3*x^4 + 1/4*A*a^2*d^3*g^2*i^3*x^4 + 1/3*A*b^2*c^3*g^2*i^3*x^3 + 2*A*a*b*c^2*d*g^2*i^3*x^3 + A*a^2*c*d^2*g^2*i^3*x^3 + A*a*b*c^3*g^2*i^3*x^2 + 3/2*A*a^2*c^2*d*g^2*i^3*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a^2*c^3*g^2*i^3 + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a*b*c^3*g^2*i^3 + 1/6*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*b^2*c^3*g^2*i^3 + 3/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a^2*c^2*d*g^2*i^3 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a*b*c^2*d*g^2*i^3 + 1/8*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*b^2*c^2*d*g^2*i^3 + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a^2*c*d^2*g^2*i^3 + 1/4*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a*b*c*d^2*g^2*i^3 + 1/20*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*b^2*c*d^2*g^2*i^3 + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a^2*d^3*g^2*i^3 + 1/30*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*a*b*d^3*g^2*i^3 + 1/360*(60*x^6*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 60*a^6*log(b*x + a)/b^6 + 60*c^6*log(d*x + c)/d^6 - (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5))*B*b^2*d^3*g^2*i^3 + A*a^2*c^3*g^2*i^3*x","B",0
22,1,1022,0,1.342374," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{5} \, A b d^{3} g i^{3} x^{5} + \frac{3}{4} \, A b c d^{2} g i^{3} x^{4} + \frac{1}{4} \, A a d^{3} g i^{3} x^{4} + A b c^{2} d g i^{3} x^{3} + A a c d^{2} g i^{3} x^{3} + \frac{1}{2} \, A b c^{3} g i^{3} x^{2} + \frac{3}{2} \, A a c^{2} d g i^{3} x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B a c^{3} g i^{3} + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B b c^{3} g i^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B a c^{2} d g i^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B b c^{2} d g i^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B a c d^{2} g i^{3} + \frac{1}{8} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B b c d^{2} g i^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B a d^{3} g i^{3} + \frac{1}{60} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} B b d^{3} g i^{3} + A a c^{3} g i^{3} x"," ",0,"1/5*A*b*d^3*g*i^3*x^5 + 3/4*A*b*c*d^2*g*i^3*x^4 + 1/4*A*a*d^3*g*i^3*x^4 + A*b*c^2*d*g*i^3*x^3 + A*a*c*d^2*g*i^3*x^3 + 1/2*A*b*c^3*g*i^3*x^2 + 3/2*A*a*c^2*d*g*i^3*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*a*c^3*g*i^3 + 1/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*b*c^3*g*i^3 + 3/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*a*c^2*d*g*i^3 + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*b*c^2*d*g*i^3 + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*a*c*d^2*g*i^3 + 1/8*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*b*c*d^2*g*i^3 + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*a*d^3*g*i^3 + 1/60*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*B*b*d^3*g*i^3 + A*a*c^3*g*i^3*x","B",0
23,1,439,0,1.145097," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{4} \, A d^{3} i^{3} x^{4} + A c d^{2} i^{3} x^{3} + \frac{3}{2} \, A c^{2} d i^{3} x^{2} + {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} B c^{3} i^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} B c^{2} d i^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} B c d^{2} i^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} B d^{3} i^{3} + A c^{3} i^{3} x"," ",0,"1/4*A*d^3*i^3*x^4 + A*c*d^2*i^3*x^3 + 3/2*A*c^2*d*i^3*x^2 + (x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*B*c^3*i^3 + 3/2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*B*c^2*d*i^3 + 1/2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*B*c*d^2*i^3 + 1/24*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*B*d^3*i^3 + A*c^3*i^3*x","B",0
24,1,850,0,1.845905," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g),x, algorithm=""maxima"")","3 \, A c^{2} d i^{3} {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} - \frac{1}{6} \, A d^{3} i^{3} {\left(\frac{6 \, a^{3} \log\left(b x + a\right)}{b^{4} g} - \frac{2 \, b^{2} x^{3} - 3 \, a b x^{2} + 6 \, a^{2} x}{b^{3} g}\right)} + \frac{3}{2} \, A c d^{2} i^{3} {\left(\frac{2 \, a^{2} \log\left(b x + a\right)}{b^{3} g} + \frac{b x^{2} - 2 \, a x}{b^{2} g}\right)} + \frac{A c^{3} i^{3} \log\left(b g x + a g\right)}{b g} - \frac{{\left(11 \, b^{2} c^{3} i^{3} - 15 \, a b c^{2} d i^{3} + 6 \, a^{2} c d^{2} i^{3}\right)} B \log\left(d x + c\right)}{6 \, b^{3} g} + \frac{{\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{4} g} + \frac{2 \, B b^{3} d^{3} i^{3} x^{3} \log\left(e\right) + {\left({\left(9 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{3} c d^{2} - {\left(3 \, i^{3} \log\left(e\right) - i^{3}\right)} a b^{2} d^{3}\right)} B x^{2} + 3 \, {\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B \log\left(b x + a\right)^{2} + {\left({\left(18 \, i^{3} \log\left(e\right) - 7 \, i^{3}\right)} b^{3} c^{2} d - 6 \, {\left(3 \, i^{3} \log\left(e\right) - 2 \, i^{3}\right)} a b^{2} c d^{2} + {\left(6 \, i^{3} \log\left(e\right) - 5 \, i^{3}\right)} a^{2} b d^{3}\right)} B x + {\left(2 \, B b^{3} d^{3} i^{3} x^{3} + 3 \, {\left(3 \, b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B x^{2} + 6 \, {\left(3 \, b^{3} c^{2} d i^{3} - 3 \, a b^{2} c d^{2} i^{3} + a^{2} b d^{3} i^{3}\right)} B x + {\left(6 \, b^{3} c^{3} i^{3} \log\left(e\right) - 18 \, {\left(i^{3} \log\left(e\right) - i^{3}\right)} a b^{2} c^{2} d + 9 \, {\left(2 \, i^{3} \log\left(e\right) - 3 \, i^{3}\right)} a^{2} b c d^{2} - {\left(6 \, i^{3} \log\left(e\right) - 11 \, i^{3}\right)} a^{3} d^{3}\right)} B\right)} \log\left(b x + a\right) - {\left(2 \, B b^{3} d^{3} i^{3} x^{3} + 3 \, {\left(3 \, b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B x^{2} + 6 \, {\left(3 \, b^{3} c^{2} d i^{3} - 3 \, a b^{2} c d^{2} i^{3} + a^{2} b d^{3} i^{3}\right)} B x + 6 \, {\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{6 \, b^{4} g}"," ",0,"3*A*c^2*d*i^3*(x/(b*g) - a*log(b*x + a)/(b^2*g)) - 1/6*A*d^3*i^3*(6*a^3*log(b*x + a)/(b^4*g) - (2*b^2*x^3 - 3*a*b*x^2 + 6*a^2*x)/(b^3*g)) + 3/2*A*c*d^2*i^3*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2*g)) + A*c^3*i^3*log(b*g*x + a*g)/(b*g) - 1/6*(11*b^2*c^3*i^3 - 15*a*b*c^2*d*i^3 + 6*a^2*c*d^2*i^3)*B*log(d*x + c)/(b^3*g) + (b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^4*g) + 1/6*(2*B*b^3*d^3*i^3*x^3*log(e) + ((9*i^3*log(e) - i^3)*b^3*c*d^2 - (3*i^3*log(e) - i^3)*a*b^2*d^3)*B*x^2 + 3*(b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B*log(b*x + a)^2 + ((18*i^3*log(e) - 7*i^3)*b^3*c^2*d - 6*(3*i^3*log(e) - 2*i^3)*a*b^2*c*d^2 + (6*i^3*log(e) - 5*i^3)*a^2*b*d^3)*B*x + (2*B*b^3*d^3*i^3*x^3 + 3*(3*b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B*x^2 + 6*(3*b^3*c^2*d*i^3 - 3*a*b^2*c*d^2*i^3 + a^2*b*d^3*i^3)*B*x + (6*b^3*c^3*i^3*log(e) - 18*(i^3*log(e) - i^3)*a*b^2*c^2*d + 9*(2*i^3*log(e) - 3*i^3)*a^2*b*c*d^2 - (6*i^3*log(e) - 11*i^3)*a^3*d^3)*B)*log(b*x + a) - (2*B*b^3*d^3*i^3*x^3 + 3*(3*b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B*x^2 + 6*(3*b^3*c^2*d*i^3 - 3*a*b^2*c*d^2*i^3 + a^2*b*d^3*i^3)*B*x + 6*(b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B*log(b*x + a))*log(d*x + c))/(b^4*g)","B",0
25,1,1501,0,1.837373," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-3 \, A {\left(\frac{a^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \frac{x}{b^{2} g^{2}} + \frac{2 \, a \log\left(b x + a\right)}{b^{3} g^{2}}\right)} c d^{2} i^{3} + \frac{1}{2} \, {\left(\frac{2 \, a^{3}}{b^{5} g^{2} x + a b^{4} g^{2}} + \frac{6 \, a^{2} \log\left(b x + a\right)}{b^{4} g^{2}} + \frac{b x^{2} - 4 \, a x}{b^{3} g^{2}}\right)} A d^{3} i^{3} + 3 \, A c^{2} d i^{3} {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - B c^{3} i^{3} {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{2} g^{2} x + a b g^{2}} + \frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{A c^{3} i^{3}}{b^{2} g^{2} x + a b g^{2}} - \frac{{\left(5 \, b^{3} c^{3} d i^{3} - 3 \, a b^{2} c^{2} d^{2} i^{3} - 2 \, a^{2} b c d^{3} i^{3} + 2 \, a^{3} d^{4} i^{3}\right)} B \log\left(d x + c\right)}{2 \, {\left(b^{5} c g^{2} - a b^{4} d g^{2}\right)}} + \frac{{\left(b^{4} c d^{3} i^{3} \log\left(e\right) - a b^{3} d^{4} i^{3} \log\left(e\right)\right)} B x^{3} + {\left({\left(6 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{4} c^{2} d^{2} - {\left(9 \, i^{3} \log\left(e\right) - 2 \, i^{3}\right)} a b^{3} c d^{3} + {\left(3 \, i^{3} \log\left(e\right) - i^{3}\right)} a^{2} b^{2} d^{4}\right)} B x^{2} + {\left({\left(6 \, i^{3} \log\left(e\right) - i^{3}\right)} a b^{3} c^{2} d^{2} - 2 \, {\left(5 \, i^{3} \log\left(e\right) - i^{3}\right)} a^{2} b^{2} c d^{3} + {\left(4 \, i^{3} \log\left(e\right) - i^{3}\right)} a^{3} b d^{4}\right)} B x + 3 \, {\left({\left(b^{4} c^{3} d i^{3} - 3 \, a b^{3} c^{2} d^{2} i^{3} + 3 \, a^{2} b^{2} c d^{3} i^{3} - a^{3} b d^{4} i^{3}\right)} B x + {\left(a b^{3} c^{3} d i^{3} - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 3 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(3 \, {\left(i^{3} \log\left(e\right) + i^{3}\right)} a b^{3} c^{3} d - 6 \, {\left(i^{3} \log\left(e\right) + i^{3}\right)} a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(i^{3} \log\left(e\right) + i^{3}\right)} a^{3} b c d^{3} - {\left(i^{3} \log\left(e\right) + i^{3}\right)} a^{4} d^{4}\right)} B + {\left({\left(b^{4} c d^{3} i^{3} - a b^{3} d^{4} i^{3}\right)} B x^{3} + 3 \, {\left(2 \, b^{4} c^{2} d^{2} i^{3} - 3 \, a b^{3} c d^{3} i^{3} + a^{2} b^{2} d^{4} i^{3}\right)} B x^{2} + {\left(6 \, b^{4} c^{3} d i^{3} \log\left(e\right) - 18 \, {\left(i^{3} \log\left(e\right) - i^{3}\right)} a b^{3} c^{2} d^{2} + 9 \, {\left(2 \, i^{3} \log\left(e\right) - 3 \, i^{3}\right)} a^{2} b^{2} c d^{3} - {\left(6 \, i^{3} \log\left(e\right) - 11 \, i^{3}\right)} a^{3} b d^{4}\right)} B x - {\left(18 \, a^{2} b^{2} c^{2} d^{2} i^{3} \log\left(e\right) - 6 \, {\left(i^{3} \log\left(e\right) + i^{3}\right)} a b^{3} c^{3} d - 9 \, {\left(2 \, i^{3} \log\left(e\right) - i^{3}\right)} a^{3} b c d^{3} + {\left(6 \, i^{3} \log\left(e\right) - 5 \, i^{3}\right)} a^{4} d^{4}\right)} B\right)} \log\left(b x + a\right) - {\left({\left(b^{4} c d^{3} i^{3} - a b^{3} d^{4} i^{3}\right)} B x^{3} + 3 \, {\left(2 \, b^{4} c^{2} d^{2} i^{3} - 3 \, a b^{3} c d^{3} i^{3} + a^{2} b^{2} d^{4} i^{3}\right)} B x^{2} + 2 \, {\left(3 \, a b^{3} c^{2} d^{2} i^{3} - 5 \, a^{2} b^{2} c d^{3} i^{3} + 2 \, a^{3} b d^{4} i^{3}\right)} B x + 2 \, {\left(3 \, a b^{3} c^{3} d i^{3} - 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 4 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B + 6 \, {\left({\left(b^{4} c^{3} d i^{3} - 3 \, a b^{3} c^{2} d^{2} i^{3} + 3 \, a^{2} b^{2} c d^{3} i^{3} - a^{3} b d^{4} i^{3}\right)} B x + {\left(a b^{3} c^{3} d i^{3} - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 3 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, {\left(a b^{5} c g^{2} - a^{2} b^{4} d g^{2} + {\left(b^{6} c g^{2} - a b^{5} d g^{2}\right)} x\right)}} + \frac{3 \, {\left(b^{2} c^{2} d i^{3} - 2 \, a b c d^{2} i^{3} + a^{2} d^{3} i^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{4} g^{2}}"," ",0,"-3*A*(a^2/(b^4*g^2*x + a*b^3*g^2) - x/(b^2*g^2) + 2*a*log(b*x + a)/(b^3*g^2))*c*d^2*i^3 + 1/2*(2*a^3/(b^5*g^2*x + a*b^4*g^2) + 6*a^2*log(b*x + a)/(b^4*g^2) + (b*x^2 - 4*a*x)/(b^3*g^2))*A*d^3*i^3 + 3*A*c^2*d*i^3*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - B*c^3*i^3*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^2*g^2*x + a*b*g^2) + 1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A*c^3*i^3/(b^2*g^2*x + a*b*g^2) - 1/2*(5*b^3*c^3*d*i^3 - 3*a*b^2*c^2*d^2*i^3 - 2*a^2*b*c*d^3*i^3 + 2*a^3*d^4*i^3)*B*log(d*x + c)/(b^5*c*g^2 - a*b^4*d*g^2) + 1/2*((b^4*c*d^3*i^3*log(e) - a*b^3*d^4*i^3*log(e))*B*x^3 + ((6*i^3*log(e) - i^3)*b^4*c^2*d^2 - (9*i^3*log(e) - 2*i^3)*a*b^3*c*d^3 + (3*i^3*log(e) - i^3)*a^2*b^2*d^4)*B*x^2 + ((6*i^3*log(e) - i^3)*a*b^3*c^2*d^2 - 2*(5*i^3*log(e) - i^3)*a^2*b^2*c*d^3 + (4*i^3*log(e) - i^3)*a^3*b*d^4)*B*x + 3*((b^4*c^3*d*i^3 - 3*a*b^3*c^2*d^2*i^3 + 3*a^2*b^2*c*d^3*i^3 - a^3*b*d^4*i^3)*B*x + (a*b^3*c^3*d*i^3 - 3*a^2*b^2*c^2*d^2*i^3 + 3*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B)*log(b*x + a)^2 + 2*(3*(i^3*log(e) + i^3)*a*b^3*c^3*d - 6*(i^3*log(e) + i^3)*a^2*b^2*c^2*d^2 + 4*(i^3*log(e) + i^3)*a^3*b*c*d^3 - (i^3*log(e) + i^3)*a^4*d^4)*B + ((b^4*c*d^3*i^3 - a*b^3*d^4*i^3)*B*x^3 + 3*(2*b^4*c^2*d^2*i^3 - 3*a*b^3*c*d^3*i^3 + a^2*b^2*d^4*i^3)*B*x^2 + (6*b^4*c^3*d*i^3*log(e) - 18*(i^3*log(e) - i^3)*a*b^3*c^2*d^2 + 9*(2*i^3*log(e) - 3*i^3)*a^2*b^2*c*d^3 - (6*i^3*log(e) - 11*i^3)*a^3*b*d^4)*B*x - (18*a^2*b^2*c^2*d^2*i^3*log(e) - 6*(i^3*log(e) + i^3)*a*b^3*c^3*d - 9*(2*i^3*log(e) - i^3)*a^3*b*c*d^3 + (6*i^3*log(e) - 5*i^3)*a^4*d^4)*B)*log(b*x + a) - ((b^4*c*d^3*i^3 - a*b^3*d^4*i^3)*B*x^3 + 3*(2*b^4*c^2*d^2*i^3 - 3*a*b^3*c*d^3*i^3 + a^2*b^2*d^4*i^3)*B*x^2 + 2*(3*a*b^3*c^2*d^2*i^3 - 5*a^2*b^2*c*d^3*i^3 + 2*a^3*b*d^4*i^3)*B*x + 2*(3*a*b^3*c^3*d*i^3 - 6*a^2*b^2*c^2*d^2*i^3 + 4*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B + 6*((b^4*c^3*d*i^3 - 3*a*b^3*c^2*d^2*i^3 + 3*a^2*b^2*c*d^3*i^3 - a^3*b*d^4*i^3)*B*x + (a*b^3*c^3*d*i^3 - 3*a^2*b^2*c^2*d^2*i^3 + 3*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B)*log(b*x + a))*log(d*x + c))/(a*b^5*c*g^2 - a^2*b^4*d*g^2 + (b^6*c*g^2 - a*b^5*d*g^2)*x) + 3*(b^2*c^2*d*i^3 - 2*a*b*c*d^2*i^3 + a^2*d^3*i^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^4*g^2)","B",0
26,1,2302,0,2.508894," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{3}{4} \, B c^{2} d i^{3} {\left(\frac{2 \, {\left(2 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} + \frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} - \frac{1}{2} \, A d^{3} i^{3} {\left(\frac{6 \, a^{2} b x + 5 \, a^{3}}{b^{6} g^{3} x^{2} + 2 \, a b^{5} g^{3} x + a^{2} b^{4} g^{3}} - \frac{2 \, x}{b^{3} g^{3}} + \frac{6 \, a \log\left(b x + a\right)}{b^{4} g^{3}}\right)} + \frac{3}{2} \, A c d^{2} i^{3} {\left(\frac{4 \, a b x + 3 \, a^{2}}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + \frac{2 \, \log\left(b x + a\right)}{b^{3} g^{3}}\right)} + \frac{1}{4} \, B c^{3} i^{3} {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{3 \, {\left(2 \, b x + a\right)} A c^{2} d i^{3}}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{A c^{3} i^{3}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{{\left(2 \, b^{3} c^{3} d^{2} i^{3} + 8 \, a b^{2} c^{2} d^{3} i^{3} - 13 \, a^{2} b c d^{4} i^{3} + 5 \, a^{3} d^{5} i^{3}\right)} B \log\left(d x + c\right)}{2 \, {\left(b^{6} c^{2} g^{3} - 2 \, a b^{5} c d g^{3} + a^{2} b^{4} d^{2} g^{3}\right)}} + \frac{4 \, {\left(b^{5} c^{2} d^{3} i^{3} \log\left(e\right) - 2 \, a b^{4} c d^{4} i^{3} \log\left(e\right) + a^{2} b^{3} d^{5} i^{3} \log\left(e\right)\right)} B x^{3} + 8 \, {\left(a b^{4} c^{2} d^{3} i^{3} \log\left(e\right) - 2 \, a^{2} b^{3} c d^{4} i^{3} \log\left(e\right) + a^{3} b^{2} d^{5} i^{3} \log\left(e\right)\right)} B x^{2} + 2 \, {\left(12 \, {\left(i^{3} \log\left(e\right) + i^{3}\right)} a b^{4} c^{3} d^{2} - {\left(28 \, i^{3} \log\left(e\right) + 27 \, i^{3}\right)} a^{2} b^{3} c^{2} d^{3} + 20 \, {\left(i^{3} \log\left(e\right) + i^{3}\right)} a^{3} b^{2} c d^{4} - {\left(4 \, i^{3} \log\left(e\right) + 5 \, i^{3}\right)} a^{4} b d^{5}\right)} B x + 6 \, {\left({\left(b^{5} c^{3} d^{2} i^{3} - 3 \, a b^{4} c^{2} d^{3} i^{3} + 3 \, a^{2} b^{3} c d^{4} i^{3} - a^{3} b^{2} d^{5} i^{3}\right)} B x^{2} + 2 \, {\left(a b^{4} c^{3} d^{2} i^{3} - 3 \, a^{2} b^{3} c^{2} d^{3} i^{3} + 3 \, a^{3} b^{2} c d^{4} i^{3} - a^{4} b d^{5} i^{3}\right)} B x + {\left(a^{2} b^{3} c^{3} d^{2} i^{3} - 3 \, a^{3} b^{2} c^{2} d^{3} i^{3} + 3 \, a^{4} b c d^{4} i^{3} - a^{5} d^{5} i^{3}\right)} B\right)} \log\left(b x + a\right)^{2} + {\left(3 \, {\left(6 \, i^{3} \log\left(e\right) + 7 \, i^{3}\right)} a^{2} b^{3} c^{3} d^{2} - {\left(46 \, i^{3} \log\left(e\right) + 47 \, i^{3}\right)} a^{3} b^{2} c^{2} d^{3} + {\left(38 \, i^{3} \log\left(e\right) + 35 \, i^{3}\right)} a^{4} b c d^{4} - {\left(10 \, i^{3} \log\left(e\right) + 9 \, i^{3}\right)} a^{5} d^{5}\right)} B + 2 \, {\left(2 \, {\left(b^{5} c^{2} d^{3} i^{3} - 2 \, a b^{4} c d^{4} i^{3} + a^{2} b^{3} d^{5} i^{3}\right)} B x^{3} + {\left(6 \, b^{5} c^{3} d^{2} i^{3} \log\left(e\right) - 18 \, {\left(i^{3} \log\left(e\right) - i^{3}\right)} a b^{4} c^{2} d^{3} + 9 \, {\left(2 \, i^{3} \log\left(e\right) - 3 \, i^{3}\right)} a^{2} b^{3} c d^{4} - {\left(6 \, i^{3} \log\left(e\right) - 11 \, i^{3}\right)} a^{3} b^{2} d^{5}\right)} B x^{2} - 2 \, {\left(18 \, a^{2} b^{3} c^{2} d^{3} i^{3} \log\left(e\right) - 6 \, {\left(i^{3} \log\left(e\right) + i^{3}\right)} a b^{4} c^{3} d^{2} - 9 \, {\left(2 \, i^{3} \log\left(e\right) - i^{3}\right)} a^{3} b^{2} c d^{4} + {\left(6 \, i^{3} \log\left(e\right) - 5 \, i^{3}\right)} a^{4} b d^{5}\right)} B x + {\left(18 \, a^{4} b c d^{4} i^{3} \log\left(e\right) + 3 \, {\left(2 \, i^{3} \log\left(e\right) + 3 \, i^{3}\right)} a^{2} b^{3} c^{3} d^{2} - 9 \, {\left(2 \, i^{3} \log\left(e\right) + i^{3}\right)} a^{3} b^{2} c^{2} d^{3} - 2 \, {\left(3 \, i^{3} \log\left(e\right) - i^{3}\right)} a^{5} d^{5}\right)} B\right)} \log\left(b x + a\right) - 2 \, {\left(2 \, {\left(b^{5} c^{2} d^{3} i^{3} - 2 \, a b^{4} c d^{4} i^{3} + a^{2} b^{3} d^{5} i^{3}\right)} B x^{3} + 4 \, {\left(a b^{4} c^{2} d^{3} i^{3} - 2 \, a^{2} b^{3} c d^{4} i^{3} + a^{3} b^{2} d^{5} i^{3}\right)} B x^{2} + 4 \, {\left(3 \, a b^{4} c^{3} d^{2} i^{3} - 7 \, a^{2} b^{3} c^{2} d^{3} i^{3} + 5 \, a^{3} b^{2} c d^{4} i^{3} - a^{4} b d^{5} i^{3}\right)} B x + {\left(9 \, a^{2} b^{3} c^{3} d^{2} i^{3} - 23 \, a^{3} b^{2} c^{2} d^{3} i^{3} + 19 \, a^{4} b c d^{4} i^{3} - 5 \, a^{5} d^{5} i^{3}\right)} B + 6 \, {\left({\left(b^{5} c^{3} d^{2} i^{3} - 3 \, a b^{4} c^{2} d^{3} i^{3} + 3 \, a^{2} b^{3} c d^{4} i^{3} - a^{3} b^{2} d^{5} i^{3}\right)} B x^{2} + 2 \, {\left(a b^{4} c^{3} d^{2} i^{3} - 3 \, a^{2} b^{3} c^{2} d^{3} i^{3} + 3 \, a^{3} b^{2} c d^{4} i^{3} - a^{4} b d^{5} i^{3}\right)} B x + {\left(a^{2} b^{3} c^{3} d^{2} i^{3} - 3 \, a^{3} b^{2} c^{2} d^{3} i^{3} + 3 \, a^{4} b c d^{4} i^{3} - a^{5} d^{5} i^{3}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{4 \, {\left(a^{2} b^{6} c^{2} g^{3} - 2 \, a^{3} b^{5} c d g^{3} + a^{4} b^{4} d^{2} g^{3} + {\left(b^{8} c^{2} g^{3} - 2 \, a b^{7} c d g^{3} + a^{2} b^{6} d^{2} g^{3}\right)} x^{2} + 2 \, {\left(a b^{7} c^{2} g^{3} - 2 \, a^{2} b^{6} c d g^{3} + a^{3} b^{5} d^{2} g^{3}\right)} x\right)}} + \frac{3 \, {\left(b c d^{2} i^{3} - a d^{3} i^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{4} g^{3}}"," ",0,"-3/4*B*c^2*d*i^3*(2*(2*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) + (3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) - 1/2*A*d^3*i^3*((6*a^2*b*x + 5*a^3)/(b^6*g^3*x^2 + 2*a*b^5*g^3*x + a^2*b^4*g^3) - 2*x/(b^3*g^3) + 6*a*log(b*x + a)/(b^4*g^3)) + 3/2*A*c*d^2*i^3*((4*a*b*x + 3*a^2)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*log(b*x + a)/(b^3*g^3)) + 1/4*B*c^3*i^3*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - 3/2*(2*b*x + a)*A*c^2*d*i^3/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*A*c^3*i^3/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*(2*b^3*c^3*d^2*i^3 + 8*a*b^2*c^2*d^3*i^3 - 13*a^2*b*c*d^4*i^3 + 5*a^3*d^5*i^3)*B*log(d*x + c)/(b^6*c^2*g^3 - 2*a*b^5*c*d*g^3 + a^2*b^4*d^2*g^3) + 1/4*(4*(b^5*c^2*d^3*i^3*log(e) - 2*a*b^4*c*d^4*i^3*log(e) + a^2*b^3*d^5*i^3*log(e))*B*x^3 + 8*(a*b^4*c^2*d^3*i^3*log(e) - 2*a^2*b^3*c*d^4*i^3*log(e) + a^3*b^2*d^5*i^3*log(e))*B*x^2 + 2*(12*(i^3*log(e) + i^3)*a*b^4*c^3*d^2 - (28*i^3*log(e) + 27*i^3)*a^2*b^3*c^2*d^3 + 20*(i^3*log(e) + i^3)*a^3*b^2*c*d^4 - (4*i^3*log(e) + 5*i^3)*a^4*b*d^5)*B*x + 6*((b^5*c^3*d^2*i^3 - 3*a*b^4*c^2*d^3*i^3 + 3*a^2*b^3*c*d^4*i^3 - a^3*b^2*d^5*i^3)*B*x^2 + 2*(a*b^4*c^3*d^2*i^3 - 3*a^2*b^3*c^2*d^3*i^3 + 3*a^3*b^2*c*d^4*i^3 - a^4*b*d^5*i^3)*B*x + (a^2*b^3*c^3*d^2*i^3 - 3*a^3*b^2*c^2*d^3*i^3 + 3*a^4*b*c*d^4*i^3 - a^5*d^5*i^3)*B)*log(b*x + a)^2 + (3*(6*i^3*log(e) + 7*i^3)*a^2*b^3*c^3*d^2 - (46*i^3*log(e) + 47*i^3)*a^3*b^2*c^2*d^3 + (38*i^3*log(e) + 35*i^3)*a^4*b*c*d^4 - (10*i^3*log(e) + 9*i^3)*a^5*d^5)*B + 2*(2*(b^5*c^2*d^3*i^3 - 2*a*b^4*c*d^4*i^3 + a^2*b^3*d^5*i^3)*B*x^3 + (6*b^5*c^3*d^2*i^3*log(e) - 18*(i^3*log(e) - i^3)*a*b^4*c^2*d^3 + 9*(2*i^3*log(e) - 3*i^3)*a^2*b^3*c*d^4 - (6*i^3*log(e) - 11*i^3)*a^3*b^2*d^5)*B*x^2 - 2*(18*a^2*b^3*c^2*d^3*i^3*log(e) - 6*(i^3*log(e) + i^3)*a*b^4*c^3*d^2 - 9*(2*i^3*log(e) - i^3)*a^3*b^2*c*d^4 + (6*i^3*log(e) - 5*i^3)*a^4*b*d^5)*B*x + (18*a^4*b*c*d^4*i^3*log(e) + 3*(2*i^3*log(e) + 3*i^3)*a^2*b^3*c^3*d^2 - 9*(2*i^3*log(e) + i^3)*a^3*b^2*c^2*d^3 - 2*(3*i^3*log(e) - i^3)*a^5*d^5)*B)*log(b*x + a) - 2*(2*(b^5*c^2*d^3*i^3 - 2*a*b^4*c*d^4*i^3 + a^2*b^3*d^5*i^3)*B*x^3 + 4*(a*b^4*c^2*d^3*i^3 - 2*a^2*b^3*c*d^4*i^3 + a^3*b^2*d^5*i^3)*B*x^2 + 4*(3*a*b^4*c^3*d^2*i^3 - 7*a^2*b^3*c^2*d^3*i^3 + 5*a^3*b^2*c*d^4*i^3 - a^4*b*d^5*i^3)*B*x + (9*a^2*b^3*c^3*d^2*i^3 - 23*a^3*b^2*c^2*d^3*i^3 + 19*a^4*b*c*d^4*i^3 - 5*a^5*d^5*i^3)*B + 6*((b^5*c^3*d^2*i^3 - 3*a*b^4*c^2*d^3*i^3 + 3*a^2*b^3*c*d^4*i^3 - a^3*b^2*d^5*i^3)*B*x^2 + 2*(a*b^4*c^3*d^2*i^3 - 3*a^2*b^3*c^2*d^3*i^3 + 3*a^3*b^2*c*d^4*i^3 - a^4*b*d^5*i^3)*B*x + (a^2*b^3*c^3*d^2*i^3 - 3*a^3*b^2*c^2*d^3*i^3 + 3*a^4*b*c*d^4*i^3 - a^5*d^5*i^3)*B)*log(b*x + a))*log(d*x + c))/(a^2*b^6*c^2*g^3 - 2*a^3*b^5*c*d*g^3 + a^4*b^4*d^2*g^3 + (b^8*c^2*g^3 - 2*a*b^7*c*d*g^3 + a^2*b^6*d^2*g^3)*x^2 + 2*(a*b^7*c^2*g^3 - 2*a^2*b^6*c*d*g^3 + a^3*b^5*d^2*g^3)*x) + 3*(b*c*d^2*i^3 - a*d^3*i^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^4*g^3)","B",0
27,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{6} \, B d^{3} i^{3} {\left(\frac{{\left(18 \, a b^{2} x^{2} + 27 \, a^{2} b x + 11 \, a^{3} + 6 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{7} g^{4} x^{3} + 3 \, a b^{6} g^{4} x^{2} + 3 \, a^{2} b^{5} g^{4} x + a^{3} b^{4} g^{4}} - 6 \, \int \frac{6 \, b^{4} d x^{4} \log\left(e\right) + 45 \, a^{2} b^{2} d x^{2} + 38 \, a^{3} b d x + 11 \, a^{4} d + 6 \, {\left(b^{4} c \log\left(e\right) + 3 \, a b^{3} d\right)} x^{3} + 6 \, {\left(2 \, b^{4} d x^{4} + 6 \, a^{2} b^{2} d x^{2} + 4 \, a^{3} b d x + a^{4} d + {\left(b^{4} c + 4 \, a b^{3} d\right)} x^{3}\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} d g^{4} x^{5} + a^{4} b^{4} c g^{4} + {\left(b^{8} c g^{4} + 4 \, a b^{7} d g^{4}\right)} x^{4} + 2 \, {\left(2 \, a b^{7} c g^{4} + 3 \, a^{2} b^{6} d g^{4}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{6} c g^{4} + 2 \, a^{3} b^{5} d g^{4}\right)} x^{2} + {\left(4 \, a^{3} b^{5} c g^{4} + a^{4} b^{4} d g^{4}\right)} x\right)}}\,{d x}\right)} - \frac{1}{6} \, B c d^{2} i^{3} {\left(\frac{6 \, {\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}} + \frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} - \frac{1}{12} \, B c^{2} d i^{3} {\left(\frac{6 \, {\left(3 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}} + \frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{1}{18} \, B c^{3} i^{3} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} + \frac{1}{6} \, A d^{3} i^{3} {\left(\frac{18 \, a b^{2} x^{2} + 27 \, a^{2} b x + 11 \, a^{3}}{b^{7} g^{4} x^{3} + 3 \, a b^{6} g^{4} x^{2} + 3 \, a^{2} b^{5} g^{4} x + a^{3} b^{4} g^{4}} + \frac{6 \, \log\left(b x + a\right)}{b^{4} g^{4}}\right)} - \frac{{\left(3 \, b x + a\right)} A c^{2} d i^{3}}{2 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A c d^{2} i^{3}}{b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}} - \frac{A c^{3} i^{3}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/6*B*d^3*i^3*((18*a*b^2*x^2 + 27*a^2*b*x + 11*a^3 + 6*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*log(b*x + a))*log(d*x + c)/(b^7*g^4*x^3 + 3*a*b^6*g^4*x^2 + 3*a^2*b^5*g^4*x + a^3*b^4*g^4) - 6*integrate(1/6*(6*b^4*d*x^4*log(e) + 45*a^2*b^2*d*x^2 + 38*a^3*b*d*x + 11*a^4*d + 6*(b^4*c*log(e) + 3*a*b^3*d)*x^3 + 6*(2*b^4*d*x^4 + 6*a^2*b^2*d*x^2 + 4*a^3*b*d*x + a^4*d + (b^4*c + 4*a*b^3*d)*x^3)*log(b*x + a))/(b^8*d*g^4*x^5 + a^4*b^4*c*g^4 + (b^8*c*g^4 + 4*a*b^7*d*g^4)*x^4 + 2*(2*a*b^7*c*g^4 + 3*a^2*b^6*d*g^4)*x^3 + 2*(3*a^2*b^6*c*g^4 + 2*a^3*b^5*d*g^4)*x^2 + (4*a^3*b^5*c*g^4 + a^4*b^4*d*g^4)*x), x)) - 1/6*B*c*d^2*i^3*(6*(3*b^2*x^2 + 3*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) + (11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4)) - 1/12*B*c^2*d*i^3*(6*(3*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) + (5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/18*B*c^3*i^3*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) + 1/6*A*d^3*i^3*((18*a*b^2*x^2 + 27*a^2*b*x + 11*a^3)/(b^7*g^4*x^3 + 3*a*b^6*g^4*x^2 + 3*a^2*b^5*g^4*x + a^3*b^4*g^4) + 6*log(b*x + a)/(b^4*g^4)) - 1/2*(3*b*x + a)*A*c^2*d*i^3/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - (3*b^2*x^2 + 3*a*b*x + a^2)*A*c*d^2*i^3/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/3*A*c^3*i^3/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","F",0
28,1,3107,0,2.708635," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{1}{48} \, B d^{3} i^{3} {\left(\frac{12 \, {\left(4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{8} g^{5} x^{4} + 4 \, a b^{7} g^{5} x^{3} + 6 \, a^{2} b^{6} g^{5} x^{2} + 4 \, a^{3} b^{5} g^{5} x + a^{4} b^{4} g^{5}} + \frac{25 \, a^{3} b^{3} c^{3} - 23 \, a^{4} b^{2} c^{2} d + 13 \, a^{5} b c d^{2} - 3 \, a^{6} d^{3} + 12 \, {\left(4 \, b^{6} c^{3} - 6 \, a b^{5} c^{2} d + 4 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(18 \, a b^{5} c^{3} - 22 \, a^{2} b^{4} c^{2} d + 13 \, a^{3} b^{3} c d^{2} - 3 \, a^{4} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(22 \, a^{2} b^{4} c^{3} - 23 \, a^{3} b^{3} c^{2} d + 13 \, a^{4} b^{2} c d^{2} - 3 \, a^{5} b d^{3}\right)} x}{{\left(b^{11} c^{3} - 3 \, a b^{10} c^{2} d + 3 \, a^{2} b^{9} c d^{2} - a^{3} b^{8} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{10} c^{3} - 3 \, a^{2} b^{9} c^{2} d + 3 \, a^{3} b^{8} c d^{2} - a^{4} b^{7} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{9} c^{3} - 3 \, a^{3} b^{8} c^{2} d + 3 \, a^{4} b^{7} c d^{2} - a^{5} b^{6} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{8} c^{3} - 3 \, a^{4} b^{7} c^{2} d + 3 \, a^{5} b^{6} c d^{2} - a^{6} b^{5} d^{3}\right)} g^{5} x + {\left(a^{4} b^{7} c^{3} - 3 \, a^{5} b^{6} c^{2} d + 3 \, a^{6} b^{5} c d^{2} - a^{7} b^{4} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{4} - 4 \, a b^{7} c^{3} d + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{3} b^{5} c d^{3} + a^{4} b^{4} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{4} - 4 \, a b^{7} c^{3} d + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{3} b^{5} c d^{3} + a^{4} b^{4} d^{4}\right)} g^{5}}\right)} - \frac{1}{48} \, B c d^{2} i^{3} {\left(\frac{12 \, {\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}} + \frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} - \frac{1}{48} \, B c^{2} d i^{3} {\left(\frac{12 \, {\left(4 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}} + \frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} + \frac{1}{48} \, B c^{3} i^{3} {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} - \frac{12 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{{\left(4 \, b x + a\right)} A c^{2} d i^{3}}{4 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} A c d^{2} i^{3}}{4 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{{\left(4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}\right)} A d^{3} i^{3}}{4 \, {\left(b^{8} g^{5} x^{4} + 4 \, a b^{7} g^{5} x^{3} + 6 \, a^{2} b^{6} g^{5} x^{2} + 4 \, a^{3} b^{5} g^{5} x + a^{4} b^{4} g^{5}\right)}} - \frac{A c^{3} i^{3}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"-1/48*B*d^3*i^3*(12*(4*b^3*x^3 + 6*a*b^2*x^2 + 4*a^2*b*x + a^3)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^8*g^5*x^4 + 4*a*b^7*g^5*x^3 + 6*a^2*b^6*g^5*x^2 + 4*a^3*b^5*g^5*x + a^4*b^4*g^5) + (25*a^3*b^3*c^3 - 23*a^4*b^2*c^2*d + 13*a^5*b*c*d^2 - 3*a^6*d^3 + 12*(4*b^6*c^3 - 6*a*b^5*c^2*d + 4*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^3 + 6*(18*a*b^5*c^3 - 22*a^2*b^4*c^2*d + 13*a^3*b^3*c*d^2 - 3*a^4*b^2*d^3)*x^2 + 4*(22*a^2*b^4*c^3 - 23*a^3*b^3*c^2*d + 13*a^4*b^2*c*d^2 - 3*a^5*b*d^3)*x)/((b^11*c^3 - 3*a*b^10*c^2*d + 3*a^2*b^9*c*d^2 - a^3*b^8*d^3)*g^5*x^4 + 4*(a*b^10*c^3 - 3*a^2*b^9*c^2*d + 3*a^3*b^8*c*d^2 - a^4*b^7*d^3)*g^5*x^3 + 6*(a^2*b^9*c^3 - 3*a^3*b^8*c^2*d + 3*a^4*b^7*c*d^2 - a^5*b^6*d^3)*g^5*x^2 + 4*(a^3*b^8*c^3 - 3*a^4*b^7*c^2*d + 3*a^5*b^6*c*d^2 - a^6*b^5*d^3)*g^5*x + (a^4*b^7*c^3 - 3*a^5*b^6*c^2*d + 3*a^6*b^5*c*d^2 - a^7*b^4*d^3)*g^5) + 12*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*log(b*x + a)/((b^8*c^4 - 4*a*b^7*c^3*d + 6*a^2*b^6*c^2*d^2 - 4*a^3*b^5*c*d^3 + a^4*b^4*d^4)*g^5) - 12*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*log(d*x + c)/((b^8*c^4 - 4*a*b^7*c^3*d + 6*a^2*b^6*c^2*d^2 - 4*a^3*b^5*c*d^3 + a^4*b^4*d^4)*g^5)) - 1/48*B*c*d^2*i^3*(12*(6*b^2*x^2 + 4*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) + (13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5)) - 1/48*B*c^2*d*i^3*(12*(4*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) + (7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) + 1/48*B*c^3*i^3*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) - 12*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/4*(4*b*x + a)*A*c^2*d*i^3/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/4*(6*b^2*x^2 + 4*a*b*x + a^2)*A*c*d^2*i^3/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/4*(4*b^3*x^3 + 6*a*b^2*x^2 + 4*a^2*b*x + a^3)*A*d^3*i^3/(b^8*g^5*x^4 + 4*a*b^7*g^5*x^3 + 6*a^2*b^6*g^5*x^2 + 4*a^3*b^5*g^5*x + a^4*b^4*g^5) - 1/4*A*c^3*i^3/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
29,1,4218,0,3.852736," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^6,x, algorithm=""maxima"")","-\frac{1}{1200} \, B d^{3} i^{3} {\left(\frac{60 \, {\left(10 \, b^{3} x^{3} + 10 \, a b^{2} x^{2} + 5 \, a^{2} b x + a^{3}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{9} g^{6} x^{5} + 5 \, a b^{8} g^{6} x^{4} + 10 \, a^{2} b^{7} g^{6} x^{3} + 10 \, a^{3} b^{6} g^{6} x^{2} + 5 \, a^{4} b^{5} g^{6} x + a^{5} b^{4} g^{6}} + \frac{77 \, a^{3} b^{4} c^{4} - 548 \, a^{4} b^{3} c^{3} d + 352 \, a^{5} b^{2} c^{2} d^{2} - 148 \, a^{6} b c d^{3} + 27 \, a^{7} d^{4} - 60 \, {\left(10 \, b^{7} c^{3} d - 10 \, a b^{6} c^{2} d^{2} + 5 \, a^{2} b^{5} c d^{3} - a^{3} b^{4} d^{4}\right)} x^{4} + 30 \, {\left(10 \, b^{7} c^{4} - 100 \, a b^{6} c^{3} d + 95 \, a^{2} b^{5} c^{2} d^{2} - 46 \, a^{3} b^{4} c d^{3} + 9 \, a^{4} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(50 \, a b^{6} c^{4} - 410 \, a^{2} b^{5} c^{3} d + 337 \, a^{3} b^{4} c^{2} d^{2} - 148 \, a^{4} b^{3} c d^{3} + 27 \, a^{5} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(65 \, a^{2} b^{5} c^{4} - 488 \, a^{3} b^{4} c^{3} d + 352 \, a^{4} b^{3} c^{2} d^{2} - 148 \, a^{5} b^{2} c d^{3} + 27 \, a^{6} b d^{4}\right)} x}{{\left(b^{13} c^{4} - 4 \, a b^{12} c^{3} d + 6 \, a^{2} b^{11} c^{2} d^{2} - 4 \, a^{3} b^{10} c d^{3} + a^{4} b^{9} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{12} c^{4} - 4 \, a^{2} b^{11} c^{3} d + 6 \, a^{3} b^{10} c^{2} d^{2} - 4 \, a^{4} b^{9} c d^{3} + a^{5} b^{8} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{11} c^{4} - 4 \, a^{3} b^{10} c^{3} d + 6 \, a^{4} b^{9} c^{2} d^{2} - 4 \, a^{5} b^{8} c d^{3} + a^{6} b^{7} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{10} c^{4} - 4 \, a^{4} b^{9} c^{3} d + 6 \, a^{5} b^{8} c^{2} d^{2} - 4 \, a^{6} b^{7} c d^{3} + a^{7} b^{6} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{9} c^{4} - 4 \, a^{5} b^{8} c^{3} d + 6 \, a^{6} b^{7} c^{2} d^{2} - 4 \, a^{7} b^{6} c d^{3} + a^{8} b^{5} d^{4}\right)} g^{6} x + {\left(a^{5} b^{8} c^{4} - 4 \, a^{6} b^{7} c^{3} d + 6 \, a^{7} b^{6} c^{2} d^{2} - 4 \, a^{8} b^{5} c d^{3} + a^{9} b^{4} d^{4}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{3} c^{3} d^{2} - 10 \, a b^{2} c^{2} d^{3} + 5 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{9} c^{5} - 5 \, a b^{8} c^{4} d + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{4} b^{5} c d^{4} - a^{5} b^{4} d^{5}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{3} c^{3} d^{2} - 10 \, a b^{2} c^{2} d^{3} + 5 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{9} c^{5} - 5 \, a b^{8} c^{4} d + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{4} b^{5} c d^{4} - a^{5} b^{4} d^{5}\right)} g^{6}}\right)} - \frac{1}{600} \, B c d^{2} i^{3} {\left(\frac{60 \, {\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}} + \frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} - \frac{1}{400} \, B c^{2} d i^{3} {\left(\frac{60 \, {\left(5 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}} + \frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} - \frac{1}{300} \, B c^{3} i^{3} {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} - \frac{3 \, {\left(5 \, b x + a\right)} A c^{2} d i^{3}}{20 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} A c d^{2} i^{3}}{10 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{{\left(10 \, b^{3} x^{3} + 10 \, a b^{2} x^{2} + 5 \, a^{2} b x + a^{3}\right)} A d^{3} i^{3}}{20 \, {\left(b^{9} g^{6} x^{5} + 5 \, a b^{8} g^{6} x^{4} + 10 \, a^{2} b^{7} g^{6} x^{3} + 10 \, a^{3} b^{6} g^{6} x^{2} + 5 \, a^{4} b^{5} g^{6} x + a^{5} b^{4} g^{6}\right)}} - \frac{A c^{3} i^{3}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}}"," ",0,"-1/1200*B*d^3*i^3*(60*(10*b^3*x^3 + 10*a*b^2*x^2 + 5*a^2*b*x + a^3)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^9*g^6*x^5 + 5*a*b^8*g^6*x^4 + 10*a^2*b^7*g^6*x^3 + 10*a^3*b^6*g^6*x^2 + 5*a^4*b^5*g^6*x + a^5*b^4*g^6) + (77*a^3*b^4*c^4 - 548*a^4*b^3*c^3*d + 352*a^5*b^2*c^2*d^2 - 148*a^6*b*c*d^3 + 27*a^7*d^4 - 60*(10*b^7*c^3*d - 10*a*b^6*c^2*d^2 + 5*a^2*b^5*c*d^3 - a^3*b^4*d^4)*x^4 + 30*(10*b^7*c^4 - 100*a*b^6*c^3*d + 95*a^2*b^5*c^2*d^2 - 46*a^3*b^4*c*d^3 + 9*a^4*b^3*d^4)*x^3 + 10*(50*a*b^6*c^4 - 410*a^2*b^5*c^3*d + 337*a^3*b^4*c^2*d^2 - 148*a^4*b^3*c*d^3 + 27*a^5*b^2*d^4)*x^2 + 5*(65*a^2*b^5*c^4 - 488*a^3*b^4*c^3*d + 352*a^4*b^3*c^2*d^2 - 148*a^5*b^2*c*d^3 + 27*a^6*b*d^4)*x)/((b^13*c^4 - 4*a*b^12*c^3*d + 6*a^2*b^11*c^2*d^2 - 4*a^3*b^10*c*d^3 + a^4*b^9*d^4)*g^6*x^5 + 5*(a*b^12*c^4 - 4*a^2*b^11*c^3*d + 6*a^3*b^10*c^2*d^2 - 4*a^4*b^9*c*d^3 + a^5*b^8*d^4)*g^6*x^4 + 10*(a^2*b^11*c^4 - 4*a^3*b^10*c^3*d + 6*a^4*b^9*c^2*d^2 - 4*a^5*b^8*c*d^3 + a^6*b^7*d^4)*g^6*x^3 + 10*(a^3*b^10*c^4 - 4*a^4*b^9*c^3*d + 6*a^5*b^8*c^2*d^2 - 4*a^6*b^7*c*d^3 + a^7*b^6*d^4)*g^6*x^2 + 5*(a^4*b^9*c^4 - 4*a^5*b^8*c^3*d + 6*a^6*b^7*c^2*d^2 - 4*a^7*b^6*c*d^3 + a^8*b^5*d^4)*g^6*x + (a^5*b^8*c^4 - 4*a^6*b^7*c^3*d + 6*a^7*b^6*c^2*d^2 - 4*a^8*b^5*c*d^3 + a^9*b^4*d^4)*g^6) - 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(b*x + a)/((b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6) + 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(d*x + c)/((b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6)) - 1/600*B*c*d^2*i^3*(60*(10*b^2*x^2 + 5*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) + (47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6)) - 1/400*B*c^2*d*i^3*(60*(5*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) + (27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6)) - 1/300*B*c^3*i^3*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6)) - 3/20*(5*b*x + a)*A*c^2*d*i^3/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/10*(10*b^2*x^2 + 5*a*b*x + a^2)*A*c*d^2*i^3/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/20*(10*b^3*x^3 + 10*a*b^2*x^2 + 5*a^2*b*x + a^3)*A*d^3*i^3/(b^9*g^6*x^5 + 5*a*b^8*g^6*x^4 + 10*a^2*b^7*g^6*x^3 + 10*a^3*b^6*g^6*x^2 + 5*a^4*b^5*g^6*x + a^5*b^4*g^6) - 1/5*A*c^3*i^3/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6)","B",0
30,1,5524,0,5.149177," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^7,x, algorithm=""maxima"")","-\frac{1}{3600} \, B d^{3} i^{3} {\left(\frac{60 \, {\left(20 \, b^{3} x^{3} + 15 \, a b^{2} x^{2} + 6 \, a^{2} b x + a^{3}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{10} g^{7} x^{6} + 6 \, a b^{9} g^{7} x^{5} + 15 \, a^{2} b^{8} g^{7} x^{4} + 20 \, a^{3} b^{7} g^{7} x^{3} + 15 \, a^{4} b^{6} g^{7} x^{2} + 6 \, a^{5} b^{5} g^{7} x + a^{6} b^{4} g^{7}} + \frac{57 \, a^{3} b^{5} c^{5} - 405 \, a^{4} b^{4} c^{4} d + 1470 \, a^{5} b^{3} c^{3} d^{2} - 730 \, a^{6} b^{2} c^{2} d^{3} + 245 \, a^{7} b c d^{4} - 37 \, a^{8} d^{5} + 60 \, {\left(20 \, b^{8} c^{3} d^{2} - 15 \, a b^{7} c^{2} d^{3} + 6 \, a^{2} b^{6} c d^{4} - a^{3} b^{5} d^{5}\right)} x^{5} - 30 \, {\left(20 \, b^{8} c^{4} d - 235 \, a b^{7} c^{3} d^{2} + 171 \, a^{2} b^{6} c^{2} d^{3} - 67 \, a^{3} b^{5} c d^{4} + 11 \, a^{4} b^{4} d^{5}\right)} x^{4} + 20 \, {\left(20 \, b^{8} c^{5} - 175 \, a b^{7} c^{4} d + 866 \, a^{2} b^{6} c^{3} d^{2} - 604 \, a^{3} b^{5} c^{2} d^{3} + 230 \, a^{4} b^{4} c d^{4} - 37 \, a^{5} b^{3} d^{5}\right)} x^{3} + 15 \, {\left(35 \, a b^{7} c^{5} - 271 \, a^{2} b^{6} c^{4} d + 1128 \, a^{3} b^{5} c^{3} d^{2} - 700 \, a^{4} b^{4} c^{2} d^{3} + 245 \, a^{5} b^{3} c d^{4} - 37 \, a^{6} b^{2} d^{5}\right)} x^{2} + 6 \, {\left(47 \, a^{2} b^{6} c^{5} - 345 \, a^{3} b^{5} c^{4} d + 1320 \, a^{4} b^{4} c^{3} d^{2} - 730 \, a^{5} b^{3} c^{2} d^{3} + 245 \, a^{6} b^{2} c d^{4} - 37 \, a^{7} b d^{5}\right)} x}{{\left(b^{15} c^{5} - 5 \, a b^{14} c^{4} d + 10 \, a^{2} b^{13} c^{3} d^{2} - 10 \, a^{3} b^{12} c^{2} d^{3} + 5 \, a^{4} b^{11} c d^{4} - a^{5} b^{10} d^{5}\right)} g^{7} x^{6} + 6 \, {\left(a b^{14} c^{5} - 5 \, a^{2} b^{13} c^{4} d + 10 \, a^{3} b^{12} c^{3} d^{2} - 10 \, a^{4} b^{11} c^{2} d^{3} + 5 \, a^{5} b^{10} c d^{4} - a^{6} b^{9} d^{5}\right)} g^{7} x^{5} + 15 \, {\left(a^{2} b^{13} c^{5} - 5 \, a^{3} b^{12} c^{4} d + 10 \, a^{4} b^{11} c^{3} d^{2} - 10 \, a^{5} b^{10} c^{2} d^{3} + 5 \, a^{6} b^{9} c d^{4} - a^{7} b^{8} d^{5}\right)} g^{7} x^{4} + 20 \, {\left(a^{3} b^{12} c^{5} - 5 \, a^{4} b^{11} c^{4} d + 10 \, a^{5} b^{10} c^{3} d^{2} - 10 \, a^{6} b^{9} c^{2} d^{3} + 5 \, a^{7} b^{8} c d^{4} - a^{8} b^{7} d^{5}\right)} g^{7} x^{3} + 15 \, {\left(a^{4} b^{11} c^{5} - 5 \, a^{5} b^{10} c^{4} d + 10 \, a^{6} b^{9} c^{3} d^{2} - 10 \, a^{7} b^{8} c^{2} d^{3} + 5 \, a^{8} b^{7} c d^{4} - a^{9} b^{6} d^{5}\right)} g^{7} x^{2} + 6 \, {\left(a^{5} b^{10} c^{5} - 5 \, a^{6} b^{9} c^{4} d + 10 \, a^{7} b^{8} c^{3} d^{2} - 10 \, a^{8} b^{7} c^{2} d^{3} + 5 \, a^{9} b^{6} c d^{4} - a^{10} b^{5} d^{5}\right)} g^{7} x + {\left(a^{6} b^{9} c^{5} - 5 \, a^{7} b^{8} c^{4} d + 10 \, a^{8} b^{7} c^{3} d^{2} - 10 \, a^{9} b^{6} c^{2} d^{3} + 5 \, a^{10} b^{5} c d^{4} - a^{11} b^{4} d^{5}\right)} g^{7}} + \frac{60 \, {\left(20 \, b^{3} c^{3} d^{3} - 15 \, a b^{2} c^{2} d^{4} + 6 \, a^{2} b c d^{5} - a^{3} d^{6}\right)} \log\left(b x + a\right)}{{\left(b^{10} c^{6} - 6 \, a b^{9} c^{5} d + 15 \, a^{2} b^{8} c^{4} d^{2} - 20 \, a^{3} b^{7} c^{3} d^{3} + 15 \, a^{4} b^{6} c^{2} d^{4} - 6 \, a^{5} b^{5} c d^{5} + a^{6} b^{4} d^{6}\right)} g^{7}} - \frac{60 \, {\left(20 \, b^{3} c^{3} d^{3} - 15 \, a b^{2} c^{2} d^{4} + 6 \, a^{2} b c d^{5} - a^{3} d^{6}\right)} \log\left(d x + c\right)}{{\left(b^{10} c^{6} - 6 \, a b^{9} c^{5} d + 15 \, a^{2} b^{8} c^{4} d^{2} - 20 \, a^{3} b^{7} c^{3} d^{3} + 15 \, a^{4} b^{6} c^{2} d^{4} - 6 \, a^{5} b^{5} c d^{5} + a^{6} b^{4} d^{6}\right)} g^{7}}\right)} - \frac{1}{1200} \, B c d^{2} i^{3} {\left(\frac{60 \, {\left(15 \, b^{2} x^{2} + 6 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{9} g^{7} x^{6} + 6 \, a b^{8} g^{7} x^{5} + 15 \, a^{2} b^{7} g^{7} x^{4} + 20 \, a^{3} b^{6} g^{7} x^{3} + 15 \, a^{4} b^{5} g^{7} x^{2} + 6 \, a^{5} b^{4} g^{7} x + a^{6} b^{3} g^{7}} + \frac{37 \, a^{2} b^{5} c^{5} - 245 \, a^{3} b^{4} c^{4} d + 730 \, a^{4} b^{3} c^{3} d^{2} - 1470 \, a^{5} b^{2} c^{2} d^{3} + 405 \, a^{6} b c d^{4} - 57 \, a^{7} d^{5} - 60 \, {\left(15 \, b^{7} c^{2} d^{3} - 6 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 30 \, {\left(15 \, b^{7} c^{3} d^{2} - 171 \, a b^{6} c^{2} d^{3} + 67 \, a^{2} b^{5} c d^{4} - 11 \, a^{3} b^{4} d^{5}\right)} x^{4} - 20 \, {\left(15 \, b^{7} c^{4} d - 126 \, a b^{6} c^{3} d^{2} + 604 \, a^{2} b^{5} c^{2} d^{3} - 230 \, a^{3} b^{4} c d^{4} + 37 \, a^{4} b^{3} d^{5}\right)} x^{3} + 15 \, {\left(15 \, b^{7} c^{5} - 111 \, a b^{6} c^{4} d + 388 \, a^{2} b^{5} c^{3} d^{2} - 1000 \, a^{3} b^{4} c^{2} d^{3} + 365 \, a^{4} b^{3} c d^{4} - 57 \, a^{5} b^{2} d^{5}\right)} x^{2} + 6 \, {\left(27 \, a b^{6} c^{5} - 185 \, a^{2} b^{5} c^{4} d + 580 \, a^{3} b^{4} c^{3} d^{2} - 1270 \, a^{4} b^{3} c^{2} d^{3} + 405 \, a^{5} b^{2} c d^{4} - 57 \, a^{6} b d^{5}\right)} x}{{\left(b^{14} c^{5} - 5 \, a b^{13} c^{4} d + 10 \, a^{2} b^{12} c^{3} d^{2} - 10 \, a^{3} b^{11} c^{2} d^{3} + 5 \, a^{4} b^{10} c d^{4} - a^{5} b^{9} d^{5}\right)} g^{7} x^{6} + 6 \, {\left(a b^{13} c^{5} - 5 \, a^{2} b^{12} c^{4} d + 10 \, a^{3} b^{11} c^{3} d^{2} - 10 \, a^{4} b^{10} c^{2} d^{3} + 5 \, a^{5} b^{9} c d^{4} - a^{6} b^{8} d^{5}\right)} g^{7} x^{5} + 15 \, {\left(a^{2} b^{12} c^{5} - 5 \, a^{3} b^{11} c^{4} d + 10 \, a^{4} b^{10} c^{3} d^{2} - 10 \, a^{5} b^{9} c^{2} d^{3} + 5 \, a^{6} b^{8} c d^{4} - a^{7} b^{7} d^{5}\right)} g^{7} x^{4} + 20 \, {\left(a^{3} b^{11} c^{5} - 5 \, a^{4} b^{10} c^{4} d + 10 \, a^{5} b^{9} c^{3} d^{2} - 10 \, a^{6} b^{8} c^{2} d^{3} + 5 \, a^{7} b^{7} c d^{4} - a^{8} b^{6} d^{5}\right)} g^{7} x^{3} + 15 \, {\left(a^{4} b^{10} c^{5} - 5 \, a^{5} b^{9} c^{4} d + 10 \, a^{6} b^{8} c^{3} d^{2} - 10 \, a^{7} b^{7} c^{2} d^{3} + 5 \, a^{8} b^{6} c d^{4} - a^{9} b^{5} d^{5}\right)} g^{7} x^{2} + 6 \, {\left(a^{5} b^{9} c^{5} - 5 \, a^{6} b^{8} c^{4} d + 10 \, a^{7} b^{7} c^{3} d^{2} - 10 \, a^{8} b^{6} c^{2} d^{3} + 5 \, a^{9} b^{5} c d^{4} - a^{10} b^{4} d^{5}\right)} g^{7} x + {\left(a^{6} b^{8} c^{5} - 5 \, a^{7} b^{7} c^{4} d + 10 \, a^{8} b^{6} c^{3} d^{2} - 10 \, a^{9} b^{5} c^{2} d^{3} + 5 \, a^{10} b^{4} c d^{4} - a^{11} b^{3} d^{5}\right)} g^{7}} - \frac{60 \, {\left(15 \, b^{2} c^{2} d^{4} - 6 \, a b c d^{5} + a^{2} d^{6}\right)} \log\left(b x + a\right)}{{\left(b^{9} c^{6} - 6 \, a b^{8} c^{5} d + 15 \, a^{2} b^{7} c^{4} d^{2} - 20 \, a^{3} b^{6} c^{3} d^{3} + 15 \, a^{4} b^{5} c^{2} d^{4} - 6 \, a^{5} b^{4} c d^{5} + a^{6} b^{3} d^{6}\right)} g^{7}} + \frac{60 \, {\left(15 \, b^{2} c^{2} d^{4} - 6 \, a b c d^{5} + a^{2} d^{6}\right)} \log\left(d x + c\right)}{{\left(b^{9} c^{6} - 6 \, a b^{8} c^{5} d + 15 \, a^{2} b^{7} c^{4} d^{2} - 20 \, a^{3} b^{6} c^{3} d^{3} + 15 \, a^{4} b^{5} c^{2} d^{4} - 6 \, a^{5} b^{4} c d^{5} + a^{6} b^{3} d^{6}\right)} g^{7}}\right)} - \frac{1}{600} \, B c^{2} d i^{3} {\left(\frac{60 \, {\left(6 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{8} g^{7} x^{6} + 6 \, a b^{7} g^{7} x^{5} + 15 \, a^{2} b^{6} g^{7} x^{4} + 20 \, a^{3} b^{5} g^{7} x^{3} + 15 \, a^{4} b^{4} g^{7} x^{2} + 6 \, a^{5} b^{3} g^{7} x + a^{6} b^{2} g^{7}} + \frac{22 \, a b^{5} c^{5} - 140 \, a^{2} b^{4} c^{4} d + 385 \, a^{3} b^{3} c^{3} d^{2} - 615 \, a^{4} b^{2} c^{2} d^{3} + 735 \, a^{5} b c d^{4} - 87 \, a^{6} d^{5} + 60 \, {\left(6 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} - 30 \, {\left(6 \, b^{6} c^{2} d^{3} - 67 \, a b^{5} c d^{4} + 11 \, a^{2} b^{4} d^{5}\right)} x^{4} + 20 \, {\left(6 \, b^{6} c^{3} d^{2} - 49 \, a b^{5} c^{2} d^{3} + 230 \, a^{2} b^{4} c d^{4} - 37 \, a^{3} b^{3} d^{5}\right)} x^{3} - 15 \, {\left(6 \, b^{6} c^{4} d - 43 \, a b^{5} c^{3} d^{2} + 145 \, a^{2} b^{4} c^{2} d^{3} - 365 \, a^{3} b^{3} c d^{4} + 57 \, a^{4} b^{2} d^{5}\right)} x^{2} + 6 \, {\left(12 \, b^{6} c^{5} - 80 \, a b^{5} c^{4} d + 235 \, a^{2} b^{4} c^{3} d^{2} - 415 \, a^{3} b^{3} c^{2} d^{3} + 585 \, a^{4} b^{2} c d^{4} - 87 \, a^{5} b d^{5}\right)} x}{{\left(b^{13} c^{5} - 5 \, a b^{12} c^{4} d + 10 \, a^{2} b^{11} c^{3} d^{2} - 10 \, a^{3} b^{10} c^{2} d^{3} + 5 \, a^{4} b^{9} c d^{4} - a^{5} b^{8} d^{5}\right)} g^{7} x^{6} + 6 \, {\left(a b^{12} c^{5} - 5 \, a^{2} b^{11} c^{4} d + 10 \, a^{3} b^{10} c^{3} d^{2} - 10 \, a^{4} b^{9} c^{2} d^{3} + 5 \, a^{5} b^{8} c d^{4} - a^{6} b^{7} d^{5}\right)} g^{7} x^{5} + 15 \, {\left(a^{2} b^{11} c^{5} - 5 \, a^{3} b^{10} c^{4} d + 10 \, a^{4} b^{9} c^{3} d^{2} - 10 \, a^{5} b^{8} c^{2} d^{3} + 5 \, a^{6} b^{7} c d^{4} - a^{7} b^{6} d^{5}\right)} g^{7} x^{4} + 20 \, {\left(a^{3} b^{10} c^{5} - 5 \, a^{4} b^{9} c^{4} d + 10 \, a^{5} b^{8} c^{3} d^{2} - 10 \, a^{6} b^{7} c^{2} d^{3} + 5 \, a^{7} b^{6} c d^{4} - a^{8} b^{5} d^{5}\right)} g^{7} x^{3} + 15 \, {\left(a^{4} b^{9} c^{5} - 5 \, a^{5} b^{8} c^{4} d + 10 \, a^{6} b^{7} c^{3} d^{2} - 10 \, a^{7} b^{6} c^{2} d^{3} + 5 \, a^{8} b^{5} c d^{4} - a^{9} b^{4} d^{5}\right)} g^{7} x^{2} + 6 \, {\left(a^{5} b^{8} c^{5} - 5 \, a^{6} b^{7} c^{4} d + 10 \, a^{7} b^{6} c^{3} d^{2} - 10 \, a^{8} b^{5} c^{2} d^{3} + 5 \, a^{9} b^{4} c d^{4} - a^{10} b^{3} d^{5}\right)} g^{7} x + {\left(a^{6} b^{7} c^{5} - 5 \, a^{7} b^{6} c^{4} d + 10 \, a^{8} b^{5} c^{3} d^{2} - 10 \, a^{9} b^{4} c^{2} d^{3} + 5 \, a^{10} b^{3} c d^{4} - a^{11} b^{2} d^{5}\right)} g^{7}} + \frac{60 \, {\left(6 \, b c d^{5} - a d^{6}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{6} - 6 \, a b^{7} c^{5} d + 15 \, a^{2} b^{6} c^{4} d^{2} - 20 \, a^{3} b^{5} c^{3} d^{3} + 15 \, a^{4} b^{4} c^{2} d^{4} - 6 \, a^{5} b^{3} c d^{5} + a^{6} b^{2} d^{6}\right)} g^{7}} - \frac{60 \, {\left(6 \, b c d^{5} - a d^{6}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{6} - 6 \, a b^{7} c^{5} d + 15 \, a^{2} b^{6} c^{4} d^{2} - 20 \, a^{3} b^{5} c^{3} d^{3} + 15 \, a^{4} b^{4} c^{2} d^{4} - 6 \, a^{5} b^{3} c d^{5} + a^{6} b^{2} d^{6}\right)} g^{7}}\right)} + \frac{1}{360} \, B c^{3} i^{3} {\left(\frac{60 \, b^{5} d^{5} x^{5} - 10 \, b^{5} c^{5} + 62 \, a b^{4} c^{4} d - 163 \, a^{2} b^{3} c^{3} d^{2} + 237 \, a^{3} b^{2} c^{2} d^{3} - 213 \, a^{4} b c d^{4} + 147 \, a^{5} d^{5} - 30 \, {\left(b^{5} c d^{4} - 11 \, a b^{4} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} - 8 \, a b^{4} c d^{4} + 37 \, a^{2} b^{3} d^{5}\right)} x^{3} - 15 \, {\left(b^{5} c^{3} d^{2} - 7 \, a b^{4} c^{2} d^{3} + 23 \, a^{2} b^{3} c d^{4} - 57 \, a^{3} b^{2} d^{5}\right)} x^{2} + 6 \, {\left(2 \, b^{5} c^{4} d - 13 \, a b^{4} c^{3} d^{2} + 37 \, a^{2} b^{3} c^{2} d^{3} - 63 \, a^{3} b^{2} c d^{4} + 87 \, a^{4} b d^{5}\right)} x}{{\left(b^{12} c^{5} - 5 \, a b^{11} c^{4} d + 10 \, a^{2} b^{10} c^{3} d^{2} - 10 \, a^{3} b^{9} c^{2} d^{3} + 5 \, a^{4} b^{8} c d^{4} - a^{5} b^{7} d^{5}\right)} g^{7} x^{6} + 6 \, {\left(a b^{11} c^{5} - 5 \, a^{2} b^{10} c^{4} d + 10 \, a^{3} b^{9} c^{3} d^{2} - 10 \, a^{4} b^{8} c^{2} d^{3} + 5 \, a^{5} b^{7} c d^{4} - a^{6} b^{6} d^{5}\right)} g^{7} x^{5} + 15 \, {\left(a^{2} b^{10} c^{5} - 5 \, a^{3} b^{9} c^{4} d + 10 \, a^{4} b^{8} c^{3} d^{2} - 10 \, a^{5} b^{7} c^{2} d^{3} + 5 \, a^{6} b^{6} c d^{4} - a^{7} b^{5} d^{5}\right)} g^{7} x^{4} + 20 \, {\left(a^{3} b^{9} c^{5} - 5 \, a^{4} b^{8} c^{4} d + 10 \, a^{5} b^{7} c^{3} d^{2} - 10 \, a^{6} b^{6} c^{2} d^{3} + 5 \, a^{7} b^{5} c d^{4} - a^{8} b^{4} d^{5}\right)} g^{7} x^{3} + 15 \, {\left(a^{4} b^{8} c^{5} - 5 \, a^{5} b^{7} c^{4} d + 10 \, a^{6} b^{6} c^{3} d^{2} - 10 \, a^{7} b^{5} c^{2} d^{3} + 5 \, a^{8} b^{4} c d^{4} - a^{9} b^{3} d^{5}\right)} g^{7} x^{2} + 6 \, {\left(a^{5} b^{7} c^{5} - 5 \, a^{6} b^{6} c^{4} d + 10 \, a^{7} b^{5} c^{3} d^{2} - 10 \, a^{8} b^{4} c^{2} d^{3} + 5 \, a^{9} b^{3} c d^{4} - a^{10} b^{2} d^{5}\right)} g^{7} x + {\left(a^{6} b^{6} c^{5} - 5 \, a^{7} b^{5} c^{4} d + 10 \, a^{8} b^{4} c^{3} d^{2} - 10 \, a^{9} b^{3} c^{2} d^{3} + 5 \, a^{10} b^{2} c d^{4} - a^{11} b d^{5}\right)} g^{7}} - \frac{60 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{7} x^{6} + 6 \, a b^{6} g^{7} x^{5} + 15 \, a^{2} b^{5} g^{7} x^{4} + 20 \, a^{3} b^{4} g^{7} x^{3} + 15 \, a^{4} b^{3} g^{7} x^{2} + 6 \, a^{5} b^{2} g^{7} x + a^{6} b g^{7}} + \frac{60 \, d^{6} \log\left(b x + a\right)}{{\left(b^{7} c^{6} - 6 \, a b^{6} c^{5} d + 15 \, a^{2} b^{5} c^{4} d^{2} - 20 \, a^{3} b^{4} c^{3} d^{3} + 15 \, a^{4} b^{3} c^{2} d^{4} - 6 \, a^{5} b^{2} c d^{5} + a^{6} b d^{6}\right)} g^{7}} - \frac{60 \, d^{6} \log\left(d x + c\right)}{{\left(b^{7} c^{6} - 6 \, a b^{6} c^{5} d + 15 \, a^{2} b^{5} c^{4} d^{2} - 20 \, a^{3} b^{4} c^{3} d^{3} + 15 \, a^{4} b^{3} c^{2} d^{4} - 6 \, a^{5} b^{2} c d^{5} + a^{6} b d^{6}\right)} g^{7}}\right)} - \frac{{\left(6 \, b x + a\right)} A c^{2} d i^{3}}{10 \, {\left(b^{8} g^{7} x^{6} + 6 \, a b^{7} g^{7} x^{5} + 15 \, a^{2} b^{6} g^{7} x^{4} + 20 \, a^{3} b^{5} g^{7} x^{3} + 15 \, a^{4} b^{4} g^{7} x^{2} + 6 \, a^{5} b^{3} g^{7} x + a^{6} b^{2} g^{7}\right)}} - \frac{{\left(15 \, b^{2} x^{2} + 6 \, a b x + a^{2}\right)} A c d^{2} i^{3}}{20 \, {\left(b^{9} g^{7} x^{6} + 6 \, a b^{8} g^{7} x^{5} + 15 \, a^{2} b^{7} g^{7} x^{4} + 20 \, a^{3} b^{6} g^{7} x^{3} + 15 \, a^{4} b^{5} g^{7} x^{2} + 6 \, a^{5} b^{4} g^{7} x + a^{6} b^{3} g^{7}\right)}} - \frac{{\left(20 \, b^{3} x^{3} + 15 \, a b^{2} x^{2} + 6 \, a^{2} b x + a^{3}\right)} A d^{3} i^{3}}{60 \, {\left(b^{10} g^{7} x^{6} + 6 \, a b^{9} g^{7} x^{5} + 15 \, a^{2} b^{8} g^{7} x^{4} + 20 \, a^{3} b^{7} g^{7} x^{3} + 15 \, a^{4} b^{6} g^{7} x^{2} + 6 \, a^{5} b^{5} g^{7} x + a^{6} b^{4} g^{7}\right)}} - \frac{A c^{3} i^{3}}{6 \, {\left(b^{7} g^{7} x^{6} + 6 \, a b^{6} g^{7} x^{5} + 15 \, a^{2} b^{5} g^{7} x^{4} + 20 \, a^{3} b^{4} g^{7} x^{3} + 15 \, a^{4} b^{3} g^{7} x^{2} + 6 \, a^{5} b^{2} g^{7} x + a^{6} b g^{7}\right)}}"," ",0,"-1/3600*B*d^3*i^3*(60*(20*b^3*x^3 + 15*a*b^2*x^2 + 6*a^2*b*x + a^3)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^10*g^7*x^6 + 6*a*b^9*g^7*x^5 + 15*a^2*b^8*g^7*x^4 + 20*a^3*b^7*g^7*x^3 + 15*a^4*b^6*g^7*x^2 + 6*a^5*b^5*g^7*x + a^6*b^4*g^7) + (57*a^3*b^5*c^5 - 405*a^4*b^4*c^4*d + 1470*a^5*b^3*c^3*d^2 - 730*a^6*b^2*c^2*d^3 + 245*a^7*b*c*d^4 - 37*a^8*d^5 + 60*(20*b^8*c^3*d^2 - 15*a*b^7*c^2*d^3 + 6*a^2*b^6*c*d^4 - a^3*b^5*d^5)*x^5 - 30*(20*b^8*c^4*d - 235*a*b^7*c^3*d^2 + 171*a^2*b^6*c^2*d^3 - 67*a^3*b^5*c*d^4 + 11*a^4*b^4*d^5)*x^4 + 20*(20*b^8*c^5 - 175*a*b^7*c^4*d + 866*a^2*b^6*c^3*d^2 - 604*a^3*b^5*c^2*d^3 + 230*a^4*b^4*c*d^4 - 37*a^5*b^3*d^5)*x^3 + 15*(35*a*b^7*c^5 - 271*a^2*b^6*c^4*d + 1128*a^3*b^5*c^3*d^2 - 700*a^4*b^4*c^2*d^3 + 245*a^5*b^3*c*d^4 - 37*a^6*b^2*d^5)*x^2 + 6*(47*a^2*b^6*c^5 - 345*a^3*b^5*c^4*d + 1320*a^4*b^4*c^3*d^2 - 730*a^5*b^3*c^2*d^3 + 245*a^6*b^2*c*d^4 - 37*a^7*b*d^5)*x)/((b^15*c^5 - 5*a*b^14*c^4*d + 10*a^2*b^13*c^3*d^2 - 10*a^3*b^12*c^2*d^3 + 5*a^4*b^11*c*d^4 - a^5*b^10*d^5)*g^7*x^6 + 6*(a*b^14*c^5 - 5*a^2*b^13*c^4*d + 10*a^3*b^12*c^3*d^2 - 10*a^4*b^11*c^2*d^3 + 5*a^5*b^10*c*d^4 - a^6*b^9*d^5)*g^7*x^5 + 15*(a^2*b^13*c^5 - 5*a^3*b^12*c^4*d + 10*a^4*b^11*c^3*d^2 - 10*a^5*b^10*c^2*d^3 + 5*a^6*b^9*c*d^4 - a^7*b^8*d^5)*g^7*x^4 + 20*(a^3*b^12*c^5 - 5*a^4*b^11*c^4*d + 10*a^5*b^10*c^3*d^2 - 10*a^6*b^9*c^2*d^3 + 5*a^7*b^8*c*d^4 - a^8*b^7*d^5)*g^7*x^3 + 15*(a^4*b^11*c^5 - 5*a^5*b^10*c^4*d + 10*a^6*b^9*c^3*d^2 - 10*a^7*b^8*c^2*d^3 + 5*a^8*b^7*c*d^4 - a^9*b^6*d^5)*g^7*x^2 + 6*(a^5*b^10*c^5 - 5*a^6*b^9*c^4*d + 10*a^7*b^8*c^3*d^2 - 10*a^8*b^7*c^2*d^3 + 5*a^9*b^6*c*d^4 - a^10*b^5*d^5)*g^7*x + (a^6*b^9*c^5 - 5*a^7*b^8*c^4*d + 10*a^8*b^7*c^3*d^2 - 10*a^9*b^6*c^2*d^3 + 5*a^10*b^5*c*d^4 - a^11*b^4*d^5)*g^7) + 60*(20*b^3*c^3*d^3 - 15*a*b^2*c^2*d^4 + 6*a^2*b*c*d^5 - a^3*d^6)*log(b*x + a)/((b^10*c^6 - 6*a*b^9*c^5*d + 15*a^2*b^8*c^4*d^2 - 20*a^3*b^7*c^3*d^3 + 15*a^4*b^6*c^2*d^4 - 6*a^5*b^5*c*d^5 + a^6*b^4*d^6)*g^7) - 60*(20*b^3*c^3*d^3 - 15*a*b^2*c^2*d^4 + 6*a^2*b*c*d^5 - a^3*d^6)*log(d*x + c)/((b^10*c^6 - 6*a*b^9*c^5*d + 15*a^2*b^8*c^4*d^2 - 20*a^3*b^7*c^3*d^3 + 15*a^4*b^6*c^2*d^4 - 6*a^5*b^5*c*d^5 + a^6*b^4*d^6)*g^7)) - 1/1200*B*c*d^2*i^3*(60*(15*b^2*x^2 + 6*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^9*g^7*x^6 + 6*a*b^8*g^7*x^5 + 15*a^2*b^7*g^7*x^4 + 20*a^3*b^6*g^7*x^3 + 15*a^4*b^5*g^7*x^2 + 6*a^5*b^4*g^7*x + a^6*b^3*g^7) + (37*a^2*b^5*c^5 - 245*a^3*b^4*c^4*d + 730*a^4*b^3*c^3*d^2 - 1470*a^5*b^2*c^2*d^3 + 405*a^6*b*c*d^4 - 57*a^7*d^5 - 60*(15*b^7*c^2*d^3 - 6*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 30*(15*b^7*c^3*d^2 - 171*a*b^6*c^2*d^3 + 67*a^2*b^5*c*d^4 - 11*a^3*b^4*d^5)*x^4 - 20*(15*b^7*c^4*d - 126*a*b^6*c^3*d^2 + 604*a^2*b^5*c^2*d^3 - 230*a^3*b^4*c*d^4 + 37*a^4*b^3*d^5)*x^3 + 15*(15*b^7*c^5 - 111*a*b^6*c^4*d + 388*a^2*b^5*c^3*d^2 - 1000*a^3*b^4*c^2*d^3 + 365*a^4*b^3*c*d^4 - 57*a^5*b^2*d^5)*x^2 + 6*(27*a*b^6*c^5 - 185*a^2*b^5*c^4*d + 580*a^3*b^4*c^3*d^2 - 1270*a^4*b^3*c^2*d^3 + 405*a^5*b^2*c*d^4 - 57*a^6*b*d^5)*x)/((b^14*c^5 - 5*a*b^13*c^4*d + 10*a^2*b^12*c^3*d^2 - 10*a^3*b^11*c^2*d^3 + 5*a^4*b^10*c*d^4 - a^5*b^9*d^5)*g^7*x^6 + 6*(a*b^13*c^5 - 5*a^2*b^12*c^4*d + 10*a^3*b^11*c^3*d^2 - 10*a^4*b^10*c^2*d^3 + 5*a^5*b^9*c*d^4 - a^6*b^8*d^5)*g^7*x^5 + 15*(a^2*b^12*c^5 - 5*a^3*b^11*c^4*d + 10*a^4*b^10*c^3*d^2 - 10*a^5*b^9*c^2*d^3 + 5*a^6*b^8*c*d^4 - a^7*b^7*d^5)*g^7*x^4 + 20*(a^3*b^11*c^5 - 5*a^4*b^10*c^4*d + 10*a^5*b^9*c^3*d^2 - 10*a^6*b^8*c^2*d^3 + 5*a^7*b^7*c*d^4 - a^8*b^6*d^5)*g^7*x^3 + 15*(a^4*b^10*c^5 - 5*a^5*b^9*c^4*d + 10*a^6*b^8*c^3*d^2 - 10*a^7*b^7*c^2*d^3 + 5*a^8*b^6*c*d^4 - a^9*b^5*d^5)*g^7*x^2 + 6*(a^5*b^9*c^5 - 5*a^6*b^8*c^4*d + 10*a^7*b^7*c^3*d^2 - 10*a^8*b^6*c^2*d^3 + 5*a^9*b^5*c*d^4 - a^10*b^4*d^5)*g^7*x + (a^6*b^8*c^5 - 5*a^7*b^7*c^4*d + 10*a^8*b^6*c^3*d^2 - 10*a^9*b^5*c^2*d^3 + 5*a^10*b^4*c*d^4 - a^11*b^3*d^5)*g^7) - 60*(15*b^2*c^2*d^4 - 6*a*b*c*d^5 + a^2*d^6)*log(b*x + a)/((b^9*c^6 - 6*a*b^8*c^5*d + 15*a^2*b^7*c^4*d^2 - 20*a^3*b^6*c^3*d^3 + 15*a^4*b^5*c^2*d^4 - 6*a^5*b^4*c*d^5 + a^6*b^3*d^6)*g^7) + 60*(15*b^2*c^2*d^4 - 6*a*b*c*d^5 + a^2*d^6)*log(d*x + c)/((b^9*c^6 - 6*a*b^8*c^5*d + 15*a^2*b^7*c^4*d^2 - 20*a^3*b^6*c^3*d^3 + 15*a^4*b^5*c^2*d^4 - 6*a^5*b^4*c*d^5 + a^6*b^3*d^6)*g^7)) - 1/600*B*c^2*d*i^3*(60*(6*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^8*g^7*x^6 + 6*a*b^7*g^7*x^5 + 15*a^2*b^6*g^7*x^4 + 20*a^3*b^5*g^7*x^3 + 15*a^4*b^4*g^7*x^2 + 6*a^5*b^3*g^7*x + a^6*b^2*g^7) + (22*a*b^5*c^5 - 140*a^2*b^4*c^4*d + 385*a^3*b^3*c^3*d^2 - 615*a^4*b^2*c^2*d^3 + 735*a^5*b*c*d^4 - 87*a^6*d^5 + 60*(6*b^6*c*d^4 - a*b^5*d^5)*x^5 - 30*(6*b^6*c^2*d^3 - 67*a*b^5*c*d^4 + 11*a^2*b^4*d^5)*x^4 + 20*(6*b^6*c^3*d^2 - 49*a*b^5*c^2*d^3 + 230*a^2*b^4*c*d^4 - 37*a^3*b^3*d^5)*x^3 - 15*(6*b^6*c^4*d - 43*a*b^5*c^3*d^2 + 145*a^2*b^4*c^2*d^3 - 365*a^3*b^3*c*d^4 + 57*a^4*b^2*d^5)*x^2 + 6*(12*b^6*c^5 - 80*a*b^5*c^4*d + 235*a^2*b^4*c^3*d^2 - 415*a^3*b^3*c^2*d^3 + 585*a^4*b^2*c*d^4 - 87*a^5*b*d^5)*x)/((b^13*c^5 - 5*a*b^12*c^4*d + 10*a^2*b^11*c^3*d^2 - 10*a^3*b^10*c^2*d^3 + 5*a^4*b^9*c*d^4 - a^5*b^8*d^5)*g^7*x^6 + 6*(a*b^12*c^5 - 5*a^2*b^11*c^4*d + 10*a^3*b^10*c^3*d^2 - 10*a^4*b^9*c^2*d^3 + 5*a^5*b^8*c*d^4 - a^6*b^7*d^5)*g^7*x^5 + 15*(a^2*b^11*c^5 - 5*a^3*b^10*c^4*d + 10*a^4*b^9*c^3*d^2 - 10*a^5*b^8*c^2*d^3 + 5*a^6*b^7*c*d^4 - a^7*b^6*d^5)*g^7*x^4 + 20*(a^3*b^10*c^5 - 5*a^4*b^9*c^4*d + 10*a^5*b^8*c^3*d^2 - 10*a^6*b^7*c^2*d^3 + 5*a^7*b^6*c*d^4 - a^8*b^5*d^5)*g^7*x^3 + 15*(a^4*b^9*c^5 - 5*a^5*b^8*c^4*d + 10*a^6*b^7*c^3*d^2 - 10*a^7*b^6*c^2*d^3 + 5*a^8*b^5*c*d^4 - a^9*b^4*d^5)*g^7*x^2 + 6*(a^5*b^8*c^5 - 5*a^6*b^7*c^4*d + 10*a^7*b^6*c^3*d^2 - 10*a^8*b^5*c^2*d^3 + 5*a^9*b^4*c*d^4 - a^10*b^3*d^5)*g^7*x + (a^6*b^7*c^5 - 5*a^7*b^6*c^4*d + 10*a^8*b^5*c^3*d^2 - 10*a^9*b^4*c^2*d^3 + 5*a^10*b^3*c*d^4 - a^11*b^2*d^5)*g^7) + 60*(6*b*c*d^5 - a*d^6)*log(b*x + a)/((b^8*c^6 - 6*a*b^7*c^5*d + 15*a^2*b^6*c^4*d^2 - 20*a^3*b^5*c^3*d^3 + 15*a^4*b^4*c^2*d^4 - 6*a^5*b^3*c*d^5 + a^6*b^2*d^6)*g^7) - 60*(6*b*c*d^5 - a*d^6)*log(d*x + c)/((b^8*c^6 - 6*a*b^7*c^5*d + 15*a^2*b^6*c^4*d^2 - 20*a^3*b^5*c^3*d^3 + 15*a^4*b^4*c^2*d^4 - 6*a^5*b^3*c*d^5 + a^6*b^2*d^6)*g^7)) + 1/360*B*c^3*i^3*((60*b^5*d^5*x^5 - 10*b^5*c^5 + 62*a*b^4*c^4*d - 163*a^2*b^3*c^3*d^2 + 237*a^3*b^2*c^2*d^3 - 213*a^4*b*c*d^4 + 147*a^5*d^5 - 30*(b^5*c*d^4 - 11*a*b^4*d^5)*x^4 + 20*(b^5*c^2*d^3 - 8*a*b^4*c*d^4 + 37*a^2*b^3*d^5)*x^3 - 15*(b^5*c^3*d^2 - 7*a*b^4*c^2*d^3 + 23*a^2*b^3*c*d^4 - 57*a^3*b^2*d^5)*x^2 + 6*(2*b^5*c^4*d - 13*a*b^4*c^3*d^2 + 37*a^2*b^3*c^2*d^3 - 63*a^3*b^2*c*d^4 + 87*a^4*b*d^5)*x)/((b^12*c^5 - 5*a*b^11*c^4*d + 10*a^2*b^10*c^3*d^2 - 10*a^3*b^9*c^2*d^3 + 5*a^4*b^8*c*d^4 - a^5*b^7*d^5)*g^7*x^6 + 6*(a*b^11*c^5 - 5*a^2*b^10*c^4*d + 10*a^3*b^9*c^3*d^2 - 10*a^4*b^8*c^2*d^3 + 5*a^5*b^7*c*d^4 - a^6*b^6*d^5)*g^7*x^5 + 15*(a^2*b^10*c^5 - 5*a^3*b^9*c^4*d + 10*a^4*b^8*c^3*d^2 - 10*a^5*b^7*c^2*d^3 + 5*a^6*b^6*c*d^4 - a^7*b^5*d^5)*g^7*x^4 + 20*(a^3*b^9*c^5 - 5*a^4*b^8*c^4*d + 10*a^5*b^7*c^3*d^2 - 10*a^6*b^6*c^2*d^3 + 5*a^7*b^5*c*d^4 - a^8*b^4*d^5)*g^7*x^3 + 15*(a^4*b^8*c^5 - 5*a^5*b^7*c^4*d + 10*a^6*b^6*c^3*d^2 - 10*a^7*b^5*c^2*d^3 + 5*a^8*b^4*c*d^4 - a^9*b^3*d^5)*g^7*x^2 + 6*(a^5*b^7*c^5 - 5*a^6*b^6*c^4*d + 10*a^7*b^5*c^3*d^2 - 10*a^8*b^4*c^2*d^3 + 5*a^9*b^3*c*d^4 - a^10*b^2*d^5)*g^7*x + (a^6*b^6*c^5 - 5*a^7*b^5*c^4*d + 10*a^8*b^4*c^3*d^2 - 10*a^9*b^3*c^2*d^3 + 5*a^10*b^2*c*d^4 - a^11*b*d^5)*g^7) - 60*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^7*x^6 + 6*a*b^6*g^7*x^5 + 15*a^2*b^5*g^7*x^4 + 20*a^3*b^4*g^7*x^3 + 15*a^4*b^3*g^7*x^2 + 6*a^5*b^2*g^7*x + a^6*b*g^7) + 60*d^6*log(b*x + a)/((b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b^2*c*d^5 + a^6*b*d^6)*g^7) - 60*d^6*log(d*x + c)/((b^7*c^6 - 6*a*b^6*c^5*d + 15*a^2*b^5*c^4*d^2 - 20*a^3*b^4*c^3*d^3 + 15*a^4*b^3*c^2*d^4 - 6*a^5*b^2*c*d^5 + a^6*b*d^6)*g^7)) - 1/10*(6*b*x + a)*A*c^2*d*i^3/(b^8*g^7*x^6 + 6*a*b^7*g^7*x^5 + 15*a^2*b^6*g^7*x^4 + 20*a^3*b^5*g^7*x^3 + 15*a^4*b^4*g^7*x^2 + 6*a^5*b^3*g^7*x + a^6*b^2*g^7) - 1/20*(15*b^2*x^2 + 6*a*b*x + a^2)*A*c*d^2*i^3/(b^9*g^7*x^6 + 6*a*b^8*g^7*x^5 + 15*a^2*b^7*g^7*x^4 + 20*a^3*b^6*g^7*x^3 + 15*a^4*b^5*g^7*x^2 + 6*a^5*b^4*g^7*x + a^6*b^3*g^7) - 1/60*(20*b^3*x^3 + 15*a*b^2*x^2 + 6*a^2*b*x + a^3)*A*d^3*i^3/(b^10*g^7*x^6 + 6*a*b^9*g^7*x^5 + 15*a^2*b^8*g^7*x^4 + 20*a^3*b^7*g^7*x^3 + 15*a^4*b^6*g^7*x^2 + 6*a^5*b^5*g^7*x + a^6*b^4*g^7) - 1/6*A*c^3*i^3/(b^7*g^7*x^6 + 6*a*b^6*g^7*x^5 + 15*a^2*b^5*g^7*x^4 + 20*a^3*b^4*g^7*x^3 + 15*a^4*b^3*g^7*x^2 + 6*a^5*b^2*g^7*x + a^6*b*g^7)","B",0
31,1,790,0,1.789242," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i),x, algorithm=""maxima"")","3 \, A a^{2} b g^{3} {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} - \frac{1}{6} \, A b^{3} g^{3} {\left(\frac{6 \, c^{3} \log\left(d x + c\right)}{d^{4} i} - \frac{2 \, d^{2} x^{3} - 3 \, c d x^{2} + 6 \, c^{2} x}{d^{3} i}\right)} + \frac{3}{2} \, A a b^{2} g^{3} {\left(\frac{2 \, c^{2} \log\left(d x + c\right)}{d^{3} i} + \frac{d x^{2} - 2 \, c x}{d^{2} i}\right)} + \frac{A a^{3} g^{3} \log\left(d i x + c i\right)}{d i} - \frac{{\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - a^{3} d^{3} g^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{4} i} + \frac{{\left(6 \, a^{3} d^{3} g^{3} \log\left(e\right) - {\left(6 \, g^{3} \log\left(e\right) + 11 \, g^{3}\right)} b^{3} c^{3} + 9 \, {\left(2 \, g^{3} \log\left(e\right) + 3 \, g^{3}\right)} a b^{2} c^{2} d - 18 \, {\left(g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b c d^{2}\right)} B \log\left(d x + c\right)}{6 \, d^{4} i} + \frac{2 \, B b^{3} d^{3} g^{3} x^{3} \log\left(e\right) - {\left({\left(3 \, g^{3} \log\left(e\right) + g^{3}\right)} b^{3} c d^{2} - {\left(9 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{2} d^{3}\right)} B x^{2} + 3 \, {\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - a^{3} d^{3} g^{3}\right)} B \log\left(d x + c\right)^{2} + {\left({\left(6 \, g^{3} \log\left(e\right) + 5 \, g^{3}\right)} b^{3} c^{2} d - 6 \, {\left(3 \, g^{3} \log\left(e\right) + 2 \, g^{3}\right)} a b^{2} c d^{2} + {\left(18 \, g^{3} \log\left(e\right) + 7 \, g^{3}\right)} a^{2} b d^{3}\right)} B x + {\left(2 \, B b^{3} d^{3} g^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} g^{3} - 3 \, a b^{2} d^{3} g^{3}\right)} B x^{2} + 6 \, {\left(b^{3} c^{2} d g^{3} - 3 \, a b^{2} c d^{2} g^{3} + 3 \, a^{2} b d^{3} g^{3}\right)} B x + {\left(6 \, a b^{2} c^{2} d g^{3} - 15 \, a^{2} b c d^{2} g^{3} + 11 \, a^{3} d^{3} g^{3}\right)} B\right)} \log\left(b x + a\right) - {\left(2 \, B b^{3} d^{3} g^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} g^{3} - 3 \, a b^{2} d^{3} g^{3}\right)} B x^{2} + 6 \, {\left(b^{3} c^{2} d g^{3} - 3 \, a b^{2} c d^{2} g^{3} + 3 \, a^{2} b d^{3} g^{3}\right)} B x\right)} \log\left(d x + c\right)}{6 \, d^{4} i}"," ",0,"3*A*a^2*b*g^3*(x/(d*i) - c*log(d*x + c)/(d^2*i)) - 1/6*A*b^3*g^3*(6*c^3*log(d*x + c)/(d^4*i) - (2*d^2*x^3 - 3*c*d*x^2 + 6*c^2*x)/(d^3*i)) + 3/2*A*a*b^2*g^3*(2*c^2*log(d*x + c)/(d^3*i) + (d*x^2 - 2*c*x)/(d^2*i)) + A*a^3*g^3*log(d*i*x + c*i)/(d*i) - (b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - a^3*d^3*g^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^4*i) + 1/6*(6*a^3*d^3*g^3*log(e) - (6*g^3*log(e) + 11*g^3)*b^3*c^3 + 9*(2*g^3*log(e) + 3*g^3)*a*b^2*c^2*d - 18*(g^3*log(e) + g^3)*a^2*b*c*d^2)*B*log(d*x + c)/(d^4*i) + 1/6*(2*B*b^3*d^3*g^3*x^3*log(e) - ((3*g^3*log(e) + g^3)*b^3*c*d^2 - (9*g^3*log(e) + g^3)*a*b^2*d^3)*B*x^2 + 3*(b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - a^3*d^3*g^3)*B*log(d*x + c)^2 + ((6*g^3*log(e) + 5*g^3)*b^3*c^2*d - 6*(3*g^3*log(e) + 2*g^3)*a*b^2*c*d^2 + (18*g^3*log(e) + 7*g^3)*a^2*b*d^3)*B*x + (2*B*b^3*d^3*g^3*x^3 - 3*(b^3*c*d^2*g^3 - 3*a*b^2*d^3*g^3)*B*x^2 + 6*(b^3*c^2*d*g^3 - 3*a*b^2*c*d^2*g^3 + 3*a^2*b*d^3*g^3)*B*x + (6*a*b^2*c^2*d*g^3 - 15*a^2*b*c*d^2*g^3 + 11*a^3*d^3*g^3)*B)*log(b*x + a) - (2*B*b^3*d^3*g^3*x^3 - 3*(b^3*c*d^2*g^3 - 3*a*b^2*d^3*g^3)*B*x^2 + 6*(b^3*c^2*d*g^3 - 3*a*b^2*c*d^2*g^3 + 3*a^2*b*d^3*g^3)*B*x)*log(d*x + c))/(d^4*i)","B",0
32,1,477,0,1.737059," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i),x, algorithm=""maxima"")","2 \, A a b g^{2} {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} + \frac{1}{2} \, A b^{2} g^{2} {\left(\frac{2 \, c^{2} \log\left(d x + c\right)}{d^{3} i} + \frac{d x^{2} - 2 \, c x}{d^{2} i}\right)} + \frac{A a^{2} g^{2} \log\left(d i x + c i\right)}{d i} + \frac{{\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + a^{2} d^{2} g^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{3} i} + \frac{{\left(2 \, a^{2} d^{2} g^{2} \log\left(e\right) + {\left(2 \, g^{2} \log\left(e\right) + 3 \, g^{2}\right)} b^{2} c^{2} - 4 \, {\left(g^{2} \log\left(e\right) + g^{2}\right)} a b c d\right)} B \log\left(d x + c\right)}{2 \, d^{3} i} + \frac{B b^{2} d^{2} g^{2} x^{2} \log\left(e\right) - {\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + a^{2} d^{2} g^{2}\right)} B \log\left(d x + c\right)^{2} - {\left({\left(2 \, g^{2} \log\left(e\right) + g^{2}\right)} b^{2} c d - {\left(4 \, g^{2} \log\left(e\right) + g^{2}\right)} a b d^{2}\right)} B x + {\left(B b^{2} d^{2} g^{2} x^{2} - 2 \, {\left(b^{2} c d g^{2} - 2 \, a b d^{2} g^{2}\right)} B x - {\left(2 \, a b c d g^{2} - 3 \, a^{2} d^{2} g^{2}\right)} B\right)} \log\left(b x + a\right) - {\left(B b^{2} d^{2} g^{2} x^{2} - 2 \, {\left(b^{2} c d g^{2} - 2 \, a b d^{2} g^{2}\right)} B x\right)} \log\left(d x + c\right)}{2 \, d^{3} i}"," ",0,"2*A*a*b*g^2*(x/(d*i) - c*log(d*x + c)/(d^2*i)) + 1/2*A*b^2*g^2*(2*c^2*log(d*x + c)/(d^3*i) + (d*x^2 - 2*c*x)/(d^2*i)) + A*a^2*g^2*log(d*i*x + c*i)/(d*i) + (b^2*c^2*g^2 - 2*a*b*c*d*g^2 + a^2*d^2*g^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^3*i) + 1/2*(2*a^2*d^2*g^2*log(e) + (2*g^2*log(e) + 3*g^2)*b^2*c^2 - 4*(g^2*log(e) + g^2)*a*b*c*d)*B*log(d*x + c)/(d^3*i) + 1/2*(B*b^2*d^2*g^2*x^2*log(e) - (b^2*c^2*g^2 - 2*a*b*c*d*g^2 + a^2*d^2*g^2)*B*log(d*x + c)^2 - ((2*g^2*log(e) + g^2)*b^2*c*d - (4*g^2*log(e) + g^2)*a*b*d^2)*B*x + (B*b^2*d^2*g^2*x^2 - 2*(b^2*c*d*g^2 - 2*a*b*d^2*g^2)*B*x - (2*a*b*c*d*g^2 - 3*a^2*d^2*g^2)*B)*log(b*x + a) - (B*b^2*d^2*g^2*x^2 - 2*(b^2*c*d*g^2 - 2*a*b*d^2*g^2)*B*x)*log(d*x + c))/(d^3*i)","B",0
33,1,221,0,1.682193," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i),x, algorithm=""maxima"")","A b g {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} + \frac{A a g \log\left(d i x + c i\right)}{d i} - \frac{{\left(b c g - a d g\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{2} i} + \frac{{\left(a d g \log\left(e\right) - {\left(g \log\left(e\right) + g\right)} b c\right)} B \log\left(d x + c\right)}{d^{2} i} - \frac{2 \, B b d g x \log\left(d x + c\right) - 2 \, B b d g x \log\left(e\right) - {\left(b c g - a d g\right)} B \log\left(d x + c\right)^{2} - 2 \, {\left(B b d g x + B a d g\right)} \log\left(b x + a\right)}{2 \, d^{2} i}"," ",0,"A*b*g*(x/(d*i) - c*log(d*x + c)/(d^2*i)) + A*a*g*log(d*i*x + c*i)/(d*i) - (b*c*g - a*d*g)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^2*i) + (a*d*g*log(e) - (g*log(e) + g)*b*c)*B*log(d*x + c)/(d^2*i) - 1/2*(2*B*b*d*g*x*log(d*x + c) - 2*B*b*d*g*x*log(e) - (b*c*g - a*d*g)*B*log(d*x + c)^2 - 2*(B*b*d*g*x + B*a*d*g)*log(b*x + a))/(d^2*i)","A",0
34,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i),x, algorithm=""maxima"")","-\frac{1}{2} \, B {\left(\frac{\log\left(d x + c\right)^{2}}{d i} - 2 \, \int \frac{\log\left(b x + a\right) + \log\left(e\right)}{d i x + c i}\,{d x}\right)} + \frac{A \log\left(d i x + c i\right)}{d i}"," ",0,"-1/2*B*(log(d*x + c)^2/(d*i) - 2*integrate((log(b*x + a) + log(e))/(d*i*x + c*i), x)) + A*log(d*i*x + c*i)/(d*i)","F",0
35,1,172,0,1.135604," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)/(d*i*x+c*i),x, algorithm=""maxima"")","B {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + A {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)} - \frac{{\left(\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right) + \log\left(d x + c\right)^{2}\right)} B}{2 \, {\left(b c g i - a d g i\right)}}"," ",0,"B*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + A*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i)) - 1/2*(log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c) + log(d*x + c)^2)*B/(b*c*g*i - a*d*g*i)","B",0
36,1,424,0,1.320365," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2/(d*i*x+c*i),x, algorithm=""maxima"")","-B {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - A {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)} + \frac{{\left({\left(b d x + a d\right)} \log\left(b x + a\right)^{2} + {\left(b d x + a d\right)} \log\left(d x + c\right)^{2} - 2 \, b c + 2 \, a d - 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right) + 2 \, {\left(b d x + a d - {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{2 \, {\left(a b^{2} c^{2} g^{2} i - 2 \, a^{2} b c d g^{2} i + a^{3} d^{2} g^{2} i + {\left(b^{3} c^{2} g^{2} i - 2 \, a b^{2} c d g^{2} i + a^{2} b d^{2} g^{2} i\right)} x\right)}}"," ",0,"-B*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - A*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i)) + 1/2*((b*d*x + a*d)*log(b*x + a)^2 + (b*d*x + a*d)*log(d*x + c)^2 - 2*b*c + 2*a*d - 2*(b*d*x + a*d)*log(b*x + a) + 2*(b*d*x + a*d - (b*d*x + a*d)*log(b*x + a))*log(d*x + c))*B/(a*b^2*c^2*g^2*i - 2*a^2*b*c*d*g^2*i + a^3*d^2*g^2*i + (b^3*c^2*g^2*i - 2*a*b^2*c*d*g^2*i + a^2*b*d^2*g^2*i)*x)","B",0
37,1,885,0,1.715229," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3/(d*i*x+c*i),x, algorithm=""maxima"")","\frac{1}{2} \, B {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{1}{2} \, A {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)} - \frac{{\left(b^{2} c^{2} - 8 \, a b c d + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d - a b d^{2}\right)} x - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{4 \, {\left(a^{2} b^{3} c^{3} g^{3} i - 3 \, a^{3} b^{2} c^{2} d g^{3} i + 3 \, a^{4} b c d^{2} g^{3} i - a^{5} d^{3} g^{3} i + {\left(b^{5} c^{3} g^{3} i - 3 \, a b^{4} c^{2} d g^{3} i + 3 \, a^{2} b^{3} c d^{2} g^{3} i - a^{3} b^{2} d^{3} g^{3} i\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} g^{3} i - 3 \, a^{2} b^{3} c^{2} d g^{3} i + 3 \, a^{3} b^{2} c d^{2} g^{3} i - a^{4} b d^{3} g^{3} i\right)} x\right)}}"," ",0,"1/2*B*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 1/2*A*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i)) - 1/4*(b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^2 - 6*(b^2*c*d - a*b*d^2)*x - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))*B/(a^2*b^3*c^3*g^3*i - 3*a^3*b^2*c^2*d*g^3*i + 3*a^4*b*c*d^2*g^3*i - a^5*d^3*g^3*i + (b^5*c^3*g^3*i - 3*a*b^4*c^2*d*g^3*i + 3*a^2*b^3*c*d^2*g^3*i - a^3*b^2*d^3*g^3*i)*x^2 + 2*(a*b^4*c^3*g^3*i - 3*a^2*b^3*c^2*d*g^3*i + 3*a^3*b^2*c*d^2*g^3*i - a^4*b*d^3*g^3*i)*x)","B",0
38,1,1469,0,2.413619," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4/(d*i*x+c*i),x, algorithm=""maxima"")","-\frac{1}{6} \, B {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{6} \, A {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)} - \frac{{\left(4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{36 \, {\left(a^{3} b^{4} c^{4} g^{4} i - 4 \, a^{4} b^{3} c^{3} d g^{4} i + 6 \, a^{5} b^{2} c^{2} d^{2} g^{4} i - 4 \, a^{6} b c d^{3} g^{4} i + a^{7} d^{4} g^{4} i + {\left(b^{7} c^{4} g^{4} i - 4 \, a b^{6} c^{3} d g^{4} i + 6 \, a^{2} b^{5} c^{2} d^{2} g^{4} i - 4 \, a^{3} b^{4} c d^{3} g^{4} i + a^{4} b^{3} d^{4} g^{4} i\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} g^{4} i - 4 \, a^{2} b^{5} c^{3} d g^{4} i + 6 \, a^{3} b^{4} c^{2} d^{2} g^{4} i - 4 \, a^{4} b^{3} c d^{3} g^{4} i + a^{5} b^{2} d^{4} g^{4} i\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} g^{4} i - 4 \, a^{3} b^{4} c^{3} d g^{4} i + 6 \, a^{4} b^{3} c^{2} d^{2} g^{4} i - 4 \, a^{5} b^{2} c d^{3} g^{4} i + a^{6} b d^{4} g^{4} i\right)} x\right)}}"," ",0,"-1/6*B*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/6*A*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i)) - 1/36*(4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*B/(a^3*b^4*c^4*g^4*i - 4*a^4*b^3*c^3*d*g^4*i + 6*a^5*b^2*c^2*d^2*g^4*i - 4*a^6*b*c*d^3*g^4*i + a^7*d^4*g^4*i + (b^7*c^4*g^4*i - 4*a*b^6*c^3*d*g^4*i + 6*a^2*b^5*c^2*d^2*g^4*i - 4*a^3*b^4*c*d^3*g^4*i + a^4*b^3*d^4*g^4*i)*x^3 + 3*(a*b^6*c^4*g^4*i - 4*a^2*b^5*c^3*d*g^4*i + 6*a^3*b^4*c^2*d^2*g^4*i - 4*a^4*b^3*c*d^3*g^4*i + a^5*b^2*d^4*g^4*i)*x^2 + 3*(a^2*b^5*c^4*g^4*i - 4*a^3*b^4*c^3*d*g^4*i + 6*a^4*b^3*c^2*d^2*g^4*i - 4*a^5*b^2*c*d^3*g^4*i + a^6*b*d^4*g^4*i)*x)","B",0
39,1,1341,0,1.892270," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{2 \, c^{3}}{d^{5} i^{2} x + c d^{4} i^{2}} + \frac{6 \, c^{2} \log\left(d x + c\right)}{d^{4} i^{2}} + \frac{d x^{2} - 4 \, c x}{d^{3} i^{2}}\right)} A b^{3} g^{3} - 3 \, A a b^{2} {\left(\frac{c^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \frac{x}{d^{2} i^{2}} + \frac{2 \, c \log\left(d x + c\right)}{d^{3} i^{2}}\right)} g^{3} + 3 \, A a^{2} b g^{3} {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - B a^{3} g^{3} {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{1}{d^{2} i^{2} x + c d i^{2}} - \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} + \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{A a^{3} g^{3}}{d^{2} i^{2} x + c d i^{2}} - \frac{{\left(6 \, a^{3} b d^{3} g^{3} \log\left(e\right) - {\left(6 \, g^{3} \log\left(e\right) + 7 \, g^{3}\right)} b^{4} c^{3} + {\left(18 \, g^{3} \log\left(e\right) + 17 \, g^{3}\right)} a b^{3} c^{2} d - 6 \, {\left(3 \, g^{3} \log\left(e\right) + 2 \, g^{3}\right)} a^{2} b^{2} c d^{2}\right)} B \log\left(d x + c\right)}{2 \, {\left(b c d^{4} i^{2} - a d^{5} i^{2}\right)}} + \frac{{\left(b^{4} c d^{3} g^{3} \log\left(e\right) - a b^{3} d^{4} g^{3} \log\left(e\right)\right)} B x^{3} - {\left({\left(3 \, g^{3} \log\left(e\right) + g^{3}\right)} b^{4} c^{2} d^{2} - {\left(9 \, g^{3} \log\left(e\right) + 2 \, g^{3}\right)} a b^{3} c d^{3} + {\left(6 \, g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b^{2} d^{4}\right)} B x^{2} - {\left({\left(4 \, g^{3} \log\left(e\right) + g^{3}\right)} b^{4} c^{3} d - 2 \, {\left(5 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{3} c^{2} d^{2} + {\left(6 \, g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b^{2} c d^{3}\right)} B x - 3 \, {\left({\left(b^{4} c^{3} d g^{3} - 3 \, a b^{3} c^{2} d^{2} g^{3} + 3 \, a^{2} b^{2} c d^{3} g^{3} - a^{3} b d^{4} g^{3}\right)} B x + {\left(b^{4} c^{4} g^{3} - 3 \, a b^{3} c^{3} d g^{3} + 3 \, a^{2} b^{2} c^{2} d^{2} g^{3} - a^{3} b c d^{3} g^{3}\right)} B\right)} \log\left(d x + c\right)^{2} + 2 \, {\left({\left(g^{3} \log\left(e\right) - g^{3}\right)} b^{4} c^{4} - 4 \, {\left(g^{3} \log\left(e\right) - g^{3}\right)} a b^{3} c^{3} d + 6 \, {\left(g^{3} \log\left(e\right) - g^{3}\right)} a^{2} b^{2} c^{2} d^{2} - 3 \, {\left(g^{3} \log\left(e\right) - g^{3}\right)} a^{3} b c d^{3}\right)} B + {\left({\left(b^{4} c d^{3} g^{3} - a b^{3} d^{4} g^{3}\right)} B x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 3 \, a b^{3} c d^{3} g^{3} + 2 \, a^{2} b^{2} d^{4} g^{3}\right)} B x^{2} - {\left(6 \, b^{4} c^{3} d g^{3} - 12 \, a b^{3} c^{2} d^{2} g^{3} + 3 \, a^{2} b^{2} c d^{3} g^{3} + 5 \, a^{3} b d^{4} g^{3}\right)} B x - {\left(6 \, a b^{3} c^{3} d g^{3} - 15 \, a^{2} b^{2} c^{2} d^{2} g^{3} + 11 \, a^{3} b c d^{3} g^{3}\right)} B\right)} \log\left(b x + a\right) - {\left({\left(b^{4} c d^{3} g^{3} - a b^{3} d^{4} g^{3}\right)} B x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 3 \, a b^{3} c d^{3} g^{3} + 2 \, a^{2} b^{2} d^{4} g^{3}\right)} B x^{2} - 2 \, {\left(2 \, b^{4} c^{3} d g^{3} - 5 \, a b^{3} c^{2} d^{2} g^{3} + 3 \, a^{2} b^{2} c d^{3} g^{3}\right)} B x + 2 \, {\left(b^{4} c^{4} g^{3} - 4 \, a b^{3} c^{3} d g^{3} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} - 3 \, a^{3} b c d^{3} g^{3}\right)} B\right)} \log\left(d x + c\right)}{2 \, {\left(b c^{2} d^{4} i^{2} - a c d^{5} i^{2} + {\left(b c d^{5} i^{2} - a d^{6} i^{2}\right)} x\right)}} + \frac{3 \, {\left(b^{3} c^{2} g^{3} - 2 \, a b^{2} c d g^{3} + a^{2} b d^{2} g^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{4} i^{2}}"," ",0,"1/2*(2*c^3/(d^5*i^2*x + c*d^4*i^2) + 6*c^2*log(d*x + c)/(d^4*i^2) + (d*x^2 - 4*c*x)/(d^3*i^2))*A*b^3*g^3 - 3*A*a*b^2*(c^2/(d^4*i^2*x + c*d^3*i^2) - x/(d^2*i^2) + 2*c*log(d*x + c)/(d^3*i^2))*g^3 + 3*A*a^2*b*g^3*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - B*a^3*g^3*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^2*i^2*x + c*d*i^2) - 1/(d^2*i^2*x + c*d*i^2) - b*log(b*x + a)/((b*c*d - a*d^2)*i^2) + b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A*a^3*g^3/(d^2*i^2*x + c*d*i^2) - 1/2*(6*a^3*b*d^3*g^3*log(e) - (6*g^3*log(e) + 7*g^3)*b^4*c^3 + (18*g^3*log(e) + 17*g^3)*a*b^3*c^2*d - 6*(3*g^3*log(e) + 2*g^3)*a^2*b^2*c*d^2)*B*log(d*x + c)/(b*c*d^4*i^2 - a*d^5*i^2) + 1/2*((b^4*c*d^3*g^3*log(e) - a*b^3*d^4*g^3*log(e))*B*x^3 - ((3*g^3*log(e) + g^3)*b^4*c^2*d^2 - (9*g^3*log(e) + 2*g^3)*a*b^3*c*d^3 + (6*g^3*log(e) + g^3)*a^2*b^2*d^4)*B*x^2 - ((4*g^3*log(e) + g^3)*b^4*c^3*d - 2*(5*g^3*log(e) + g^3)*a*b^3*c^2*d^2 + (6*g^3*log(e) + g^3)*a^2*b^2*c*d^3)*B*x - 3*((b^4*c^3*d*g^3 - 3*a*b^3*c^2*d^2*g^3 + 3*a^2*b^2*c*d^3*g^3 - a^3*b*d^4*g^3)*B*x + (b^4*c^4*g^3 - 3*a*b^3*c^3*d*g^3 + 3*a^2*b^2*c^2*d^2*g^3 - a^3*b*c*d^3*g^3)*B)*log(d*x + c)^2 + 2*((g^3*log(e) - g^3)*b^4*c^4 - 4*(g^3*log(e) - g^3)*a*b^3*c^3*d + 6*(g^3*log(e) - g^3)*a^2*b^2*c^2*d^2 - 3*(g^3*log(e) - g^3)*a^3*b*c*d^3)*B + ((b^4*c*d^3*g^3 - a*b^3*d^4*g^3)*B*x^3 - 3*(b^4*c^2*d^2*g^3 - 3*a*b^3*c*d^3*g^3 + 2*a^2*b^2*d^4*g^3)*B*x^2 - (6*b^4*c^3*d*g^3 - 12*a*b^3*c^2*d^2*g^3 + 3*a^2*b^2*c*d^3*g^3 + 5*a^3*b*d^4*g^3)*B*x - (6*a*b^3*c^3*d*g^3 - 15*a^2*b^2*c^2*d^2*g^3 + 11*a^3*b*c*d^3*g^3)*B)*log(b*x + a) - ((b^4*c*d^3*g^3 - a*b^3*d^4*g^3)*B*x^3 - 3*(b^4*c^2*d^2*g^3 - 3*a*b^3*c*d^3*g^3 + 2*a^2*b^2*d^4*g^3)*B*x^2 - 2*(2*b^4*c^3*d*g^3 - 5*a*b^3*c^2*d^2*g^3 + 3*a^2*b^2*c*d^3*g^3)*B*x + 2*(b^4*c^4*g^3 - 4*a*b^3*c^3*d*g^3 + 6*a^2*b^2*c^2*d^2*g^3 - 3*a^3*b*c*d^3*g^3)*B)*log(d*x + c))/(b*c^2*d^4*i^2 - a*c*d^5*i^2 + (b*c*d^5*i^2 - a*d^6*i^2)*x) + 3*(b^3*c^2*g^3 - 2*a*b^2*c*d*g^3 + a^2*b*d^2*g^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^4*i^2)","B",0
40,1,886,0,1.899737," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-A b^{2} {\left(\frac{c^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \frac{x}{d^{2} i^{2}} + \frac{2 \, c \log\left(d x + c\right)}{d^{3} i^{2}}\right)} g^{2} + 2 \, A a b g^{2} {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - B a^{2} g^{2} {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{1}{d^{2} i^{2} x + c d i^{2}} - \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} + \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{A a^{2} g^{2}}{d^{2} i^{2} x + c d i^{2}} - \frac{{\left(2 \, a^{2} b d^{2} g^{2} \log\left(e\right) + 2 \, {\left(g^{2} \log\left(e\right) + g^{2}\right)} b^{3} c^{2} - {\left(4 \, g^{2} \log\left(e\right) + 3 \, g^{2}\right)} a b^{2} c d\right)} B \log\left(d x + c\right)}{b c d^{3} i^{2} - a d^{4} i^{2}} + \frac{{\left(b^{3} c d^{2} g^{2} \log\left(e\right) - a b^{2} d^{3} g^{2} \log\left(e\right)\right)} B x^{2} + {\left(b^{3} c^{2} d g^{2} \log\left(e\right) - a b^{2} c d^{2} g^{2} \log\left(e\right)\right)} B x + {\left({\left(b^{3} c^{2} d g^{2} - 2 \, a b^{2} c d^{2} g^{2} + a^{2} b d^{3} g^{2}\right)} B x + {\left(b^{3} c^{3} g^{2} - 2 \, a b^{2} c^{2} d g^{2} + a^{2} b c d^{2} g^{2}\right)} B\right)} \log\left(d x + c\right)^{2} - {\left({\left(g^{2} \log\left(e\right) - g^{2}\right)} b^{3} c^{3} - 3 \, {\left(g^{2} \log\left(e\right) - g^{2}\right)} a b^{2} c^{2} d + 2 \, {\left(g^{2} \log\left(e\right) - g^{2}\right)} a^{2} b c d^{2}\right)} B + {\left({\left(b^{3} c d^{2} g^{2} - a b^{2} d^{3} g^{2}\right)} B x^{2} + {\left(2 \, b^{3} c^{2} d g^{2} - 2 \, a b^{2} c d^{2} g^{2} - a^{2} b d^{3} g^{2}\right)} B x + {\left(2 \, a b^{2} c^{2} d g^{2} - 3 \, a^{2} b c d^{2} g^{2}\right)} B\right)} \log\left(b x + a\right) - {\left({\left(b^{3} c d^{2} g^{2} - a b^{2} d^{3} g^{2}\right)} B x^{2} + {\left(b^{3} c^{2} d g^{2} - a b^{2} c d^{2} g^{2}\right)} B x - {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 2 \, a^{2} b c d^{2} g^{2}\right)} B\right)} \log\left(d x + c\right)}{b c^{2} d^{3} i^{2} - a c d^{4} i^{2} + {\left(b c d^{4} i^{2} - a d^{5} i^{2}\right)} x} - \frac{2 \, {\left(b^{2} c g^{2} - a b d g^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{3} i^{2}}"," ",0,"-A*b^2*(c^2/(d^4*i^2*x + c*d^3*i^2) - x/(d^2*i^2) + 2*c*log(d*x + c)/(d^3*i^2))*g^2 + 2*A*a*b*g^2*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - B*a^2*g^2*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^2*i^2*x + c*d*i^2) - 1/(d^2*i^2*x + c*d*i^2) - b*log(b*x + a)/((b*c*d - a*d^2)*i^2) + b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A*a^2*g^2/(d^2*i^2*x + c*d*i^2) - (2*a^2*b*d^2*g^2*log(e) + 2*(g^2*log(e) + g^2)*b^3*c^2 - (4*g^2*log(e) + 3*g^2)*a*b^2*c*d)*B*log(d*x + c)/(b*c*d^3*i^2 - a*d^4*i^2) + ((b^3*c*d^2*g^2*log(e) - a*b^2*d^3*g^2*log(e))*B*x^2 + (b^3*c^2*d*g^2*log(e) - a*b^2*c*d^2*g^2*log(e))*B*x + ((b^3*c^2*d*g^2 - 2*a*b^2*c*d^2*g^2 + a^2*b*d^3*g^2)*B*x + (b^3*c^3*g^2 - 2*a*b^2*c^2*d*g^2 + a^2*b*c*d^2*g^2)*B)*log(d*x + c)^2 - ((g^2*log(e) - g^2)*b^3*c^3 - 3*(g^2*log(e) - g^2)*a*b^2*c^2*d + 2*(g^2*log(e) - g^2)*a^2*b*c*d^2)*B + ((b^3*c*d^2*g^2 - a*b^2*d^3*g^2)*B*x^2 + (2*b^3*c^2*d*g^2 - 2*a*b^2*c*d^2*g^2 - a^2*b*d^3*g^2)*B*x + (2*a*b^2*c^2*d*g^2 - 3*a^2*b*c*d^2*g^2)*B)*log(b*x + a) - ((b^3*c*d^2*g^2 - a*b^2*d^3*g^2)*B*x^2 + (b^3*c^2*d*g^2 - a*b^2*c*d^2*g^2)*B*x - (b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 2*a^2*b*c*d^2*g^2)*B)*log(d*x + c))/(b*c^2*d^3*i^2 - a*c*d^4*i^2 + (b*c*d^4*i^2 - a*d^5*i^2)*x) - 2*(b^2*c*g^2 - a*b*d*g^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^3*i^2)","B",0
41,0,0,0,0.000000," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, B b g {\left(\frac{{\left(d x + c\right)} \log\left(d x + c\right)^{2} + 2 \, c \log\left(d x + c\right)}{d^{3} i^{2} x + c d^{2} i^{2}} - 2 \, \int \frac{d x \log\left(b x + a\right) + d x \log\left(e\right) + c}{d^{3} i^{2} x^{2} + 2 \, c d^{2} i^{2} x + c^{2} d i^{2}}\,{d x}\right)} + A b g {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - B a g {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{1}{d^{2} i^{2} x + c d i^{2}} - \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} + \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{A a g}{d^{2} i^{2} x + c d i^{2}}"," ",0,"-1/2*B*b*g*(((d*x + c)*log(d*x + c)^2 + 2*c*log(d*x + c))/(d^3*i^2*x + c*d^2*i^2) - 2*integrate((d*x*log(b*x + a) + d*x*log(e) + c)/(d^3*i^2*x^2 + 2*c*d^2*i^2*x + c^2*d*i^2), x)) + A*b*g*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - B*a*g*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^2*i^2*x + c*d*i^2) - 1/(d^2*i^2*x + c*d*i^2) - b*log(b*x + a)/((b*c*d - a*d^2)*i^2) + b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A*a*g/(d^2*i^2*x + c*d*i^2)","F",0
42,1,134,0,1.095047," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-B {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{1}{d^{2} i^{2} x + c d i^{2}} - \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} + \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{A}{d^{2} i^{2} x + c d i^{2}}"," ",0,"-B*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^2*i^2*x + c*d*i^2) - 1/(d^2*i^2*x + c*d*i^2) - b*log(b*x + a)/((b*c*d - a*d^2)*i^2) + b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A/(d^2*i^2*x + c*d*i^2)","A",0
43,1,421,0,1.324873," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)/(d*i*x+c*i)^2,x, algorithm=""maxima"")","B {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + A {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)} - \frac{{\left({\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} + 2 \, b c - 2 \, a d + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 2 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{2 \, {\left(b^{2} c^{3} g i^{2} - 2 \, a b c^{2} d g i^{2} + a^{2} c d^{2} g i^{2} + {\left(b^{2} c^{2} d g i^{2} - 2 \, a b c d^{2} g i^{2} + a^{2} d^{3} g i^{2}\right)} x\right)}}"," ",0,"B*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + A*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2)) - 1/2*((b*d*x + b*c)*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 + 2*b*c - 2*a*d + 2*(b*d*x + b*c)*log(b*x + a) - 2*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c))*B/(b^2*c^3*g*i^2 - 2*a*b*c^2*d*g*i^2 + a^2*c*d^2*g*i^2 + (b^2*c^2*d*g*i^2 - 2*a*b*c*d^2*g*i^2 + a^2*d^3*g*i^2)*x)","B",0
44,1,859,0,1.406440," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-B {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - A {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)} - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)^{2}\right)} B}{a b^{3} c^{4} g^{2} i^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} i^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} i^{2} - a^{4} c d^{3} g^{2} i^{2} + {\left(b^{4} c^{3} d g^{2} i^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} i^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} i^{2} - a^{3} b d^{4} g^{2} i^{2}\right)} x^{2} + {\left(b^{4} c^{4} g^{2} i^{2} - 2 \, a b^{3} c^{3} d g^{2} i^{2} + 2 \, a^{3} b c d^{3} g^{2} i^{2} - a^{4} d^{4} g^{2} i^{2}\right)} x}"," ",0,"-B*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - A*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2)) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)*log(d*x + c) - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c)^2)*B/(a*b^3*c^4*g^2*i^2 - 3*a^2*b^2*c^3*d*g^2*i^2 + 3*a^3*b*c^2*d^2*g^2*i^2 - a^4*c*d^3*g^2*i^2 + (b^4*c^3*d*g^2*i^2 - 3*a*b^3*c^2*d^2*g^2*i^2 + 3*a^2*b^2*c*d^3*g^2*i^2 - a^3*b*d^4*g^2*i^2)*x^2 + (b^4*c^4*g^2*i^2 - 2*a*b^3*c^3*d*g^2*i^2 + 2*a^3*b*c*d^3*g^2*i^2 - a^4*d^4*g^2*i^2)*x)","B",0
45,1,1721,0,2.369771," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3/(d*i*x+c*i)^2,x, algorithm=""maxima"")","\frac{1}{2} \, B {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{1}{2} \, A {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)} - \frac{{\left(b^{3} c^{3} - 12 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{4 \, {\left(a^{2} b^{4} c^{5} g^{3} i^{2} - 4 \, a^{3} b^{3} c^{4} d g^{3} i^{2} + 6 \, a^{4} b^{2} c^{3} d^{2} g^{3} i^{2} - 4 \, a^{5} b c^{2} d^{3} g^{3} i^{2} + a^{6} c d^{4} g^{3} i^{2} + {\left(b^{6} c^{4} d g^{3} i^{2} - 4 \, a b^{5} c^{3} d^{2} g^{3} i^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} g^{3} i^{2} - 4 \, a^{3} b^{3} c d^{4} g^{3} i^{2} + a^{4} b^{2} d^{5} g^{3} i^{2}\right)} x^{3} + {\left(b^{6} c^{5} g^{3} i^{2} - 2 \, a b^{5} c^{4} d g^{3} i^{2} - 2 \, a^{2} b^{4} c^{3} d^{2} g^{3} i^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} g^{3} i^{2} - 7 \, a^{4} b^{2} c d^{4} g^{3} i^{2} + 2 \, a^{5} b d^{5} g^{3} i^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} g^{3} i^{2} - 7 \, a^{2} b^{4} c^{4} d g^{3} i^{2} + 8 \, a^{3} b^{3} c^{3} d^{2} g^{3} i^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} g^{3} i^{2} - 2 \, a^{5} b c d^{4} g^{3} i^{2} + a^{6} d^{5} g^{3} i^{2}\right)} x\right)}}"," ",0,"1/2*B*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 1/2*A*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2)) - 1/4*(b^3*c^3 - 12*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c)^2 - 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c))*B/(a^2*b^4*c^5*g^3*i^2 - 4*a^3*b^3*c^4*d*g^3*i^2 + 6*a^4*b^2*c^3*d^2*g^3*i^2 - 4*a^5*b*c^2*d^3*g^3*i^2 + a^6*c*d^4*g^3*i^2 + (b^6*c^4*d*g^3*i^2 - 4*a*b^5*c^3*d^2*g^3*i^2 + 6*a^2*b^4*c^2*d^3*g^3*i^2 - 4*a^3*b^3*c*d^4*g^3*i^2 + a^4*b^2*d^5*g^3*i^2)*x^3 + (b^6*c^5*g^3*i^2 - 2*a*b^5*c^4*d*g^3*i^2 - 2*a^2*b^4*c^3*d^2*g^3*i^2 + 8*a^3*b^3*c^2*d^3*g^3*i^2 - 7*a^4*b^2*c*d^4*g^3*i^2 + 2*a^5*b*d^5*g^3*i^2)*x^2 + (2*a*b^5*c^5*g^3*i^2 - 7*a^2*b^4*c^4*d*g^3*i^2 + 8*a^3*b^3*c^3*d^2*g^3*i^2 - 2*a^4*b^2*c^2*d^3*g^3*i^2 - 2*a^5*b*c*d^4*g^3*i^2 + a^6*d^5*g^3*i^2)*x)","B",0
46,1,2560,0,3.449288," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, B {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{3} \, A {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)} - \frac{{\left(b^{4} c^{4} - 9 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} - 55 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4} + 30 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(11 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} - 19 \, a^{2} b^{2} d^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - {\left(5 \, b^{4} c^{3} d - 81 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} + 19 \, a^{3} b d^{4}\right)} x + 30 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{3} b c d^{3} + 5 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 15 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 6 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{9 \, {\left(a^{3} b^{5} c^{6} g^{4} i^{2} - 5 \, a^{4} b^{4} c^{5} d g^{4} i^{2} + 10 \, a^{5} b^{3} c^{4} d^{2} g^{4} i^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{7} b c^{2} d^{4} g^{4} i^{2} - a^{8} c d^{5} g^{4} i^{2} + {\left(b^{8} c^{5} d g^{4} i^{2} - 5 \, a b^{7} c^{4} d^{2} g^{4} i^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} g^{4} i^{2} - 10 \, a^{3} b^{5} c^{2} d^{4} g^{4} i^{2} + 5 \, a^{4} b^{4} c d^{5} g^{4} i^{2} - a^{5} b^{3} d^{6} g^{4} i^{2}\right)} x^{4} + {\left(b^{8} c^{6} g^{4} i^{2} - 2 \, a b^{7} c^{5} d g^{4} i^{2} - 5 \, a^{2} b^{6} c^{4} d^{2} g^{4} i^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} g^{4} i^{2} - 25 \, a^{4} b^{4} c^{2} d^{4} g^{4} i^{2} + 14 \, a^{5} b^{3} c d^{5} g^{4} i^{2} - 3 \, a^{6} b^{2} d^{6} g^{4} i^{2}\right)} x^{3} + 3 \, {\left(a b^{7} c^{6} g^{4} i^{2} - 4 \, a^{2} b^{6} c^{5} d g^{4} i^{2} + 5 \, a^{3} b^{5} c^{4} d^{2} g^{4} i^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} g^{4} i^{2} + 4 \, a^{6} b^{2} c d^{5} g^{4} i^{2} - a^{7} b d^{6} g^{4} i^{2}\right)} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} g^{4} i^{2} - 14 \, a^{3} b^{5} c^{5} d g^{4} i^{2} + 25 \, a^{4} b^{4} c^{4} d^{2} g^{4} i^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{6} b^{2} c^{2} d^{4} g^{4} i^{2} + 2 \, a^{7} b c d^{5} g^{4} i^{2} - a^{8} d^{6} g^{4} i^{2}\right)} x\right)}}"," ",0,"-1/3*B*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/3*A*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2)) - 1/9*(b^4*c^4 - 9*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 - 55*a^3*b*c*d^3 + 9*a^4*d^4 + 30*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 3*(11*b^4*c^2*d^2 + 8*a*b^3*c*d^3 - 19*a^2*b^2*d^4)*x^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(d*x + c)^2 - (5*b^4*c^3*d - 81*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 + 19*a^3*b*d^4)*x + 30*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a) - 6*(5*b^4*d^4*x^4 + 5*a^3*b*c*d^3 + 5*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 15*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 5*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 6*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c))*B/(a^3*b^5*c^6*g^4*i^2 - 5*a^4*b^4*c^5*d*g^4*i^2 + 10*a^5*b^3*c^4*d^2*g^4*i^2 - 10*a^6*b^2*c^3*d^3*g^4*i^2 + 5*a^7*b*c^2*d^4*g^4*i^2 - a^8*c*d^5*g^4*i^2 + (b^8*c^5*d*g^4*i^2 - 5*a*b^7*c^4*d^2*g^4*i^2 + 10*a^2*b^6*c^3*d^3*g^4*i^2 - 10*a^3*b^5*c^2*d^4*g^4*i^2 + 5*a^4*b^4*c*d^5*g^4*i^2 - a^5*b^3*d^6*g^4*i^2)*x^4 + (b^8*c^6*g^4*i^2 - 2*a*b^7*c^5*d*g^4*i^2 - 5*a^2*b^6*c^4*d^2*g^4*i^2 + 20*a^3*b^5*c^3*d^3*g^4*i^2 - 25*a^4*b^4*c^2*d^4*g^4*i^2 + 14*a^5*b^3*c*d^5*g^4*i^2 - 3*a^6*b^2*d^6*g^4*i^2)*x^3 + 3*(a*b^7*c^6*g^4*i^2 - 4*a^2*b^6*c^5*d*g^4*i^2 + 5*a^3*b^5*c^4*d^2*g^4*i^2 - 5*a^5*b^3*c^2*d^4*g^4*i^2 + 4*a^6*b^2*c*d^5*g^4*i^2 - a^7*b*d^6*g^4*i^2)*x^2 + (3*a^2*b^6*c^6*g^4*i^2 - 14*a^3*b^5*c^5*d*g^4*i^2 + 25*a^4*b^4*c^4*d^2*g^4*i^2 - 20*a^5*b^3*c^3*d^3*g^4*i^2 + 5*a^6*b^2*c^2*d^4*g^4*i^2 + 2*a^7*b*c*d^5*g^4*i^2 - a^8*d^6*g^4*i^2)*x)","B",0
47,1,2037,0,2.306041," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{3}{4} \, B a^{2} b g^{3} {\left(\frac{2 \, {\left(2 \, d x + c\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} - \frac{1}{2} \, A b^{3} g^{3} {\left(\frac{6 \, c^{2} d x + 5 \, c^{3}}{d^{6} i^{3} x^{2} + 2 \, c d^{5} i^{3} x + c^{2} d^{4} i^{3}} - \frac{2 \, x}{d^{3} i^{3}} + \frac{6 \, c \log\left(d x + c\right)}{d^{4} i^{3}}\right)} + \frac{1}{4} \, B a^{3} g^{3} {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} + \frac{3}{2} \, A a b^{2} g^{3} {\left(\frac{4 \, c d x + 3 \, c^{2}}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} + \frac{2 \, \log\left(d x + c\right)}{d^{3} i^{3}}\right)} - \frac{3 \, {\left(2 \, d x + c\right)} A a^{2} b g^{3}}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{A a^{3} g^{3}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} + \frac{{\left(6 \, a^{3} b^{2} d^{3} g^{3} \log\left(e\right) - {\left(6 \, g^{3} \log\left(e\right) + 7 \, g^{3}\right)} b^{5} c^{3} + {\left(18 \, g^{3} \log\left(e\right) + 19 \, g^{3}\right)} a b^{4} c^{2} d - 2 \, {\left(9 \, g^{3} \log\left(e\right) + 7 \, g^{3}\right)} a^{2} b^{3} c d^{2}\right)} B \log\left(d x + c\right)}{2 \, {\left(b^{2} c^{2} d^{4} i^{3} - 2 \, a b c d^{5} i^{3} + a^{2} d^{6} i^{3}\right)}} + \frac{4 \, {\left(b^{5} c^{2} d^{3} g^{3} \log\left(e\right) - 2 \, a b^{4} c d^{4} g^{3} \log\left(e\right) + a^{2} b^{3} d^{5} g^{3} \log\left(e\right)\right)} B x^{3} + 8 \, {\left(b^{5} c^{3} d^{2} g^{3} \log\left(e\right) - 2 \, a b^{4} c^{2} d^{3} g^{3} \log\left(e\right) + a^{2} b^{3} c d^{4} g^{3} \log\left(e\right)\right)} B x^{2} - 2 \, {\left({\left(4 \, g^{3} \log\left(e\right) - 5 \, g^{3}\right)} b^{5} c^{4} d - 20 \, {\left(g^{3} \log\left(e\right) - g^{3}\right)} a b^{4} c^{3} d^{2} + {\left(28 \, g^{3} \log\left(e\right) - 27 \, g^{3}\right)} a^{2} b^{3} c^{2} d^{3} - 12 \, {\left(g^{3} \log\left(e\right) - g^{3}\right)} a^{3} b^{2} c d^{4}\right)} B x + 6 \, {\left({\left(b^{5} c^{3} d^{2} g^{3} - 3 \, a b^{4} c^{2} d^{3} g^{3} + 3 \, a^{2} b^{3} c d^{4} g^{3} - a^{3} b^{2} d^{5} g^{3}\right)} B x^{2} + 2 \, {\left(b^{5} c^{4} d g^{3} - 3 \, a b^{4} c^{3} d^{2} g^{3} + 3 \, a^{2} b^{3} c^{2} d^{3} g^{3} - a^{3} b^{2} c d^{4} g^{3}\right)} B x + {\left(b^{5} c^{5} g^{3} - 3 \, a b^{4} c^{4} d g^{3} + 3 \, a^{2} b^{3} c^{3} d^{2} g^{3} - a^{3} b^{2} c^{2} d^{3} g^{3}\right)} B\right)} \log\left(d x + c\right)^{2} - {\left({\left(10 \, g^{3} \log\left(e\right) - 9 \, g^{3}\right)} b^{5} c^{5} - {\left(38 \, g^{3} \log\left(e\right) - 35 \, g^{3}\right)} a b^{4} c^{4} d + {\left(46 \, g^{3} \log\left(e\right) - 47 \, g^{3}\right)} a^{2} b^{3} c^{3} d^{2} - 3 \, {\left(6 \, g^{3} \log\left(e\right) - 7 \, g^{3}\right)} a^{3} b^{2} c^{2} d^{3}\right)} B + 2 \, {\left(2 \, {\left(b^{5} c^{2} d^{3} g^{3} - 2 \, a b^{4} c d^{4} g^{3} + a^{2} b^{3} d^{5} g^{3}\right)} B x^{3} + {\left(9 \, b^{5} c^{3} d^{2} g^{3} - 21 \, a b^{4} c^{2} d^{3} g^{3} + 12 \, a^{2} b^{3} c d^{4} g^{3} + 2 \, a^{3} b^{2} d^{5} g^{3}\right)} B x^{2} + 2 \, {\left(3 \, b^{5} c^{4} d g^{3} - 3 \, a b^{4} c^{3} d^{2} g^{3} - 6 \, a^{2} b^{3} c^{2} d^{3} g^{3} + 8 \, a^{3} b^{2} c d^{4} g^{3}\right)} B x + {\left(6 \, a b^{4} c^{4} d g^{3} - 15 \, a^{2} b^{3} c^{3} d^{2} g^{3} + 11 \, a^{3} b^{2} c^{2} d^{3} g^{3}\right)} B\right)} \log\left(b x + a\right) - 2 \, {\left(2 \, {\left(b^{5} c^{2} d^{3} g^{3} - 2 \, a b^{4} c d^{4} g^{3} + a^{2} b^{3} d^{5} g^{3}\right)} B x^{3} + 4 \, {\left(b^{5} c^{3} d^{2} g^{3} - 2 \, a b^{4} c^{2} d^{3} g^{3} + a^{2} b^{3} c d^{4} g^{3}\right)} B x^{2} - 4 \, {\left(b^{5} c^{4} d g^{3} - 5 \, a b^{4} c^{3} d^{2} g^{3} + 7 \, a^{2} b^{3} c^{2} d^{3} g^{3} - 3 \, a^{3} b^{2} c d^{4} g^{3}\right)} B x - {\left(5 \, b^{5} c^{5} g^{3} - 19 \, a b^{4} c^{4} d g^{3} + 23 \, a^{2} b^{3} c^{3} d^{2} g^{3} - 9 \, a^{3} b^{2} c^{2} d^{3} g^{3}\right)} B\right)} \log\left(d x + c\right)}{4 \, {\left(b^{2} c^{4} d^{4} i^{3} - 2 \, a b c^{3} d^{5} i^{3} + a^{2} c^{2} d^{6} i^{3} + {\left(b^{2} c^{2} d^{6} i^{3} - 2 \, a b c d^{7} i^{3} + a^{2} d^{8} i^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{5} i^{3} - 2 \, a b c^{2} d^{6} i^{3} + a^{2} c d^{7} i^{3}\right)} x\right)}} - \frac{3 \, {\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{4} i^{3}}"," ",0,"-3/4*B*a^2*b*g^3*(2*(2*d*x + c)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - (b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) - 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) + 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) - 1/2*A*b^3*g^3*((6*c^2*d*x + 5*c^3)/(d^6*i^3*x^2 + 2*c*d^5*i^3*x + c^2*d^4*i^3) - 2*x/(d^3*i^3) + 6*c*log(d*x + c)/(d^4*i^3)) + 1/4*B*a^3*g^3*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) + 3/2*A*a*b^2*g^3*((4*c*d*x + 3*c^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) + 2*log(d*x + c)/(d^3*i^3)) - 3/2*(2*d*x + c)*A*a^2*b*g^3/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*A*a^3*g^3/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 1/2*(6*a^3*b^2*d^3*g^3*log(e) - (6*g^3*log(e) + 7*g^3)*b^5*c^3 + (18*g^3*log(e) + 19*g^3)*a*b^4*c^2*d - 2*(9*g^3*log(e) + 7*g^3)*a^2*b^3*c*d^2)*B*log(d*x + c)/(b^2*c^2*d^4*i^3 - 2*a*b*c*d^5*i^3 + a^2*d^6*i^3) + 1/4*(4*(b^5*c^2*d^3*g^3*log(e) - 2*a*b^4*c*d^4*g^3*log(e) + a^2*b^3*d^5*g^3*log(e))*B*x^3 + 8*(b^5*c^3*d^2*g^3*log(e) - 2*a*b^4*c^2*d^3*g^3*log(e) + a^2*b^3*c*d^4*g^3*log(e))*B*x^2 - 2*((4*g^3*log(e) - 5*g^3)*b^5*c^4*d - 20*(g^3*log(e) - g^3)*a*b^4*c^3*d^2 + (28*g^3*log(e) - 27*g^3)*a^2*b^3*c^2*d^3 - 12*(g^3*log(e) - g^3)*a^3*b^2*c*d^4)*B*x + 6*((b^5*c^3*d^2*g^3 - 3*a*b^4*c^2*d^3*g^3 + 3*a^2*b^3*c*d^4*g^3 - a^3*b^2*d^5*g^3)*B*x^2 + 2*(b^5*c^4*d*g^3 - 3*a*b^4*c^3*d^2*g^3 + 3*a^2*b^3*c^2*d^3*g^3 - a^3*b^2*c*d^4*g^3)*B*x + (b^5*c^5*g^3 - 3*a*b^4*c^4*d*g^3 + 3*a^2*b^3*c^3*d^2*g^3 - a^3*b^2*c^2*d^3*g^3)*B)*log(d*x + c)^2 - ((10*g^3*log(e) - 9*g^3)*b^5*c^5 - (38*g^3*log(e) - 35*g^3)*a*b^4*c^4*d + (46*g^3*log(e) - 47*g^3)*a^2*b^3*c^3*d^2 - 3*(6*g^3*log(e) - 7*g^3)*a^3*b^2*c^2*d^3)*B + 2*(2*(b^5*c^2*d^3*g^3 - 2*a*b^4*c*d^4*g^3 + a^2*b^3*d^5*g^3)*B*x^3 + (9*b^5*c^3*d^2*g^3 - 21*a*b^4*c^2*d^3*g^3 + 12*a^2*b^3*c*d^4*g^3 + 2*a^3*b^2*d^5*g^3)*B*x^2 + 2*(3*b^5*c^4*d*g^3 - 3*a*b^4*c^3*d^2*g^3 - 6*a^2*b^3*c^2*d^3*g^3 + 8*a^3*b^2*c*d^4*g^3)*B*x + (6*a*b^4*c^4*d*g^3 - 15*a^2*b^3*c^3*d^2*g^3 + 11*a^3*b^2*c^2*d^3*g^3)*B)*log(b*x + a) - 2*(2*(b^5*c^2*d^3*g^3 - 2*a*b^4*c*d^4*g^3 + a^2*b^3*d^5*g^3)*B*x^3 + 4*(b^5*c^3*d^2*g^3 - 2*a*b^4*c^2*d^3*g^3 + a^2*b^3*c*d^4*g^3)*B*x^2 - 4*(b^5*c^4*d*g^3 - 5*a*b^4*c^3*d^2*g^3 + 7*a^2*b^3*c^2*d^3*g^3 - 3*a^3*b^2*c*d^4*g^3)*B*x - (5*b^5*c^5*g^3 - 19*a*b^4*c^4*d*g^3 + 23*a^2*b^3*c^3*d^2*g^3 - 9*a^3*b^2*c^2*d^3*g^3)*B)*log(d*x + c))/(b^2*c^4*d^4*i^3 - 2*a*b*c^3*d^5*i^3 + a^2*c^2*d^6*i^3 + (b^2*c^2*d^6*i^3 - 2*a*b*c*d^7*i^3 + a^2*d^8*i^3)*x^2 + 2*(b^2*c^3*d^5*i^3 - 2*a*b*c^2*d^6*i^3 + a^2*c*d^7*i^3)*x) - 3*(b^3*c*g^3 - a*b^2*d*g^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^4*i^3)","B",0
48,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B a b g^{2} {\left(\frac{2 \, {\left(2 \, d x + c\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{4} \, B a^{2} g^{2} {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} + \frac{1}{2} \, A b^{2} g^{2} {\left(\frac{4 \, c d x + 3 \, c^{2}}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} + \frac{2 \, \log\left(d x + c\right)}{d^{3} i^{3}}\right)} - \frac{1}{2} \, B b^{2} g^{2} {\left(\frac{{\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d x + c\right)^{2} + {\left(4 \, c d x + 3 \, c^{2}\right)} \log\left(d x + c\right)}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} - 2 \, \int \frac{2 \, d^{2} x^{2} \log\left(b x + a\right) + 2 \, d^{2} x^{2} \log\left(e\right) + 4 \, c d x + 3 \, c^{2}}{2 \, {\left(d^{5} i^{3} x^{3} + 3 \, c d^{4} i^{3} x^{2} + 3 \, c^{2} d^{3} i^{3} x + c^{3} d^{2} i^{3}\right)}}\,{d x}\right)} - \frac{{\left(2 \, d x + c\right)} A a b g^{2}}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{A a^{2} g^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"-1/2*B*a*b*g^2*(2*(2*d*x + c)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - (b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) - 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) + 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/4*B*a^2*g^2*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) + 1/2*A*b^2*g^2*((4*c*d*x + 3*c^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) + 2*log(d*x + c)/(d^3*i^3)) - 1/2*B*b^2*g^2*(((d^2*x^2 + 2*c*d*x + c^2)*log(d*x + c)^2 + (4*c*d*x + 3*c^2)*log(d*x + c))/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) - 2*integrate(1/2*(2*d^2*x^2*log(b*x + a) + 2*d^2*x^2*log(e) + 4*c*d*x + 3*c^2)/(d^5*i^3*x^3 + 3*c*d^4*i^3*x^2 + 3*c^2*d^3*i^3*x + c^3*d^2*i^3), x)) - (2*d*x + c)*A*a*b*g^2/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*A*a^2*g^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","F",0
49,1,567,0,1.200702," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, B b g {\left(\frac{2 \, {\left(2 \, d x + c\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{4} \, B a g {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{{\left(2 \, d x + c\right)} A b g}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{A a g}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"-1/4*B*b*g*(2*(2*d*x + c)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - (b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) - 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) + 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/4*B*a*g*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*(2*d*x + c)*A*b*g/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*A*a*g/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","B",0
50,1,255,0,1.134100," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{4} \, B {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{A}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"1/4*B*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*A/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","A",0
51,1,885,0,1.689634," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{1}{2} \, A {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)} - \frac{{\left(7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{4 \, {\left(b^{3} c^{5} g i^{3} - 3 \, a b^{2} c^{4} d g i^{3} + 3 \, a^{2} b c^{3} d^{2} g i^{3} - a^{3} c^{2} d^{3} g i^{3} + {\left(b^{3} c^{3} d^{2} g i^{3} - 3 \, a b^{2} c^{2} d^{3} g i^{3} + 3 \, a^{2} b c d^{4} g i^{3} - a^{3} d^{5} g i^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d g i^{3} - 3 \, a b^{2} c^{3} d^{2} g i^{3} + 3 \, a^{2} b c^{2} d^{3} g i^{3} - a^{3} c d^{4} g i^{3}\right)} x\right)}}"," ",0,"1/2*B*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 1/2*A*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3)) - 1/4*(7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*B/(b^3*c^5*g*i^3 - 3*a*b^2*c^4*d*g*i^3 + 3*a^2*b*c^3*d^2*g*i^3 - a^3*c^2*d^3*g*i^3 + (b^3*c^3*d^2*g*i^3 - 3*a*b^2*c^2*d^3*g*i^3 + 3*a^2*b*c*d^4*g*i^3 - a^3*d^5*g*i^3)*x^2 + 2*(b^3*c^4*d*g*i^3 - 3*a*b^2*c^3*d^2*g*i^3 + 3*a^2*b*c^2*d^3*g*i^3 - a^3*c*d^4*g*i^3)*x)","B",0
52,1,1721,0,2.594541," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{2} \, A {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)} - \frac{{\left(4 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} - a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{4 \, {\left(a b^{4} c^{6} g^{2} i^{3} - 4 \, a^{2} b^{3} c^{5} d g^{2} i^{3} + 6 \, a^{3} b^{2} c^{4} d^{2} g^{2} i^{3} - 4 \, a^{4} b c^{3} d^{3} g^{2} i^{3} + a^{5} c^{2} d^{4} g^{2} i^{3} + {\left(b^{5} c^{4} d^{2} g^{2} i^{3} - 4 \, a b^{4} c^{3} d^{3} g^{2} i^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} g^{2} i^{3} - 4 \, a^{3} b^{2} c d^{5} g^{2} i^{3} + a^{4} b d^{6} g^{2} i^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d g^{2} i^{3} - 7 \, a b^{4} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{2} b^{3} c^{3} d^{3} g^{2} i^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} g^{2} i^{3} - 2 \, a^{4} b c d^{5} g^{2} i^{3} + a^{5} d^{6} g^{2} i^{3}\right)} x^{2} + {\left(b^{5} c^{6} g^{2} i^{3} - 2 \, a b^{4} c^{5} d g^{2} i^{3} - 2 \, a^{2} b^{3} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 7 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 2 \, a^{5} c d^{5} g^{2} i^{3}\right)} x\right)}}"," ",0,"-1/2*B*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/2*A*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3)) - 1/4*(4*b^3*c^3 - 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 - a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c)^2 - 3*(b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c))*B/(a*b^4*c^6*g^2*i^3 - 4*a^2*b^3*c^5*d*g^2*i^3 + 6*a^3*b^2*c^4*d^2*g^2*i^3 - 4*a^4*b*c^3*d^3*g^2*i^3 + a^5*c^2*d^4*g^2*i^3 + (b^5*c^4*d^2*g^2*i^3 - 4*a*b^4*c^3*d^3*g^2*i^3 + 6*a^2*b^3*c^2*d^4*g^2*i^3 - 4*a^3*b^2*c*d^5*g^2*i^3 + a^4*b*d^6*g^2*i^3)*x^3 + (2*b^5*c^5*d*g^2*i^3 - 7*a*b^4*c^4*d^2*g^2*i^3 + 8*a^2*b^3*c^3*d^3*g^2*i^3 - 2*a^3*b^2*c^2*d^4*g^2*i^3 - 2*a^4*b*c*d^5*g^2*i^3 + a^5*d^6*g^2*i^3)*x^2 + (b^5*c^6*g^2*i^3 - 2*a*b^4*c^5*d*g^2*i^3 - 2*a^2*b^3*c^4*d^2*g^2*i^3 + 8*a^3*b^2*c^3*d^3*g^2*i^3 - 7*a^4*b*c^2*d^4*g^2*i^3 + 2*a^5*c*d^5*g^2*i^3)*x)","B",0
53,1,2380,0,2.789208," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{1}{2} \, A {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)} - \frac{{\left(b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} - 16 \, a^{3} b c d^{3} + a^{4} d^{4} - 12 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} - 24 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 12 \, {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} B}{4 \, {\left(a^{2} b^{5} c^{7} g^{3} i^{3} - 5 \, a^{3} b^{4} c^{6} d g^{3} i^{3} + 10 \, a^{4} b^{3} c^{5} d^{2} g^{3} i^{3} - 10 \, a^{5} b^{2} c^{4} d^{3} g^{3} i^{3} + 5 \, a^{6} b c^{3} d^{4} g^{3} i^{3} - a^{7} c^{2} d^{5} g^{3} i^{3} + {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 5 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} - 10 \, a^{3} b^{4} c^{2} d^{5} g^{3} i^{3} + 5 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d g^{3} i^{3} - 4 \, a b^{6} c^{5} d^{2} g^{3} i^{3} + 5 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} + 4 \, a^{5} b^{2} c d^{6} g^{3} i^{3} - a^{6} b d^{7} g^{3} i^{3}\right)} x^{3} + {\left(b^{7} c^{7} g^{3} i^{3} - a b^{6} c^{6} d g^{3} i^{3} - 9 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 25 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} + 9 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} g^{3} i^{3} - 4 \, a^{2} b^{5} c^{6} d g^{3} i^{3} + 5 \, a^{3} b^{4} c^{5} d^{2} g^{3} i^{3} - 5 \, a^{5} b^{2} c^{3} d^{4} g^{3} i^{3} + 4 \, a^{6} b c^{2} d^{5} g^{3} i^{3} - a^{7} c d^{6} g^{3} i^{3}\right)} x\right)}}"," ",0,"1/2*B*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 1/2*A*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3)) - 1/4*(b^4*c^4 - 16*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 - 16*a^3*b*c*d^3 + a^4*d^4 - 12*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^2 - 24*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)*log(d*x + c) + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c)^2 - 12*(b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x)*B/(a^2*b^5*c^7*g^3*i^3 - 5*a^3*b^4*c^6*d*g^3*i^3 + 10*a^4*b^3*c^5*d^2*g^3*i^3 - 10*a^5*b^2*c^4*d^3*g^3*i^3 + 5*a^6*b*c^3*d^4*g^3*i^3 - a^7*c^2*d^5*g^3*i^3 + (b^7*c^5*d^2*g^3*i^3 - 5*a*b^6*c^4*d^3*g^3*i^3 + 10*a^2*b^5*c^3*d^4*g^3*i^3 - 10*a^3*b^4*c^2*d^5*g^3*i^3 + 5*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3)*x^4 + 2*(b^7*c^6*d*g^3*i^3 - 4*a*b^6*c^5*d^2*g^3*i^3 + 5*a^2*b^5*c^4*d^3*g^3*i^3 - 5*a^4*b^3*c^2*d^5*g^3*i^3 + 4*a^5*b^2*c*d^6*g^3*i^3 - a^6*b*d^7*g^3*i^3)*x^3 + (b^7*c^7*g^3*i^3 - a*b^6*c^6*d*g^3*i^3 - 9*a^2*b^5*c^5*d^2*g^3*i^3 + 25*a^3*b^4*c^4*d^3*g^3*i^3 - 25*a^4*b^3*c^3*d^4*g^3*i^3 + 9*a^5*b^2*c^2*d^5*g^3*i^3 + a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*x^2 + 2*(a*b^6*c^7*g^3*i^3 - 4*a^2*b^5*c^6*d*g^3*i^3 + 5*a^3*b^4*c^5*d^2*g^3*i^3 - 5*a^5*b^2*c^3*d^4*g^3*i^3 + 4*a^6*b*c^2*d^5*g^3*i^3 - a^7*c*d^6*g^3*i^3)*x)","B",0
54,1,3816,0,5.651773," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{6} \, B {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{6} \, A {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)} - \frac{{\left(4 \, b^{5} c^{5} - 45 \, a b^{4} c^{4} d + 360 \, a^{2} b^{3} c^{3} d^{2} - 490 \, a^{3} b^{2} c^{2} d^{3} + 180 \, a^{4} b c d^{4} - 9 \, a^{5} d^{5} + 120 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 120 \, {\left(3 \, b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} - a^{2} b^{3} d^{5}\right)} x^{3} + 20 \, {\left(11 \, b^{5} c^{3} d^{2} + 21 \, a b^{4} c^{2} d^{3} - 39 \, a^{2} b^{3} c d^{4} + 7 \, a^{3} b^{2} d^{5}\right)} x^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(5 \, b^{5} c^{4} d - 108 \, a b^{4} c^{3} d^{2} + 78 \, a^{2} b^{3} c^{2} d^{3} + 52 \, a^{3} b^{2} c d^{4} - 27 \, a^{4} b d^{5}\right)} x + 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 3 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B}{36 \, {\left(a^{3} b^{6} c^{8} g^{4} i^{3} - 6 \, a^{4} b^{5} c^{7} d g^{4} i^{3} + 15 \, a^{5} b^{4} c^{6} d^{2} g^{4} i^{3} - 20 \, a^{6} b^{3} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} g^{4} i^{3} - 6 \, a^{8} b c^{3} d^{5} g^{4} i^{3} + a^{9} c^{2} d^{6} g^{4} i^{3} + {\left(b^{9} c^{6} d^{2} g^{4} i^{3} - 6 \, a b^{8} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} g^{4} i^{3} - 20 \, a^{3} b^{6} c^{3} d^{5} g^{4} i^{3} + 15 \, a^{4} b^{5} c^{2} d^{6} g^{4} i^{3} - 6 \, a^{5} b^{4} c d^{7} g^{4} i^{3} + a^{6} b^{3} d^{8} g^{4} i^{3}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d g^{4} i^{3} - 9 \, a b^{8} c^{6} d^{2} g^{4} i^{3} + 12 \, a^{2} b^{7} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} g^{4} i^{3} - 30 \, a^{4} b^{5} c^{3} d^{5} g^{4} i^{3} + 33 \, a^{5} b^{4} c^{2} d^{6} g^{4} i^{3} - 16 \, a^{6} b^{3} c d^{7} g^{4} i^{3} + 3 \, a^{7} b^{2} d^{8} g^{4} i^{3}\right)} x^{4} + {\left(b^{9} c^{8} g^{4} i^{3} - 18 \, a^{2} b^{7} c^{6} d^{2} g^{4} i^{3} + 52 \, a^{3} b^{6} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} g^{4} i^{3} + 24 \, a^{5} b^{4} c^{3} d^{5} g^{4} i^{3} + 10 \, a^{6} b^{3} c^{2} d^{6} g^{4} i^{3} - 12 \, a^{7} b^{2} c d^{7} g^{4} i^{3} + 3 \, a^{8} b d^{8} g^{4} i^{3}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} g^{4} i^{3} - 12 \, a^{2} b^{7} c^{7} d g^{4} i^{3} + 10 \, a^{3} b^{6} c^{6} d^{2} g^{4} i^{3} + 24 \, a^{4} b^{5} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} g^{4} i^{3} + 52 \, a^{6} b^{3} c^{3} d^{5} g^{4} i^{3} - 18 \, a^{7} b^{2} c^{2} d^{6} g^{4} i^{3} + a^{9} d^{8} g^{4} i^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} g^{4} i^{3} - 16 \, a^{3} b^{6} c^{7} d g^{4} i^{3} + 33 \, a^{4} b^{5} c^{6} d^{2} g^{4} i^{3} - 30 \, a^{5} b^{4} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} g^{4} i^{3} + 12 \, a^{7} b^{2} c^{3} d^{5} g^{4} i^{3} - 9 \, a^{8} b c^{2} d^{6} g^{4} i^{3} + 2 \, a^{9} c d^{7} g^{4} i^{3}\right)} x\right)}}"," ",0,"-1/6*B*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/6*A*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3)) - 1/36*(4*b^5*c^5 - 45*a*b^4*c^4*d + 360*a^2*b^3*c^3*d^2 - 490*a^3*b^2*c^2*d^3 + 180*a^4*b*c*d^4 - 9*a^5*d^5 + 120*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 120*(3*b^5*c^2*d^3 - 2*a*b^4*c*d^4 - a^2*b^3*d^5)*x^3 + 20*(11*b^5*c^3*d^2 + 21*a*b^4*c^2*d^3 - 39*a^2*b^3*c*d^4 + 7*a^3*b^2*d^5)*x^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c)^2 - 5*(5*b^5*c^4*d - 108*a*b^4*c^3*d^2 + 78*a^2*b^3*c^2*d^3 + 52*a^3*b^2*c*d^4 - 27*a^4*b*d^5)*x + 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 3*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c))*B/(a^3*b^6*c^8*g^4*i^3 - 6*a^4*b^5*c^7*d*g^4*i^3 + 15*a^5*b^4*c^6*d^2*g^4*i^3 - 20*a^6*b^3*c^5*d^3*g^4*i^3 + 15*a^7*b^2*c^4*d^4*g^4*i^3 - 6*a^8*b*c^3*d^5*g^4*i^3 + a^9*c^2*d^6*g^4*i^3 + (b^9*c^6*d^2*g^4*i^3 - 6*a*b^8*c^5*d^3*g^4*i^3 + 15*a^2*b^7*c^4*d^4*g^4*i^3 - 20*a^3*b^6*c^3*d^5*g^4*i^3 + 15*a^4*b^5*c^2*d^6*g^4*i^3 - 6*a^5*b^4*c*d^7*g^4*i^3 + a^6*b^3*d^8*g^4*i^3)*x^5 + (2*b^9*c^7*d*g^4*i^3 - 9*a*b^8*c^6*d^2*g^4*i^3 + 12*a^2*b^7*c^5*d^3*g^4*i^3 + 5*a^3*b^6*c^4*d^4*g^4*i^3 - 30*a^4*b^5*c^3*d^5*g^4*i^3 + 33*a^5*b^4*c^2*d^6*g^4*i^3 - 16*a^6*b^3*c*d^7*g^4*i^3 + 3*a^7*b^2*d^8*g^4*i^3)*x^4 + (b^9*c^8*g^4*i^3 - 18*a^2*b^7*c^6*d^2*g^4*i^3 + 52*a^3*b^6*c^5*d^3*g^4*i^3 - 60*a^4*b^5*c^4*d^4*g^4*i^3 + 24*a^5*b^4*c^3*d^5*g^4*i^3 + 10*a^6*b^3*c^2*d^6*g^4*i^3 - 12*a^7*b^2*c*d^7*g^4*i^3 + 3*a^8*b*d^8*g^4*i^3)*x^3 + (3*a*b^8*c^8*g^4*i^3 - 12*a^2*b^7*c^7*d*g^4*i^3 + 10*a^3*b^6*c^6*d^2*g^4*i^3 + 24*a^4*b^5*c^5*d^3*g^4*i^3 - 60*a^5*b^4*c^4*d^4*g^4*i^3 + 52*a^6*b^3*c^3*d^5*g^4*i^3 - 18*a^7*b^2*c^2*d^6*g^4*i^3 + a^9*d^8*g^4*i^3)*x^2 + (3*a^2*b^7*c^8*g^4*i^3 - 16*a^3*b^6*c^7*d*g^4*i^3 + 33*a^4*b^5*c^6*d^2*g^4*i^3 - 30*a^5*b^4*c^5*d^3*g^4*i^3 + 5*a^6*b^3*c^4*d^4*g^4*i^3 + 12*a^7*b^2*c^3*d^5*g^4*i^3 - 9*a^8*b*c^2*d^6*g^4*i^3 + 2*a^9*c*d^7*g^4*i^3)*x)","B",0
55,1,3186,0,2.598430," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{5} \, A^{2} b^{3} d g^{3} i x^{5} + \frac{1}{4} \, A^{2} b^{3} c g^{3} i x^{4} + \frac{3}{4} \, A^{2} a b^{2} d g^{3} i x^{4} + A^{2} a b^{2} c g^{3} i x^{3} + A^{2} a^{2} b d g^{3} i x^{3} + \frac{3}{2} \, A^{2} a^{2} b c g^{3} i x^{2} + \frac{1}{2} \, A^{2} a^{3} d g^{3} i x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{3} c g^{3} i + 3 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{2} b c g^{3} i + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a b^{2} c g^{3} i + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B b^{3} c g^{3} i + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{3} d g^{3} i + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a^{2} b d g^{3} i + \frac{1}{4} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a b^{2} d g^{3} i + \frac{1}{30} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B b^{3} d g^{3} i + A^{2} a^{3} c g^{3} i x - \frac{{\left(6 \, a^{4} c d^{4} g^{3} i - {\left(6 \, g^{3} i \log\left(e\right) + 5 \, g^{3} i\right)} b^{4} c^{5} + {\left(30 \, g^{3} i \log\left(e\right) + 19 \, g^{3} i\right)} a b^{3} c^{4} d - {\left(60 \, g^{3} i \log\left(e\right) + 23 \, g^{3} i\right)} a^{2} b^{2} c^{3} d^{2} + 3 \, {\left(20 \, g^{3} i \log\left(e\right) + g^{3} i\right)} a^{3} b c^{2} d^{3}\right)} B^{2} \log\left(d x + c\right)}{60 \, b d^{4}} + \frac{{\left(b^{5} c^{5} g^{3} i - 5 \, a b^{4} c^{4} d g^{3} i + 10 \, a^{2} b^{3} c^{3} d^{2} g^{3} i - 10 \, a^{3} b^{2} c^{2} d^{3} g^{3} i + 5 \, a^{4} b c d^{4} g^{3} i - a^{5} d^{5} g^{3} i\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{10 \, b^{2} d^{4}} + \frac{12 \, B^{2} b^{5} d^{5} g^{3} i x^{5} \log\left(e\right)^{2} + 3 \, {\left({\left(5 \, g^{3} i \log\left(e\right)^{2} - 2 \, g^{3} i \log\left(e\right)\right)} b^{5} c d^{4} + {\left(15 \, g^{3} i \log\left(e\right)^{2} + 2 \, g^{3} i \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 2 \, {\left({\left(g^{3} i \log\left(e\right) - g^{3} i\right)} b^{5} c^{2} d^{3} - 2 \, {\left(15 \, g^{3} i \log\left(e\right)^{2} - 5 \, g^{3} i \log\left(e\right) - g^{3} i\right)} a b^{4} c d^{4} - {\left(30 \, g^{3} i \log\left(e\right)^{2} + 11 \, g^{3} i \log\left(e\right) + g^{3} i\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + {\left({\left(3 \, g^{3} i \log\left(e\right) - 2 \, g^{3} i\right)} b^{5} c^{3} d^{2} - 3 \, {\left(5 \, g^{3} i \log\left(e\right) - 4 \, g^{3} i\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(30 \, g^{3} i \log\left(e\right)^{2} - 5 \, g^{3} i \log\left(e\right) - 6 \, g^{3} i\right)} a^{2} b^{3} c d^{4} + {\left(30 \, g^{3} i \log\left(e\right)^{2} + 27 \, g^{3} i \log\left(e\right) + 8 \, g^{3} i\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - {\left({\left(6 \, g^{3} i \log\left(e\right) - g^{3} i\right)} b^{5} c^{4} d - 2 \, {\left(15 \, g^{3} i \log\left(e\right) - 4 \, g^{3} i\right)} a b^{4} c^{3} d^{2} + 12 \, {\left(5 \, g^{3} i \log\left(e\right) - 2 \, g^{3} i\right)} a^{2} b^{3} c^{2} d^{3} - 2 \, {\left(30 \, g^{3} i \log\left(e\right)^{2} + 15 \, g^{3} i \log\left(e\right) - 14 \, g^{3} i\right)} a^{3} b^{2} c d^{4} - {\left(6 \, g^{3} i \log\left(e\right) + 11 \, g^{3} i\right)} a^{4} b d^{5}\right)} B^{2} x + 3 \, {\left(4 \, B^{2} b^{5} d^{5} g^{3} i x^{5} + 20 \, B^{2} a^{3} b^{2} c d^{4} g^{3} i x + 5 \, {\left(b^{5} c d^{4} g^{3} i + 3 \, a b^{4} d^{5} g^{3} i\right)} B^{2} x^{4} + 20 \, {\left(a b^{4} c d^{4} g^{3} i + a^{2} b^{3} d^{5} g^{3} i\right)} B^{2} x^{3} + 10 \, {\left(3 \, a^{2} b^{3} c d^{4} g^{3} i + a^{3} b^{2} d^{5} g^{3} i\right)} B^{2} x^{2} + {\left(5 \, a^{4} b c d^{4} g^{3} i - a^{5} d^{5} g^{3} i\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(4 \, B^{2} b^{5} d^{5} g^{3} i x^{5} + 20 \, B^{2} a^{3} b^{2} c d^{4} g^{3} i x + 5 \, {\left(b^{5} c d^{4} g^{3} i + 3 \, a b^{4} d^{5} g^{3} i\right)} B^{2} x^{4} + 20 \, {\left(a b^{4} c d^{4} g^{3} i + a^{2} b^{3} d^{5} g^{3} i\right)} B^{2} x^{3} + 10 \, {\left(3 \, a^{2} b^{3} c d^{4} g^{3} i + a^{3} b^{2} d^{5} g^{3} i\right)} B^{2} x^{2} - {\left(b^{5} c^{5} g^{3} i - 5 \, a b^{4} c^{4} d g^{3} i + 10 \, a^{2} b^{3} c^{3} d^{2} g^{3} i - 10 \, a^{3} b^{2} c^{2} d^{3} g^{3} i\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + {\left(24 \, B^{2} b^{5} d^{5} g^{3} i x^{5} \log\left(e\right) + 6 \, {\left({\left(5 \, g^{3} i \log\left(e\right) - g^{3} i\right)} b^{5} c d^{4} + {\left(15 \, g^{3} i \log\left(e\right) + g^{3} i\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 2 \, {\left(b^{5} c^{2} d^{3} g^{3} i - 10 \, {\left(6 \, g^{3} i \log\left(e\right) - g^{3} i\right)} a b^{4} c d^{4} - {\left(60 \, g^{3} i \log\left(e\right) + 11 \, g^{3} i\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + 3 \, {\left(b^{5} c^{3} d^{2} g^{3} i - 5 \, a b^{4} c^{2} d^{3} g^{3} i + 5 \, {\left(12 \, g^{3} i \log\left(e\right) - g^{3} i\right)} a^{2} b^{3} c d^{4} + {\left(20 \, g^{3} i \log\left(e\right) + 9 \, g^{3} i\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{5} c^{4} d g^{3} i - 5 \, a b^{4} c^{3} d^{2} g^{3} i + 10 \, a^{2} b^{3} c^{2} d^{3} g^{3} i - a^{4} b d^{5} g^{3} i - 5 \, {\left(4 \, g^{3} i \log\left(e\right) + g^{3} i\right)} a^{3} b^{2} c d^{4}\right)} B^{2} x - {\left(6 \, a b^{4} c^{4} d g^{3} i - 27 \, a^{2} b^{3} c^{3} d^{2} g^{3} i + 47 \, a^{3} b^{2} c^{2} d^{3} g^{3} i - {\left(30 \, g^{3} i \log\left(e\right) + 31 \, g^{3} i\right)} a^{4} b c d^{4} + {\left(6 \, g^{3} i \log\left(e\right) + 5 \, g^{3} i\right)} a^{5} d^{5}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(24 \, B^{2} b^{5} d^{5} g^{3} i x^{5} \log\left(e\right) + 6 \, {\left({\left(5 \, g^{3} i \log\left(e\right) - g^{3} i\right)} b^{5} c d^{4} + {\left(15 \, g^{3} i \log\left(e\right) + g^{3} i\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 2 \, {\left(b^{5} c^{2} d^{3} g^{3} i - 10 \, {\left(6 \, g^{3} i \log\left(e\right) - g^{3} i\right)} a b^{4} c d^{4} - {\left(60 \, g^{3} i \log\left(e\right) + 11 \, g^{3} i\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + 3 \, {\left(b^{5} c^{3} d^{2} g^{3} i - 5 \, a b^{4} c^{2} d^{3} g^{3} i + 5 \, {\left(12 \, g^{3} i \log\left(e\right) - g^{3} i\right)} a^{2} b^{3} c d^{4} + {\left(20 \, g^{3} i \log\left(e\right) + 9 \, g^{3} i\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{5} c^{4} d g^{3} i - 5 \, a b^{4} c^{3} d^{2} g^{3} i + 10 \, a^{2} b^{3} c^{2} d^{3} g^{3} i - a^{4} b d^{5} g^{3} i - 5 \, {\left(4 \, g^{3} i \log\left(e\right) + g^{3} i\right)} a^{3} b^{2} c d^{4}\right)} B^{2} x + 6 \, {\left(4 \, B^{2} b^{5} d^{5} g^{3} i x^{5} + 20 \, B^{2} a^{3} b^{2} c d^{4} g^{3} i x + 5 \, {\left(b^{5} c d^{4} g^{3} i + 3 \, a b^{4} d^{5} g^{3} i\right)} B^{2} x^{4} + 20 \, {\left(a b^{4} c d^{4} g^{3} i + a^{2} b^{3} d^{5} g^{3} i\right)} B^{2} x^{3} + 10 \, {\left(3 \, a^{2} b^{3} c d^{4} g^{3} i + a^{3} b^{2} d^{5} g^{3} i\right)} B^{2} x^{2} + {\left(5 \, a^{4} b c d^{4} g^{3} i - a^{5} d^{5} g^{3} i\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{60 \, b^{2} d^{4}}"," ",0,"1/5*A^2*b^3*d*g^3*i*x^5 + 1/4*A^2*b^3*c*g^3*i*x^4 + 3/4*A^2*a*b^2*d*g^3*i*x^4 + A^2*a*b^2*c*g^3*i*x^3 + A^2*a^2*b*d*g^3*i*x^3 + 3/2*A^2*a^2*b*c*g^3*i*x^2 + 1/2*A^2*a^3*d*g^3*i*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a^3*c*g^3*i + 3*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^2*b*c*g^3*i + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a*b^2*c*g^3*i + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*b^3*c*g^3*i + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^3*d*g^3*i + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a^2*b*d*g^3*i + 1/4*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a*b^2*d*g^3*i + 1/30*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*b^3*d*g^3*i + A^2*a^3*c*g^3*i*x - 1/60*(6*a^4*c*d^4*g^3*i - (6*g^3*i*log(e) + 5*g^3*i)*b^4*c^5 + (30*g^3*i*log(e) + 19*g^3*i)*a*b^3*c^4*d - (60*g^3*i*log(e) + 23*g^3*i)*a^2*b^2*c^3*d^2 + 3*(20*g^3*i*log(e) + g^3*i)*a^3*b*c^2*d^3)*B^2*log(d*x + c)/(b*d^4) + 1/10*(b^5*c^5*g^3*i - 5*a*b^4*c^4*d*g^3*i + 10*a^2*b^3*c^3*d^2*g^3*i - 10*a^3*b^2*c^2*d^3*g^3*i + 5*a^4*b*c*d^4*g^3*i - a^5*d^5*g^3*i)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^2*d^4) + 1/60*(12*B^2*b^5*d^5*g^3*i*x^5*log(e)^2 + 3*((5*g^3*i*log(e)^2 - 2*g^3*i*log(e))*b^5*c*d^4 + (15*g^3*i*log(e)^2 + 2*g^3*i*log(e))*a*b^4*d^5)*B^2*x^4 - 2*((g^3*i*log(e) - g^3*i)*b^5*c^2*d^3 - 2*(15*g^3*i*log(e)^2 - 5*g^3*i*log(e) - g^3*i)*a*b^4*c*d^4 - (30*g^3*i*log(e)^2 + 11*g^3*i*log(e) + g^3*i)*a^2*b^3*d^5)*B^2*x^3 + ((3*g^3*i*log(e) - 2*g^3*i)*b^5*c^3*d^2 - 3*(5*g^3*i*log(e) - 4*g^3*i)*a*b^4*c^2*d^3 + 3*(30*g^3*i*log(e)^2 - 5*g^3*i*log(e) - 6*g^3*i)*a^2*b^3*c*d^4 + (30*g^3*i*log(e)^2 + 27*g^3*i*log(e) + 8*g^3*i)*a^3*b^2*d^5)*B^2*x^2 - ((6*g^3*i*log(e) - g^3*i)*b^5*c^4*d - 2*(15*g^3*i*log(e) - 4*g^3*i)*a*b^4*c^3*d^2 + 12*(5*g^3*i*log(e) - 2*g^3*i)*a^2*b^3*c^2*d^3 - 2*(30*g^3*i*log(e)^2 + 15*g^3*i*log(e) - 14*g^3*i)*a^3*b^2*c*d^4 - (6*g^3*i*log(e) + 11*g^3*i)*a^4*b*d^5)*B^2*x + 3*(4*B^2*b^5*d^5*g^3*i*x^5 + 20*B^2*a^3*b^2*c*d^4*g^3*i*x + 5*(b^5*c*d^4*g^3*i + 3*a*b^4*d^5*g^3*i)*B^2*x^4 + 20*(a*b^4*c*d^4*g^3*i + a^2*b^3*d^5*g^3*i)*B^2*x^3 + 10*(3*a^2*b^3*c*d^4*g^3*i + a^3*b^2*d^5*g^3*i)*B^2*x^2 + (5*a^4*b*c*d^4*g^3*i - a^5*d^5*g^3*i)*B^2)*log(b*x + a)^2 + 3*(4*B^2*b^5*d^5*g^3*i*x^5 + 20*B^2*a^3*b^2*c*d^4*g^3*i*x + 5*(b^5*c*d^4*g^3*i + 3*a*b^4*d^5*g^3*i)*B^2*x^4 + 20*(a*b^4*c*d^4*g^3*i + a^2*b^3*d^5*g^3*i)*B^2*x^3 + 10*(3*a^2*b^3*c*d^4*g^3*i + a^3*b^2*d^5*g^3*i)*B^2*x^2 - (b^5*c^5*g^3*i - 5*a*b^4*c^4*d*g^3*i + 10*a^2*b^3*c^3*d^2*g^3*i - 10*a^3*b^2*c^2*d^3*g^3*i)*B^2)*log(d*x + c)^2 + (24*B^2*b^5*d^5*g^3*i*x^5*log(e) + 6*((5*g^3*i*log(e) - g^3*i)*b^5*c*d^4 + (15*g^3*i*log(e) + g^3*i)*a*b^4*d^5)*B^2*x^4 - 2*(b^5*c^2*d^3*g^3*i - 10*(6*g^3*i*log(e) - g^3*i)*a*b^4*c*d^4 - (60*g^3*i*log(e) + 11*g^3*i)*a^2*b^3*d^5)*B^2*x^3 + 3*(b^5*c^3*d^2*g^3*i - 5*a*b^4*c^2*d^3*g^3*i + 5*(12*g^3*i*log(e) - g^3*i)*a^2*b^3*c*d^4 + (20*g^3*i*log(e) + 9*g^3*i)*a^3*b^2*d^5)*B^2*x^2 - 6*(b^5*c^4*d*g^3*i - 5*a*b^4*c^3*d^2*g^3*i + 10*a^2*b^3*c^2*d^3*g^3*i - a^4*b*d^5*g^3*i - 5*(4*g^3*i*log(e) + g^3*i)*a^3*b^2*c*d^4)*B^2*x - (6*a*b^4*c^4*d*g^3*i - 27*a^2*b^3*c^3*d^2*g^3*i + 47*a^3*b^2*c^2*d^3*g^3*i - (30*g^3*i*log(e) + 31*g^3*i)*a^4*b*c*d^4 + (6*g^3*i*log(e) + 5*g^3*i)*a^5*d^5)*B^2)*log(b*x + a) - (24*B^2*b^5*d^5*g^3*i*x^5*log(e) + 6*((5*g^3*i*log(e) - g^3*i)*b^5*c*d^4 + (15*g^3*i*log(e) + g^3*i)*a*b^4*d^5)*B^2*x^4 - 2*(b^5*c^2*d^3*g^3*i - 10*(6*g^3*i*log(e) - g^3*i)*a*b^4*c*d^4 - (60*g^3*i*log(e) + 11*g^3*i)*a^2*b^3*d^5)*B^2*x^3 + 3*(b^5*c^3*d^2*g^3*i - 5*a*b^4*c^2*d^3*g^3*i + 5*(12*g^3*i*log(e) - g^3*i)*a^2*b^3*c*d^4 + (20*g^3*i*log(e) + 9*g^3*i)*a^3*b^2*d^5)*B^2*x^2 - 6*(b^5*c^4*d*g^3*i - 5*a*b^4*c^3*d^2*g^3*i + 10*a^2*b^3*c^2*d^3*g^3*i - a^4*b*d^5*g^3*i - 5*(4*g^3*i*log(e) + g^3*i)*a^3*b^2*c*d^4)*B^2*x + 6*(4*B^2*b^5*d^5*g^3*i*x^5 + 20*B^2*a^3*b^2*c*d^4*g^3*i*x + 5*(b^5*c*d^4*g^3*i + 3*a*b^4*d^5*g^3*i)*B^2*x^4 + 20*(a*b^4*c*d^4*g^3*i + a^2*b^3*d^5*g^3*i)*B^2*x^3 + 10*(3*a^2*b^3*c*d^4*g^3*i + a^3*b^2*d^5*g^3*i)*B^2*x^2 + (5*a^4*b*c*d^4*g^3*i - a^5*d^5*g^3*i)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d^4)","B",0
56,1,2243,0,2.244979," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} b^{2} d g^{2} i x^{4} + \frac{1}{3} \, A^{2} b^{2} c g^{2} i x^{3} + \frac{2}{3} \, A^{2} a b d g^{2} i x^{3} + A^{2} a b c g^{2} i x^{2} + \frac{1}{2} \, A^{2} a^{2} d g^{2} i x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{2} c g^{2} i + 2 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a b c g^{2} i + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B b^{2} c g^{2} i + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{2} d g^{2} i + \frac{2}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a b d g^{2} i + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B b^{2} d g^{2} i + A^{2} a^{2} c g^{2} i x - \frac{{\left(2 \, a^{3} c d^{3} g^{2} i + {\left(2 \, g^{2} i \log\left(e\right) + g^{2} i\right)} b^{3} c^{4} - 2 \, {\left(4 \, g^{2} i \log\left(e\right) + g^{2} i\right)} a b^{2} c^{3} d + {\left(12 \, g^{2} i \log\left(e\right) - g^{2} i\right)} a^{2} b c^{2} d^{2}\right)} B^{2} \log\left(d x + c\right)}{12 \, b d^{3}} - \frac{{\left(b^{4} c^{4} g^{2} i - 4 \, a b^{3} c^{3} d g^{2} i + 6 \, a^{2} b^{2} c^{2} d^{2} g^{2} i - 4 \, a^{3} b c d^{3} g^{2} i + a^{4} d^{4} g^{2} i\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{6 \, b^{2} d^{3}} + \frac{3 \, B^{2} b^{4} d^{4} g^{2} i x^{4} \log\left(e\right)^{2} + 2 \, {\left({\left(2 \, g^{2} i \log\left(e\right)^{2} - g^{2} i \log\left(e\right)\right)} b^{4} c d^{3} + {\left(4 \, g^{2} i \log\left(e\right)^{2} + g^{2} i \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - {\left({\left(g^{2} i \log\left(e\right) - g^{2} i\right)} b^{4} c^{2} d^{2} - 2 \, {\left(6 \, g^{2} i \log\left(e\right)^{2} - 2 \, g^{2} i \log\left(e\right) - g^{2} i\right)} a b^{3} c d^{3} - {\left(6 \, g^{2} i \log\left(e\right)^{2} + 5 \, g^{2} i \log\left(e\right) + g^{2} i\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + {\left({\left(2 \, g^{2} i \log\left(e\right) - g^{2} i\right)} b^{4} c^{3} d - {\left(8 \, g^{2} i \log\left(e\right) - 5 \, g^{2} i\right)} a b^{3} c^{2} d^{2} + {\left(12 \, g^{2} i \log\left(e\right)^{2} + 4 \, g^{2} i \log\left(e\right) - 7 \, g^{2} i\right)} a^{2} b^{2} c d^{3} + {\left(2 \, g^{2} i \log\left(e\right) + 3 \, g^{2} i\right)} a^{3} b d^{4}\right)} B^{2} x + {\left(3 \, B^{2} b^{4} d^{4} g^{2} i x^{4} + 12 \, B^{2} a^{2} b^{2} c d^{3} g^{2} i x + 4 \, {\left(b^{4} c d^{3} g^{2} i + 2 \, a b^{3} d^{4} g^{2} i\right)} B^{2} x^{3} + 6 \, {\left(2 \, a b^{3} c d^{3} g^{2} i + a^{2} b^{2} d^{4} g^{2} i\right)} B^{2} x^{2} + {\left(4 \, a^{3} b c d^{3} g^{2} i - a^{4} d^{4} g^{2} i\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + {\left(3 \, B^{2} b^{4} d^{4} g^{2} i x^{4} + 12 \, B^{2} a^{2} b^{2} c d^{3} g^{2} i x + 4 \, {\left(b^{4} c d^{3} g^{2} i + 2 \, a b^{3} d^{4} g^{2} i\right)} B^{2} x^{3} + 6 \, {\left(2 \, a b^{3} c d^{3} g^{2} i + a^{2} b^{2} d^{4} g^{2} i\right)} B^{2} x^{2} + {\left(b^{4} c^{4} g^{2} i - 4 \, a b^{3} c^{3} d g^{2} i + 6 \, a^{2} b^{2} c^{2} d^{2} g^{2} i\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g^{2} i x^{4} \log\left(e\right) + 2 \, {\left({\left(4 \, g^{2} i \log\left(e\right) - g^{2} i\right)} b^{4} c d^{3} + {\left(8 \, g^{2} i \log\left(e\right) + g^{2} i\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - {\left(b^{4} c^{2} d^{2} g^{2} i - 4 \, {\left(6 \, g^{2} i \log\left(e\right) - g^{2} i\right)} a b^{3} c d^{3} - {\left(12 \, g^{2} i \log\left(e\right) + 5 \, g^{2} i\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 2 \, {\left(b^{4} c^{3} d g^{2} i - 4 \, a b^{3} c^{2} d^{2} g^{2} i + a^{3} b d^{4} g^{2} i + 2 \, {\left(6 \, g^{2} i \log\left(e\right) + g^{2} i\right)} a^{2} b^{2} c d^{3}\right)} B^{2} x + {\left(2 \, a b^{3} c^{3} d g^{2} i - 7 \, a^{2} b^{2} c^{2} d^{2} g^{2} i + 2 \, {\left(4 \, g^{2} i \log\left(e\right) + 3 \, g^{2} i\right)} a^{3} b c d^{3} - {\left(2 \, g^{2} i \log\left(e\right) + g^{2} i\right)} a^{4} d^{4}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(6 \, B^{2} b^{4} d^{4} g^{2} i x^{4} \log\left(e\right) + 2 \, {\left({\left(4 \, g^{2} i \log\left(e\right) - g^{2} i\right)} b^{4} c d^{3} + {\left(8 \, g^{2} i \log\left(e\right) + g^{2} i\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - {\left(b^{4} c^{2} d^{2} g^{2} i - 4 \, {\left(6 \, g^{2} i \log\left(e\right) - g^{2} i\right)} a b^{3} c d^{3} - {\left(12 \, g^{2} i \log\left(e\right) + 5 \, g^{2} i\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 2 \, {\left(b^{4} c^{3} d g^{2} i - 4 \, a b^{3} c^{2} d^{2} g^{2} i + a^{3} b d^{4} g^{2} i + 2 \, {\left(6 \, g^{2} i \log\left(e\right) + g^{2} i\right)} a^{2} b^{2} c d^{3}\right)} B^{2} x + 2 \, {\left(3 \, B^{2} b^{4} d^{4} g^{2} i x^{4} + 12 \, B^{2} a^{2} b^{2} c d^{3} g^{2} i x + 4 \, {\left(b^{4} c d^{3} g^{2} i + 2 \, a b^{3} d^{4} g^{2} i\right)} B^{2} x^{3} + 6 \, {\left(2 \, a b^{3} c d^{3} g^{2} i + a^{2} b^{2} d^{4} g^{2} i\right)} B^{2} x^{2} + {\left(4 \, a^{3} b c d^{3} g^{2} i - a^{4} d^{4} g^{2} i\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b^{2} d^{3}}"," ",0,"1/4*A^2*b^2*d*g^2*i*x^4 + 1/3*A^2*b^2*c*g^2*i*x^3 + 2/3*A^2*a*b*d*g^2*i*x^3 + A^2*a*b*c*g^2*i*x^2 + 1/2*A^2*a^2*d*g^2*i*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a^2*c*g^2*i + 2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a*b*c*g^2*i + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*b^2*c*g^2*i + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^2*d*g^2*i + 2/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a*b*d*g^2*i + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*b^2*d*g^2*i + A^2*a^2*c*g^2*i*x - 1/12*(2*a^3*c*d^3*g^2*i + (2*g^2*i*log(e) + g^2*i)*b^3*c^4 - 2*(4*g^2*i*log(e) + g^2*i)*a*b^2*c^3*d + (12*g^2*i*log(e) - g^2*i)*a^2*b*c^2*d^2)*B^2*log(d*x + c)/(b*d^3) - 1/6*(b^4*c^4*g^2*i - 4*a*b^3*c^3*d*g^2*i + 6*a^2*b^2*c^2*d^2*g^2*i - 4*a^3*b*c*d^3*g^2*i + a^4*d^4*g^2*i)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^2*d^3) + 1/12*(3*B^2*b^4*d^4*g^2*i*x^4*log(e)^2 + 2*((2*g^2*i*log(e)^2 - g^2*i*log(e))*b^4*c*d^3 + (4*g^2*i*log(e)^2 + g^2*i*log(e))*a*b^3*d^4)*B^2*x^3 - ((g^2*i*log(e) - g^2*i)*b^4*c^2*d^2 - 2*(6*g^2*i*log(e)^2 - 2*g^2*i*log(e) - g^2*i)*a*b^3*c*d^3 - (6*g^2*i*log(e)^2 + 5*g^2*i*log(e) + g^2*i)*a^2*b^2*d^4)*B^2*x^2 + ((2*g^2*i*log(e) - g^2*i)*b^4*c^3*d - (8*g^2*i*log(e) - 5*g^2*i)*a*b^3*c^2*d^2 + (12*g^2*i*log(e)^2 + 4*g^2*i*log(e) - 7*g^2*i)*a^2*b^2*c*d^3 + (2*g^2*i*log(e) + 3*g^2*i)*a^3*b*d^4)*B^2*x + (3*B^2*b^4*d^4*g^2*i*x^4 + 12*B^2*a^2*b^2*c*d^3*g^2*i*x + 4*(b^4*c*d^3*g^2*i + 2*a*b^3*d^4*g^2*i)*B^2*x^3 + 6*(2*a*b^3*c*d^3*g^2*i + a^2*b^2*d^4*g^2*i)*B^2*x^2 + (4*a^3*b*c*d^3*g^2*i - a^4*d^4*g^2*i)*B^2)*log(b*x + a)^2 + (3*B^2*b^4*d^4*g^2*i*x^4 + 12*B^2*a^2*b^2*c*d^3*g^2*i*x + 4*(b^4*c*d^3*g^2*i + 2*a*b^3*d^4*g^2*i)*B^2*x^3 + 6*(2*a*b^3*c*d^3*g^2*i + a^2*b^2*d^4*g^2*i)*B^2*x^2 + (b^4*c^4*g^2*i - 4*a*b^3*c^3*d*g^2*i + 6*a^2*b^2*c^2*d^2*g^2*i)*B^2)*log(d*x + c)^2 + (6*B^2*b^4*d^4*g^2*i*x^4*log(e) + 2*((4*g^2*i*log(e) - g^2*i)*b^4*c*d^3 + (8*g^2*i*log(e) + g^2*i)*a*b^3*d^4)*B^2*x^3 - (b^4*c^2*d^2*g^2*i - 4*(6*g^2*i*log(e) - g^2*i)*a*b^3*c*d^3 - (12*g^2*i*log(e) + 5*g^2*i)*a^2*b^2*d^4)*B^2*x^2 + 2*(b^4*c^3*d*g^2*i - 4*a*b^3*c^2*d^2*g^2*i + a^3*b*d^4*g^2*i + 2*(6*g^2*i*log(e) + g^2*i)*a^2*b^2*c*d^3)*B^2*x + (2*a*b^3*c^3*d*g^2*i - 7*a^2*b^2*c^2*d^2*g^2*i + 2*(4*g^2*i*log(e) + 3*g^2*i)*a^3*b*c*d^3 - (2*g^2*i*log(e) + g^2*i)*a^4*d^4)*B^2)*log(b*x + a) - (6*B^2*b^4*d^4*g^2*i*x^4*log(e) + 2*((4*g^2*i*log(e) - g^2*i)*b^4*c*d^3 + (8*g^2*i*log(e) + g^2*i)*a*b^3*d^4)*B^2*x^3 - (b^4*c^2*d^2*g^2*i - 4*(6*g^2*i*log(e) - g^2*i)*a*b^3*c*d^3 - (12*g^2*i*log(e) + 5*g^2*i)*a^2*b^2*d^4)*B^2*x^2 + 2*(b^4*c^3*d*g^2*i - 4*a*b^3*c^2*d^2*g^2*i + a^3*b*d^4*g^2*i + 2*(6*g^2*i*log(e) + g^2*i)*a^2*b^2*c*d^3)*B^2*x + 2*(3*B^2*b^4*d^4*g^2*i*x^4 + 12*B^2*a^2*b^2*c*d^3*g^2*i*x + 4*(b^4*c*d^3*g^2*i + 2*a*b^3*d^4*g^2*i)*B^2*x^3 + 6*(2*a*b^3*c*d^3*g^2*i + a^2*b^2*d^4*g^2*i)*B^2*x^2 + (4*a^3*b*c*d^3*g^2*i - a^4*d^4*g^2*i)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d^3)","B",0
57,1,1252,0,2.171642," ","integrate((b*g*x+a*g)*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A^{2} b d g i x^{3} + \frac{1}{2} \, A^{2} b c g i x^{2} + \frac{1}{2} \, A^{2} a d g i x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a c g i + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B b c g i + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a d g i + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B b d g i + A^{2} a c g i x + \frac{{\left(b^{2} c^{3} g i \log\left(e\right) - a^{2} c d^{2} g i - {\left(3 \, g i \log\left(e\right) - g i\right)} a b c^{2} d\right)} B^{2} \log\left(d x + c\right)}{3 \, b d^{2}} + \frac{{\left(b^{3} c^{3} g i - 3 \, a b^{2} c^{2} d g i + 3 \, a^{2} b c d^{2} g i - a^{3} d^{3} g i\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{3 \, b^{2} d^{2}} + \frac{2 \, B^{2} b^{3} d^{3} g i x^{3} \log\left(e\right)^{2} + {\left({\left(3 \, g i \log\left(e\right)^{2} - 2 \, g i \log\left(e\right)\right)} b^{3} c d^{2} + {\left(3 \, g i \log\left(e\right)^{2} + 2 \, g i \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - 2 \, {\left({\left(g i \log\left(e\right) - g i\right)} b^{3} c^{2} d - {\left(3 \, g i \log\left(e\right)^{2} - 2 \, g i\right)} a b^{2} c d^{2} - {\left(g i \log\left(e\right) + g i\right)} a^{2} b d^{3}\right)} B^{2} x + {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} + 6 \, B^{2} a b^{2} c d^{2} g i x + 3 \, {\left(b^{3} c d^{2} g i + a b^{2} d^{3} g i\right)} B^{2} x^{2} + {\left(3 \, a^{2} b c d^{2} g i - a^{3} d^{3} g i\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} + 6 \, B^{2} a b^{2} c d^{2} g i x + 3 \, {\left(b^{3} c d^{2} g i + a b^{2} d^{3} g i\right)} B^{2} x^{2} - {\left(b^{3} c^{3} g i - 3 \, a b^{2} c^{2} d g i\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} \log\left(e\right) + {\left({\left(3 \, g i \log\left(e\right) - g i\right)} b^{3} c d^{2} + {\left(3 \, g i \log\left(e\right) + g i\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + {\left(6 \, a b^{2} c d^{2} g i \log\left(e\right) - b^{3} c^{2} d g i + a^{2} b d^{3} g i\right)} B^{2} x - {\left(a^{3} d^{3} g i \log\left(e\right) + a b^{2} c^{2} d g i - {\left(3 \, g i \log\left(e\right) + g i\right)} a^{2} b c d^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} \log\left(e\right) + {\left({\left(3 \, g i \log\left(e\right) - g i\right)} b^{3} c d^{2} + {\left(3 \, g i \log\left(e\right) + g i\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + {\left(6 \, a b^{2} c d^{2} g i \log\left(e\right) - b^{3} c^{2} d g i + a^{2} b d^{3} g i\right)} B^{2} x + {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} + 6 \, B^{2} a b^{2} c d^{2} g i x + 3 \, {\left(b^{3} c d^{2} g i + a b^{2} d^{3} g i\right)} B^{2} x^{2} + {\left(3 \, a^{2} b c d^{2} g i - a^{3} d^{3} g i\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{6 \, b^{2} d^{2}}"," ",0,"1/3*A^2*b*d*g*i*x^3 + 1/2*A^2*b*c*g*i*x^2 + 1/2*A^2*a*d*g*i*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a*c*g*i + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*b*c*g*i + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a*d*g*i + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*b*d*g*i + A^2*a*c*g*i*x + 1/3*(b^2*c^3*g*i*log(e) - a^2*c*d^2*g*i - (3*g*i*log(e) - g*i)*a*b*c^2*d)*B^2*log(d*x + c)/(b*d^2) + 1/3*(b^3*c^3*g*i - 3*a*b^2*c^2*d*g*i + 3*a^2*b*c*d^2*g*i - a^3*d^3*g*i)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^2*d^2) + 1/6*(2*B^2*b^3*d^3*g*i*x^3*log(e)^2 + ((3*g*i*log(e)^2 - 2*g*i*log(e))*b^3*c*d^2 + (3*g*i*log(e)^2 + 2*g*i*log(e))*a*b^2*d^3)*B^2*x^2 - 2*((g*i*log(e) - g*i)*b^3*c^2*d - (3*g*i*log(e)^2 - 2*g*i)*a*b^2*c*d^2 - (g*i*log(e) + g*i)*a^2*b*d^3)*B^2*x + (2*B^2*b^3*d^3*g*i*x^3 + 6*B^2*a*b^2*c*d^2*g*i*x + 3*(b^3*c*d^2*g*i + a*b^2*d^3*g*i)*B^2*x^2 + (3*a^2*b*c*d^2*g*i - a^3*d^3*g*i)*B^2)*log(b*x + a)^2 + (2*B^2*b^3*d^3*g*i*x^3 + 6*B^2*a*b^2*c*d^2*g*i*x + 3*(b^3*c*d^2*g*i + a*b^2*d^3*g*i)*B^2*x^2 - (b^3*c^3*g*i - 3*a*b^2*c^2*d*g*i)*B^2)*log(d*x + c)^2 + 2*(2*B^2*b^3*d^3*g*i*x^3*log(e) + ((3*g*i*log(e) - g*i)*b^3*c*d^2 + (3*g*i*log(e) + g*i)*a*b^2*d^3)*B^2*x^2 + (6*a*b^2*c*d^2*g*i*log(e) - b^3*c^2*d*g*i + a^2*b*d^3*g*i)*B^2*x - (a^3*d^3*g*i*log(e) + a*b^2*c^2*d*g*i - (3*g*i*log(e) + g*i)*a^2*b*c*d^2)*B^2)*log(b*x + a) - 2*(2*B^2*b^3*d^3*g*i*x^3*log(e) + ((3*g*i*log(e) - g*i)*b^3*c*d^2 + (3*g*i*log(e) + g*i)*a*b^2*d^3)*B^2*x^2 + (6*a*b^2*c*d^2*g*i*log(e) - b^3*c^2*d*g*i + a^2*b*d^3*g*i)*B^2*x + (2*B^2*b^3*d^3*g*i*x^3 + 6*B^2*a*b^2*c*d^2*g*i*x + 3*(b^3*c*d^2*g*i + a*b^2*d^3*g*i)*B^2*x^2 + (3*a^2*b*c*d^2*g*i - a^3*d^3*g*i)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d^2)","B",0
58,1,633,0,1.965466," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A^{2} d i x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B c i + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B d i + A^{2} c i x - \frac{{\left({\left(i \log\left(e\right) - i\right)} b c^{2} + a c d i\right)} B^{2} \log\left(d x + c\right)}{b d} - \frac{{\left(b^{2} c^{2} i - 2 \, a b c d i + a^{2} d^{2} i\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{b^{2} d} + \frac{B^{2} b^{2} d^{2} i x^{2} \log\left(e\right)^{2} + 2 \, {\left(a b d^{2} i \log\left(e\right) + {\left(i \log\left(e\right)^{2} - i \log\left(e\right)\right)} b^{2} c d\right)} B^{2} x + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + {\left(2 \, a b c d i - a^{2} d^{2} i\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + B^{2} b^{2} c^{2} i\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(B^{2} b^{2} d^{2} i x^{2} \log\left(e\right) + {\left({\left(2 \, i \log\left(e\right) - i\right)} b^{2} c d + a b d^{2} i\right)} B^{2} x + {\left({\left(2 \, i \log\left(e\right) - i\right)} a b c d - {\left(i \log\left(e\right) - i\right)} a^{2} d^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} b^{2} d^{2} i x^{2} \log\left(e\right) + {\left({\left(2 \, i \log\left(e\right) - i\right)} b^{2} c d + a b d^{2} i\right)} B^{2} x + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + {\left(2 \, a b c d i - a^{2} d^{2} i\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b^{2} d}"," ",0,"1/2*A^2*d*i*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*c*i + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*d*i + A^2*c*i*x - ((i*log(e) - i)*b*c^2 + a*c*d*i)*B^2*log(d*x + c)/(b*d) - (b^2*c^2*i - 2*a*b*c*d*i + a^2*d^2*i)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^2*d) + 1/2*(B^2*b^2*d^2*i*x^2*log(e)^2 + 2*(a*b*d^2*i*log(e) + (i*log(e)^2 - i*log(e))*b^2*c*d)*B^2*x + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + (2*a*b*c*d*i - a^2*d^2*i)*B^2)*log(b*x + a)^2 + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + B^2*b^2*c^2*i)*log(d*x + c)^2 + 2*(B^2*b^2*d^2*i*x^2*log(e) + ((2*i*log(e) - i)*b^2*c*d + a*b*d^2*i)*B^2*x + ((2*i*log(e) - i)*a*b*c*d - (i*log(e) - i)*a^2*d^2)*B^2)*log(b*x + a) - 2*(B^2*b^2*d^2*i*x^2*log(e) + ((2*i*log(e) - i)*b^2*c*d + a*b*d^2*i)*B^2*x + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + (2*a*b*c*d*i - a^2*d^2*i)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d)","B",0
59,0,0,0,0.000000," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g),x, algorithm=""maxima"")","A^{2} d i {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} + \frac{A^{2} c i \log\left(b g x + a g\right)}{b g} + \frac{{\left(B^{2} b d i x + {\left(b c i - a d i\right)} B^{2} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2}}{b^{2} g} - \int -\frac{B^{2} b^{2} c^{2} i \log\left(e\right)^{2} + 2 \, A B b^{2} c^{2} i \log\left(e\right) + {\left(B^{2} b^{2} d^{2} i \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} i \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + B^{2} b^{2} c^{2} i\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(B^{2} b^{2} c d i \log\left(e\right)^{2} + 2 \, A B b^{2} c d i \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{2} c^{2} i \log\left(e\right) + A B b^{2} c^{2} i + {\left(B^{2} b^{2} d^{2} i \log\left(e\right) + A B b^{2} d^{2} i\right)} x^{2} + 2 \, {\left(B^{2} b^{2} c d i \log\left(e\right) + A B b^{2} c d i\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} b^{2} c^{2} i \log\left(e\right) + A B b^{2} c^{2} i + {\left({\left(i \log\left(e\right) + i\right)} B^{2} b^{2} d^{2} + A B b^{2} d^{2} i\right)} x^{2} + {\left(2 \, A B b^{2} c d i + {\left(2 \, b^{2} c d i \log\left(e\right) + a b d^{2} i\right)} B^{2}\right)} x + {\left(B^{2} b^{2} d^{2} i x^{2} + {\left(3 \, b^{2} c d i - a b d^{2} i\right)} B^{2} x + {\left(b^{2} c^{2} i + a b c d i - a^{2} d^{2} i\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{3} d g x^{2} + a b^{2} c g + {\left(b^{3} c g + a b^{2} d g\right)} x}\,{d x}"," ",0,"A^2*d*i*(x/(b*g) - a*log(b*x + a)/(b^2*g)) + A^2*c*i*log(b*g*x + a*g)/(b*g) + (B^2*b*d*i*x + (b*c*i - a*d*i)*B^2*log(b*x + a))*log(d*x + c)^2/(b^2*g) - integrate(-(B^2*b^2*c^2*i*log(e)^2 + 2*A*B*b^2*c^2*i*log(e) + (B^2*b^2*d^2*i*log(e)^2 + 2*A*B*b^2*d^2*i*log(e))*x^2 + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + B^2*b^2*c^2*i)*log(b*x + a)^2 + 2*(B^2*b^2*c*d*i*log(e)^2 + 2*A*B*b^2*c*d*i*log(e))*x + 2*(B^2*b^2*c^2*i*log(e) + A*B*b^2*c^2*i + (B^2*b^2*d^2*i*log(e) + A*B*b^2*d^2*i)*x^2 + 2*(B^2*b^2*c*d*i*log(e) + A*B*b^2*c*d*i)*x)*log(b*x + a) - 2*(B^2*b^2*c^2*i*log(e) + A*B*b^2*c^2*i + ((i*log(e) + i)*B^2*b^2*d^2 + A*B*b^2*d^2*i)*x^2 + (2*A*B*b^2*c*d*i + (2*b^2*c*d*i*log(e) + a*b*d^2*i)*B^2)*x + (B^2*b^2*d^2*i*x^2 + (3*b^2*c*d*i - a*b*d^2*i)*B^2*x + (b^2*c^2*i + a*b*c*d*i - a^2*d^2*i)*B^2)*log(b*x + a))*log(d*x + c))/(b^3*d*g*x^2 + a*b^2*c*g + (b^3*c*g + a*b^2*d*g)*x), x)","F",0
60,0,0,0,0.000000," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","A^{2} d i {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - 2 \, A B c i {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{2} g^{2} x + a b g^{2}} + \frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{A^{2} c i}{b^{2} g^{2} x + a b g^{2}} - \frac{{\left({\left(b c i - a d i\right)} B^{2} - {\left(B^{2} b d i x + B^{2} a d i\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2}}{b^{3} g^{2} x + a b^{2} g^{2}} - \int -\frac{B^{2} b^{2} c^{2} i \log\left(e\right)^{2} + {\left(B^{2} b^{2} d^{2} i \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} i \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + B^{2} b^{2} c^{2} i\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(B^{2} b^{2} c d i \log\left(e\right)^{2} + A B b^{2} c d i \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{2} c^{2} i \log\left(e\right) + {\left(B^{2} b^{2} d^{2} i \log\left(e\right) + A B b^{2} d^{2} i\right)} x^{2} + {\left(2 \, B^{2} b^{2} c d i \log\left(e\right) + A B b^{2} c d i\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b^{2} c^{2} i \log\left(e\right) - a b c d i + a^{2} d^{2} i\right)} B^{2} + {\left(B^{2} b^{2} d^{2} i \log\left(e\right) + A B b^{2} d^{2} i\right)} x^{2} + {\left(A B b^{2} c d i + {\left({\left(2 \, i \log\left(e\right) - i\right)} b^{2} c d + a b d^{2} i\right)} B^{2}\right)} x + {\left(2 \, B^{2} b^{2} d^{2} i x^{2} + 2 \, {\left(b^{2} c d i + a b d^{2} i\right)} B^{2} x + {\left(b^{2} c^{2} i + a^{2} d^{2} i\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{4} d g^{2} x^{3} + a^{2} b^{2} c g^{2} + {\left(b^{4} c g^{2} + 2 \, a b^{3} d g^{2}\right)} x^{2} + {\left(2 \, a b^{3} c g^{2} + a^{2} b^{2} d g^{2}\right)} x}\,{d x}"," ",0,"A^2*d*i*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - 2*A*B*c*i*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^2*g^2*x + a*b*g^2) + 1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A^2*c*i/(b^2*g^2*x + a*b*g^2) - ((b*c*i - a*d*i)*B^2 - (B^2*b*d*i*x + B^2*a*d*i)*log(b*x + a))*log(d*x + c)^2/(b^3*g^2*x + a*b^2*g^2) - integrate(-(B^2*b^2*c^2*i*log(e)^2 + (B^2*b^2*d^2*i*log(e)^2 + 2*A*B*b^2*d^2*i*log(e))*x^2 + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + B^2*b^2*c^2*i)*log(b*x + a)^2 + 2*(B^2*b^2*c*d*i*log(e)^2 + A*B*b^2*c*d*i*log(e))*x + 2*(B^2*b^2*c^2*i*log(e) + (B^2*b^2*d^2*i*log(e) + A*B*b^2*d^2*i)*x^2 + (2*B^2*b^2*c*d*i*log(e) + A*B*b^2*c*d*i)*x)*log(b*x + a) - 2*((b^2*c^2*i*log(e) - a*b*c*d*i + a^2*d^2*i)*B^2 + (B^2*b^2*d^2*i*log(e) + A*B*b^2*d^2*i)*x^2 + (A*B*b^2*c*d*i + ((2*i*log(e) - i)*b^2*c*d + a*b*d^2*i)*B^2)*x + (2*B^2*b^2*d^2*i*x^2 + 2*(b^2*c*d*i + a*b*d^2*i)*B^2*x + (b^2*c^2*i + a^2*d^2*i)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d*g^2*x^3 + a^2*b^2*c*g^2 + (b^4*c*g^2 + 2*a*b^3*d*g^2)*x^2 + (2*a*b^3*c*g^2 + a^2*b^2*d*g^2)*x), x)","F",0
61,1,1987,0,2.388489," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, b x + a\right)} B^{2} d i \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} + \frac{1}{4} \, {\left(2 \, {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{b^{2} c^{2} - 8 \, a b c d + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d - a b d^{2}\right)} x - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{2} b^{3} c^{2} g^{3} - 2 \, a^{3} b^{2} c d g^{3} + a^{4} b d^{2} g^{3} + {\left(b^{5} c^{2} g^{3} - 2 \, a b^{4} c d g^{3} + a^{2} b^{3} d^{2} g^{3}\right)} x^{2} + 2 \, {\left(a b^{4} c^{2} g^{3} - 2 \, a^{2} b^{3} c d g^{3} + a^{3} b^{2} d^{2} g^{3}\right)} x}\right)} B^{2} c i - \frac{1}{4} \, {\left(2 \, {\left(\frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{7 \, a b^{2} c^{2} - 8 \, a^{2} b c d + a^{3} d^{2} - 2 \, {\left(2 \, a^{2} b c d - a^{3} d^{2} + {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} - 2 \, {\left(2 \, a^{2} b c d - a^{3} d^{2} + {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d + a^{2} b d^{2}\right)} x + 2 \, {\left(4 \, a^{2} b c d - a^{3} d^{2} + {\left(4 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(4 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(4 \, a^{2} b c d - a^{3} d^{2} + {\left(4 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(4 \, a b^{2} c d - a^{2} b d^{2}\right)} x - 2 \, {\left(2 \, a^{2} b c d - a^{3} d^{2} + {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{2} b^{4} c^{2} g^{3} - 2 \, a^{3} b^{3} c d g^{3} + a^{4} b^{2} d^{2} g^{3} + {\left(b^{6} c^{2} g^{3} - 2 \, a b^{5} c d g^{3} + a^{2} b^{4} d^{2} g^{3}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} g^{3} - 2 \, a^{2} b^{4} c d g^{3} + a^{3} b^{3} d^{2} g^{3}\right)} x}\right)} B^{2} d i - \frac{1}{2} \, A B d i {\left(\frac{2 \, {\left(2 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} + \frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{2} \, A B c i {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{B^{2} c i \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{{\left(2 \, b x + a\right)} A^{2} d i}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{A^{2} c i}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"-1/2*(2*b*x + a)*B^2*d*i*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) + 1/4*(2*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - (b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^2 - 6*(b^2*c*d - a*b*d^2)*x - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))/(a^2*b^3*c^2*g^3 - 2*a^3*b^2*c*d*g^3 + a^4*b*d^2*g^3 + (b^5*c^2*g^3 - 2*a*b^4*c*d*g^3 + a^2*b^3*d^2*g^3)*x^2 + 2*(a*b^4*c^2*g^3 - 2*a^2*b^3*c*d*g^3 + a^3*b^2*d^2*g^3)*x))*B^2*c*i - 1/4*(2*((3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (7*a*b^2*c^2 - 8*a^2*b*c*d + a^3*d^2 - 2*(2*a^2*b*c*d - a^3*d^2 + (2*b^3*c*d - a*b^2*d^2)*x^2 + 2*(2*a*b^2*c*d - a^2*b*d^2)*x)*log(b*x + a)^2 - 2*(2*a^2*b*c*d - a^3*d^2 + (2*b^3*c*d - a*b^2*d^2)*x^2 + 2*(2*a*b^2*c*d - a^2*b*d^2)*x)*log(d*x + c)^2 + 2*(4*b^3*c^2 - 5*a*b^2*c*d + a^2*b*d^2)*x + 2*(4*a^2*b*c*d - a^3*d^2 + (4*b^3*c*d - a*b^2*d^2)*x^2 + 2*(4*a*b^2*c*d - a^2*b*d^2)*x)*log(b*x + a) - 2*(4*a^2*b*c*d - a^3*d^2 + (4*b^3*c*d - a*b^2*d^2)*x^2 + 2*(4*a*b^2*c*d - a^2*b*d^2)*x - 2*(2*a^2*b*c*d - a^3*d^2 + (2*b^3*c*d - a*b^2*d^2)*x^2 + 2*(2*a*b^2*c*d - a^2*b*d^2)*x)*log(b*x + a))*log(d*x + c))/(a^2*b^4*c^2*g^3 - 2*a^3*b^3*c*d*g^3 + a^4*b^2*d^2*g^3 + (b^6*c^2*g^3 - 2*a*b^5*c*d*g^3 + a^2*b^4*d^2*g^3)*x^2 + 2*(a*b^5*c^2*g^3 - 2*a^2*b^4*c*d*g^3 + a^3*b^3*d^2*g^3)*x))*B^2*d*i - 1/2*A*B*d*i*(2*(2*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) + (3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/2*A*B*c*i*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - 1/2*B^2*c*i*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*(2*b*x + a)*A^2*d*i/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*A^2*c*i/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
62,1,3282,0,3.461578," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{{\left(3 \, b x + a\right)} B^{2} d i \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{6 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{1}{54} \, {\left(6 \, {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{3} b^{4} c^{3} g^{4} - 3 \, a^{4} b^{3} c^{2} d g^{4} + 3 \, a^{5} b^{2} c d^{2} g^{4} - a^{6} b d^{3} g^{4} + {\left(b^{7} c^{3} g^{4} - 3 \, a b^{6} c^{2} d g^{4} + 3 \, a^{2} b^{5} c d^{2} g^{4} - a^{3} b^{4} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{6} c^{3} g^{4} - 3 \, a^{2} b^{5} c^{2} d g^{4} + 3 \, a^{3} b^{4} c d^{2} g^{4} - a^{4} b^{3} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{3} g^{4} - 3 \, a^{3} b^{4} c^{2} d g^{4} + 3 \, a^{4} b^{3} c d^{2} g^{4} - a^{5} b^{2} d^{3} g^{4}\right)} x}\right)} B^{2} c i - \frac{1}{108} \, {\left(6 \, {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{19 \, a b^{3} c^{3} - 189 \, a^{2} b^{2} c^{2} d + 189 \, a^{3} b c d^{2} - 19 \, a^{4} d^{3} - 6 \, {\left(27 \, b^{4} c^{2} d - 32 \, a b^{3} c d^{2} + 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 18 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 18 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(9 \, b^{4} c^{3} - 125 \, a b^{3} c^{2} d + 135 \, a^{2} b^{2} c d^{2} - 19 \, a^{3} b d^{3}\right)} x - 6 \, {\left(27 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(27 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(27 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(27 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(27 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(27 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(27 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(27 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x - 6 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{3} b^{5} c^{3} g^{4} - 3 \, a^{4} b^{4} c^{2} d g^{4} + 3 \, a^{5} b^{3} c d^{2} g^{4} - a^{6} b^{2} d^{3} g^{4} + {\left(b^{8} c^{3} g^{4} - 3 \, a b^{7} c^{2} d g^{4} + 3 \, a^{2} b^{6} c d^{2} g^{4} - a^{3} b^{5} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{7} c^{3} g^{4} - 3 \, a^{2} b^{6} c^{2} d g^{4} + 3 \, a^{3} b^{5} c d^{2} g^{4} - a^{4} b^{4} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} c^{3} g^{4} - 3 \, a^{3} b^{5} c^{2} d g^{4} + 3 \, a^{4} b^{4} c d^{2} g^{4} - a^{5} b^{3} d^{3} g^{4}\right)} x}\right)} B^{2} d i - \frac{1}{18} \, A B d i {\left(\frac{6 \, {\left(3 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}} + \frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{1}{9} \, A B c i {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{B^{2} c i \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{{\left(3 \, b x + a\right)} A^{2} d i}{6 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{A^{2} c i}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/6*(3*b*x + a)*B^2*d*i*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/54*(6*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))/(a^3*b^4*c^3*g^4 - 3*a^4*b^3*c^2*d*g^4 + 3*a^5*b^2*c*d^2*g^4 - a^6*b*d^3*g^4 + (b^7*c^3*g^4 - 3*a*b^6*c^2*d*g^4 + 3*a^2*b^5*c*d^2*g^4 - a^3*b^4*d^3*g^4)*x^3 + 3*(a*b^6*c^3*g^4 - 3*a^2*b^5*c^2*d*g^4 + 3*a^3*b^4*c*d^2*g^4 - a^4*b^3*d^3*g^4)*x^2 + 3*(a^2*b^5*c^3*g^4 - 3*a^3*b^4*c^2*d*g^4 + 3*a^4*b^3*c*d^2*g^4 - a^5*b^2*d^3*g^4)*x))*B^2*c*i - 1/108*(6*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (19*a*b^3*c^3 - 189*a^2*b^2*c^2*d + 189*a^3*b*c*d^2 - 19*a^4*d^3 - 6*(27*b^4*c^2*d - 32*a*b^3*c*d^2 + 5*a^2*b^2*d^3)*x^2 + 18*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(b*x + a)^2 + 18*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(d*x + c)^2 + 3*(9*b^4*c^3 - 125*a*b^3*c^2*d + 135*a^2*b^2*c*d^2 - 19*a^3*b*d^3)*x - 6*(27*a^3*b*c*d^2 - 5*a^4*d^3 + (27*b^4*c*d^2 - 5*a*b^3*d^3)*x^3 + 3*(27*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^2 + 3*(27*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x)*log(b*x + a) + 6*(27*a^3*b*c*d^2 - 5*a^4*d^3 + (27*b^4*c*d^2 - 5*a*b^3*d^3)*x^3 + 3*(27*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^2 + 3*(27*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x - 6*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(b*x + a))*log(d*x + c))/(a^3*b^5*c^3*g^4 - 3*a^4*b^4*c^2*d*g^4 + 3*a^5*b^3*c*d^2*g^4 - a^6*b^2*d^3*g^4 + (b^8*c^3*g^4 - 3*a*b^7*c^2*d*g^4 + 3*a^2*b^6*c*d^2*g^4 - a^3*b^5*d^3*g^4)*x^3 + 3*(a*b^7*c^3*g^4 - 3*a^2*b^6*c^2*d*g^4 + 3*a^3*b^5*c*d^2*g^4 - a^4*b^4*d^3*g^4)*x^2 + 3*(a^2*b^6*c^3*g^4 - 3*a^3*b^5*c^2*d*g^4 + 3*a^4*b^4*c*d^2*g^4 - a^5*b^3*d^3*g^4)*x))*B^2*d*i - 1/18*A*B*d*i*(6*(3*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) + (5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/9*A*B*c*i*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/3*B^2*c*i*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/6*(3*b*x + a)*A^2*d*i/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*A^2*c*i/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","B",0
63,1,4808,0,5.053678," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{{\left(4 \, b x + a\right)} B^{2} d i \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{12 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} + \frac{1}{288} \, {\left(12 \, {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{9 \, b^{4} c^{4} - 64 \, a b^{3} c^{3} d + 216 \, a^{2} b^{2} c^{2} d^{2} - 576 \, a^{3} b c d^{3} + 415 \, a^{4} d^{4} - 300 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(13 \, b^{4} c^{2} d^{2} - 176 \, a b^{3} c d^{3} + 163 \, a^{2} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(7 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 324 \, a^{2} b^{2} c d^{3} - 271 \, a^{3} b d^{4}\right)} x - 300 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(25 \, b^{4} d^{4} x^{4} + 100 \, a b^{3} d^{4} x^{3} + 150 \, a^{2} b^{2} d^{4} x^{2} + 100 \, a^{3} b d^{4} x + 25 \, a^{4} d^{4} - 12 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{5} c^{4} g^{5} - 4 \, a^{5} b^{4} c^{3} d g^{5} + 6 \, a^{6} b^{3} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{2} c d^{3} g^{5} + a^{8} b d^{4} g^{5} + {\left(b^{9} c^{4} g^{5} - 4 \, a b^{8} c^{3} d g^{5} + 6 \, a^{2} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{6} c d^{3} g^{5} + a^{4} b^{5} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} g^{5} - 4 \, a^{2} b^{7} c^{3} d g^{5} + 6 \, a^{3} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{5} c d^{3} g^{5} + a^{5} b^{4} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} g^{5} - 4 \, a^{3} b^{6} c^{3} d g^{5} + 6 \, a^{4} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{4} c d^{3} g^{5} + a^{6} b^{3} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} g^{5} - 4 \, a^{4} b^{5} c^{3} d g^{5} + 6 \, a^{5} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{3} c d^{3} g^{5} + a^{7} b^{2} d^{4} g^{5}\right)} x}\right)} B^{2} c i - \frac{1}{864} \, {\left(12 \, {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{37 \, a b^{4} c^{4} - 304 \, a^{2} b^{3} c^{3} d + 1512 \, a^{3} b^{2} c^{2} d^{2} - 1360 \, a^{4} b c d^{3} + 115 \, a^{5} d^{4} + 12 \, {\left(88 \, b^{5} c^{2} d^{2} - 101 \, a b^{4} c d^{3} + 13 \, a^{2} b^{3} d^{4}\right)} x^{3} - 6 \, {\left(40 \, b^{5} c^{3} d - 609 \, a b^{4} c^{2} d^{2} + 648 \, a^{2} b^{3} c d^{3} - 79 \, a^{3} b^{2} d^{4}\right)} x^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(16 \, b^{5} c^{4} - 163 \, a b^{4} c^{3} d + 1068 \, a^{2} b^{3} c^{2} d^{2} - 1036 \, a^{3} b^{2} c d^{3} + 115 \, a^{4} b d^{4}\right)} x + 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x - 12 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{6} c^{4} g^{5} - 4 \, a^{5} b^{5} c^{3} d g^{5} + 6 \, a^{6} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{3} c d^{3} g^{5} + a^{8} b^{2} d^{4} g^{5} + {\left(b^{10} c^{4} g^{5} - 4 \, a b^{9} c^{3} d g^{5} + 6 \, a^{2} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{7} c d^{3} g^{5} + a^{4} b^{6} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{9} c^{4} g^{5} - 4 \, a^{2} b^{8} c^{3} d g^{5} + 6 \, a^{3} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{6} c d^{3} g^{5} + a^{5} b^{5} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} c^{4} g^{5} - 4 \, a^{3} b^{7} c^{3} d g^{5} + 6 \, a^{4} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{5} c d^{3} g^{5} + a^{6} b^{4} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} c^{4} g^{5} - 4 \, a^{4} b^{6} c^{3} d g^{5} + 6 \, a^{5} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{4} c d^{3} g^{5} + a^{7} b^{3} d^{4} g^{5}\right)} x}\right)} B^{2} d i - \frac{1}{72} \, A B d i {\left(\frac{12 \, {\left(4 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}} + \frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} + \frac{1}{24} \, A B c i {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} - \frac{12 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{B^{2} c i \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{{\left(4 \, b x + a\right)} A^{2} d i}{12 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{A^{2} c i}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"-1/12*(4*b*x + a)*B^2*d*i*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) + 1/288*(12*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - (9*b^4*c^4 - 64*a*b^3*c^3*d + 216*a^2*b^2*c^2*d^2 - 576*a^3*b*c*d^3 + 415*a^4*d^4 - 300*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 6*(13*b^4*c^2*d^2 - 176*a*b^3*c*d^3 + 163*a^2*b^2*d^4)*x^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a)^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(d*x + c)^2 - 4*(7*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 324*a^2*b^2*c*d^3 - 271*a^3*b*d^4)*x - 300*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a) + 12*(25*b^4*d^4*x^4 + 100*a*b^3*d^4*x^3 + 150*a^2*b^2*d^4*x^2 + 100*a^3*b*d^4*x + 25*a^4*d^4 - 12*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a))*log(d*x + c))/(a^4*b^5*c^4*g^5 - 4*a^5*b^4*c^3*d*g^5 + 6*a^6*b^3*c^2*d^2*g^5 - 4*a^7*b^2*c*d^3*g^5 + a^8*b*d^4*g^5 + (b^9*c^4*g^5 - 4*a*b^8*c^3*d*g^5 + 6*a^2*b^7*c^2*d^2*g^5 - 4*a^3*b^6*c*d^3*g^5 + a^4*b^5*d^4*g^5)*x^4 + 4*(a*b^8*c^4*g^5 - 4*a^2*b^7*c^3*d*g^5 + 6*a^3*b^6*c^2*d^2*g^5 - 4*a^4*b^5*c*d^3*g^5 + a^5*b^4*d^4*g^5)*x^3 + 6*(a^2*b^7*c^4*g^5 - 4*a^3*b^6*c^3*d*g^5 + 6*a^4*b^5*c^2*d^2*g^5 - 4*a^5*b^4*c*d^3*g^5 + a^6*b^3*d^4*g^5)*x^2 + 4*(a^3*b^6*c^4*g^5 - 4*a^4*b^5*c^3*d*g^5 + 6*a^5*b^4*c^2*d^2*g^5 - 4*a^6*b^3*c*d^3*g^5 + a^7*b^2*d^4*g^5)*x))*B^2*c*i - 1/864*(12*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (37*a*b^4*c^4 - 304*a^2*b^3*c^3*d + 1512*a^3*b^2*c^2*d^2 - 1360*a^4*b*c*d^3 + 115*a^5*d^4 + 12*(88*b^5*c^2*d^2 - 101*a*b^4*c*d^3 + 13*a^2*b^3*d^4)*x^3 - 6*(40*b^5*c^3*d - 609*a*b^4*c^2*d^2 + 648*a^2*b^3*c*d^3 - 79*a^3*b^2*d^4)*x^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a)^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(d*x + c)^2 + 4*(16*b^5*c^4 - 163*a*b^4*c^3*d + 1068*a^2*b^3*c^2*d^2 - 1036*a^3*b^2*c*d^3 + 115*a^4*b*d^4)*x + 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x)*log(b*x + a) - 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x - 12*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a))*log(d*x + c))/(a^4*b^6*c^4*g^5 - 4*a^5*b^5*c^3*d*g^5 + 6*a^6*b^4*c^2*d^2*g^5 - 4*a^7*b^3*c*d^3*g^5 + a^8*b^2*d^4*g^5 + (b^10*c^4*g^5 - 4*a*b^9*c^3*d*g^5 + 6*a^2*b^8*c^2*d^2*g^5 - 4*a^3*b^7*c*d^3*g^5 + a^4*b^6*d^4*g^5)*x^4 + 4*(a*b^9*c^4*g^5 - 4*a^2*b^8*c^3*d*g^5 + 6*a^3*b^7*c^2*d^2*g^5 - 4*a^4*b^6*c*d^3*g^5 + a^5*b^5*d^4*g^5)*x^3 + 6*(a^2*b^8*c^4*g^5 - 4*a^3*b^7*c^3*d*g^5 + 6*a^4*b^6*c^2*d^2*g^5 - 4*a^5*b^5*c*d^3*g^5 + a^6*b^4*d^4*g^5)*x^2 + 4*(a^3*b^7*c^4*g^5 - 4*a^4*b^6*c^3*d*g^5 + 6*a^5*b^5*c^2*d^2*g^5 - 4*a^6*b^4*c*d^3*g^5 + a^7*b^3*d^4*g^5)*x))*B^2*d*i - 1/72*A*B*d*i*(12*(4*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) + (7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) + 1/24*A*B*c*i*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) - 12*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/4*B^2*c*i*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/12*(4*b*x + a)*A^2*d*i/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/4*A^2*c*i/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
64,1,5178,0,2.990385," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{6} \, A^{2} b^{3} d^{2} g^{3} i^{2} x^{6} + \frac{2}{5} \, A^{2} b^{3} c d g^{3} i^{2} x^{5} + \frac{3}{5} \, A^{2} a b^{2} d^{2} g^{3} i^{2} x^{5} + \frac{1}{4} \, A^{2} b^{3} c^{2} g^{3} i^{2} x^{4} + \frac{3}{2} \, A^{2} a b^{2} c d g^{3} i^{2} x^{4} + \frac{3}{4} \, A^{2} a^{2} b d^{2} g^{3} i^{2} x^{4} + A^{2} a b^{2} c^{2} g^{3} i^{2} x^{3} + 2 \, A^{2} a^{2} b c d g^{3} i^{2} x^{3} + \frac{1}{3} \, A^{2} a^{3} d^{2} g^{3} i^{2} x^{3} + \frac{3}{2} \, A^{2} a^{2} b c^{2} g^{3} i^{2} x^{2} + A^{2} a^{3} c d g^{3} i^{2} x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{3} c^{2} g^{3} i^{2} + 3 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{2} b c^{2} g^{3} i^{2} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a b^{2} c^{2} g^{3} i^{2} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B b^{3} c^{2} g^{3} i^{2} + 2 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{3} c d g^{3} i^{2} + 2 \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a^{2} b c d g^{3} i^{2} + \frac{1}{2} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a b^{2} c d g^{3} i^{2} + \frac{1}{15} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B b^{3} c d g^{3} i^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a^{3} d^{2} g^{3} i^{2} + \frac{1}{4} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a^{2} b d^{2} g^{3} i^{2} + \frac{1}{10} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B a b^{2} d^{2} g^{3} i^{2} + \frac{1}{180} \, {\left(60 \, x^{6} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} + \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} - \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} A B b^{3} d^{2} g^{3} i^{2} + A^{2} a^{3} c^{2} g^{3} i^{2} x - \frac{{\left(33 \, a^{4} b c^{2} d^{4} g^{3} i^{2} - 6 \, a^{5} c d^{5} g^{3} i^{2} - 2 \, {\left(3 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} b^{5} c^{6} + 6 \, {\left(6 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a b^{4} c^{5} d - 3 \, {\left(30 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} a^{2} b^{3} c^{4} d^{2} + 2 \, {\left(60 \, g^{3} i^{2} \log\left(e\right) - 17 \, g^{3} i^{2}\right)} a^{3} b^{2} c^{3} d^{3}\right)} B^{2} \log\left(d x + c\right)}{180 \, b^{2} d^{4}} + \frac{{\left(b^{6} c^{6} g^{3} i^{2} - 6 \, a b^{5} c^{5} d g^{3} i^{2} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2} + 15 \, a^{4} b^{2} c^{2} d^{4} g^{3} i^{2} - 6 \, a^{5} b c d^{5} g^{3} i^{2} + a^{6} d^{6} g^{3} i^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{30 \, b^{3} d^{4}} + \frac{60 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} \log\left(e\right)^{2} + 24 \, {\left({\left(6 \, g^{3} i^{2} \log\left(e\right)^{2} - g^{3} i^{2} \log\left(e\right)\right)} b^{6} c d^{5} + {\left(9 \, g^{3} i^{2} \log\left(e\right)^{2} + g^{3} i^{2} \log\left(e\right)\right)} a b^{5} d^{6}\right)} B^{2} x^{5} + 6 \, {\left({\left(15 \, g^{3} i^{2} \log\left(e\right)^{2} - 7 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} b^{6} c^{2} d^{4} + 2 \, {\left(45 \, g^{3} i^{2} \log\left(e\right)^{2} - 3 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} a b^{5} c d^{5} + {\left(45 \, g^{3} i^{2} \log\left(e\right)^{2} + 13 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} - 2 \, {\left({\left(2 \, g^{3} i^{2} \log\left(e\right) - 3 \, g^{3} i^{2}\right)} b^{6} c^{3} d^{3} - 3 \, {\left(60 \, g^{3} i^{2} \log\left(e\right)^{2} - 26 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a b^{5} c^{2} d^{4} - 3 \, {\left(120 \, g^{3} i^{2} \log\left(e\right)^{2} + 14 \, g^{3} i^{2} \log\left(e\right) - 5 \, g^{3} i^{2}\right)} a^{2} b^{4} c d^{5} - {\left(60 \, g^{3} i^{2} \log\left(e\right)^{2} + 38 \, g^{3} i^{2} \log\left(e\right) + 9 \, g^{3} i^{2}\right)} a^{3} b^{3} d^{6}\right)} B^{2} x^{3} + {\left({\left(6 \, g^{3} i^{2} \log\left(e\right) - 7 \, g^{3} i^{2}\right)} b^{6} c^{4} d^{2} - 2 \, {\left(18 \, g^{3} i^{2} \log\left(e\right) - 23 \, g^{3} i^{2}\right)} a b^{5} c^{3} d^{3} + 60 \, {\left(9 \, g^{3} i^{2} \log\left(e\right)^{2} - 3 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} a^{2} b^{4} c^{2} d^{4} + 2 \, {\left(180 \, g^{3} i^{2} \log\left(e\right)^{2} + 102 \, g^{3} i^{2} \log\left(e\right) + 5 \, g^{3} i^{2}\right)} a^{3} b^{3} c d^{5} + {\left(6 \, g^{3} i^{2} \log\left(e\right) + 11 \, g^{3} i^{2}\right)} a^{4} b^{2} d^{6}\right)} B^{2} x^{2} - 2 \, {\left(2 \, {\left(3 \, g^{3} i^{2} \log\left(e\right) - 2 \, g^{3} i^{2}\right)} b^{6} c^{5} d - 9 \, {\left(4 \, g^{3} i^{2} \log\left(e\right) - 3 \, g^{3} i^{2}\right)} a b^{5} c^{4} d^{2} + {\left(90 \, g^{3} i^{2} \log\left(e\right) - 77 \, g^{3} i^{2}\right)} a^{2} b^{4} c^{3} d^{3} - {\left(180 \, g^{3} i^{2} \log\left(e\right)^{2} + 30 \, g^{3} i^{2} \log\left(e\right) - 97 \, g^{3} i^{2}\right)} a^{3} b^{3} c^{2} d^{4} - 3 \, {\left(12 \, g^{3} i^{2} \log\left(e\right) + 17 \, g^{3} i^{2}\right)} a^{4} b^{2} c d^{5} + 2 \, {\left(3 \, g^{3} i^{2} \log\left(e\right) + 4 \, g^{3} i^{2}\right)} a^{5} b d^{6}\right)} B^{2} x + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} + 60 \, B^{2} a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} x + 12 \, {\left(2 \, b^{6} c d^{5} g^{3} i^{2} + 3 \, a b^{5} d^{6} g^{3} i^{2}\right)} B^{2} x^{5} + 15 \, {\left(b^{6} c^{2} d^{4} g^{3} i^{2} + 6 \, a b^{5} c d^{5} g^{3} i^{2} + 3 \, a^{2} b^{4} d^{6} g^{3} i^{2}\right)} B^{2} x^{4} + 20 \, {\left(3 \, a b^{5} c^{2} d^{4} g^{3} i^{2} + 6 \, a^{2} b^{4} c d^{5} g^{3} i^{2} + a^{3} b^{3} d^{6} g^{3} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(3 \, a^{2} b^{4} c^{2} d^{4} g^{3} i^{2} + 2 \, a^{3} b^{3} c d^{5} g^{3} i^{2}\right)} B^{2} x^{2} + {\left(15 \, a^{4} b^{2} c^{2} d^{4} g^{3} i^{2} - 6 \, a^{5} b c d^{5} g^{3} i^{2} + a^{6} d^{6} g^{3} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} + 60 \, B^{2} a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} x + 12 \, {\left(2 \, b^{6} c d^{5} g^{3} i^{2} + 3 \, a b^{5} d^{6} g^{3} i^{2}\right)} B^{2} x^{5} + 15 \, {\left(b^{6} c^{2} d^{4} g^{3} i^{2} + 6 \, a b^{5} c d^{5} g^{3} i^{2} + 3 \, a^{2} b^{4} d^{6} g^{3} i^{2}\right)} B^{2} x^{4} + 20 \, {\left(3 \, a b^{5} c^{2} d^{4} g^{3} i^{2} + 6 \, a^{2} b^{4} c d^{5} g^{3} i^{2} + a^{3} b^{3} d^{6} g^{3} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(3 \, a^{2} b^{4} c^{2} d^{4} g^{3} i^{2} + 2 \, a^{3} b^{3} c d^{5} g^{3} i^{2}\right)} B^{2} x^{2} - {\left(b^{6} c^{6} g^{3} i^{2} - 6 \, a b^{5} c^{5} d g^{3} i^{2} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(60 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} \log\left(e\right) + 12 \, {\left({\left(12 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} b^{6} c d^{5} + {\left(18 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a b^{5} d^{6}\right)} B^{2} x^{5} + 3 \, {\left({\left(30 \, g^{3} i^{2} \log\left(e\right) - 7 \, g^{3} i^{2}\right)} b^{6} c^{2} d^{4} + 6 \, {\left(30 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} a b^{5} c d^{5} + {\left(90 \, g^{3} i^{2} \log\left(e\right) + 13 \, g^{3} i^{2}\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} - 2 \, {\left(b^{6} c^{3} d^{3} g^{3} i^{2} - 3 \, {\left(60 \, g^{3} i^{2} \log\left(e\right) - 13 \, g^{3} i^{2}\right)} a b^{5} c^{2} d^{4} - 3 \, {\left(120 \, g^{3} i^{2} \log\left(e\right) + 7 \, g^{3} i^{2}\right)} a^{2} b^{4} c d^{5} - {\left(60 \, g^{3} i^{2} \log\left(e\right) + 19 \, g^{3} i^{2}\right)} a^{3} b^{3} d^{6}\right)} B^{2} x^{3} + 3 \, {\left(b^{6} c^{4} d^{2} g^{3} i^{2} - 6 \, a b^{5} c^{3} d^{3} g^{3} i^{2} + a^{4} b^{2} d^{6} g^{3} i^{2} + 30 \, {\left(6 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} a^{2} b^{4} c^{2} d^{4} + 2 \, {\left(60 \, g^{3} i^{2} \log\left(e\right) + 17 \, g^{3} i^{2}\right)} a^{3} b^{3} c d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{6} c^{5} d g^{3} i^{2} - 6 \, a b^{5} c^{4} d^{2} g^{3} i^{2} + 15 \, a^{2} b^{4} c^{3} d^{3} g^{3} i^{2} - 6 \, a^{4} b^{2} c d^{5} g^{3} i^{2} + a^{5} b d^{6} g^{3} i^{2} - 5 \, {\left(12 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a^{3} b^{3} c^{2} d^{4}\right)} B^{2} x - {\left(6 \, a b^{5} c^{5} d g^{3} i^{2} - 33 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} + 74 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2} - 9 \, {\left(10 \, g^{3} i^{2} \log\left(e\right) + 7 \, g^{3} i^{2}\right)} a^{4} b^{2} c^{2} d^{4} + 18 \, {\left(2 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a^{5} b c d^{5} - 2 \, {\left(3 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a^{6} d^{6}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(60 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} \log\left(e\right) + 12 \, {\left({\left(12 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} b^{6} c d^{5} + {\left(18 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a b^{5} d^{6}\right)} B^{2} x^{5} + 3 \, {\left({\left(30 \, g^{3} i^{2} \log\left(e\right) - 7 \, g^{3} i^{2}\right)} b^{6} c^{2} d^{4} + 6 \, {\left(30 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} a b^{5} c d^{5} + {\left(90 \, g^{3} i^{2} \log\left(e\right) + 13 \, g^{3} i^{2}\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} - 2 \, {\left(b^{6} c^{3} d^{3} g^{3} i^{2} - 3 \, {\left(60 \, g^{3} i^{2} \log\left(e\right) - 13 \, g^{3} i^{2}\right)} a b^{5} c^{2} d^{4} - 3 \, {\left(120 \, g^{3} i^{2} \log\left(e\right) + 7 \, g^{3} i^{2}\right)} a^{2} b^{4} c d^{5} - {\left(60 \, g^{3} i^{2} \log\left(e\right) + 19 \, g^{3} i^{2}\right)} a^{3} b^{3} d^{6}\right)} B^{2} x^{3} + 3 \, {\left(b^{6} c^{4} d^{2} g^{3} i^{2} - 6 \, a b^{5} c^{3} d^{3} g^{3} i^{2} + a^{4} b^{2} d^{6} g^{3} i^{2} + 30 \, {\left(6 \, g^{3} i^{2} \log\left(e\right) - g^{3} i^{2}\right)} a^{2} b^{4} c^{2} d^{4} + 2 \, {\left(60 \, g^{3} i^{2} \log\left(e\right) + 17 \, g^{3} i^{2}\right)} a^{3} b^{3} c d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{6} c^{5} d g^{3} i^{2} - 6 \, a b^{5} c^{4} d^{2} g^{3} i^{2} + 15 \, a^{2} b^{4} c^{3} d^{3} g^{3} i^{2} - 6 \, a^{4} b^{2} c d^{5} g^{3} i^{2} + a^{5} b d^{6} g^{3} i^{2} - 5 \, {\left(12 \, g^{3} i^{2} \log\left(e\right) + g^{3} i^{2}\right)} a^{3} b^{3} c^{2} d^{4}\right)} B^{2} x + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} + 60 \, B^{2} a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} x + 12 \, {\left(2 \, b^{6} c d^{5} g^{3} i^{2} + 3 \, a b^{5} d^{6} g^{3} i^{2}\right)} B^{2} x^{5} + 15 \, {\left(b^{6} c^{2} d^{4} g^{3} i^{2} + 6 \, a b^{5} c d^{5} g^{3} i^{2} + 3 \, a^{2} b^{4} d^{6} g^{3} i^{2}\right)} B^{2} x^{4} + 20 \, {\left(3 \, a b^{5} c^{2} d^{4} g^{3} i^{2} + 6 \, a^{2} b^{4} c d^{5} g^{3} i^{2} + a^{3} b^{3} d^{6} g^{3} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(3 \, a^{2} b^{4} c^{2} d^{4} g^{3} i^{2} + 2 \, a^{3} b^{3} c d^{5} g^{3} i^{2}\right)} B^{2} x^{2} + {\left(15 \, a^{4} b^{2} c^{2} d^{4} g^{3} i^{2} - 6 \, a^{5} b c d^{5} g^{3} i^{2} + a^{6} d^{6} g^{3} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{360 \, b^{3} d^{4}}"," ",0,"1/6*A^2*b^3*d^2*g^3*i^2*x^6 + 2/5*A^2*b^3*c*d*g^3*i^2*x^5 + 3/5*A^2*a*b^2*d^2*g^3*i^2*x^5 + 1/4*A^2*b^3*c^2*g^3*i^2*x^4 + 3/2*A^2*a*b^2*c*d*g^3*i^2*x^4 + 3/4*A^2*a^2*b*d^2*g^3*i^2*x^4 + A^2*a*b^2*c^2*g^3*i^2*x^3 + 2*A^2*a^2*b*c*d*g^3*i^2*x^3 + 1/3*A^2*a^3*d^2*g^3*i^2*x^3 + 3/2*A^2*a^2*b*c^2*g^3*i^2*x^2 + A^2*a^3*c*d*g^3*i^2*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a^3*c^2*g^3*i^2 + 3*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^2*b*c^2*g^3*i^2 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a*b^2*c^2*g^3*i^2 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*b^3*c^2*g^3*i^2 + 2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^3*c*d*g^3*i^2 + 2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a^2*b*c*d*g^3*i^2 + 1/2*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a*b^2*c*d*g^3*i^2 + 1/15*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*b^3*c*d*g^3*i^2 + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a^3*d^2*g^3*i^2 + 1/4*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a^2*b*d^2*g^3*i^2 + 1/10*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*a*b^2*d^2*g^3*i^2 + 1/180*(60*x^6*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 60*a^6*log(b*x + a)/b^6 + 60*c^6*log(d*x + c)/d^6 - (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5))*A*B*b^3*d^2*g^3*i^2 + A^2*a^3*c^2*g^3*i^2*x - 1/180*(33*a^4*b*c^2*d^4*g^3*i^2 - 6*a^5*c*d^5*g^3*i^2 - 2*(3*g^3*i^2*log(e) + g^3*i^2)*b^5*c^6 + 6*(6*g^3*i^2*log(e) + g^3*i^2)*a*b^4*c^5*d - 3*(30*g^3*i^2*log(e) - g^3*i^2)*a^2*b^3*c^4*d^2 + 2*(60*g^3*i^2*log(e) - 17*g^3*i^2)*a^3*b^2*c^3*d^3)*B^2*log(d*x + c)/(b^2*d^4) + 1/30*(b^6*c^6*g^3*i^2 - 6*a*b^5*c^5*d*g^3*i^2 + 15*a^2*b^4*c^4*d^2*g^3*i^2 - 20*a^3*b^3*c^3*d^3*g^3*i^2 + 15*a^4*b^2*c^2*d^4*g^3*i^2 - 6*a^5*b*c*d^5*g^3*i^2 + a^6*d^6*g^3*i^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^3*d^4) + 1/360*(60*B^2*b^6*d^6*g^3*i^2*x^6*log(e)^2 + 24*((6*g^3*i^2*log(e)^2 - g^3*i^2*log(e))*b^6*c*d^5 + (9*g^3*i^2*log(e)^2 + g^3*i^2*log(e))*a*b^5*d^6)*B^2*x^5 + 6*((15*g^3*i^2*log(e)^2 - 7*g^3*i^2*log(e) + g^3*i^2)*b^6*c^2*d^4 + 2*(45*g^3*i^2*log(e)^2 - 3*g^3*i^2*log(e) - g^3*i^2)*a*b^5*c*d^5 + (45*g^3*i^2*log(e)^2 + 13*g^3*i^2*log(e) + g^3*i^2)*a^2*b^4*d^6)*B^2*x^4 - 2*((2*g^3*i^2*log(e) - 3*g^3*i^2)*b^6*c^3*d^3 - 3*(60*g^3*i^2*log(e)^2 - 26*g^3*i^2*log(e) + g^3*i^2)*a*b^5*c^2*d^4 - 3*(120*g^3*i^2*log(e)^2 + 14*g^3*i^2*log(e) - 5*g^3*i^2)*a^2*b^4*c*d^5 - (60*g^3*i^2*log(e)^2 + 38*g^3*i^2*log(e) + 9*g^3*i^2)*a^3*b^3*d^6)*B^2*x^3 + ((6*g^3*i^2*log(e) - 7*g^3*i^2)*b^6*c^4*d^2 - 2*(18*g^3*i^2*log(e) - 23*g^3*i^2)*a*b^5*c^3*d^3 + 60*(9*g^3*i^2*log(e)^2 - 3*g^3*i^2*log(e) - g^3*i^2)*a^2*b^4*c^2*d^4 + 2*(180*g^3*i^2*log(e)^2 + 102*g^3*i^2*log(e) + 5*g^3*i^2)*a^3*b^3*c*d^5 + (6*g^3*i^2*log(e) + 11*g^3*i^2)*a^4*b^2*d^6)*B^2*x^2 - 2*(2*(3*g^3*i^2*log(e) - 2*g^3*i^2)*b^6*c^5*d - 9*(4*g^3*i^2*log(e) - 3*g^3*i^2)*a*b^5*c^4*d^2 + (90*g^3*i^2*log(e) - 77*g^3*i^2)*a^2*b^4*c^3*d^3 - (180*g^3*i^2*log(e)^2 + 30*g^3*i^2*log(e) - 97*g^3*i^2)*a^3*b^3*c^2*d^4 - 3*(12*g^3*i^2*log(e) + 17*g^3*i^2)*a^4*b^2*c*d^5 + 2*(3*g^3*i^2*log(e) + 4*g^3*i^2)*a^5*b*d^6)*B^2*x + 6*(10*B^2*b^6*d^6*g^3*i^2*x^6 + 60*B^2*a^3*b^3*c^2*d^4*g^3*i^2*x + 12*(2*b^6*c*d^5*g^3*i^2 + 3*a*b^5*d^6*g^3*i^2)*B^2*x^5 + 15*(b^6*c^2*d^4*g^3*i^2 + 6*a*b^5*c*d^5*g^3*i^2 + 3*a^2*b^4*d^6*g^3*i^2)*B^2*x^4 + 20*(3*a*b^5*c^2*d^4*g^3*i^2 + 6*a^2*b^4*c*d^5*g^3*i^2 + a^3*b^3*d^6*g^3*i^2)*B^2*x^3 + 30*(3*a^2*b^4*c^2*d^4*g^3*i^2 + 2*a^3*b^3*c*d^5*g^3*i^2)*B^2*x^2 + (15*a^4*b^2*c^2*d^4*g^3*i^2 - 6*a^5*b*c*d^5*g^3*i^2 + a^6*d^6*g^3*i^2)*B^2)*log(b*x + a)^2 + 6*(10*B^2*b^6*d^6*g^3*i^2*x^6 + 60*B^2*a^3*b^3*c^2*d^4*g^3*i^2*x + 12*(2*b^6*c*d^5*g^3*i^2 + 3*a*b^5*d^6*g^3*i^2)*B^2*x^5 + 15*(b^6*c^2*d^4*g^3*i^2 + 6*a*b^5*c*d^5*g^3*i^2 + 3*a^2*b^4*d^6*g^3*i^2)*B^2*x^4 + 20*(3*a*b^5*c^2*d^4*g^3*i^2 + 6*a^2*b^4*c*d^5*g^3*i^2 + a^3*b^3*d^6*g^3*i^2)*B^2*x^3 + 30*(3*a^2*b^4*c^2*d^4*g^3*i^2 + 2*a^3*b^3*c*d^5*g^3*i^2)*B^2*x^2 - (b^6*c^6*g^3*i^2 - 6*a*b^5*c^5*d*g^3*i^2 + 15*a^2*b^4*c^4*d^2*g^3*i^2 - 20*a^3*b^3*c^3*d^3*g^3*i^2)*B^2)*log(d*x + c)^2 + 2*(60*B^2*b^6*d^6*g^3*i^2*x^6*log(e) + 12*((12*g^3*i^2*log(e) - g^3*i^2)*b^6*c*d^5 + (18*g^3*i^2*log(e) + g^3*i^2)*a*b^5*d^6)*B^2*x^5 + 3*((30*g^3*i^2*log(e) - 7*g^3*i^2)*b^6*c^2*d^4 + 6*(30*g^3*i^2*log(e) - g^3*i^2)*a*b^5*c*d^5 + (90*g^3*i^2*log(e) + 13*g^3*i^2)*a^2*b^4*d^6)*B^2*x^4 - 2*(b^6*c^3*d^3*g^3*i^2 - 3*(60*g^3*i^2*log(e) - 13*g^3*i^2)*a*b^5*c^2*d^4 - 3*(120*g^3*i^2*log(e) + 7*g^3*i^2)*a^2*b^4*c*d^5 - (60*g^3*i^2*log(e) + 19*g^3*i^2)*a^3*b^3*d^6)*B^2*x^3 + 3*(b^6*c^4*d^2*g^3*i^2 - 6*a*b^5*c^3*d^3*g^3*i^2 + a^4*b^2*d^6*g^3*i^2 + 30*(6*g^3*i^2*log(e) - g^3*i^2)*a^2*b^4*c^2*d^4 + 2*(60*g^3*i^2*log(e) + 17*g^3*i^2)*a^3*b^3*c*d^5)*B^2*x^2 - 6*(b^6*c^5*d*g^3*i^2 - 6*a*b^5*c^4*d^2*g^3*i^2 + 15*a^2*b^4*c^3*d^3*g^3*i^2 - 6*a^4*b^2*c*d^5*g^3*i^2 + a^5*b*d^6*g^3*i^2 - 5*(12*g^3*i^2*log(e) + g^3*i^2)*a^3*b^3*c^2*d^4)*B^2*x - (6*a*b^5*c^5*d*g^3*i^2 - 33*a^2*b^4*c^4*d^2*g^3*i^2 + 74*a^3*b^3*c^3*d^3*g^3*i^2 - 9*(10*g^3*i^2*log(e) + 7*g^3*i^2)*a^4*b^2*c^2*d^4 + 18*(2*g^3*i^2*log(e) + g^3*i^2)*a^5*b*c*d^5 - 2*(3*g^3*i^2*log(e) + g^3*i^2)*a^6*d^6)*B^2)*log(b*x + a) - 2*(60*B^2*b^6*d^6*g^3*i^2*x^6*log(e) + 12*((12*g^3*i^2*log(e) - g^3*i^2)*b^6*c*d^5 + (18*g^3*i^2*log(e) + g^3*i^2)*a*b^5*d^6)*B^2*x^5 + 3*((30*g^3*i^2*log(e) - 7*g^3*i^2)*b^6*c^2*d^4 + 6*(30*g^3*i^2*log(e) - g^3*i^2)*a*b^5*c*d^5 + (90*g^3*i^2*log(e) + 13*g^3*i^2)*a^2*b^4*d^6)*B^2*x^4 - 2*(b^6*c^3*d^3*g^3*i^2 - 3*(60*g^3*i^2*log(e) - 13*g^3*i^2)*a*b^5*c^2*d^4 - 3*(120*g^3*i^2*log(e) + 7*g^3*i^2)*a^2*b^4*c*d^5 - (60*g^3*i^2*log(e) + 19*g^3*i^2)*a^3*b^3*d^6)*B^2*x^3 + 3*(b^6*c^4*d^2*g^3*i^2 - 6*a*b^5*c^3*d^3*g^3*i^2 + a^4*b^2*d^6*g^3*i^2 + 30*(6*g^3*i^2*log(e) - g^3*i^2)*a^2*b^4*c^2*d^4 + 2*(60*g^3*i^2*log(e) + 17*g^3*i^2)*a^3*b^3*c*d^5)*B^2*x^2 - 6*(b^6*c^5*d*g^3*i^2 - 6*a*b^5*c^4*d^2*g^3*i^2 + 15*a^2*b^4*c^3*d^3*g^3*i^2 - 6*a^4*b^2*c*d^5*g^3*i^2 + a^5*b*d^6*g^3*i^2 - 5*(12*g^3*i^2*log(e) + g^3*i^2)*a^3*b^3*c^2*d^4)*B^2*x + 6*(10*B^2*b^6*d^6*g^3*i^2*x^6 + 60*B^2*a^3*b^3*c^2*d^4*g^3*i^2*x + 12*(2*b^6*c*d^5*g^3*i^2 + 3*a*b^5*d^6*g^3*i^2)*B^2*x^5 + 15*(b^6*c^2*d^4*g^3*i^2 + 6*a*b^5*c*d^5*g^3*i^2 + 3*a^2*b^4*d^6*g^3*i^2)*B^2*x^4 + 20*(3*a*b^5*c^2*d^4*g^3*i^2 + 6*a^2*b^4*c*d^5*g^3*i^2 + a^3*b^3*d^6*g^3*i^2)*B^2*x^3 + 30*(3*a^2*b^4*c^2*d^4*g^3*i^2 + 2*a^3*b^3*c*d^5*g^3*i^2)*B^2*x^2 + (15*a^4*b^2*c^2*d^4*g^3*i^2 - 6*a^5*b*c*d^5*g^3*i^2 + a^6*d^6*g^3*i^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^3*d^4)","B",0
65,1,3656,0,2.625489," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{5} \, A^{2} b^{2} d^{2} g^{2} i^{2} x^{5} + \frac{1}{2} \, A^{2} b^{2} c d g^{2} i^{2} x^{4} + \frac{1}{2} \, A^{2} a b d^{2} g^{2} i^{2} x^{4} + \frac{1}{3} \, A^{2} b^{2} c^{2} g^{2} i^{2} x^{3} + \frac{4}{3} \, A^{2} a b c d g^{2} i^{2} x^{3} + \frac{1}{3} \, A^{2} a^{2} d^{2} g^{2} i^{2} x^{3} + A^{2} a b c^{2} g^{2} i^{2} x^{2} + A^{2} a^{2} c d g^{2} i^{2} x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{2} c^{2} g^{2} i^{2} + 2 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a b c^{2} g^{2} i^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B b^{2} c^{2} g^{2} i^{2} + 2 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{2} c d g^{2} i^{2} + \frac{4}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a b c d g^{2} i^{2} + \frac{1}{6} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B b^{2} c d g^{2} i^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a^{2} d^{2} g^{2} i^{2} + \frac{1}{6} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a b d^{2} g^{2} i^{2} + \frac{1}{30} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B b^{2} d^{2} g^{2} i^{2} + A^{2} a^{2} c^{2} g^{2} i^{2} x - \frac{{\left(2 \, b^{4} c^{5} g^{2} i^{2} \log\left(e\right) + 9 \, a^{3} b c^{2} d^{3} g^{2} i^{2} - 2 \, a^{4} c d^{4} g^{2} i^{2} - 2 \, {\left(5 \, g^{2} i^{2} \log\left(e\right) - g^{2} i^{2}\right)} a b^{3} c^{4} d + {\left(20 \, g^{2} i^{2} \log\left(e\right) - 9 \, g^{2} i^{2}\right)} a^{2} b^{2} c^{3} d^{2}\right)} B^{2} \log\left(d x + c\right)}{30 \, b^{2} d^{3}} - \frac{{\left(b^{5} c^{5} g^{2} i^{2} - 5 \, a b^{4} c^{4} d g^{2} i^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{2} i^{2} + 5 \, a^{4} b c d^{4} g^{2} i^{2} - a^{5} d^{5} g^{2} i^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{15 \, b^{3} d^{3}} + \frac{12 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} \log\left(e\right)^{2} + 6 \, {\left({\left(5 \, g^{2} i^{2} \log\left(e\right)^{2} - g^{2} i^{2} \log\left(e\right)\right)} b^{5} c d^{4} + {\left(5 \, g^{2} i^{2} \log\left(e\right)^{2} + g^{2} i^{2} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left({\left(10 \, g^{2} i^{2} \log\left(e\right)^{2} - 6 \, g^{2} i^{2} \log\left(e\right) + g^{2} i^{2}\right)} b^{5} c^{2} d^{3} + 2 \, {\left(20 \, g^{2} i^{2} \log\left(e\right)^{2} - g^{2} i^{2}\right)} a b^{4} c d^{4} + {\left(10 \, g^{2} i^{2} \log\left(e\right)^{2} + 6 \, g^{2} i^{2} \log\left(e\right) + g^{2} i^{2}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left({\left(2 \, g^{2} i^{2} \log\left(e\right) - 3 \, g^{2} i^{2}\right)} b^{5} c^{3} d^{2} - 3 \, {\left(20 \, g^{2} i^{2} \log\left(e\right)^{2} - 10 \, g^{2} i^{2} \log\left(e\right) - g^{2} i^{2}\right)} a b^{4} c^{2} d^{3} - 3 \, {\left(20 \, g^{2} i^{2} \log\left(e\right)^{2} + 10 \, g^{2} i^{2} \log\left(e\right) - g^{2} i^{2}\right)} a^{2} b^{3} c d^{4} - {\left(2 \, g^{2} i^{2} \log\left(e\right) + 3 \, g^{2} i^{2}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 2 \, {\left(2 \, {\left(g^{2} i^{2} \log\left(e\right) - g^{2} i^{2}\right)} b^{5} c^{4} d - {\left(10 \, g^{2} i^{2} \log\left(e\right) - 11 \, g^{2} i^{2}\right)} a b^{4} c^{3} d^{2} + 6 \, {\left(5 \, g^{2} i^{2} \log\left(e\right)^{2} - 3 \, g^{2} i^{2}\right)} a^{2} b^{3} c^{2} d^{3} + {\left(10 \, g^{2} i^{2} \log\left(e\right) + 11 \, g^{2} i^{2}\right)} a^{3} b^{2} c d^{4} - 2 \, {\left(g^{2} i^{2} \log\left(e\right) + g^{2} i^{2}\right)} a^{4} b d^{5}\right)} B^{2} x + 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} + 30 \, B^{2} a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} x + 15 \, {\left(b^{5} c d^{4} g^{2} i^{2} + a b^{4} d^{5} g^{2} i^{2}\right)} B^{2} x^{4} + 10 \, {\left(b^{5} c^{2} d^{3} g^{2} i^{2} + 4 \, a b^{4} c d^{4} g^{2} i^{2} + a^{2} b^{3} d^{5} g^{2} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(a b^{4} c^{2} d^{3} g^{2} i^{2} + a^{2} b^{3} c d^{4} g^{2} i^{2}\right)} B^{2} x^{2} + {\left(10 \, a^{3} b^{2} c^{2} d^{3} g^{2} i^{2} - 5 \, a^{4} b c d^{4} g^{2} i^{2} + a^{5} d^{5} g^{2} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} + 30 \, B^{2} a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} x + 15 \, {\left(b^{5} c d^{4} g^{2} i^{2} + a b^{4} d^{5} g^{2} i^{2}\right)} B^{2} x^{4} + 10 \, {\left(b^{5} c^{2} d^{3} g^{2} i^{2} + 4 \, a b^{4} c d^{4} g^{2} i^{2} + a^{2} b^{3} d^{5} g^{2} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(a b^{4} c^{2} d^{3} g^{2} i^{2} + a^{2} b^{3} c d^{4} g^{2} i^{2}\right)} B^{2} x^{2} + {\left(b^{5} c^{5} g^{2} i^{2} - 5 \, a b^{4} c^{4} d g^{2} i^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} \log\left(e\right) + 3 \, {\left({\left(10 \, g^{2} i^{2} \log\left(e\right) - g^{2} i^{2}\right)} b^{5} c d^{4} + {\left(10 \, g^{2} i^{2} \log\left(e\right) + g^{2} i^{2}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left(40 \, a b^{4} c d^{4} g^{2} i^{2} \log\left(e\right) + {\left(10 \, g^{2} i^{2} \log\left(e\right) - 3 \, g^{2} i^{2}\right)} b^{5} c^{2} d^{3} + {\left(10 \, g^{2} i^{2} \log\left(e\right) + 3 \, g^{2} i^{2}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left(b^{5} c^{3} d^{2} g^{2} i^{2} - a^{3} b^{2} d^{5} g^{2} i^{2} - 15 \, {\left(4 \, g^{2} i^{2} \log\left(e\right) - g^{2} i^{2}\right)} a b^{4} c^{2} d^{3} - 15 \, {\left(4 \, g^{2} i^{2} \log\left(e\right) + g^{2} i^{2}\right)} a^{2} b^{3} c d^{4}\right)} B^{2} x^{2} + 2 \, {\left(30 \, a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} \log\left(e\right) + b^{5} c^{4} d g^{2} i^{2} - 5 \, a b^{4} c^{3} d^{2} g^{2} i^{2} + 5 \, a^{3} b^{2} c d^{4} g^{2} i^{2} - a^{4} b d^{5} g^{2} i^{2}\right)} B^{2} x + {\left(2 \, a^{5} d^{5} g^{2} i^{2} \log\left(e\right) + 2 \, a b^{4} c^{4} d g^{2} i^{2} - 9 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2} + {\left(20 \, g^{2} i^{2} \log\left(e\right) + 9 \, g^{2} i^{2}\right)} a^{3} b^{2} c^{2} d^{3} - 2 \, {\left(5 \, g^{2} i^{2} \log\left(e\right) + g^{2} i^{2}\right)} a^{4} b c d^{4}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} \log\left(e\right) + 3 \, {\left({\left(10 \, g^{2} i^{2} \log\left(e\right) - g^{2} i^{2}\right)} b^{5} c d^{4} + {\left(10 \, g^{2} i^{2} \log\left(e\right) + g^{2} i^{2}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left(40 \, a b^{4} c d^{4} g^{2} i^{2} \log\left(e\right) + {\left(10 \, g^{2} i^{2} \log\left(e\right) - 3 \, g^{2} i^{2}\right)} b^{5} c^{2} d^{3} + {\left(10 \, g^{2} i^{2} \log\left(e\right) + 3 \, g^{2} i^{2}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left(b^{5} c^{3} d^{2} g^{2} i^{2} - a^{3} b^{2} d^{5} g^{2} i^{2} - 15 \, {\left(4 \, g^{2} i^{2} \log\left(e\right) - g^{2} i^{2}\right)} a b^{4} c^{2} d^{3} - 15 \, {\left(4 \, g^{2} i^{2} \log\left(e\right) + g^{2} i^{2}\right)} a^{2} b^{3} c d^{4}\right)} B^{2} x^{2} + 2 \, {\left(30 \, a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} \log\left(e\right) + b^{5} c^{4} d g^{2} i^{2} - 5 \, a b^{4} c^{3} d^{2} g^{2} i^{2} + 5 \, a^{3} b^{2} c d^{4} g^{2} i^{2} - a^{4} b d^{5} g^{2} i^{2}\right)} B^{2} x + 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} + 30 \, B^{2} a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} x + 15 \, {\left(b^{5} c d^{4} g^{2} i^{2} + a b^{4} d^{5} g^{2} i^{2}\right)} B^{2} x^{4} + 10 \, {\left(b^{5} c^{2} d^{3} g^{2} i^{2} + 4 \, a b^{4} c d^{4} g^{2} i^{2} + a^{2} b^{3} d^{5} g^{2} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(a b^{4} c^{2} d^{3} g^{2} i^{2} + a^{2} b^{3} c d^{4} g^{2} i^{2}\right)} B^{2} x^{2} + {\left(10 \, a^{3} b^{2} c^{2} d^{3} g^{2} i^{2} - 5 \, a^{4} b c d^{4} g^{2} i^{2} + a^{5} d^{5} g^{2} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{60 \, b^{3} d^{3}}"," ",0,"1/5*A^2*b^2*d^2*g^2*i^2*x^5 + 1/2*A^2*b^2*c*d*g^2*i^2*x^4 + 1/2*A^2*a*b*d^2*g^2*i^2*x^4 + 1/3*A^2*b^2*c^2*g^2*i^2*x^3 + 4/3*A^2*a*b*c*d*g^2*i^2*x^3 + 1/3*A^2*a^2*d^2*g^2*i^2*x^3 + A^2*a*b*c^2*g^2*i^2*x^2 + A^2*a^2*c*d*g^2*i^2*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a^2*c^2*g^2*i^2 + 2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a*b*c^2*g^2*i^2 + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*b^2*c^2*g^2*i^2 + 2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^2*c*d*g^2*i^2 + 4/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a*b*c*d*g^2*i^2 + 1/6*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*b^2*c*d*g^2*i^2 + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a^2*d^2*g^2*i^2 + 1/6*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a*b*d^2*g^2*i^2 + 1/30*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*b^2*d^2*g^2*i^2 + A^2*a^2*c^2*g^2*i^2*x - 1/30*(2*b^4*c^5*g^2*i^2*log(e) + 9*a^3*b*c^2*d^3*g^2*i^2 - 2*a^4*c*d^4*g^2*i^2 - 2*(5*g^2*i^2*log(e) - g^2*i^2)*a*b^3*c^4*d + (20*g^2*i^2*log(e) - 9*g^2*i^2)*a^2*b^2*c^3*d^2)*B^2*log(d*x + c)/(b^2*d^3) - 1/15*(b^5*c^5*g^2*i^2 - 5*a*b^4*c^4*d*g^2*i^2 + 10*a^2*b^3*c^3*d^2*g^2*i^2 - 10*a^3*b^2*c^2*d^3*g^2*i^2 + 5*a^4*b*c*d^4*g^2*i^2 - a^5*d^5*g^2*i^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^3*d^3) + 1/60*(12*B^2*b^5*d^5*g^2*i^2*x^5*log(e)^2 + 6*((5*g^2*i^2*log(e)^2 - g^2*i^2*log(e))*b^5*c*d^4 + (5*g^2*i^2*log(e)^2 + g^2*i^2*log(e))*a*b^4*d^5)*B^2*x^4 + 2*((10*g^2*i^2*log(e)^2 - 6*g^2*i^2*log(e) + g^2*i^2)*b^5*c^2*d^3 + 2*(20*g^2*i^2*log(e)^2 - g^2*i^2)*a*b^4*c*d^4 + (10*g^2*i^2*log(e)^2 + 6*g^2*i^2*log(e) + g^2*i^2)*a^2*b^3*d^5)*B^2*x^3 - ((2*g^2*i^2*log(e) - 3*g^2*i^2)*b^5*c^3*d^2 - 3*(20*g^2*i^2*log(e)^2 - 10*g^2*i^2*log(e) - g^2*i^2)*a*b^4*c^2*d^3 - 3*(20*g^2*i^2*log(e)^2 + 10*g^2*i^2*log(e) - g^2*i^2)*a^2*b^3*c*d^4 - (2*g^2*i^2*log(e) + 3*g^2*i^2)*a^3*b^2*d^5)*B^2*x^2 + 2*(2*(g^2*i^2*log(e) - g^2*i^2)*b^5*c^4*d - (10*g^2*i^2*log(e) - 11*g^2*i^2)*a*b^4*c^3*d^2 + 6*(5*g^2*i^2*log(e)^2 - 3*g^2*i^2)*a^2*b^3*c^2*d^3 + (10*g^2*i^2*log(e) + 11*g^2*i^2)*a^3*b^2*c*d^4 - 2*(g^2*i^2*log(e) + g^2*i^2)*a^4*b*d^5)*B^2*x + 2*(6*B^2*b^5*d^5*g^2*i^2*x^5 + 30*B^2*a^2*b^3*c^2*d^3*g^2*i^2*x + 15*(b^5*c*d^4*g^2*i^2 + a*b^4*d^5*g^2*i^2)*B^2*x^4 + 10*(b^5*c^2*d^3*g^2*i^2 + 4*a*b^4*c*d^4*g^2*i^2 + a^2*b^3*d^5*g^2*i^2)*B^2*x^3 + 30*(a*b^4*c^2*d^3*g^2*i^2 + a^2*b^3*c*d^4*g^2*i^2)*B^2*x^2 + (10*a^3*b^2*c^2*d^3*g^2*i^2 - 5*a^4*b*c*d^4*g^2*i^2 + a^5*d^5*g^2*i^2)*B^2)*log(b*x + a)^2 + 2*(6*B^2*b^5*d^5*g^2*i^2*x^5 + 30*B^2*a^2*b^3*c^2*d^3*g^2*i^2*x + 15*(b^5*c*d^4*g^2*i^2 + a*b^4*d^5*g^2*i^2)*B^2*x^4 + 10*(b^5*c^2*d^3*g^2*i^2 + 4*a*b^4*c*d^4*g^2*i^2 + a^2*b^3*d^5*g^2*i^2)*B^2*x^3 + 30*(a*b^4*c^2*d^3*g^2*i^2 + a^2*b^3*c*d^4*g^2*i^2)*B^2*x^2 + (b^5*c^5*g^2*i^2 - 5*a*b^4*c^4*d*g^2*i^2 + 10*a^2*b^3*c^3*d^2*g^2*i^2)*B^2)*log(d*x + c)^2 + 2*(12*B^2*b^5*d^5*g^2*i^2*x^5*log(e) + 3*((10*g^2*i^2*log(e) - g^2*i^2)*b^5*c*d^4 + (10*g^2*i^2*log(e) + g^2*i^2)*a*b^4*d^5)*B^2*x^4 + 2*(40*a*b^4*c*d^4*g^2*i^2*log(e) + (10*g^2*i^2*log(e) - 3*g^2*i^2)*b^5*c^2*d^3 + (10*g^2*i^2*log(e) + 3*g^2*i^2)*a^2*b^3*d^5)*B^2*x^3 - (b^5*c^3*d^2*g^2*i^2 - a^3*b^2*d^5*g^2*i^2 - 15*(4*g^2*i^2*log(e) - g^2*i^2)*a*b^4*c^2*d^3 - 15*(4*g^2*i^2*log(e) + g^2*i^2)*a^2*b^3*c*d^4)*B^2*x^2 + 2*(30*a^2*b^3*c^2*d^3*g^2*i^2*log(e) + b^5*c^4*d*g^2*i^2 - 5*a*b^4*c^3*d^2*g^2*i^2 + 5*a^3*b^2*c*d^4*g^2*i^2 - a^4*b*d^5*g^2*i^2)*B^2*x + (2*a^5*d^5*g^2*i^2*log(e) + 2*a*b^4*c^4*d*g^2*i^2 - 9*a^2*b^3*c^3*d^2*g^2*i^2 + (20*g^2*i^2*log(e) + 9*g^2*i^2)*a^3*b^2*c^2*d^3 - 2*(5*g^2*i^2*log(e) + g^2*i^2)*a^4*b*c*d^4)*B^2)*log(b*x + a) - 2*(12*B^2*b^5*d^5*g^2*i^2*x^5*log(e) + 3*((10*g^2*i^2*log(e) - g^2*i^2)*b^5*c*d^4 + (10*g^2*i^2*log(e) + g^2*i^2)*a*b^4*d^5)*B^2*x^4 + 2*(40*a*b^4*c*d^4*g^2*i^2*log(e) + (10*g^2*i^2*log(e) - 3*g^2*i^2)*b^5*c^2*d^3 + (10*g^2*i^2*log(e) + 3*g^2*i^2)*a^2*b^3*d^5)*B^2*x^3 - (b^5*c^3*d^2*g^2*i^2 - a^3*b^2*d^5*g^2*i^2 - 15*(4*g^2*i^2*log(e) - g^2*i^2)*a*b^4*c^2*d^3 - 15*(4*g^2*i^2*log(e) + g^2*i^2)*a^2*b^3*c*d^4)*B^2*x^2 + 2*(30*a^2*b^3*c^2*d^3*g^2*i^2*log(e) + b^5*c^4*d*g^2*i^2 - 5*a*b^4*c^3*d^2*g^2*i^2 + 5*a^3*b^2*c*d^4*g^2*i^2 - a^4*b*d^5*g^2*i^2)*B^2*x + 2*(6*B^2*b^5*d^5*g^2*i^2*x^5 + 30*B^2*a^2*b^3*c^2*d^3*g^2*i^2*x + 15*(b^5*c*d^4*g^2*i^2 + a*b^4*d^5*g^2*i^2)*B^2*x^4 + 10*(b^5*c^2*d^3*g^2*i^2 + 4*a*b^4*c*d^4*g^2*i^2 + a^2*b^3*d^5*g^2*i^2)*B^2*x^3 + 30*(a*b^4*c^2*d^3*g^2*i^2 + a^2*b^3*c*d^4*g^2*i^2)*B^2*x^2 + (10*a^3*b^2*c^2*d^3*g^2*i^2 - 5*a^4*b*c*d^4*g^2*i^2 + a^5*d^5*g^2*i^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^3*d^3)","B",0
66,1,2259,0,2.339567," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} b d^{2} g i^{2} x^{4} + \frac{2}{3} \, A^{2} b c d g i^{2} x^{3} + \frac{1}{3} \, A^{2} a d^{2} g i^{2} x^{3} + \frac{1}{2} \, A^{2} b c^{2} g i^{2} x^{2} + A^{2} a c d g i^{2} x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a c^{2} g i^{2} + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B b c^{2} g i^{2} + 2 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a c d g i^{2} + \frac{2}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B b c d g i^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a d^{2} g i^{2} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B b d^{2} g i^{2} + A^{2} a c^{2} g i^{2} x - \frac{{\left(7 \, a^{2} b c^{2} d^{2} g i^{2} - 2 \, a^{3} c d^{3} g i^{2} - {\left(2 \, g i^{2} \log\left(e\right) - g i^{2}\right)} b^{3} c^{4} + 2 \, {\left(4 \, g i^{2} \log\left(e\right) - 3 \, g i^{2}\right)} a b^{2} c^{3} d\right)} B^{2} \log\left(d x + c\right)}{12 \, b^{2} d^{2}} + \frac{{\left(b^{4} c^{4} g i^{2} - 4 \, a b^{3} c^{3} d g i^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g i^{2} - 4 \, a^{3} b c d^{3} g i^{2} + a^{4} d^{4} g i^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{6 \, b^{3} d^{2}} + \frac{3 \, B^{2} b^{4} d^{4} g i^{2} x^{4} \log\left(e\right)^{2} + 2 \, {\left({\left(4 \, g i^{2} \log\left(e\right)^{2} - g i^{2} \log\left(e\right)\right)} b^{4} c d^{3} + {\left(2 \, g i^{2} \log\left(e\right)^{2} + g i^{2} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left({\left(6 \, g i^{2} \log\left(e\right)^{2} - 5 \, g i^{2} \log\left(e\right) + g i^{2}\right)} b^{4} c^{2} d^{2} + 2 \, {\left(6 \, g i^{2} \log\left(e\right)^{2} + 2 \, g i^{2} \log\left(e\right) - g i^{2}\right)} a b^{3} c d^{3} + {\left(g i^{2} \log\left(e\right) + g i^{2}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - {\left({\left(2 \, g i^{2} \log\left(e\right) - 3 \, g i^{2}\right)} b^{4} c^{3} d - {\left(12 \, g i^{2} \log\left(e\right)^{2} - 4 \, g i^{2} \log\left(e\right) - 7 \, g i^{2}\right)} a b^{3} c^{2} d^{2} - {\left(8 \, g i^{2} \log\left(e\right) + 5 \, g i^{2}\right)} a^{2} b^{2} c d^{3} + {\left(2 \, g i^{2} \log\left(e\right) + g i^{2}\right)} a^{3} b d^{4}\right)} B^{2} x + {\left(3 \, B^{2} b^{4} d^{4} g i^{2} x^{4} + 12 \, B^{2} a b^{3} c^{2} d^{2} g i^{2} x + 4 \, {\left(2 \, b^{4} c d^{3} g i^{2} + a b^{3} d^{4} g i^{2}\right)} B^{2} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} g i^{2} + 2 \, a b^{3} c d^{3} g i^{2}\right)} B^{2} x^{2} + {\left(6 \, a^{2} b^{2} c^{2} d^{2} g i^{2} - 4 \, a^{3} b c d^{3} g i^{2} + a^{4} d^{4} g i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + {\left(3 \, B^{2} b^{4} d^{4} g i^{2} x^{4} + 12 \, B^{2} a b^{3} c^{2} d^{2} g i^{2} x + 4 \, {\left(2 \, b^{4} c d^{3} g i^{2} + a b^{3} d^{4} g i^{2}\right)} B^{2} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} g i^{2} + 2 \, a b^{3} c d^{3} g i^{2}\right)} B^{2} x^{2} - {\left(b^{4} c^{4} g i^{2} - 4 \, a b^{3} c^{3} d g i^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g i^{2} x^{4} \log\left(e\right) + 2 \, {\left({\left(8 \, g i^{2} \log\left(e\right) - g i^{2}\right)} b^{4} c d^{3} + {\left(4 \, g i^{2} \log\left(e\right) + g i^{2}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left(a^{2} b^{2} d^{4} g i^{2} + {\left(12 \, g i^{2} \log\left(e\right) - 5 \, g i^{2}\right)} b^{4} c^{2} d^{2} + 4 \, {\left(6 \, g i^{2} \log\left(e\right) + g i^{2}\right)} a b^{3} c d^{3}\right)} B^{2} x^{2} - 2 \, {\left(b^{4} c^{3} d g i^{2} - 4 \, a^{2} b^{2} c d^{3} g i^{2} + a^{3} b d^{4} g i^{2} - 2 \, {\left(6 \, g i^{2} \log\left(e\right) - g i^{2}\right)} a b^{3} c^{2} d^{2}\right)} B^{2} x - {\left(2 \, a b^{3} c^{3} d g i^{2} - {\left(12 \, g i^{2} \log\left(e\right) + g i^{2}\right)} a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(4 \, g i^{2} \log\left(e\right) - g i^{2}\right)} a^{3} b c d^{3} - {\left(2 \, g i^{2} \log\left(e\right) - g i^{2}\right)} a^{4} d^{4}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(6 \, B^{2} b^{4} d^{4} g i^{2} x^{4} \log\left(e\right) + 2 \, {\left({\left(8 \, g i^{2} \log\left(e\right) - g i^{2}\right)} b^{4} c d^{3} + {\left(4 \, g i^{2} \log\left(e\right) + g i^{2}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left(a^{2} b^{2} d^{4} g i^{2} + {\left(12 \, g i^{2} \log\left(e\right) - 5 \, g i^{2}\right)} b^{4} c^{2} d^{2} + 4 \, {\left(6 \, g i^{2} \log\left(e\right) + g i^{2}\right)} a b^{3} c d^{3}\right)} B^{2} x^{2} - 2 \, {\left(b^{4} c^{3} d g i^{2} - 4 \, a^{2} b^{2} c d^{3} g i^{2} + a^{3} b d^{4} g i^{2} - 2 \, {\left(6 \, g i^{2} \log\left(e\right) - g i^{2}\right)} a b^{3} c^{2} d^{2}\right)} B^{2} x + 2 \, {\left(3 \, B^{2} b^{4} d^{4} g i^{2} x^{4} + 12 \, B^{2} a b^{3} c^{2} d^{2} g i^{2} x + 4 \, {\left(2 \, b^{4} c d^{3} g i^{2} + a b^{3} d^{4} g i^{2}\right)} B^{2} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} g i^{2} + 2 \, a b^{3} c d^{3} g i^{2}\right)} B^{2} x^{2} + {\left(6 \, a^{2} b^{2} c^{2} d^{2} g i^{2} - 4 \, a^{3} b c d^{3} g i^{2} + a^{4} d^{4} g i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b^{3} d^{2}}"," ",0,"1/4*A^2*b*d^2*g*i^2*x^4 + 2/3*A^2*b*c*d*g*i^2*x^3 + 1/3*A^2*a*d^2*g*i^2*x^3 + 1/2*A^2*b*c^2*g*i^2*x^2 + A^2*a*c*d*g*i^2*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a*c^2*g*i^2 + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*b*c^2*g*i^2 + 2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a*c*d*g*i^2 + 2/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*b*c*d*g*i^2 + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a*d^2*g*i^2 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*b*d^2*g*i^2 + A^2*a*c^2*g*i^2*x - 1/12*(7*a^2*b*c^2*d^2*g*i^2 - 2*a^3*c*d^3*g*i^2 - (2*g*i^2*log(e) - g*i^2)*b^3*c^4 + 2*(4*g*i^2*log(e) - 3*g*i^2)*a*b^2*c^3*d)*B^2*log(d*x + c)/(b^2*d^2) + 1/6*(b^4*c^4*g*i^2 - 4*a*b^3*c^3*d*g*i^2 + 6*a^2*b^2*c^2*d^2*g*i^2 - 4*a^3*b*c*d^3*g*i^2 + a^4*d^4*g*i^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^3*d^2) + 1/12*(3*B^2*b^4*d^4*g*i^2*x^4*log(e)^2 + 2*((4*g*i^2*log(e)^2 - g*i^2*log(e))*b^4*c*d^3 + (2*g*i^2*log(e)^2 + g*i^2*log(e))*a*b^3*d^4)*B^2*x^3 + ((6*g*i^2*log(e)^2 - 5*g*i^2*log(e) + g*i^2)*b^4*c^2*d^2 + 2*(6*g*i^2*log(e)^2 + 2*g*i^2*log(e) - g*i^2)*a*b^3*c*d^3 + (g*i^2*log(e) + g*i^2)*a^2*b^2*d^4)*B^2*x^2 - ((2*g*i^2*log(e) - 3*g*i^2)*b^4*c^3*d - (12*g*i^2*log(e)^2 - 4*g*i^2*log(e) - 7*g*i^2)*a*b^3*c^2*d^2 - (8*g*i^2*log(e) + 5*g*i^2)*a^2*b^2*c*d^3 + (2*g*i^2*log(e) + g*i^2)*a^3*b*d^4)*B^2*x + (3*B^2*b^4*d^4*g*i^2*x^4 + 12*B^2*a*b^3*c^2*d^2*g*i^2*x + 4*(2*b^4*c*d^3*g*i^2 + a*b^3*d^4*g*i^2)*B^2*x^3 + 6*(b^4*c^2*d^2*g*i^2 + 2*a*b^3*c*d^3*g*i^2)*B^2*x^2 + (6*a^2*b^2*c^2*d^2*g*i^2 - 4*a^3*b*c*d^3*g*i^2 + a^4*d^4*g*i^2)*B^2)*log(b*x + a)^2 + (3*B^2*b^4*d^4*g*i^2*x^4 + 12*B^2*a*b^3*c^2*d^2*g*i^2*x + 4*(2*b^4*c*d^3*g*i^2 + a*b^3*d^4*g*i^2)*B^2*x^3 + 6*(b^4*c^2*d^2*g*i^2 + 2*a*b^3*c*d^3*g*i^2)*B^2*x^2 - (b^4*c^4*g*i^2 - 4*a*b^3*c^3*d*g*i^2)*B^2)*log(d*x + c)^2 + (6*B^2*b^4*d^4*g*i^2*x^4*log(e) + 2*((8*g*i^2*log(e) - g*i^2)*b^4*c*d^3 + (4*g*i^2*log(e) + g*i^2)*a*b^3*d^4)*B^2*x^3 + (a^2*b^2*d^4*g*i^2 + (12*g*i^2*log(e) - 5*g*i^2)*b^4*c^2*d^2 + 4*(6*g*i^2*log(e) + g*i^2)*a*b^3*c*d^3)*B^2*x^2 - 2*(b^4*c^3*d*g*i^2 - 4*a^2*b^2*c*d^3*g*i^2 + a^3*b*d^4*g*i^2 - 2*(6*g*i^2*log(e) - g*i^2)*a*b^3*c^2*d^2)*B^2*x - (2*a*b^3*c^3*d*g*i^2 - (12*g*i^2*log(e) + g*i^2)*a^2*b^2*c^2*d^2 + 2*(4*g*i^2*log(e) - g*i^2)*a^3*b*c*d^3 - (2*g*i^2*log(e) - g*i^2)*a^4*d^4)*B^2)*log(b*x + a) - (6*B^2*b^4*d^4*g*i^2*x^4*log(e) + 2*((8*g*i^2*log(e) - g*i^2)*b^4*c*d^3 + (4*g*i^2*log(e) + g*i^2)*a*b^3*d^4)*B^2*x^3 + (a^2*b^2*d^4*g*i^2 + (12*g*i^2*log(e) - 5*g*i^2)*b^4*c^2*d^2 + 4*(6*g*i^2*log(e) + g*i^2)*a*b^3*c*d^3)*B^2*x^2 - 2*(b^4*c^3*d*g*i^2 - 4*a^2*b^2*c*d^3*g*i^2 + a^3*b*d^4*g*i^2 - 2*(6*g*i^2*log(e) - g*i^2)*a*b^3*c^2*d^2)*B^2*x + 2*(3*B^2*b^4*d^4*g*i^2*x^4 + 12*B^2*a*b^3*c^2*d^2*g*i^2*x + 4*(2*b^4*c*d^3*g*i^2 + a*b^3*d^4*g*i^2)*B^2*x^3 + 6*(b^4*c^2*d^2*g*i^2 + 2*a*b^3*c*d^3*g*i^2)*B^2*x^2 + (6*a^2*b^2*c^2*d^2*g*i^2 - 4*a^3*b*c*d^3*g*i^2 + a^4*d^4*g*i^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^3*d^2)","B",0
67,1,1202,0,2.031031," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A^{2} d^{2} i^{2} x^{3} + A^{2} c d i^{2} x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B c^{2} i^{2} + 2 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B c d i^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B d^{2} i^{2} + A^{2} c^{2} i^{2} x - \frac{{\left(5 \, a b c^{2} d i^{2} - 2 \, a^{2} c d^{2} i^{2} + {\left(2 \, i^{2} \log\left(e\right) - 3 \, i^{2}\right)} b^{2} c^{3}\right)} B^{2} \log\left(d x + c\right)}{3 \, b^{2} d} - \frac{2 \, {\left(b^{3} c^{3} i^{2} - 3 \, a b^{2} c^{2} d i^{2} + 3 \, a^{2} b c d^{2} i^{2} - a^{3} d^{3} i^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{3 \, b^{3} d} + \frac{B^{2} b^{3} d^{3} i^{2} x^{3} \log\left(e\right)^{2} + {\left(a b^{2} d^{3} i^{2} \log\left(e\right) + {\left(3 \, i^{2} \log\left(e\right)^{2} - i^{2} \log\left(e\right)\right)} b^{3} c d^{2}\right)} B^{2} x^{2} + {\left({\left(3 \, i^{2} \log\left(e\right)^{2} - 4 \, i^{2} \log\left(e\right) + i^{2}\right)} b^{3} c^{2} d + 2 \, {\left(3 \, i^{2} \log\left(e\right) - i^{2}\right)} a b^{2} c d^{2} - {\left(2 \, i^{2} \log\left(e\right) - i^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + {\left(3 \, a b^{2} c^{2} d i^{2} - 3 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left(d x + c\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} i^{2} x^{3} \log\left(e\right) + {\left(a b^{2} d^{3} i^{2} + {\left(6 \, i^{2} \log\left(e\right) - i^{2}\right)} b^{3} c d^{2}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} c d^{2} i^{2} - a^{2} b d^{3} i^{2} + {\left(3 \, i^{2} \log\left(e\right) - 2 \, i^{2}\right)} b^{3} c^{2} d\right)} B^{2} x + {\left(2 \, {\left(3 \, i^{2} \log\left(e\right) - 2 \, i^{2}\right)} a b^{2} c^{2} d - {\left(6 \, i^{2} \log\left(e\right) - 7 \, i^{2}\right)} a^{2} b c d^{2} + {\left(2 \, i^{2} \log\left(e\right) - 3 \, i^{2}\right)} a^{3} d^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(2 \, B^{2} b^{3} d^{3} i^{2} x^{3} \log\left(e\right) + {\left(a b^{2} d^{3} i^{2} + {\left(6 \, i^{2} \log\left(e\right) - i^{2}\right)} b^{3} c d^{2}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} c d^{2} i^{2} - a^{2} b d^{3} i^{2} + {\left(3 \, i^{2} \log\left(e\right) - 2 \, i^{2}\right)} b^{3} c^{2} d\right)} B^{2} x + 2 \, {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + {\left(3 \, a b^{2} c^{2} d i^{2} - 3 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, b^{3} d}"," ",0,"1/3*A^2*d^2*i^2*x^3 + A^2*c*d*i^2*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*c^2*i^2 + 2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*c*d*i^2 + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*d^2*i^2 + A^2*c^2*i^2*x - 1/3*(5*a*b*c^2*d*i^2 - 2*a^2*c*d^2*i^2 + (2*i^2*log(e) - 3*i^2)*b^2*c^3)*B^2*log(d*x + c)/(b^2*d) - 2/3*(b^3*c^3*i^2 - 3*a*b^2*c^2*d*i^2 + 3*a^2*b*c*d^2*i^2 - a^3*d^3*i^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^3*d) + 1/3*(B^2*b^3*d^3*i^2*x^3*log(e)^2 + (a*b^2*d^3*i^2*log(e) + (3*i^2*log(e)^2 - i^2*log(e))*b^3*c*d^2)*B^2*x^2 + ((3*i^2*log(e)^2 - 4*i^2*log(e) + i^2)*b^3*c^2*d + 2*(3*i^2*log(e) - i^2)*a*b^2*c*d^2 - (2*i^2*log(e) - i^2)*a^2*b*d^3)*B^2*x + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + (3*a*b^2*c^2*d*i^2 - 3*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B^2)*log(b*x + a)^2 + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log(d*x + c)^2 + (2*B^2*b^3*d^3*i^2*x^3*log(e) + (a*b^2*d^3*i^2 + (6*i^2*log(e) - i^2)*b^3*c*d^2)*B^2*x^2 + 2*(3*a*b^2*c*d^2*i^2 - a^2*b*d^3*i^2 + (3*i^2*log(e) - 2*i^2)*b^3*c^2*d)*B^2*x + (2*(3*i^2*log(e) - 2*i^2)*a*b^2*c^2*d - (6*i^2*log(e) - 7*i^2)*a^2*b*c*d^2 + (2*i^2*log(e) - 3*i^2)*a^3*d^3)*B^2)*log(b*x + a) - (2*B^2*b^3*d^3*i^2*x^3*log(e) + (a*b^2*d^3*i^2 + (6*i^2*log(e) - i^2)*b^3*c*d^2)*B^2*x^2 + 2*(3*a*b^2*c*d^2*i^2 - a^2*b*d^3*i^2 + (3*i^2*log(e) - 2*i^2)*b^3*c^2*d)*B^2*x + 2*(B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + (3*a*b^2*c^2*d*i^2 - 3*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^3*d)","B",0
68,0,0,0,0.000000," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g),x, algorithm=""maxima"")","2 \, A^{2} c d i^{2} {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} + \frac{1}{2} \, A^{2} d^{2} i^{2} {\left(\frac{2 \, a^{2} \log\left(b x + a\right)}{b^{3} g} + \frac{b x^{2} - 2 \, a x}{b^{2} g}\right)} + \frac{A^{2} c^{2} i^{2} \log\left(b g x + a g\right)}{b g} + \frac{{\left(B^{2} b^{2} d^{2} i^{2} x^{2} + 2 \, {\left(2 \, b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B^{2} x + 2 \, {\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} B^{2} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2}}{2 \, b^{3} g} - \int -\frac{B^{2} b^{3} c^{3} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c^{3} i^{2} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} i^{2} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c d^{2} i^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(B^{2} b^{3} c^{2} d i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c^{2} d i^{2} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{3} c^{3} i^{2} \log\left(e\right) + A B b^{3} c^{3} i^{2} + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right) + A B b^{3} d^{3} i^{2}\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} \log\left(e\right) + A B b^{3} c d^{2} i^{2}\right)} x^{2} + 3 \, {\left(B^{2} b^{3} c^{2} d i^{2} \log\left(e\right) + A B b^{3} c^{2} d i^{2}\right)} x\right)} \log\left(b x + a\right) - {\left(2 \, B^{2} b^{3} c^{3} i^{2} \log\left(e\right) + 2 \, A B b^{3} c^{3} i^{2} + {\left(2 \, A B b^{3} d^{3} i^{2} + {\left(2 \, i^{2} \log\left(e\right) + i^{2}\right)} B^{2} b^{3} d^{3}\right)} x^{3} + {\left(6 \, A B b^{3} c d^{2} i^{2} - {\left(a b^{2} d^{3} i^{2} - 2 \, {\left(3 \, i^{2} \log\left(e\right) + 2 \, i^{2}\right)} b^{3} c d^{2}\right)} B^{2}\right)} x^{2} + 2 \, {\left(3 \, A B b^{3} c^{2} d i^{2} + {\left(3 \, b^{3} c^{2} d i^{2} \log\left(e\right) + 2 \, a b^{2} c d^{2} i^{2} - a^{2} b d^{3} i^{2}\right)} B^{2}\right)} x + 2 \, {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + {\left(4 \, b^{3} c^{2} d i^{2} - 2 \, a b^{2} c d^{2} i^{2} + a^{2} b d^{3} i^{2}\right)} B^{2} x + {\left(b^{3} c^{3} i^{2} + a b^{2} c^{2} d i^{2} - 2 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{4} d g x^{2} + a b^{3} c g + {\left(b^{4} c g + a b^{3} d g\right)} x}\,{d x}"," ",0,"2*A^2*c*d*i^2*(x/(b*g) - a*log(b*x + a)/(b^2*g)) + 1/2*A^2*d^2*i^2*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2*g)) + A^2*c^2*i^2*log(b*g*x + a*g)/(b*g) + 1/2*(B^2*b^2*d^2*i^2*x^2 + 2*(2*b^2*c*d*i^2 - a*b*d^2*i^2)*B^2*x + 2*(b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*B^2*log(b*x + a))*log(d*x + c)^2/(b^3*g) - integrate(-(B^2*b^3*c^3*i^2*log(e)^2 + 2*A*B*b^3*c^3*i^2*log(e) + (B^2*b^3*d^3*i^2*log(e)^2 + 2*A*B*b^3*d^3*i^2*log(e))*x^3 + 3*(B^2*b^3*c*d^2*i^2*log(e)^2 + 2*A*B*b^3*c*d^2*i^2*log(e))*x^2 + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log(b*x + a)^2 + 3*(B^2*b^3*c^2*d*i^2*log(e)^2 + 2*A*B*b^3*c^2*d*i^2*log(e))*x + 2*(B^2*b^3*c^3*i^2*log(e) + A*B*b^3*c^3*i^2 + (B^2*b^3*d^3*i^2*log(e) + A*B*b^3*d^3*i^2)*x^3 + 3*(B^2*b^3*c*d^2*i^2*log(e) + A*B*b^3*c*d^2*i^2)*x^2 + 3*(B^2*b^3*c^2*d*i^2*log(e) + A*B*b^3*c^2*d*i^2)*x)*log(b*x + a) - (2*B^2*b^3*c^3*i^2*log(e) + 2*A*B*b^3*c^3*i^2 + (2*A*B*b^3*d^3*i^2 + (2*i^2*log(e) + i^2)*B^2*b^3*d^3)*x^3 + (6*A*B*b^3*c*d^2*i^2 - (a*b^2*d^3*i^2 - 2*(3*i^2*log(e) + 2*i^2)*b^3*c*d^2)*B^2)*x^2 + 2*(3*A*B*b^3*c^2*d*i^2 + (3*b^3*c^2*d*i^2*log(e) + 2*a*b^2*c*d^2*i^2 - a^2*b*d^3*i^2)*B^2)*x + 2*(B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + (4*b^3*c^2*d*i^2 - 2*a*b^2*c*d^2*i^2 + a^2*b*d^3*i^2)*B^2*x + (b^3*c^3*i^2 + a*b^2*c^2*d*i^2 - 2*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d*g*x^2 + a*b^3*c*g + (b^4*c*g + a*b^3*d*g)*x), x)","F",0
69,0,0,0,0.000000," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-A^{2} {\left(\frac{a^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \frac{x}{b^{2} g^{2}} + \frac{2 \, a \log\left(b x + a\right)}{b^{3} g^{2}}\right)} d^{2} i^{2} + 2 \, A^{2} c d i^{2} {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - 2 \, A B c^{2} i^{2} {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{2} g^{2} x + a b g^{2}} + \frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{A^{2} c^{2} i^{2}}{b^{2} g^{2} x + a b g^{2}} + \frac{{\left(B^{2} b^{2} d^{2} i^{2} x^{2} + B^{2} a b d^{2} i^{2} x - {\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} B^{2} + 2 \, {\left({\left(b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B^{2} x + {\left(a b c d i^{2} - a^{2} d^{2} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \int -\frac{B^{2} b^{3} c^{3} i^{2} \log\left(e\right)^{2} + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} i^{2} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c d^{2} i^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left(b x + a\right)^{2} + {\left(3 \, B^{2} b^{3} c^{2} d i^{2} \log\left(e\right)^{2} + 4 \, A B b^{3} c^{2} d i^{2} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{3} c^{3} i^{2} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right) + A B b^{3} d^{3} i^{2}\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} \log\left(e\right) + A B b^{3} c d^{2} i^{2}\right)} x^{2} + {\left(3 \, B^{2} b^{3} c^{2} d i^{2} \log\left(e\right) + 2 \, A B b^{3} c^{2} d i^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left({\left(A B b^{3} d^{3} i^{2} + {\left(i^{2} \log\left(e\right) + i^{2}\right)} B^{2} b^{3} d^{3}\right)} x^{3} + {\left(b^{3} c^{3} i^{2} \log\left(e\right) - a b^{2} c^{2} d i^{2} + 2 \, a^{2} b c d^{2} i^{2} - a^{3} d^{3} i^{2}\right)} B^{2} + {\left(3 \, A B b^{3} c d^{2} i^{2} + {\left(3 \, b^{3} c d^{2} i^{2} \log\left(e\right) + 2 \, a b^{2} d^{3} i^{2}\right)} B^{2}\right)} x^{2} + {\left(2 \, A B b^{3} c^{2} d i^{2} + {\left(2 \, a b^{2} c d^{2} i^{2} + {\left(3 \, i^{2} \log\left(e\right) - i^{2}\right)} b^{3} c^{2} d\right)} B^{2}\right)} x + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + {\left(5 \, b^{3} c d^{2} i^{2} - 2 \, a b^{2} d^{3} i^{2}\right)} B^{2} x^{2} + {\left(3 \, b^{3} c^{2} d i^{2} + 4 \, a b^{2} c d^{2} i^{2} - 4 \, a^{2} b d^{3} i^{2}\right)} B^{2} x + {\left(b^{3} c^{3} i^{2} + 2 \, a^{2} b c d^{2} i^{2} - 2 \, a^{3} d^{3} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{5} d g^{2} x^{3} + a^{2} b^{3} c g^{2} + {\left(b^{5} c g^{2} + 2 \, a b^{4} d g^{2}\right)} x^{2} + {\left(2 \, a b^{4} c g^{2} + a^{2} b^{3} d g^{2}\right)} x}\,{d x}"," ",0,"-A^2*(a^2/(b^4*g^2*x + a*b^3*g^2) - x/(b^2*g^2) + 2*a*log(b*x + a)/(b^3*g^2))*d^2*i^2 + 2*A^2*c*d*i^2*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - 2*A*B*c^2*i^2*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^2*g^2*x + a*b*g^2) + 1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A^2*c^2*i^2/(b^2*g^2*x + a*b*g^2) + (B^2*b^2*d^2*i^2*x^2 + B^2*a*b*d^2*i^2*x - (b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*B^2 + 2*((b^2*c*d*i^2 - a*b*d^2*i^2)*B^2*x + (a*b*c*d*i^2 - a^2*d^2*i^2)*B^2)*log(b*x + a))*log(d*x + c)^2/(b^4*g^2*x + a*b^3*g^2) - integrate(-(B^2*b^3*c^3*i^2*log(e)^2 + (B^2*b^3*d^3*i^2*log(e)^2 + 2*A*B*b^3*d^3*i^2*log(e))*x^3 + 3*(B^2*b^3*c*d^2*i^2*log(e)^2 + 2*A*B*b^3*c*d^2*i^2*log(e))*x^2 + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log(b*x + a)^2 + (3*B^2*b^3*c^2*d*i^2*log(e)^2 + 4*A*B*b^3*c^2*d*i^2*log(e))*x + 2*(B^2*b^3*c^3*i^2*log(e) + (B^2*b^3*d^3*i^2*log(e) + A*B*b^3*d^3*i^2)*x^3 + 3*(B^2*b^3*c*d^2*i^2*log(e) + A*B*b^3*c*d^2*i^2)*x^2 + (3*B^2*b^3*c^2*d*i^2*log(e) + 2*A*B*b^3*c^2*d*i^2)*x)*log(b*x + a) - 2*((A*B*b^3*d^3*i^2 + (i^2*log(e) + i^2)*B^2*b^3*d^3)*x^3 + (b^3*c^3*i^2*log(e) - a*b^2*c^2*d*i^2 + 2*a^2*b*c*d^2*i^2 - a^3*d^3*i^2)*B^2 + (3*A*B*b^3*c*d^2*i^2 + (3*b^3*c*d^2*i^2*log(e) + 2*a*b^2*d^3*i^2)*B^2)*x^2 + (2*A*B*b^3*c^2*d*i^2 + (2*a*b^2*c*d^2*i^2 + (3*i^2*log(e) - i^2)*b^3*c^2*d)*B^2)*x + (B^2*b^3*d^3*i^2*x^3 + (5*b^3*c*d^2*i^2 - 2*a*b^2*d^3*i^2)*B^2*x^2 + (3*b^3*c^2*d*i^2 + 4*a*b^2*c*d^2*i^2 - 4*a^2*b*d^3*i^2)*B^2*x + (b^3*c^3*i^2 + 2*a^2*b*c*d^2*i^2 - 2*a^3*d^3*i^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^5*d*g^2*x^3 + a^2*b^3*c*g^2 + (b^5*c*g^2 + 2*a*b^4*d*g^2)*x^2 + (2*a*b^4*c*g^2 + a^2*b^3*d*g^2)*x), x)","F",0
70,0,0,0,0.000000," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-A B c d i^{2} {\left(\frac{2 \, {\left(2 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} + \frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{2} \, A^{2} d^{2} i^{2} {\left(\frac{4 \, a b x + 3 \, a^{2}}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + \frac{2 \, \log\left(b x + a\right)}{b^{3} g^{3}}\right)} + \frac{1}{2} \, A B c^{2} i^{2} {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{{\left(2 \, b x + a\right)} A^{2} c d i^{2}}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} - \frac{A^{2} c^{2} i^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{{\left(4 \, {\left(b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B^{2} x + {\left(b^{2} c^{2} i^{2} + 2 \, a b c d i^{2} - 3 \, a^{2} d^{2} i^{2}\right)} B^{2} - 2 \, {\left(B^{2} b^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} a b d^{2} i^{2} x + B^{2} a^{2} d^{2} i^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2}}{2 \, {\left(b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}\right)}} - \int -\frac{3 \, B^{2} b^{3} c^{2} d i^{2} x \log\left(e\right)^{2} + B^{2} b^{3} c^{3} i^{2} \log\left(e\right)^{2} + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} i^{2} \log\left(e\right)\right)} x^{3} + {\left(3 \, B^{2} b^{3} c d^{2} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c d^{2} i^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(3 \, B^{2} b^{3} c^{2} d i^{2} x \log\left(e\right) + B^{2} b^{3} c^{3} i^{2} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right) + A B b^{3} d^{3} i^{2}\right)} x^{3} + {\left(3 \, B^{2} b^{3} c d^{2} i^{2} \log\left(e\right) + A B b^{3} c d^{2} i^{2}\right)} x^{2}\right)} \log\left(b x + a\right) + {\left({\left(6 \, a b^{2} c d^{2} i^{2} - 7 \, a^{2} b d^{3} i^{2} - {\left(6 \, i^{2} \log\left(e\right) - i^{2}\right)} b^{3} c^{2} d\right)} B^{2} x - 2 \, {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right) + A B b^{3} d^{3} i^{2}\right)} x^{3} - {\left(2 \, b^{3} c^{3} i^{2} \log\left(e\right) - a b^{2} c^{2} d i^{2} - 2 \, a^{2} b c d^{2} i^{2} + 3 \, a^{3} d^{3} i^{2}\right)} B^{2} - 2 \, {\left(A B b^{3} c d^{2} i^{2} + {\left(2 \, a b^{2} d^{3} i^{2} + {\left(3 \, i^{2} \log\left(e\right) - 2 \, i^{2}\right)} b^{3} c d^{2}\right)} B^{2}\right)} x^{2} - 2 \, {\left(2 \, B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, {\left(b^{3} c d^{2} i^{2} + a b^{2} d^{3} i^{2}\right)} B^{2} x^{2} + 3 \, {\left(b^{3} c^{2} d i^{2} + a^{2} b d^{3} i^{2}\right)} B^{2} x + {\left(b^{3} c^{3} i^{2} + a^{3} d^{3} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{6} d g^{3} x^{4} + a^{3} b^{3} c g^{3} + {\left(b^{6} c g^{3} + 3 \, a b^{5} d g^{3}\right)} x^{3} + 3 \, {\left(a b^{5} c g^{3} + a^{2} b^{4} d g^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{4} c g^{3} + a^{3} b^{3} d g^{3}\right)} x}\,{d x}"," ",0,"-A*B*c*d*i^2*(2*(2*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) + (3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/2*A^2*d^2*i^2*((4*a*b*x + 3*a^2)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*log(b*x + a)/(b^3*g^3)) + 1/2*A*B*c^2*i^2*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - (2*b*x + a)*A^2*c*d*i^2/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*A^2*c^2*i^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*(4*(b^2*c*d*i^2 - a*b*d^2*i^2)*B^2*x + (b^2*c^2*i^2 + 2*a*b*c*d*i^2 - 3*a^2*d^2*i^2)*B^2 - 2*(B^2*b^2*d^2*i^2*x^2 + 2*B^2*a*b*d^2*i^2*x + B^2*a^2*d^2*i^2)*log(b*x + a))*log(d*x + c)^2/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) - integrate(-(3*B^2*b^3*c^2*d*i^2*x*log(e)^2 + B^2*b^3*c^3*i^2*log(e)^2 + (B^2*b^3*d^3*i^2*log(e)^2 + 2*A*B*b^3*d^3*i^2*log(e))*x^3 + (3*B^2*b^3*c*d^2*i^2*log(e)^2 + 2*A*B*b^3*c*d^2*i^2*log(e))*x^2 + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log(b*x + a)^2 + 2*(3*B^2*b^3*c^2*d*i^2*x*log(e) + B^2*b^3*c^3*i^2*log(e) + (B^2*b^3*d^3*i^2*log(e) + A*B*b^3*d^3*i^2)*x^3 + (3*B^2*b^3*c*d^2*i^2*log(e) + A*B*b^3*c*d^2*i^2)*x^2)*log(b*x + a) + ((6*a*b^2*c*d^2*i^2 - 7*a^2*b*d^3*i^2 - (6*i^2*log(e) - i^2)*b^3*c^2*d)*B^2*x - 2*(B^2*b^3*d^3*i^2*log(e) + A*B*b^3*d^3*i^2)*x^3 - (2*b^3*c^3*i^2*log(e) - a*b^2*c^2*d*i^2 - 2*a^2*b*c*d^2*i^2 + 3*a^3*d^3*i^2)*B^2 - 2*(A*B*b^3*c*d^2*i^2 + (2*a*b^2*d^3*i^2 + (3*i^2*log(e) - 2*i^2)*b^3*c*d^2)*B^2)*x^2 - 2*(2*B^2*b^3*d^3*i^2*x^3 + 3*(b^3*c*d^2*i^2 + a*b^2*d^3*i^2)*B^2*x^2 + 3*(b^3*c^2*d*i^2 + a^2*b*d^3*i^2)*B^2*x + (b^3*c^3*i^2 + a^3*d^3*i^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^6*d*g^3*x^4 + a^3*b^3*c*g^3 + (b^6*c*g^3 + 3*a*b^5*d*g^3)*x^3 + 3*(a*b^5*c*g^3 + a^2*b^4*d*g^3)*x^2 + (3*a^2*b^4*c*g^3 + a^3*b^3*d*g^3)*x), x)","F",0
71,1,5532,0,5.280356," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{{\left(3 \, b x + a\right)} B^{2} c d i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} B^{2} d^{2} i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{3 \, {\left(b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}\right)}} - \frac{1}{54} \, {\left(6 \, {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{3} b^{4} c^{3} g^{4} - 3 \, a^{4} b^{3} c^{2} d g^{4} + 3 \, a^{5} b^{2} c d^{2} g^{4} - a^{6} b d^{3} g^{4} + {\left(b^{7} c^{3} g^{4} - 3 \, a b^{6} c^{2} d g^{4} + 3 \, a^{2} b^{5} c d^{2} g^{4} - a^{3} b^{4} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{6} c^{3} g^{4} - 3 \, a^{2} b^{5} c^{2} d g^{4} + 3 \, a^{3} b^{4} c d^{2} g^{4} - a^{4} b^{3} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{3} g^{4} - 3 \, a^{3} b^{4} c^{2} d g^{4} + 3 \, a^{4} b^{3} c d^{2} g^{4} - a^{5} b^{2} d^{3} g^{4}\right)} x}\right)} B^{2} c^{2} i^{2} - \frac{1}{54} \, {\left(6 \, {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{19 \, a b^{3} c^{3} - 189 \, a^{2} b^{2} c^{2} d + 189 \, a^{3} b c d^{2} - 19 \, a^{4} d^{3} - 6 \, {\left(27 \, b^{4} c^{2} d - 32 \, a b^{3} c d^{2} + 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 18 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 18 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(9 \, b^{4} c^{3} - 125 \, a b^{3} c^{2} d + 135 \, a^{2} b^{2} c d^{2} - 19 \, a^{3} b d^{3}\right)} x - 6 \, {\left(27 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(27 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(27 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(27 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(27 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(27 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(27 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(27 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x - 6 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{3} b^{5} c^{3} g^{4} - 3 \, a^{4} b^{4} c^{2} d g^{4} + 3 \, a^{5} b^{3} c d^{2} g^{4} - a^{6} b^{2} d^{3} g^{4} + {\left(b^{8} c^{3} g^{4} - 3 \, a b^{7} c^{2} d g^{4} + 3 \, a^{2} b^{6} c d^{2} g^{4} - a^{3} b^{5} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{7} c^{3} g^{4} - 3 \, a^{2} b^{6} c^{2} d g^{4} + 3 \, a^{3} b^{5} c d^{2} g^{4} - a^{4} b^{4} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} c^{3} g^{4} - 3 \, a^{3} b^{5} c^{2} d g^{4} + 3 \, a^{4} b^{4} c d^{2} g^{4} - a^{5} b^{3} d^{3} g^{4}\right)} x}\right)} B^{2} c d i^{2} - \frac{1}{54} \, {\left(6 \, {\left(\frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{85 \, a^{2} b^{3} c^{3} - 108 \, a^{3} b^{2} c^{2} d + 27 \, a^{4} b c d^{2} - 4 \, a^{5} d^{3} + 6 \, {\left(18 \, b^{5} c^{3} - 27 \, a b^{4} c^{2} d + 11 \, a^{2} b^{3} c d^{2} - 2 \, a^{3} b^{2} d^{3}\right)} x^{2} - 18 \, {\left(3 \, a^{3} b^{2} c^{2} d - 3 \, a^{4} b c d^{2} + a^{5} d^{3} + {\left(3 \, b^{5} c^{2} d - 3 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{4} c^{2} d - 3 \, a^{2} b^{3} c d^{2} + a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{3} c^{2} d - 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(3 \, a^{3} b^{2} c^{2} d - 3 \, a^{4} b c d^{2} + a^{5} d^{3} + {\left(3 \, b^{5} c^{2} d - 3 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{4} c^{2} d - 3 \, a^{2} b^{3} c d^{2} + a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{3} c^{2} d - 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(63 \, a b^{4} c^{3} - 86 \, a^{2} b^{3} c^{2} d + 27 \, a^{3} b^{2} c d^{2} - 4 \, a^{4} b d^{3}\right)} x + 6 \, {\left(18 \, a^{3} b^{2} c^{2} d - 9 \, a^{4} b c d^{2} + 2 \, a^{5} d^{3} + {\left(18 \, b^{5} c^{2} d - 9 \, a b^{4} c d^{2} + 2 \, a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(18 \, a b^{4} c^{2} d - 9 \, a^{2} b^{3} c d^{2} + 2 \, a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(18 \, a^{2} b^{3} c^{2} d - 9 \, a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(18 \, a^{3} b^{2} c^{2} d - 9 \, a^{4} b c d^{2} + 2 \, a^{5} d^{3} + {\left(18 \, b^{5} c^{2} d - 9 \, a b^{4} c d^{2} + 2 \, a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(18 \, a b^{4} c^{2} d - 9 \, a^{2} b^{3} c d^{2} + 2 \, a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(18 \, a^{2} b^{3} c^{2} d - 9 \, a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x - 6 \, {\left(3 \, a^{3} b^{2} c^{2} d - 3 \, a^{4} b c d^{2} + a^{5} d^{3} + {\left(3 \, b^{5} c^{2} d - 3 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{4} c^{2} d - 3 \, a^{2} b^{3} c d^{2} + a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{3} c^{2} d - 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{3} b^{6} c^{3} g^{4} - 3 \, a^{4} b^{5} c^{2} d g^{4} + 3 \, a^{5} b^{4} c d^{2} g^{4} - a^{6} b^{3} d^{3} g^{4} + {\left(b^{9} c^{3} g^{4} - 3 \, a b^{8} c^{2} d g^{4} + 3 \, a^{2} b^{7} c d^{2} g^{4} - a^{3} b^{6} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{8} c^{3} g^{4} - 3 \, a^{2} b^{7} c^{2} d g^{4} + 3 \, a^{3} b^{6} c d^{2} g^{4} - a^{4} b^{5} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} c^{3} g^{4} - 3 \, a^{3} b^{6} c^{2} d g^{4} + 3 \, a^{4} b^{5} c d^{2} g^{4} - a^{5} b^{4} d^{3} g^{4}\right)} x}\right)} B^{2} d^{2} i^{2} - \frac{1}{9} \, A B d^{2} i^{2} {\left(\frac{6 \, {\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}} + \frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} - \frac{1}{9} \, A B c d i^{2} {\left(\frac{6 \, {\left(3 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}} + \frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{1}{9} \, A B c^{2} i^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{B^{2} c^{2} i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{{\left(3 \, b x + a\right)} A^{2} c d i^{2}}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A^{2} d^{2} i^{2}}{3 \, {\left(b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}\right)}} - \frac{A^{2} c^{2} i^{2}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/3*(3*b*x + a)*B^2*c*d*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*(3*b^2*x^2 + 3*a*b*x + a^2)*B^2*d^2*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/54*(6*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))/(a^3*b^4*c^3*g^4 - 3*a^4*b^3*c^2*d*g^4 + 3*a^5*b^2*c*d^2*g^4 - a^6*b*d^3*g^4 + (b^7*c^3*g^4 - 3*a*b^6*c^2*d*g^4 + 3*a^2*b^5*c*d^2*g^4 - a^3*b^4*d^3*g^4)*x^3 + 3*(a*b^6*c^3*g^4 - 3*a^2*b^5*c^2*d*g^4 + 3*a^3*b^4*c*d^2*g^4 - a^4*b^3*d^3*g^4)*x^2 + 3*(a^2*b^5*c^3*g^4 - 3*a^3*b^4*c^2*d*g^4 + 3*a^4*b^3*c*d^2*g^4 - a^5*b^2*d^3*g^4)*x))*B^2*c^2*i^2 - 1/54*(6*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (19*a*b^3*c^3 - 189*a^2*b^2*c^2*d + 189*a^3*b*c*d^2 - 19*a^4*d^3 - 6*(27*b^4*c^2*d - 32*a*b^3*c*d^2 + 5*a^2*b^2*d^3)*x^2 + 18*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(b*x + a)^2 + 18*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(d*x + c)^2 + 3*(9*b^4*c^3 - 125*a*b^3*c^2*d + 135*a^2*b^2*c*d^2 - 19*a^3*b*d^3)*x - 6*(27*a^3*b*c*d^2 - 5*a^4*d^3 + (27*b^4*c*d^2 - 5*a*b^3*d^3)*x^3 + 3*(27*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^2 + 3*(27*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x)*log(b*x + a) + 6*(27*a^3*b*c*d^2 - 5*a^4*d^3 + (27*b^4*c*d^2 - 5*a*b^3*d^3)*x^3 + 3*(27*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^2 + 3*(27*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x - 6*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(b*x + a))*log(d*x + c))/(a^3*b^5*c^3*g^4 - 3*a^4*b^4*c^2*d*g^4 + 3*a^5*b^3*c*d^2*g^4 - a^6*b^2*d^3*g^4 + (b^8*c^3*g^4 - 3*a*b^7*c^2*d*g^4 + 3*a^2*b^6*c*d^2*g^4 - a^3*b^5*d^3*g^4)*x^3 + 3*(a*b^7*c^3*g^4 - 3*a^2*b^6*c^2*d*g^4 + 3*a^3*b^5*c*d^2*g^4 - a^4*b^4*d^3*g^4)*x^2 + 3*(a^2*b^6*c^3*g^4 - 3*a^3*b^5*c^2*d*g^4 + 3*a^4*b^4*c*d^2*g^4 - a^5*b^3*d^3*g^4)*x))*B^2*c*d*i^2 - 1/54*(6*((11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (85*a^2*b^3*c^3 - 108*a^3*b^2*c^2*d + 27*a^4*b*c*d^2 - 4*a^5*d^3 + 6*(18*b^5*c^3 - 27*a*b^4*c^2*d + 11*a^2*b^3*c*d^2 - 2*a^3*b^2*d^3)*x^2 - 18*(3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2 + a^5*d^3 + (3*b^5*c^2*d - 3*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 3*(3*a*b^4*c^2*d - 3*a^2*b^3*c*d^2 + a^3*b^2*d^3)*x^2 + 3*(3*a^2*b^3*c^2*d - 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x)*log(b*x + a)^2 - 18*(3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2 + a^5*d^3 + (3*b^5*c^2*d - 3*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 3*(3*a*b^4*c^2*d - 3*a^2*b^3*c*d^2 + a^3*b^2*d^3)*x^2 + 3*(3*a^2*b^3*c^2*d - 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x)*log(d*x + c)^2 + 3*(63*a*b^4*c^3 - 86*a^2*b^3*c^2*d + 27*a^3*b^2*c*d^2 - 4*a^4*b*d^3)*x + 6*(18*a^3*b^2*c^2*d - 9*a^4*b*c*d^2 + 2*a^5*d^3 + (18*b^5*c^2*d - 9*a*b^4*c*d^2 + 2*a^2*b^3*d^3)*x^3 + 3*(18*a*b^4*c^2*d - 9*a^2*b^3*c*d^2 + 2*a^3*b^2*d^3)*x^2 + 3*(18*a^2*b^3*c^2*d - 9*a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x)*log(b*x + a) - 6*(18*a^3*b^2*c^2*d - 9*a^4*b*c*d^2 + 2*a^5*d^3 + (18*b^5*c^2*d - 9*a*b^4*c*d^2 + 2*a^2*b^3*d^3)*x^3 + 3*(18*a*b^4*c^2*d - 9*a^2*b^3*c*d^2 + 2*a^3*b^2*d^3)*x^2 + 3*(18*a^2*b^3*c^2*d - 9*a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x - 6*(3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2 + a^5*d^3 + (3*b^5*c^2*d - 3*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 3*(3*a*b^4*c^2*d - 3*a^2*b^3*c*d^2 + a^3*b^2*d^3)*x^2 + 3*(3*a^2*b^3*c^2*d - 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x)*log(b*x + a))*log(d*x + c))/(a^3*b^6*c^3*g^4 - 3*a^4*b^5*c^2*d*g^4 + 3*a^5*b^4*c*d^2*g^4 - a^6*b^3*d^3*g^4 + (b^9*c^3*g^4 - 3*a*b^8*c^2*d*g^4 + 3*a^2*b^7*c*d^2*g^4 - a^3*b^6*d^3*g^4)*x^3 + 3*(a*b^8*c^3*g^4 - 3*a^2*b^7*c^2*d*g^4 + 3*a^3*b^6*c*d^2*g^4 - a^4*b^5*d^3*g^4)*x^2 + 3*(a^2*b^7*c^3*g^4 - 3*a^3*b^6*c^2*d*g^4 + 3*a^4*b^5*c*d^2*g^4 - a^5*b^4*d^3*g^4)*x))*B^2*d^2*i^2 - 1/9*A*B*d^2*i^2*(6*(3*b^2*x^2 + 3*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) + (11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4)) - 1/9*A*B*c*d*i^2*(6*(3*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) + (5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/9*A*B*c^2*i^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/3*B^2*c^2*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/3*(3*b*x + a)*A^2*c*d*i^2/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*(3*b^2*x^2 + 3*a*b*x + a^2)*A^2*d^2*i^2/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/3*A^2*c^2*i^2/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","B",0
72,1,8031,0,8.093752," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{{\left(4 \, b x + a\right)} B^{2} c d i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{6 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} B^{2} d^{2} i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{12 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} + \frac{1}{288} \, {\left(12 \, {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{9 \, b^{4} c^{4} - 64 \, a b^{3} c^{3} d + 216 \, a^{2} b^{2} c^{2} d^{2} - 576 \, a^{3} b c d^{3} + 415 \, a^{4} d^{4} - 300 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(13 \, b^{4} c^{2} d^{2} - 176 \, a b^{3} c d^{3} + 163 \, a^{2} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(7 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 324 \, a^{2} b^{2} c d^{3} - 271 \, a^{3} b d^{4}\right)} x - 300 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(25 \, b^{4} d^{4} x^{4} + 100 \, a b^{3} d^{4} x^{3} + 150 \, a^{2} b^{2} d^{4} x^{2} + 100 \, a^{3} b d^{4} x + 25 \, a^{4} d^{4} - 12 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{5} c^{4} g^{5} - 4 \, a^{5} b^{4} c^{3} d g^{5} + 6 \, a^{6} b^{3} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{2} c d^{3} g^{5} + a^{8} b d^{4} g^{5} + {\left(b^{9} c^{4} g^{5} - 4 \, a b^{8} c^{3} d g^{5} + 6 \, a^{2} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{6} c d^{3} g^{5} + a^{4} b^{5} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} g^{5} - 4 \, a^{2} b^{7} c^{3} d g^{5} + 6 \, a^{3} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{5} c d^{3} g^{5} + a^{5} b^{4} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} g^{5} - 4 \, a^{3} b^{6} c^{3} d g^{5} + 6 \, a^{4} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{4} c d^{3} g^{5} + a^{6} b^{3} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} g^{5} - 4 \, a^{4} b^{5} c^{3} d g^{5} + 6 \, a^{5} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{3} c d^{3} g^{5} + a^{7} b^{2} d^{4} g^{5}\right)} x}\right)} B^{2} c^{2} i^{2} - \frac{1}{432} \, {\left(12 \, {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{37 \, a b^{4} c^{4} - 304 \, a^{2} b^{3} c^{3} d + 1512 \, a^{3} b^{2} c^{2} d^{2} - 1360 \, a^{4} b c d^{3} + 115 \, a^{5} d^{4} + 12 \, {\left(88 \, b^{5} c^{2} d^{2} - 101 \, a b^{4} c d^{3} + 13 \, a^{2} b^{3} d^{4}\right)} x^{3} - 6 \, {\left(40 \, b^{5} c^{3} d - 609 \, a b^{4} c^{2} d^{2} + 648 \, a^{2} b^{3} c d^{3} - 79 \, a^{3} b^{2} d^{4}\right)} x^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(16 \, b^{5} c^{4} - 163 \, a b^{4} c^{3} d + 1068 \, a^{2} b^{3} c^{2} d^{2} - 1036 \, a^{3} b^{2} c d^{3} + 115 \, a^{4} b d^{4}\right)} x + 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x - 12 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{6} c^{4} g^{5} - 4 \, a^{5} b^{5} c^{3} d g^{5} + 6 \, a^{6} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{3} c d^{3} g^{5} + a^{8} b^{2} d^{4} g^{5} + {\left(b^{10} c^{4} g^{5} - 4 \, a b^{9} c^{3} d g^{5} + 6 \, a^{2} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{7} c d^{3} g^{5} + a^{4} b^{6} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{9} c^{4} g^{5} - 4 \, a^{2} b^{8} c^{3} d g^{5} + 6 \, a^{3} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{6} c d^{3} g^{5} + a^{5} b^{5} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} c^{4} g^{5} - 4 \, a^{3} b^{7} c^{3} d g^{5} + 6 \, a^{4} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{5} c d^{3} g^{5} + a^{6} b^{4} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} c^{4} g^{5} - 4 \, a^{4} b^{6} c^{3} d g^{5} + 6 \, a^{5} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{4} c d^{3} g^{5} + a^{7} b^{3} d^{4} g^{5}\right)} x}\right)} B^{2} c d i^{2} - \frac{1}{864} \, {\left(12 \, {\left(\frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{115 \, a^{2} b^{4} c^{4} - 1360 \, a^{3} b^{3} c^{3} d + 1512 \, a^{4} b^{2} c^{2} d^{2} - 304 \, a^{5} b c d^{3} + 37 \, a^{6} d^{4} - 12 \, {\left(108 \, b^{6} c^{3} d - 148 \, a b^{5} c^{2} d^{2} + 47 \, a^{2} b^{4} c d^{3} - 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(36 \, b^{6} c^{4} - 712 \, a b^{5} c^{3} d + 903 \, a^{2} b^{4} c^{2} d^{2} - 264 \, a^{3} b^{3} c d^{3} + 37 \, a^{4} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(76 \, a b^{5} c^{4} - 1057 \, a^{2} b^{4} c^{3} d + 1248 \, a^{3} b^{3} c^{2} d^{2} - 304 \, a^{4} b^{2} c d^{3} + 37 \, a^{5} b d^{4}\right)} x - 12 \, {\left(108 \, a^{4} b^{2} c^{2} d^{2} - 40 \, a^{5} b c d^{3} + 7 \, a^{6} d^{4} + {\left(108 \, b^{6} c^{2} d^{2} - 40 \, a b^{5} c d^{3} + 7 \, a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(108 \, a b^{5} c^{2} d^{2} - 40 \, a^{2} b^{4} c d^{3} + 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(108 \, a^{2} b^{4} c^{2} d^{2} - 40 \, a^{3} b^{3} c d^{3} + 7 \, a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(108 \, a^{3} b^{3} c^{2} d^{2} - 40 \, a^{4} b^{2} c d^{3} + 7 \, a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(108 \, a^{4} b^{2} c^{2} d^{2} - 40 \, a^{5} b c d^{3} + 7 \, a^{6} d^{4} + {\left(108 \, b^{6} c^{2} d^{2} - 40 \, a b^{5} c d^{3} + 7 \, a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(108 \, a b^{5} c^{2} d^{2} - 40 \, a^{2} b^{4} c d^{3} + 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(108 \, a^{2} b^{4} c^{2} d^{2} - 40 \, a^{3} b^{3} c d^{3} + 7 \, a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(108 \, a^{3} b^{3} c^{2} d^{2} - 40 \, a^{4} b^{2} c d^{3} + 7 \, a^{5} b d^{4}\right)} x - 12 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{7} c^{4} g^{5} - 4 \, a^{5} b^{6} c^{3} d g^{5} + 6 \, a^{6} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{4} c d^{3} g^{5} + a^{8} b^{3} d^{4} g^{5} + {\left(b^{11} c^{4} g^{5} - 4 \, a b^{10} c^{3} d g^{5} + 6 \, a^{2} b^{9} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{8} c d^{3} g^{5} + a^{4} b^{7} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{10} c^{4} g^{5} - 4 \, a^{2} b^{9} c^{3} d g^{5} + 6 \, a^{3} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{7} c d^{3} g^{5} + a^{5} b^{6} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} c^{4} g^{5} - 4 \, a^{3} b^{8} c^{3} d g^{5} + 6 \, a^{4} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{6} c d^{3} g^{5} + a^{6} b^{5} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} c^{4} g^{5} - 4 \, a^{4} b^{7} c^{3} d g^{5} + 6 \, a^{5} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{5} c d^{3} g^{5} + a^{7} b^{4} d^{4} g^{5}\right)} x}\right)} B^{2} d^{2} i^{2} - \frac{1}{72} \, A B d^{2} i^{2} {\left(\frac{12 \, {\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}} + \frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} - \frac{1}{36} \, A B c d i^{2} {\left(\frac{12 \, {\left(4 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}} + \frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} + \frac{1}{24} \, A B c^{2} i^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} - \frac{12 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{B^{2} c^{2} i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{{\left(4 \, b x + a\right)} A^{2} c d i^{2}}{6 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} A^{2} d^{2} i^{2}}{12 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{A^{2} c^{2} i^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"-1/6*(4*b*x + a)*B^2*c*d*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/12*(6*b^2*x^2 + 4*a*b*x + a^2)*B^2*d^2*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) + 1/288*(12*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - (9*b^4*c^4 - 64*a*b^3*c^3*d + 216*a^2*b^2*c^2*d^2 - 576*a^3*b*c*d^3 + 415*a^4*d^4 - 300*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 6*(13*b^4*c^2*d^2 - 176*a*b^3*c*d^3 + 163*a^2*b^2*d^4)*x^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a)^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(d*x + c)^2 - 4*(7*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 324*a^2*b^2*c*d^3 - 271*a^3*b*d^4)*x - 300*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a) + 12*(25*b^4*d^4*x^4 + 100*a*b^3*d^4*x^3 + 150*a^2*b^2*d^4*x^2 + 100*a^3*b*d^4*x + 25*a^4*d^4 - 12*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a))*log(d*x + c))/(a^4*b^5*c^4*g^5 - 4*a^5*b^4*c^3*d*g^5 + 6*a^6*b^3*c^2*d^2*g^5 - 4*a^7*b^2*c*d^3*g^5 + a^8*b*d^4*g^5 + (b^9*c^4*g^5 - 4*a*b^8*c^3*d*g^5 + 6*a^2*b^7*c^2*d^2*g^5 - 4*a^3*b^6*c*d^3*g^5 + a^4*b^5*d^4*g^5)*x^4 + 4*(a*b^8*c^4*g^5 - 4*a^2*b^7*c^3*d*g^5 + 6*a^3*b^6*c^2*d^2*g^5 - 4*a^4*b^5*c*d^3*g^5 + a^5*b^4*d^4*g^5)*x^3 + 6*(a^2*b^7*c^4*g^5 - 4*a^3*b^6*c^3*d*g^5 + 6*a^4*b^5*c^2*d^2*g^5 - 4*a^5*b^4*c*d^3*g^5 + a^6*b^3*d^4*g^5)*x^2 + 4*(a^3*b^6*c^4*g^5 - 4*a^4*b^5*c^3*d*g^5 + 6*a^5*b^4*c^2*d^2*g^5 - 4*a^6*b^3*c*d^3*g^5 + a^7*b^2*d^4*g^5)*x))*B^2*c^2*i^2 - 1/432*(12*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (37*a*b^4*c^4 - 304*a^2*b^3*c^3*d + 1512*a^3*b^2*c^2*d^2 - 1360*a^4*b*c*d^3 + 115*a^5*d^4 + 12*(88*b^5*c^2*d^2 - 101*a*b^4*c*d^3 + 13*a^2*b^3*d^4)*x^3 - 6*(40*b^5*c^3*d - 609*a*b^4*c^2*d^2 + 648*a^2*b^3*c*d^3 - 79*a^3*b^2*d^4)*x^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a)^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(d*x + c)^2 + 4*(16*b^5*c^4 - 163*a*b^4*c^3*d + 1068*a^2*b^3*c^2*d^2 - 1036*a^3*b^2*c*d^3 + 115*a^4*b*d^4)*x + 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x)*log(b*x + a) - 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x - 12*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a))*log(d*x + c))/(a^4*b^6*c^4*g^5 - 4*a^5*b^5*c^3*d*g^5 + 6*a^6*b^4*c^2*d^2*g^5 - 4*a^7*b^3*c*d^3*g^5 + a^8*b^2*d^4*g^5 + (b^10*c^4*g^5 - 4*a*b^9*c^3*d*g^5 + 6*a^2*b^8*c^2*d^2*g^5 - 4*a^3*b^7*c*d^3*g^5 + a^4*b^6*d^4*g^5)*x^4 + 4*(a*b^9*c^4*g^5 - 4*a^2*b^8*c^3*d*g^5 + 6*a^3*b^7*c^2*d^2*g^5 - 4*a^4*b^6*c*d^3*g^5 + a^5*b^5*d^4*g^5)*x^3 + 6*(a^2*b^8*c^4*g^5 - 4*a^3*b^7*c^3*d*g^5 + 6*a^4*b^6*c^2*d^2*g^5 - 4*a^5*b^5*c*d^3*g^5 + a^6*b^4*d^4*g^5)*x^2 + 4*(a^3*b^7*c^4*g^5 - 4*a^4*b^6*c^3*d*g^5 + 6*a^5*b^5*c^2*d^2*g^5 - 4*a^6*b^4*c*d^3*g^5 + a^7*b^3*d^4*g^5)*x))*B^2*c*d*i^2 - 1/864*(12*((13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (115*a^2*b^4*c^4 - 1360*a^3*b^3*c^3*d + 1512*a^4*b^2*c^2*d^2 - 304*a^5*b*c*d^3 + 37*a^6*d^4 - 12*(108*b^6*c^3*d - 148*a*b^5*c^2*d^2 + 47*a^2*b^4*c*d^3 - 7*a^3*b^3*d^4)*x^3 + 6*(36*b^6*c^4 - 712*a*b^5*c^3*d + 903*a^2*b^4*c^2*d^2 - 264*a^3*b^3*c*d^3 + 37*a^4*b^2*d^4)*x^2 + 72*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(b*x + a)^2 + 72*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(d*x + c)^2 + 4*(76*a*b^5*c^4 - 1057*a^2*b^4*c^3*d + 1248*a^3*b^3*c^2*d^2 - 304*a^4*b^2*c*d^3 + 37*a^5*b*d^4)*x - 12*(108*a^4*b^2*c^2*d^2 - 40*a^5*b*c*d^3 + 7*a^6*d^4 + (108*b^6*c^2*d^2 - 40*a*b^5*c*d^3 + 7*a^2*b^4*d^4)*x^4 + 4*(108*a*b^5*c^2*d^2 - 40*a^2*b^4*c*d^3 + 7*a^3*b^3*d^4)*x^3 + 6*(108*a^2*b^4*c^2*d^2 - 40*a^3*b^3*c*d^3 + 7*a^4*b^2*d^4)*x^2 + 4*(108*a^3*b^3*c^2*d^2 - 40*a^4*b^2*c*d^3 + 7*a^5*b*d^4)*x)*log(b*x + a) + 12*(108*a^4*b^2*c^2*d^2 - 40*a^5*b*c*d^3 + 7*a^6*d^4 + (108*b^6*c^2*d^2 - 40*a*b^5*c*d^3 + 7*a^2*b^4*d^4)*x^4 + 4*(108*a*b^5*c^2*d^2 - 40*a^2*b^4*c*d^3 + 7*a^3*b^3*d^4)*x^3 + 6*(108*a^2*b^4*c^2*d^2 - 40*a^3*b^3*c*d^3 + 7*a^4*b^2*d^4)*x^2 + 4*(108*a^3*b^3*c^2*d^2 - 40*a^4*b^2*c*d^3 + 7*a^5*b*d^4)*x - 12*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(b*x + a))*log(d*x + c))/(a^4*b^7*c^4*g^5 - 4*a^5*b^6*c^3*d*g^5 + 6*a^6*b^5*c^2*d^2*g^5 - 4*a^7*b^4*c*d^3*g^5 + a^8*b^3*d^4*g^5 + (b^11*c^4*g^5 - 4*a*b^10*c^3*d*g^5 + 6*a^2*b^9*c^2*d^2*g^5 - 4*a^3*b^8*c*d^3*g^5 + a^4*b^7*d^4*g^5)*x^4 + 4*(a*b^10*c^4*g^5 - 4*a^2*b^9*c^3*d*g^5 + 6*a^3*b^8*c^2*d^2*g^5 - 4*a^4*b^7*c*d^3*g^5 + a^5*b^6*d^4*g^5)*x^3 + 6*(a^2*b^9*c^4*g^5 - 4*a^3*b^8*c^3*d*g^5 + 6*a^4*b^7*c^2*d^2*g^5 - 4*a^5*b^6*c*d^3*g^5 + a^6*b^5*d^4*g^5)*x^2 + 4*(a^3*b^8*c^4*g^5 - 4*a^4*b^7*c^3*d*g^5 + 6*a^5*b^6*c^2*d^2*g^5 - 4*a^6*b^5*c*d^3*g^5 + a^7*b^4*d^4*g^5)*x))*B^2*d^2*i^2 - 1/72*A*B*d^2*i^2*(12*(6*b^2*x^2 + 4*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) + (13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5)) - 1/36*A*B*c*d*i^2*(12*(4*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) + (7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) + 1/24*A*B*c^2*i^2*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) - 12*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/4*B^2*c^2*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/6*(4*b*x + a)*A^2*c*d*i^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/12*(6*b^2*x^2 + 4*a*b*x + a^2)*A^2*d^2*i^2/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/4*A^2*c^2*i^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
73,1,10880,0,12.026056," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^6,x, algorithm=""maxima"")","-\frac{{\left(5 \, b x + a\right)} B^{2} c d i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{10 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} B^{2} d^{2} i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{30 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{1}{9000} \, {\left(60 \, {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{144 \, b^{5} c^{5} - 1125 \, a b^{4} c^{4} d + 4000 \, a^{2} b^{3} c^{3} d^{2} - 9000 \, a^{3} b^{2} c^{2} d^{3} + 18000 \, a^{4} b c d^{4} - 12019 \, a^{5} d^{5} + 8220 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} - 30 \, {\left(77 \, b^{5} c^{2} d^{3} - 1250 \, a b^{4} c d^{4} + 1173 \, a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(94 \, b^{5} c^{3} d^{2} - 975 \, a b^{4} c^{2} d^{3} + 6600 \, a^{2} b^{3} c d^{4} - 5719 \, a^{3} b^{2} d^{5}\right)} x^{2} - 1800 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right)^{2} - 1800 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(81 \, b^{5} c^{4} d - 700 \, a b^{4} c^{3} d^{2} + 3000 \, a^{2} b^{3} c^{2} d^{3} - 10800 \, a^{3} b^{2} c d^{4} + 8419 \, a^{4} b d^{5}\right)} x + 8220 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right) - 60 \, {\left(137 \, b^{5} d^{5} x^{5} + 685 \, a b^{4} d^{5} x^{4} + 1370 \, a^{2} b^{3} d^{5} x^{3} + 1370 \, a^{3} b^{2} d^{5} x^{2} + 685 \, a^{4} b d^{5} x + 137 \, a^{5} d^{5} - 60 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{5} b^{6} c^{5} g^{6} - 5 \, a^{6} b^{5} c^{4} d g^{6} + 10 \, a^{7} b^{4} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{3} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{2} c d^{4} g^{6} - a^{10} b d^{5} g^{6} + {\left(b^{11} c^{5} g^{6} - 5 \, a b^{10} c^{4} d g^{6} + 10 \, a^{2} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{7} c d^{4} g^{6} - a^{5} b^{6} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{10} c^{5} g^{6} - 5 \, a^{2} b^{9} c^{4} d g^{6} + 10 \, a^{3} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{6} c d^{4} g^{6} - a^{6} b^{5} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{9} c^{5} g^{6} - 5 \, a^{3} b^{8} c^{4} d g^{6} + 10 \, a^{4} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{5} c d^{4} g^{6} - a^{7} b^{4} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{8} c^{5} g^{6} - 5 \, a^{4} b^{7} c^{4} d g^{6} + 10 \, a^{5} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{4} c d^{4} g^{6} - a^{8} b^{3} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{7} c^{5} g^{6} - 5 \, a^{5} b^{6} c^{4} d g^{6} + 10 \, a^{6} b^{5} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{4} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{3} c d^{4} g^{6} - a^{9} b^{2} d^{5} g^{6}\right)} x}\right)} B^{2} c^{2} i^{2} - \frac{1}{18000} \, {\left(60 \, {\left(\frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{549 \, a b^{5} c^{5} - 4625 \, a^{2} b^{4} c^{4} d + 19000 \, a^{3} b^{3} c^{3} d^{2} - 63000 \, a^{4} b^{2} c^{2} d^{3} + 51875 \, a^{5} b c d^{4} - 3799 \, a^{6} d^{5} - 60 \, {\left(625 \, b^{6} c^{2} d^{3} - 702 \, a b^{5} c d^{4} + 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 30 \, {\left(325 \, b^{6} c^{3} d^{2} - 5667 \, a b^{5} c^{2} d^{3} + 5975 \, a^{2} b^{4} c d^{4} - 633 \, a^{3} b^{3} d^{5}\right)} x^{3} - 10 \, {\left(350 \, b^{6} c^{4} d - 3949 \, a b^{5} c^{3} d^{2} + 29475 \, a^{2} b^{4} c^{2} d^{3} - 28775 \, a^{3} b^{3} c d^{4} + 2899 \, a^{4} b^{2} d^{5}\right)} x^{2} + 1800 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right)^{2} + 1800 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(d x + c\right)^{2} + 5 \, {\left(225 \, b^{6} c^{5} - 2201 \, a b^{5} c^{4} d + 10900 \, a^{2} b^{4} c^{3} d^{2} - 46200 \, a^{3} b^{3} c^{2} d^{3} + 41075 \, a^{4} b^{2} c d^{4} - 3799 \, a^{5} b d^{5}\right)} x - 60 \, {\left(625 \, a^{5} b c d^{4} - 77 \, a^{6} d^{5} + {\left(625 \, b^{6} c d^{4} - 77 \, a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(625 \, a b^{5} c d^{4} - 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(625 \, a^{2} b^{4} c d^{4} - 77 \, a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(625 \, a^{3} b^{3} c d^{4} - 77 \, a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(625 \, a^{4} b^{2} c d^{4} - 77 \, a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(625 \, a^{5} b c d^{4} - 77 \, a^{6} d^{5} + {\left(625 \, b^{6} c d^{4} - 77 \, a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(625 \, a b^{5} c d^{4} - 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(625 \, a^{2} b^{4} c d^{4} - 77 \, a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(625 \, a^{3} b^{3} c d^{4} - 77 \, a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(625 \, a^{4} b^{2} c d^{4} - 77 \, a^{5} b d^{5}\right)} x - 60 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{5} b^{7} c^{5} g^{6} - 5 \, a^{6} b^{6} c^{4} d g^{6} + 10 \, a^{7} b^{5} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{4} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{3} c d^{4} g^{6} - a^{10} b^{2} d^{5} g^{6} + {\left(b^{12} c^{5} g^{6} - 5 \, a b^{11} c^{4} d g^{6} + 10 \, a^{2} b^{10} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{9} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{8} c d^{4} g^{6} - a^{5} b^{7} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{11} c^{5} g^{6} - 5 \, a^{2} b^{10} c^{4} d g^{6} + 10 \, a^{3} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{7} c d^{4} g^{6} - a^{6} b^{6} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} c^{5} g^{6} - 5 \, a^{3} b^{9} c^{4} d g^{6} + 10 \, a^{4} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{6} c d^{4} g^{6} - a^{7} b^{5} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} c^{5} g^{6} - 5 \, a^{4} b^{8} c^{4} d g^{6} + 10 \, a^{5} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{5} c d^{4} g^{6} - a^{8} b^{4} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} c^{5} g^{6} - 5 \, a^{5} b^{7} c^{4} d g^{6} + 10 \, a^{6} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{4} c d^{4} g^{6} - a^{9} b^{3} d^{5} g^{6}\right)} x}\right)} B^{2} c d i^{2} - \frac{1}{54000} \, {\left(60 \, {\left(\frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{1489 \, a^{2} b^{5} c^{5} - 14375 \, a^{3} b^{4} c^{4} d + 85000 \, a^{4} b^{3} c^{3} d^{2} - 85000 \, a^{5} b^{2} c^{2} d^{3} + 14375 \, a^{6} b c d^{4} - 1489 \, a^{7} d^{5} + 60 \, {\left(1100 \, b^{7} c^{3} d^{2} - 1425 \, a b^{6} c^{2} d^{3} + 372 \, a^{2} b^{5} c d^{4} - 47 \, a^{3} b^{4} d^{5}\right)} x^{4} - 30 \, {\left(500 \, b^{7} c^{4} d - 9825 \, a b^{6} c^{3} d^{2} + 11937 \, a^{2} b^{5} c^{2} d^{3} - 2975 \, a^{3} b^{4} c d^{4} + 363 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(400 \, b^{7} c^{5} - 5450 \, a b^{6} c^{4} d + 49189 \, a^{2} b^{5} c^{3} d^{2} - 55525 \, a^{3} b^{4} c^{2} d^{3} + 12875 \, a^{4} b^{3} c d^{4} - 1489 \, a^{5} b^{2} d^{5}\right)} x^{2} - 1800 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right)^{2} - 1800 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(d x + c\right)^{2} + 5 \, {\left(925 \, a b^{6} c^{5} - 9911 \, a^{2} b^{5} c^{4} d + 67900 \, a^{3} b^{4} c^{3} d^{2} - 71800 \, a^{4} b^{3} c^{2} d^{3} + 14375 \, a^{5} b^{2} c d^{4} - 1489 \, a^{6} b d^{5}\right)} x + 60 \, {\left(1100 \, a^{5} b^{2} c^{2} d^{3} - 325 \, a^{6} b c d^{4} + 47 \, a^{7} d^{5} + {\left(1100 \, b^{7} c^{2} d^{3} - 325 \, a b^{6} c d^{4} + 47 \, a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(1100 \, a b^{6} c^{2} d^{3} - 325 \, a^{2} b^{5} c d^{4} + 47 \, a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(1100 \, a^{2} b^{5} c^{2} d^{3} - 325 \, a^{3} b^{4} c d^{4} + 47 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(1100 \, a^{3} b^{4} c^{2} d^{3} - 325 \, a^{4} b^{3} c d^{4} + 47 \, a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(1100 \, a^{4} b^{3} c^{2} d^{3} - 325 \, a^{5} b^{2} c d^{4} + 47 \, a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(1100 \, a^{5} b^{2} c^{2} d^{3} - 325 \, a^{6} b c d^{4} + 47 \, a^{7} d^{5} + {\left(1100 \, b^{7} c^{2} d^{3} - 325 \, a b^{6} c d^{4} + 47 \, a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(1100 \, a b^{6} c^{2} d^{3} - 325 \, a^{2} b^{5} c d^{4} + 47 \, a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(1100 \, a^{2} b^{5} c^{2} d^{3} - 325 \, a^{3} b^{4} c d^{4} + 47 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(1100 \, a^{3} b^{4} c^{2} d^{3} - 325 \, a^{4} b^{3} c d^{4} + 47 \, a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(1100 \, a^{4} b^{3} c^{2} d^{3} - 325 \, a^{5} b^{2} c d^{4} + 47 \, a^{6} b d^{5}\right)} x - 60 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{5} b^{8} c^{5} g^{6} - 5 \, a^{6} b^{7} c^{4} d g^{6} + 10 \, a^{7} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{4} c d^{4} g^{6} - a^{10} b^{3} d^{5} g^{6} + {\left(b^{13} c^{5} g^{6} - 5 \, a b^{12} c^{4} d g^{6} + 10 \, a^{2} b^{11} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{10} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{9} c d^{4} g^{6} - a^{5} b^{8} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{12} c^{5} g^{6} - 5 \, a^{2} b^{11} c^{4} d g^{6} + 10 \, a^{3} b^{10} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{9} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{8} c d^{4} g^{6} - a^{6} b^{7} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} c^{5} g^{6} - 5 \, a^{3} b^{10} c^{4} d g^{6} + 10 \, a^{4} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{7} c d^{4} g^{6} - a^{7} b^{6} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} c^{5} g^{6} - 5 \, a^{4} b^{9} c^{4} d g^{6} + 10 \, a^{5} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{6} c d^{4} g^{6} - a^{8} b^{5} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} c^{5} g^{6} - 5 \, a^{5} b^{8} c^{4} d g^{6} + 10 \, a^{6} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{5} c d^{4} g^{6} - a^{9} b^{4} d^{5} g^{6}\right)} x}\right)} B^{2} d^{2} i^{2} - \frac{1}{900} \, A B d^{2} i^{2} {\left(\frac{60 \, {\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}} + \frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} - \frac{1}{300} \, A B c d i^{2} {\left(\frac{60 \, {\left(5 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}} + \frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} - \frac{1}{150} \, A B c^{2} i^{2} {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} - \frac{B^{2} c^{2} i^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}} - \frac{{\left(5 \, b x + a\right)} A^{2} c d i^{2}}{10 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} A^{2} d^{2} i^{2}}{30 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{A^{2} c^{2} i^{2}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}}"," ",0,"-1/10*(5*b*x + a)*B^2*c*d*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/30*(10*b^2*x^2 + 5*a*b*x + a^2)*B^2*d^2*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/9000*(60*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (144*b^5*c^5 - 1125*a*b^4*c^4*d + 4000*a^2*b^3*c^3*d^2 - 9000*a^3*b^2*c^2*d^3 + 18000*a^4*b*c*d^4 - 12019*a^5*d^5 + 8220*(b^5*c*d^4 - a*b^4*d^5)*x^4 - 30*(77*b^5*c^2*d^3 - 1250*a*b^4*c*d^4 + 1173*a^2*b^3*d^5)*x^3 + 10*(94*b^5*c^3*d^2 - 975*a*b^4*c^2*d^3 + 6600*a^2*b^3*c*d^4 - 5719*a^3*b^2*d^5)*x^2 - 1800*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a)^2 - 1800*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(d*x + c)^2 - 5*(81*b^5*c^4*d - 700*a*b^4*c^3*d^2 + 3000*a^2*b^3*c^2*d^3 - 10800*a^3*b^2*c*d^4 + 8419*a^4*b*d^5)*x + 8220*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a) - 60*(137*b^5*d^5*x^5 + 685*a*b^4*d^5*x^4 + 1370*a^2*b^3*d^5*x^3 + 1370*a^3*b^2*d^5*x^2 + 685*a^4*b*d^5*x + 137*a^5*d^5 - 60*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a))*log(d*x + c))/(a^5*b^6*c^5*g^6 - 5*a^6*b^5*c^4*d*g^6 + 10*a^7*b^4*c^3*d^2*g^6 - 10*a^8*b^3*c^2*d^3*g^6 + 5*a^9*b^2*c*d^4*g^6 - a^10*b*d^5*g^6 + (b^11*c^5*g^6 - 5*a*b^10*c^4*d*g^6 + 10*a^2*b^9*c^3*d^2*g^6 - 10*a^3*b^8*c^2*d^3*g^6 + 5*a^4*b^7*c*d^4*g^6 - a^5*b^6*d^5*g^6)*x^5 + 5*(a*b^10*c^5*g^6 - 5*a^2*b^9*c^4*d*g^6 + 10*a^3*b^8*c^3*d^2*g^6 - 10*a^4*b^7*c^2*d^3*g^6 + 5*a^5*b^6*c*d^4*g^6 - a^6*b^5*d^5*g^6)*x^4 + 10*(a^2*b^9*c^5*g^6 - 5*a^3*b^8*c^4*d*g^6 + 10*a^4*b^7*c^3*d^2*g^6 - 10*a^5*b^6*c^2*d^3*g^6 + 5*a^6*b^5*c*d^4*g^6 - a^7*b^4*d^5*g^6)*x^3 + 10*(a^3*b^8*c^5*g^6 - 5*a^4*b^7*c^4*d*g^6 + 10*a^5*b^6*c^3*d^2*g^6 - 10*a^6*b^5*c^2*d^3*g^6 + 5*a^7*b^4*c*d^4*g^6 - a^8*b^3*d^5*g^6)*x^2 + 5*(a^4*b^7*c^5*g^6 - 5*a^5*b^6*c^4*d*g^6 + 10*a^6*b^5*c^3*d^2*g^6 - 10*a^7*b^4*c^2*d^3*g^6 + 5*a^8*b^3*c*d^4*g^6 - a^9*b^2*d^5*g^6)*x))*B^2*c^2*i^2 - 1/18000*(60*((27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (549*a*b^5*c^5 - 4625*a^2*b^4*c^4*d + 19000*a^3*b^3*c^3*d^2 - 63000*a^4*b^2*c^2*d^3 + 51875*a^5*b*c*d^4 - 3799*a^6*d^5 - 60*(625*b^6*c^2*d^3 - 702*a*b^5*c*d^4 + 77*a^2*b^4*d^5)*x^4 + 30*(325*b^6*c^3*d^2 - 5667*a*b^5*c^2*d^3 + 5975*a^2*b^4*c*d^4 - 633*a^3*b^3*d^5)*x^3 - 10*(350*b^6*c^4*d - 3949*a*b^5*c^3*d^2 + 29475*a^2*b^4*c^2*d^3 - 28775*a^3*b^3*c*d^4 + 2899*a^4*b^2*d^5)*x^2 + 1800*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(b*x + a)^2 + 1800*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(d*x + c)^2 + 5*(225*b^6*c^5 - 2201*a*b^5*c^4*d + 10900*a^2*b^4*c^3*d^2 - 46200*a^3*b^3*c^2*d^3 + 41075*a^4*b^2*c*d^4 - 3799*a^5*b*d^5)*x - 60*(625*a^5*b*c*d^4 - 77*a^6*d^5 + (625*b^6*c*d^4 - 77*a*b^5*d^5)*x^5 + 5*(625*a*b^5*c*d^4 - 77*a^2*b^4*d^5)*x^4 + 10*(625*a^2*b^4*c*d^4 - 77*a^3*b^3*d^5)*x^3 + 10*(625*a^3*b^3*c*d^4 - 77*a^4*b^2*d^5)*x^2 + 5*(625*a^4*b^2*c*d^4 - 77*a^5*b*d^5)*x)*log(b*x + a) + 60*(625*a^5*b*c*d^4 - 77*a^6*d^5 + (625*b^6*c*d^4 - 77*a*b^5*d^5)*x^5 + 5*(625*a*b^5*c*d^4 - 77*a^2*b^4*d^5)*x^4 + 10*(625*a^2*b^4*c*d^4 - 77*a^3*b^3*d^5)*x^3 + 10*(625*a^3*b^3*c*d^4 - 77*a^4*b^2*d^5)*x^2 + 5*(625*a^4*b^2*c*d^4 - 77*a^5*b*d^5)*x - 60*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(b*x + a))*log(d*x + c))/(a^5*b^7*c^5*g^6 - 5*a^6*b^6*c^4*d*g^6 + 10*a^7*b^5*c^3*d^2*g^6 - 10*a^8*b^4*c^2*d^3*g^6 + 5*a^9*b^3*c*d^4*g^6 - a^10*b^2*d^5*g^6 + (b^12*c^5*g^6 - 5*a*b^11*c^4*d*g^6 + 10*a^2*b^10*c^3*d^2*g^6 - 10*a^3*b^9*c^2*d^3*g^6 + 5*a^4*b^8*c*d^4*g^6 - a^5*b^7*d^5*g^6)*x^5 + 5*(a*b^11*c^5*g^6 - 5*a^2*b^10*c^4*d*g^6 + 10*a^3*b^9*c^3*d^2*g^6 - 10*a^4*b^8*c^2*d^3*g^6 + 5*a^5*b^7*c*d^4*g^6 - a^6*b^6*d^5*g^6)*x^4 + 10*(a^2*b^10*c^5*g^6 - 5*a^3*b^9*c^4*d*g^6 + 10*a^4*b^8*c^3*d^2*g^6 - 10*a^5*b^7*c^2*d^3*g^6 + 5*a^6*b^6*c*d^4*g^6 - a^7*b^5*d^5*g^6)*x^3 + 10*(a^3*b^9*c^5*g^6 - 5*a^4*b^8*c^4*d*g^6 + 10*a^5*b^7*c^3*d^2*g^6 - 10*a^6*b^6*c^2*d^3*g^6 + 5*a^7*b^5*c*d^4*g^6 - a^8*b^4*d^5*g^6)*x^2 + 5*(a^4*b^8*c^5*g^6 - 5*a^5*b^7*c^4*d*g^6 + 10*a^6*b^6*c^3*d^2*g^6 - 10*a^7*b^5*c^2*d^3*g^6 + 5*a^8*b^4*c*d^4*g^6 - a^9*b^3*d^5*g^6)*x))*B^2*c*d*i^2 - 1/54000*(60*((47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (1489*a^2*b^5*c^5 - 14375*a^3*b^4*c^4*d + 85000*a^4*b^3*c^3*d^2 - 85000*a^5*b^2*c^2*d^3 + 14375*a^6*b*c*d^4 - 1489*a^7*d^5 + 60*(1100*b^7*c^3*d^2 - 1425*a*b^6*c^2*d^3 + 372*a^2*b^5*c*d^4 - 47*a^3*b^4*d^5)*x^4 - 30*(500*b^7*c^4*d - 9825*a*b^6*c^3*d^2 + 11937*a^2*b^5*c^2*d^3 - 2975*a^3*b^4*c*d^4 + 363*a^4*b^3*d^5)*x^3 + 10*(400*b^7*c^5 - 5450*a*b^6*c^4*d + 49189*a^2*b^5*c^3*d^2 - 55525*a^3*b^4*c^2*d^3 + 12875*a^4*b^3*c*d^4 - 1489*a^5*b^2*d^5)*x^2 - 1800*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(b*x + a)^2 - 1800*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(d*x + c)^2 + 5*(925*a*b^6*c^5 - 9911*a^2*b^5*c^4*d + 67900*a^3*b^4*c^3*d^2 - 71800*a^4*b^3*c^2*d^3 + 14375*a^5*b^2*c*d^4 - 1489*a^6*b*d^5)*x + 60*(1100*a^5*b^2*c^2*d^3 - 325*a^6*b*c*d^4 + 47*a^7*d^5 + (1100*b^7*c^2*d^3 - 325*a*b^6*c*d^4 + 47*a^2*b^5*d^5)*x^5 + 5*(1100*a*b^6*c^2*d^3 - 325*a^2*b^5*c*d^4 + 47*a^3*b^4*d^5)*x^4 + 10*(1100*a^2*b^5*c^2*d^3 - 325*a^3*b^4*c*d^4 + 47*a^4*b^3*d^5)*x^3 + 10*(1100*a^3*b^4*c^2*d^3 - 325*a^4*b^3*c*d^4 + 47*a^5*b^2*d^5)*x^2 + 5*(1100*a^4*b^3*c^2*d^3 - 325*a^5*b^2*c*d^4 + 47*a^6*b*d^5)*x)*log(b*x + a) - 60*(1100*a^5*b^2*c^2*d^3 - 325*a^6*b*c*d^4 + 47*a^7*d^5 + (1100*b^7*c^2*d^3 - 325*a*b^6*c*d^4 + 47*a^2*b^5*d^5)*x^5 + 5*(1100*a*b^6*c^2*d^3 - 325*a^2*b^5*c*d^4 + 47*a^3*b^4*d^5)*x^4 + 10*(1100*a^2*b^5*c^2*d^3 - 325*a^3*b^4*c*d^4 + 47*a^4*b^3*d^5)*x^3 + 10*(1100*a^3*b^4*c^2*d^3 - 325*a^4*b^3*c*d^4 + 47*a^5*b^2*d^5)*x^2 + 5*(1100*a^4*b^3*c^2*d^3 - 325*a^5*b^2*c*d^4 + 47*a^6*b*d^5)*x - 60*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(b*x + a))*log(d*x + c))/(a^5*b^8*c^5*g^6 - 5*a^6*b^7*c^4*d*g^6 + 10*a^7*b^6*c^3*d^2*g^6 - 10*a^8*b^5*c^2*d^3*g^6 + 5*a^9*b^4*c*d^4*g^6 - a^10*b^3*d^5*g^6 + (b^13*c^5*g^6 - 5*a*b^12*c^4*d*g^6 + 10*a^2*b^11*c^3*d^2*g^6 - 10*a^3*b^10*c^2*d^3*g^6 + 5*a^4*b^9*c*d^4*g^6 - a^5*b^8*d^5*g^6)*x^5 + 5*(a*b^12*c^5*g^6 - 5*a^2*b^11*c^4*d*g^6 + 10*a^3*b^10*c^3*d^2*g^6 - 10*a^4*b^9*c^2*d^3*g^6 + 5*a^5*b^8*c*d^4*g^6 - a^6*b^7*d^5*g^6)*x^4 + 10*(a^2*b^11*c^5*g^6 - 5*a^3*b^10*c^4*d*g^6 + 10*a^4*b^9*c^3*d^2*g^6 - 10*a^5*b^8*c^2*d^3*g^6 + 5*a^6*b^7*c*d^4*g^6 - a^7*b^6*d^5*g^6)*x^3 + 10*(a^3*b^10*c^5*g^6 - 5*a^4*b^9*c^4*d*g^6 + 10*a^5*b^8*c^3*d^2*g^6 - 10*a^6*b^7*c^2*d^3*g^6 + 5*a^7*b^6*c*d^4*g^6 - a^8*b^5*d^5*g^6)*x^2 + 5*(a^4*b^9*c^5*g^6 - 5*a^5*b^8*c^4*d*g^6 + 10*a^6*b^7*c^3*d^2*g^6 - 10*a^7*b^6*c^2*d^3*g^6 + 5*a^8*b^5*c*d^4*g^6 - a^9*b^4*d^5*g^6)*x))*B^2*d^2*i^2 - 1/900*A*B*d^2*i^2*(60*(10*b^2*x^2 + 5*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) + (47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6)) - 1/300*A*B*c*d*i^2*(60*(5*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) + (27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6)) - 1/150*A*B*c^2*i^2*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6)) - 1/5*B^2*c^2*i^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) - 1/10*(5*b*x + a)*A^2*c*d*i^2/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/30*(10*b^2*x^2 + 5*a*b*x + a^2)*A^2*d^2*i^2/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/5*A^2*c^2*i^2/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6)","B",0
74,1,6921,0,3.441584," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{7} \, A^{2} b^{3} d^{3} g^{3} i^{3} x^{7} + \frac{1}{2} \, A^{2} b^{3} c d^{2} g^{3} i^{3} x^{6} + \frac{1}{2} \, A^{2} a b^{2} d^{3} g^{3} i^{3} x^{6} + \frac{3}{5} \, A^{2} b^{3} c^{2} d g^{3} i^{3} x^{5} + \frac{9}{5} \, A^{2} a b^{2} c d^{2} g^{3} i^{3} x^{5} + \frac{3}{5} \, A^{2} a^{2} b d^{3} g^{3} i^{3} x^{5} + \frac{1}{4} \, A^{2} b^{3} c^{3} g^{3} i^{3} x^{4} + \frac{9}{4} \, A^{2} a b^{2} c^{2} d g^{3} i^{3} x^{4} + \frac{9}{4} \, A^{2} a^{2} b c d^{2} g^{3} i^{3} x^{4} + \frac{1}{4} \, A^{2} a^{3} d^{3} g^{3} i^{3} x^{4} + A^{2} a b^{2} c^{3} g^{3} i^{3} x^{3} + 3 \, A^{2} a^{2} b c^{2} d g^{3} i^{3} x^{3} + A^{2} a^{3} c d^{2} g^{3} i^{3} x^{3} + \frac{3}{2} \, A^{2} a^{2} b c^{3} g^{3} i^{3} x^{2} + \frac{3}{2} \, A^{2} a^{3} c^{2} d g^{3} i^{3} x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{3} c^{3} g^{3} i^{3} + 3 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{2} b c^{3} g^{3} i^{3} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a b^{2} c^{3} g^{3} i^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B b^{3} c^{3} g^{3} i^{3} + 3 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{3} c^{2} d g^{3} i^{3} + 3 \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a^{2} b c^{2} d g^{3} i^{3} + \frac{3}{4} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a b^{2} c^{2} d g^{3} i^{3} + \frac{1}{10} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B b^{3} c^{2} d g^{3} i^{3} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a^{3} c d^{2} g^{3} i^{3} + \frac{3}{4} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a^{2} b c d^{2} g^{3} i^{3} + \frac{3}{10} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B a b^{2} c d^{2} g^{3} i^{3} + \frac{1}{60} \, {\left(60 \, x^{6} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} + \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} - \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} A B b^{3} c d^{2} g^{3} i^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a^{3} d^{3} g^{3} i^{3} + \frac{1}{10} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B a^{2} b d^{3} g^{3} i^{3} + \frac{1}{60} \, {\left(60 \, x^{6} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} + \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} - \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} A B a b^{2} d^{3} g^{3} i^{3} + \frac{1}{210} \, {\left(60 \, x^{7} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{60 \, a^{7} \log\left(b x + a\right)}{b^{7}} - \frac{60 \, c^{7} \log\left(d x + c\right)}{d^{7}} - \frac{10 \, {\left(b^{6} c d^{5} - a b^{5} d^{6}\right)} x^{6} - 12 \, {\left(b^{6} c^{2} d^{4} - a^{2} b^{4} d^{6}\right)} x^{5} + 15 \, {\left(b^{6} c^{3} d^{3} - a^{3} b^{3} d^{6}\right)} x^{4} - 20 \, {\left(b^{6} c^{4} d^{2} - a^{4} b^{2} d^{6}\right)} x^{3} + 30 \, {\left(b^{6} c^{5} d - a^{5} b d^{6}\right)} x^{2} - 60 \, {\left(b^{6} c^{6} - a^{6} d^{6}\right)} x}{b^{6} d^{6}}\right)} A B b^{3} d^{3} g^{3} i^{3} + A^{2} a^{3} c^{3} g^{3} i^{3} x + \frac{{\left(6 \, b^{6} c^{7} g^{3} i^{3} \log\left(e\right) - 107 \, a^{4} b^{2} c^{3} d^{4} g^{3} i^{3} + 39 \, a^{5} b c^{2} d^{5} g^{3} i^{3} - 6 \, a^{6} c d^{6} g^{3} i^{3} - 6 \, {\left(7 \, g^{3} i^{3} \log\left(e\right) - g^{3} i^{3}\right)} a b^{5} c^{6} d + 3 \, {\left(42 \, g^{3} i^{3} \log\left(e\right) - 13 \, g^{3} i^{3}\right)} a^{2} b^{4} c^{5} d^{2} - {\left(210 \, g^{3} i^{3} \log\left(e\right) - 107 \, g^{3} i^{3}\right)} a^{3} b^{3} c^{4} d^{3}\right)} B^{2} \log\left(d x + c\right)}{420 \, b^{3} d^{4}} + \frac{{\left(b^{7} c^{7} g^{3} i^{3} - 7 \, a b^{6} c^{6} d g^{3} i^{3} + 21 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} - 35 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} + 35 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} - 21 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + 7 \, a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{70 \, b^{4} d^{4}} + \frac{360 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} \log\left(e\right)^{2} + 60 \, {\left({\left(21 \, g^{3} i^{3} \log\left(e\right)^{2} - 2 \, g^{3} i^{3} \log\left(e\right)\right)} b^{7} c d^{6} + {\left(21 \, g^{3} i^{3} \log\left(e\right)^{2} + 2 \, g^{3} i^{3} \log\left(e\right)\right)} a b^{6} d^{7}\right)} B^{2} x^{6} + 24 \, {\left({\left(63 \, g^{3} i^{3} \log\left(e\right)^{2} - 15 \, g^{3} i^{3} \log\left(e\right) + g^{3} i^{3}\right)} b^{7} c^{2} d^{5} + {\left(189 \, g^{3} i^{3} \log\left(e\right)^{2} - 2 \, g^{3} i^{3}\right)} a b^{6} c d^{6} + {\left(63 \, g^{3} i^{3} \log\left(e\right)^{2} + 15 \, g^{3} i^{3} \log\left(e\right) + g^{3} i^{3}\right)} a^{2} b^{5} d^{7}\right)} B^{2} x^{5} + 6 \, {\left({\left(105 \, g^{3} i^{3} \log\left(e\right)^{2} - 51 \, g^{3} i^{3} \log\left(e\right) + 10 \, g^{3} i^{3}\right)} b^{7} c^{3} d^{4} + {\left(945 \, g^{3} i^{3} \log\left(e\right)^{2} - 147 \, g^{3} i^{3} \log\left(e\right) - 10 \, g^{3} i^{3}\right)} a b^{6} c^{2} d^{5} + {\left(945 \, g^{3} i^{3} \log\left(e\right)^{2} + 147 \, g^{3} i^{3} \log\left(e\right) - 10 \, g^{3} i^{3}\right)} a^{2} b^{5} c d^{6} + {\left(105 \, g^{3} i^{3} \log\left(e\right)^{2} + 51 \, g^{3} i^{3} \log\left(e\right) + 10 \, g^{3} i^{3}\right)} a^{3} b^{4} d^{7}\right)} B^{2} x^{4} - 2 \, {\left({\left(6 \, g^{3} i^{3} \log\left(e\right) - 11 \, g^{3} i^{3}\right)} b^{7} c^{4} d^{3} - 4 \, {\left(315 \, g^{3} i^{3} \log\left(e\right)^{2} - 147 \, g^{3} i^{3} \log\left(e\right) + 19 \, g^{3} i^{3}\right)} a b^{6} c^{3} d^{4} - 6 \, {\left(630 \, g^{3} i^{3} \log\left(e\right)^{2} - 29 \, g^{3} i^{3}\right)} a^{2} b^{5} c^{2} d^{5} - 4 \, {\left(315 \, g^{3} i^{3} \log\left(e\right)^{2} + 147 \, g^{3} i^{3} \log\left(e\right) + 19 \, g^{3} i^{3}\right)} a^{3} b^{4} c d^{6} - {\left(6 \, g^{3} i^{3} \log\left(e\right) + 11 \, g^{3} i^{3}\right)} a^{4} b^{3} d^{7}\right)} B^{2} x^{3} + 3 \, {\left(3 \, {\left(2 \, g^{3} i^{3} \log\left(e\right) - 3 \, g^{3} i^{3}\right)} b^{7} c^{5} d^{2} - {\left(42 \, g^{3} i^{3} \log\left(e\right) - 67 \, g^{3} i^{3}\right)} a b^{6} c^{4} d^{3} + 2 \, {\left(630 \, g^{3} i^{3} \log\left(e\right)^{2} - 252 \, g^{3} i^{3} \log\left(e\right) - 29 \, g^{3} i^{3}\right)} a^{2} b^{5} c^{3} d^{4} + 2 \, {\left(630 \, g^{3} i^{3} \log\left(e\right)^{2} + 252 \, g^{3} i^{3} \log\left(e\right) - 29 \, g^{3} i^{3}\right)} a^{3} b^{4} c^{2} d^{5} + {\left(42 \, g^{3} i^{3} \log\left(e\right) + 67 \, g^{3} i^{3}\right)} a^{4} b^{3} c d^{6} - 3 \, {\left(2 \, g^{3} i^{3} \log\left(e\right) + 3 \, g^{3} i^{3}\right)} a^{5} b^{2} d^{7}\right)} B^{2} x^{2} - 6 \, {\left(6 \, {\left(g^{3} i^{3} \log\left(e\right) - g^{3} i^{3}\right)} b^{7} c^{6} d - 3 \, {\left(14 \, g^{3} i^{3} \log\left(e\right) - 15 \, g^{3} i^{3}\right)} a b^{6} c^{5} d^{2} + 2 \, {\left(63 \, g^{3} i^{3} \log\left(e\right) - 73 \, g^{3} i^{3}\right)} a^{2} b^{5} c^{4} d^{3} - 2 \, {\left(210 \, g^{3} i^{3} \log\left(e\right)^{2} - 107 \, g^{3} i^{3}\right)} a^{3} b^{4} c^{3} d^{4} - 2 \, {\left(63 \, g^{3} i^{3} \log\left(e\right) + 73 \, g^{3} i^{3}\right)} a^{4} b^{3} c^{2} d^{5} + 3 \, {\left(14 \, g^{3} i^{3} \log\left(e\right) + 15 \, g^{3} i^{3}\right)} a^{5} b^{2} c d^{6} - 6 \, {\left(g^{3} i^{3} \log\left(e\right) + g^{3} i^{3}\right)} a^{6} b d^{7}\right)} B^{2} x + 18 \, {\left(20 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} + 140 \, B^{2} a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} x + 70 \, {\left(b^{7} c d^{6} g^{3} i^{3} + a b^{6} d^{7} g^{3} i^{3}\right)} B^{2} x^{6} + 84 \, {\left(b^{7} c^{2} d^{5} g^{3} i^{3} + 3 \, a b^{6} c d^{6} g^{3} i^{3} + a^{2} b^{5} d^{7} g^{3} i^{3}\right)} B^{2} x^{5} + 35 \, {\left(b^{7} c^{3} d^{4} g^{3} i^{3} + 9 \, a b^{6} c^{2} d^{5} g^{3} i^{3} + 9 \, a^{2} b^{5} c d^{6} g^{3} i^{3} + a^{3} b^{4} d^{7} g^{3} i^{3}\right)} B^{2} x^{4} + 140 \, {\left(a b^{6} c^{3} d^{4} g^{3} i^{3} + 3 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} + a^{3} b^{4} c d^{6} g^{3} i^{3}\right)} B^{2} x^{3} + 210 \, {\left(a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} + a^{3} b^{4} c^{2} d^{5} g^{3} i^{3}\right)} B^{2} x^{2} + {\left(35 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} - 21 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + 7 \, a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 18 \, {\left(20 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} + 140 \, B^{2} a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} x + 70 \, {\left(b^{7} c d^{6} g^{3} i^{3} + a b^{6} d^{7} g^{3} i^{3}\right)} B^{2} x^{6} + 84 \, {\left(b^{7} c^{2} d^{5} g^{3} i^{3} + 3 \, a b^{6} c d^{6} g^{3} i^{3} + a^{2} b^{5} d^{7} g^{3} i^{3}\right)} B^{2} x^{5} + 35 \, {\left(b^{7} c^{3} d^{4} g^{3} i^{3} + 9 \, a b^{6} c^{2} d^{5} g^{3} i^{3} + 9 \, a^{2} b^{5} c d^{6} g^{3} i^{3} + a^{3} b^{4} d^{7} g^{3} i^{3}\right)} B^{2} x^{4} + 140 \, {\left(a b^{6} c^{3} d^{4} g^{3} i^{3} + 3 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} + a^{3} b^{4} c d^{6} g^{3} i^{3}\right)} B^{2} x^{3} + 210 \, {\left(a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} + a^{3} b^{4} c^{2} d^{5} g^{3} i^{3}\right)} B^{2} x^{2} - {\left(b^{7} c^{7} g^{3} i^{3} - 7 \, a b^{6} c^{6} d g^{3} i^{3} + 21 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} - 35 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(120 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} \log\left(e\right) + 20 \, {\left({\left(21 \, g^{3} i^{3} \log\left(e\right) - g^{3} i^{3}\right)} b^{7} c d^{6} + {\left(21 \, g^{3} i^{3} \log\left(e\right) + g^{3} i^{3}\right)} a b^{6} d^{7}\right)} B^{2} x^{6} + 12 \, {\left(126 \, a b^{6} c d^{6} g^{3} i^{3} \log\left(e\right) + {\left(42 \, g^{3} i^{3} \log\left(e\right) - 5 \, g^{3} i^{3}\right)} b^{7} c^{2} d^{5} + {\left(42 \, g^{3} i^{3} \log\left(e\right) + 5 \, g^{3} i^{3}\right)} a^{2} b^{5} d^{7}\right)} B^{2} x^{5} + 3 \, {\left({\left(70 \, g^{3} i^{3} \log\left(e\right) - 17 \, g^{3} i^{3}\right)} b^{7} c^{3} d^{4} + 7 \, {\left(90 \, g^{3} i^{3} \log\left(e\right) - 7 \, g^{3} i^{3}\right)} a b^{6} c^{2} d^{5} + 7 \, {\left(90 \, g^{3} i^{3} \log\left(e\right) + 7 \, g^{3} i^{3}\right)} a^{2} b^{5} c d^{6} + {\left(70 \, g^{3} i^{3} \log\left(e\right) + 17 \, g^{3} i^{3}\right)} a^{3} b^{4} d^{7}\right)} B^{2} x^{4} + 2 \, {\left(1260 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} \log\left(e\right) - b^{7} c^{4} d^{3} g^{3} i^{3} + a^{4} b^{3} d^{7} g^{3} i^{3} + 14 \, {\left(30 \, g^{3} i^{3} \log\left(e\right) - 7 \, g^{3} i^{3}\right)} a b^{6} c^{3} d^{4} + 14 \, {\left(30 \, g^{3} i^{3} \log\left(e\right) + 7 \, g^{3} i^{3}\right)} a^{3} b^{4} c d^{6}\right)} B^{2} x^{3} + 3 \, {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 7 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 7 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3} + 84 \, {\left(5 \, g^{3} i^{3} \log\left(e\right) - g^{3} i^{3}\right)} a^{2} b^{5} c^{3} d^{4} + 84 \, {\left(5 \, g^{3} i^{3} \log\left(e\right) + g^{3} i^{3}\right)} a^{3} b^{4} c^{2} d^{5}\right)} B^{2} x^{2} + 6 \, {\left(140 \, a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} \log\left(e\right) - b^{7} c^{6} d g^{3} i^{3} + 7 \, a b^{6} c^{5} d^{2} g^{3} i^{3} - 21 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} + 21 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} - 7 \, a^{5} b^{2} c d^{6} g^{3} i^{3} + a^{6} b d^{7} g^{3} i^{3}\right)} B^{2} x - {\left(6 \, a^{7} d^{7} g^{3} i^{3} \log\left(e\right) + 6 \, a b^{6} c^{6} d g^{3} i^{3} - 39 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 107 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - {\left(210 \, g^{3} i^{3} \log\left(e\right) + 107 \, g^{3} i^{3}\right)} a^{4} b^{3} c^{3} d^{4} + 3 \, {\left(42 \, g^{3} i^{3} \log\left(e\right) + 13 \, g^{3} i^{3}\right)} a^{5} b^{2} c^{2} d^{5} - 6 \, {\left(7 \, g^{3} i^{3} \log\left(e\right) + g^{3} i^{3}\right)} a^{6} b c d^{6}\right)} B^{2}\right)} \log\left(b x + a\right) - 6 \, {\left(120 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} \log\left(e\right) + 20 \, {\left({\left(21 \, g^{3} i^{3} \log\left(e\right) - g^{3} i^{3}\right)} b^{7} c d^{6} + {\left(21 \, g^{3} i^{3} \log\left(e\right) + g^{3} i^{3}\right)} a b^{6} d^{7}\right)} B^{2} x^{6} + 12 \, {\left(126 \, a b^{6} c d^{6} g^{3} i^{3} \log\left(e\right) + {\left(42 \, g^{3} i^{3} \log\left(e\right) - 5 \, g^{3} i^{3}\right)} b^{7} c^{2} d^{5} + {\left(42 \, g^{3} i^{3} \log\left(e\right) + 5 \, g^{3} i^{3}\right)} a^{2} b^{5} d^{7}\right)} B^{2} x^{5} + 3 \, {\left({\left(70 \, g^{3} i^{3} \log\left(e\right) - 17 \, g^{3} i^{3}\right)} b^{7} c^{3} d^{4} + 7 \, {\left(90 \, g^{3} i^{3} \log\left(e\right) - 7 \, g^{3} i^{3}\right)} a b^{6} c^{2} d^{5} + 7 \, {\left(90 \, g^{3} i^{3} \log\left(e\right) + 7 \, g^{3} i^{3}\right)} a^{2} b^{5} c d^{6} + {\left(70 \, g^{3} i^{3} \log\left(e\right) + 17 \, g^{3} i^{3}\right)} a^{3} b^{4} d^{7}\right)} B^{2} x^{4} + 2 \, {\left(1260 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} \log\left(e\right) - b^{7} c^{4} d^{3} g^{3} i^{3} + a^{4} b^{3} d^{7} g^{3} i^{3} + 14 \, {\left(30 \, g^{3} i^{3} \log\left(e\right) - 7 \, g^{3} i^{3}\right)} a b^{6} c^{3} d^{4} + 14 \, {\left(30 \, g^{3} i^{3} \log\left(e\right) + 7 \, g^{3} i^{3}\right)} a^{3} b^{4} c d^{6}\right)} B^{2} x^{3} + 3 \, {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 7 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 7 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3} + 84 \, {\left(5 \, g^{3} i^{3} \log\left(e\right) - g^{3} i^{3}\right)} a^{2} b^{5} c^{3} d^{4} + 84 \, {\left(5 \, g^{3} i^{3} \log\left(e\right) + g^{3} i^{3}\right)} a^{3} b^{4} c^{2} d^{5}\right)} B^{2} x^{2} + 6 \, {\left(140 \, a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} \log\left(e\right) - b^{7} c^{6} d g^{3} i^{3} + 7 \, a b^{6} c^{5} d^{2} g^{3} i^{3} - 21 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} + 21 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} - 7 \, a^{5} b^{2} c d^{6} g^{3} i^{3} + a^{6} b d^{7} g^{3} i^{3}\right)} B^{2} x + 6 \, {\left(20 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} + 140 \, B^{2} a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} x + 70 \, {\left(b^{7} c d^{6} g^{3} i^{3} + a b^{6} d^{7} g^{3} i^{3}\right)} B^{2} x^{6} + 84 \, {\left(b^{7} c^{2} d^{5} g^{3} i^{3} + 3 \, a b^{6} c d^{6} g^{3} i^{3} + a^{2} b^{5} d^{7} g^{3} i^{3}\right)} B^{2} x^{5} + 35 \, {\left(b^{7} c^{3} d^{4} g^{3} i^{3} + 9 \, a b^{6} c^{2} d^{5} g^{3} i^{3} + 9 \, a^{2} b^{5} c d^{6} g^{3} i^{3} + a^{3} b^{4} d^{7} g^{3} i^{3}\right)} B^{2} x^{4} + 140 \, {\left(a b^{6} c^{3} d^{4} g^{3} i^{3} + 3 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} + a^{3} b^{4} c d^{6} g^{3} i^{3}\right)} B^{2} x^{3} + 210 \, {\left(a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} + a^{3} b^{4} c^{2} d^{5} g^{3} i^{3}\right)} B^{2} x^{2} + {\left(35 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} - 21 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + 7 \, a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2520 \, b^{4} d^{4}}"," ",0,"1/7*A^2*b^3*d^3*g^3*i^3*x^7 + 1/2*A^2*b^3*c*d^2*g^3*i^3*x^6 + 1/2*A^2*a*b^2*d^3*g^3*i^3*x^6 + 3/5*A^2*b^3*c^2*d*g^3*i^3*x^5 + 9/5*A^2*a*b^2*c*d^2*g^3*i^3*x^5 + 3/5*A^2*a^2*b*d^3*g^3*i^3*x^5 + 1/4*A^2*b^3*c^3*g^3*i^3*x^4 + 9/4*A^2*a*b^2*c^2*d*g^3*i^3*x^4 + 9/4*A^2*a^2*b*c*d^2*g^3*i^3*x^4 + 1/4*A^2*a^3*d^3*g^3*i^3*x^4 + A^2*a*b^2*c^3*g^3*i^3*x^3 + 3*A^2*a^2*b*c^2*d*g^3*i^3*x^3 + A^2*a^3*c*d^2*g^3*i^3*x^3 + 3/2*A^2*a^2*b*c^3*g^3*i^3*x^2 + 3/2*A^2*a^3*c^2*d*g^3*i^3*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a^3*c^3*g^3*i^3 + 3*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^2*b*c^3*g^3*i^3 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a*b^2*c^3*g^3*i^3 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*b^3*c^3*g^3*i^3 + 3*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^3*c^2*d*g^3*i^3 + 3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a^2*b*c^2*d*g^3*i^3 + 3/4*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a*b^2*c^2*d*g^3*i^3 + 1/10*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*b^3*c^2*d*g^3*i^3 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a^3*c*d^2*g^3*i^3 + 3/4*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a^2*b*c*d^2*g^3*i^3 + 3/10*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*a*b^2*c*d^2*g^3*i^3 + 1/60*(60*x^6*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 60*a^6*log(b*x + a)/b^6 + 60*c^6*log(d*x + c)/d^6 - (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5))*A*B*b^3*c*d^2*g^3*i^3 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a^3*d^3*g^3*i^3 + 1/10*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*a^2*b*d^3*g^3*i^3 + 1/60*(60*x^6*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 60*a^6*log(b*x + a)/b^6 + 60*c^6*log(d*x + c)/d^6 - (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5))*A*B*a*b^2*d^3*g^3*i^3 + 1/210*(60*x^7*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 60*a^7*log(b*x + a)/b^7 - 60*c^7*log(d*x + c)/d^7 - (10*(b^6*c*d^5 - a*b^5*d^6)*x^6 - 12*(b^6*c^2*d^4 - a^2*b^4*d^6)*x^5 + 15*(b^6*c^3*d^3 - a^3*b^3*d^6)*x^4 - 20*(b^6*c^4*d^2 - a^4*b^2*d^6)*x^3 + 30*(b^6*c^5*d - a^5*b*d^6)*x^2 - 60*(b^6*c^6 - a^6*d^6)*x)/(b^6*d^6))*A*B*b^3*d^3*g^3*i^3 + A^2*a^3*c^3*g^3*i^3*x + 1/420*(6*b^6*c^7*g^3*i^3*log(e) - 107*a^4*b^2*c^3*d^4*g^3*i^3 + 39*a^5*b*c^2*d^5*g^3*i^3 - 6*a^6*c*d^6*g^3*i^3 - 6*(7*g^3*i^3*log(e) - g^3*i^3)*a*b^5*c^6*d + 3*(42*g^3*i^3*log(e) - 13*g^3*i^3)*a^2*b^4*c^5*d^2 - (210*g^3*i^3*log(e) - 107*g^3*i^3)*a^3*b^3*c^4*d^3)*B^2*log(d*x + c)/(b^3*d^4) + 1/70*(b^7*c^7*g^3*i^3 - 7*a*b^6*c^6*d*g^3*i^3 + 21*a^2*b^5*c^5*d^2*g^3*i^3 - 35*a^3*b^4*c^4*d^3*g^3*i^3 + 35*a^4*b^3*c^3*d^4*g^3*i^3 - 21*a^5*b^2*c^2*d^5*g^3*i^3 + 7*a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^4*d^4) + 1/2520*(360*B^2*b^7*d^7*g^3*i^3*x^7*log(e)^2 + 60*((21*g^3*i^3*log(e)^2 - 2*g^3*i^3*log(e))*b^7*c*d^6 + (21*g^3*i^3*log(e)^2 + 2*g^3*i^3*log(e))*a*b^6*d^7)*B^2*x^6 + 24*((63*g^3*i^3*log(e)^2 - 15*g^3*i^3*log(e) + g^3*i^3)*b^7*c^2*d^5 + (189*g^3*i^3*log(e)^2 - 2*g^3*i^3)*a*b^6*c*d^6 + (63*g^3*i^3*log(e)^2 + 15*g^3*i^3*log(e) + g^3*i^3)*a^2*b^5*d^7)*B^2*x^5 + 6*((105*g^3*i^3*log(e)^2 - 51*g^3*i^3*log(e) + 10*g^3*i^3)*b^7*c^3*d^4 + (945*g^3*i^3*log(e)^2 - 147*g^3*i^3*log(e) - 10*g^3*i^3)*a*b^6*c^2*d^5 + (945*g^3*i^3*log(e)^2 + 147*g^3*i^3*log(e) - 10*g^3*i^3)*a^2*b^5*c*d^6 + (105*g^3*i^3*log(e)^2 + 51*g^3*i^3*log(e) + 10*g^3*i^3)*a^3*b^4*d^7)*B^2*x^4 - 2*((6*g^3*i^3*log(e) - 11*g^3*i^3)*b^7*c^4*d^3 - 4*(315*g^3*i^3*log(e)^2 - 147*g^3*i^3*log(e) + 19*g^3*i^3)*a*b^6*c^3*d^4 - 6*(630*g^3*i^3*log(e)^2 - 29*g^3*i^3)*a^2*b^5*c^2*d^5 - 4*(315*g^3*i^3*log(e)^2 + 147*g^3*i^3*log(e) + 19*g^3*i^3)*a^3*b^4*c*d^6 - (6*g^3*i^3*log(e) + 11*g^3*i^3)*a^4*b^3*d^7)*B^2*x^3 + 3*(3*(2*g^3*i^3*log(e) - 3*g^3*i^3)*b^7*c^5*d^2 - (42*g^3*i^3*log(e) - 67*g^3*i^3)*a*b^6*c^4*d^3 + 2*(630*g^3*i^3*log(e)^2 - 252*g^3*i^3*log(e) - 29*g^3*i^3)*a^2*b^5*c^3*d^4 + 2*(630*g^3*i^3*log(e)^2 + 252*g^3*i^3*log(e) - 29*g^3*i^3)*a^3*b^4*c^2*d^5 + (42*g^3*i^3*log(e) + 67*g^3*i^3)*a^4*b^3*c*d^6 - 3*(2*g^3*i^3*log(e) + 3*g^3*i^3)*a^5*b^2*d^7)*B^2*x^2 - 6*(6*(g^3*i^3*log(e) - g^3*i^3)*b^7*c^6*d - 3*(14*g^3*i^3*log(e) - 15*g^3*i^3)*a*b^6*c^5*d^2 + 2*(63*g^3*i^3*log(e) - 73*g^3*i^3)*a^2*b^5*c^4*d^3 - 2*(210*g^3*i^3*log(e)^2 - 107*g^3*i^3)*a^3*b^4*c^3*d^4 - 2*(63*g^3*i^3*log(e) + 73*g^3*i^3)*a^4*b^3*c^2*d^5 + 3*(14*g^3*i^3*log(e) + 15*g^3*i^3)*a^5*b^2*c*d^6 - 6*(g^3*i^3*log(e) + g^3*i^3)*a^6*b*d^7)*B^2*x + 18*(20*B^2*b^7*d^7*g^3*i^3*x^7 + 140*B^2*a^3*b^4*c^3*d^4*g^3*i^3*x + 70*(b^7*c*d^6*g^3*i^3 + a*b^6*d^7*g^3*i^3)*B^2*x^6 + 84*(b^7*c^2*d^5*g^3*i^3 + 3*a*b^6*c*d^6*g^3*i^3 + a^2*b^5*d^7*g^3*i^3)*B^2*x^5 + 35*(b^7*c^3*d^4*g^3*i^3 + 9*a*b^6*c^2*d^5*g^3*i^3 + 9*a^2*b^5*c*d^6*g^3*i^3 + a^3*b^4*d^7*g^3*i^3)*B^2*x^4 + 140*(a*b^6*c^3*d^4*g^3*i^3 + 3*a^2*b^5*c^2*d^5*g^3*i^3 + a^3*b^4*c*d^6*g^3*i^3)*B^2*x^3 + 210*(a^2*b^5*c^3*d^4*g^3*i^3 + a^3*b^4*c^2*d^5*g^3*i^3)*B^2*x^2 + (35*a^4*b^3*c^3*d^4*g^3*i^3 - 21*a^5*b^2*c^2*d^5*g^3*i^3 + 7*a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*B^2)*log(b*x + a)^2 + 18*(20*B^2*b^7*d^7*g^3*i^3*x^7 + 140*B^2*a^3*b^4*c^3*d^4*g^3*i^3*x + 70*(b^7*c*d^6*g^3*i^3 + a*b^6*d^7*g^3*i^3)*B^2*x^6 + 84*(b^7*c^2*d^5*g^3*i^3 + 3*a*b^6*c*d^6*g^3*i^3 + a^2*b^5*d^7*g^3*i^3)*B^2*x^5 + 35*(b^7*c^3*d^4*g^3*i^3 + 9*a*b^6*c^2*d^5*g^3*i^3 + 9*a^2*b^5*c*d^6*g^3*i^3 + a^3*b^4*d^7*g^3*i^3)*B^2*x^4 + 140*(a*b^6*c^3*d^4*g^3*i^3 + 3*a^2*b^5*c^2*d^5*g^3*i^3 + a^3*b^4*c*d^6*g^3*i^3)*B^2*x^3 + 210*(a^2*b^5*c^3*d^4*g^3*i^3 + a^3*b^4*c^2*d^5*g^3*i^3)*B^2*x^2 - (b^7*c^7*g^3*i^3 - 7*a*b^6*c^6*d*g^3*i^3 + 21*a^2*b^5*c^5*d^2*g^3*i^3 - 35*a^3*b^4*c^4*d^3*g^3*i^3)*B^2)*log(d*x + c)^2 + 6*(120*B^2*b^7*d^7*g^3*i^3*x^7*log(e) + 20*((21*g^3*i^3*log(e) - g^3*i^3)*b^7*c*d^6 + (21*g^3*i^3*log(e) + g^3*i^3)*a*b^6*d^7)*B^2*x^6 + 12*(126*a*b^6*c*d^6*g^3*i^3*log(e) + (42*g^3*i^3*log(e) - 5*g^3*i^3)*b^7*c^2*d^5 + (42*g^3*i^3*log(e) + 5*g^3*i^3)*a^2*b^5*d^7)*B^2*x^5 + 3*((70*g^3*i^3*log(e) - 17*g^3*i^3)*b^7*c^3*d^4 + 7*(90*g^3*i^3*log(e) - 7*g^3*i^3)*a*b^6*c^2*d^5 + 7*(90*g^3*i^3*log(e) + 7*g^3*i^3)*a^2*b^5*c*d^6 + (70*g^3*i^3*log(e) + 17*g^3*i^3)*a^3*b^4*d^7)*B^2*x^4 + 2*(1260*a^2*b^5*c^2*d^5*g^3*i^3*log(e) - b^7*c^4*d^3*g^3*i^3 + a^4*b^3*d^7*g^3*i^3 + 14*(30*g^3*i^3*log(e) - 7*g^3*i^3)*a*b^6*c^3*d^4 + 14*(30*g^3*i^3*log(e) + 7*g^3*i^3)*a^3*b^4*c*d^6)*B^2*x^3 + 3*(b^7*c^5*d^2*g^3*i^3 - 7*a*b^6*c^4*d^3*g^3*i^3 + 7*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3 + 84*(5*g^3*i^3*log(e) - g^3*i^3)*a^2*b^5*c^3*d^4 + 84*(5*g^3*i^3*log(e) + g^3*i^3)*a^3*b^4*c^2*d^5)*B^2*x^2 + 6*(140*a^3*b^4*c^3*d^4*g^3*i^3*log(e) - b^7*c^6*d*g^3*i^3 + 7*a*b^6*c^5*d^2*g^3*i^3 - 21*a^2*b^5*c^4*d^3*g^3*i^3 + 21*a^4*b^3*c^2*d^5*g^3*i^3 - 7*a^5*b^2*c*d^6*g^3*i^3 + a^6*b*d^7*g^3*i^3)*B^2*x - (6*a^7*d^7*g^3*i^3*log(e) + 6*a*b^6*c^6*d*g^3*i^3 - 39*a^2*b^5*c^5*d^2*g^3*i^3 + 107*a^3*b^4*c^4*d^3*g^3*i^3 - (210*g^3*i^3*log(e) + 107*g^3*i^3)*a^4*b^3*c^3*d^4 + 3*(42*g^3*i^3*log(e) + 13*g^3*i^3)*a^5*b^2*c^2*d^5 - 6*(7*g^3*i^3*log(e) + g^3*i^3)*a^6*b*c*d^6)*B^2)*log(b*x + a) - 6*(120*B^2*b^7*d^7*g^3*i^3*x^7*log(e) + 20*((21*g^3*i^3*log(e) - g^3*i^3)*b^7*c*d^6 + (21*g^3*i^3*log(e) + g^3*i^3)*a*b^6*d^7)*B^2*x^6 + 12*(126*a*b^6*c*d^6*g^3*i^3*log(e) + (42*g^3*i^3*log(e) - 5*g^3*i^3)*b^7*c^2*d^5 + (42*g^3*i^3*log(e) + 5*g^3*i^3)*a^2*b^5*d^7)*B^2*x^5 + 3*((70*g^3*i^3*log(e) - 17*g^3*i^3)*b^7*c^3*d^4 + 7*(90*g^3*i^3*log(e) - 7*g^3*i^3)*a*b^6*c^2*d^5 + 7*(90*g^3*i^3*log(e) + 7*g^3*i^3)*a^2*b^5*c*d^6 + (70*g^3*i^3*log(e) + 17*g^3*i^3)*a^3*b^4*d^7)*B^2*x^4 + 2*(1260*a^2*b^5*c^2*d^5*g^3*i^3*log(e) - b^7*c^4*d^3*g^3*i^3 + a^4*b^3*d^7*g^3*i^3 + 14*(30*g^3*i^3*log(e) - 7*g^3*i^3)*a*b^6*c^3*d^4 + 14*(30*g^3*i^3*log(e) + 7*g^3*i^3)*a^3*b^4*c*d^6)*B^2*x^3 + 3*(b^7*c^5*d^2*g^3*i^3 - 7*a*b^6*c^4*d^3*g^3*i^3 + 7*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3 + 84*(5*g^3*i^3*log(e) - g^3*i^3)*a^2*b^5*c^3*d^4 + 84*(5*g^3*i^3*log(e) + g^3*i^3)*a^3*b^4*c^2*d^5)*B^2*x^2 + 6*(140*a^3*b^4*c^3*d^4*g^3*i^3*log(e) - b^7*c^6*d*g^3*i^3 + 7*a*b^6*c^5*d^2*g^3*i^3 - 21*a^2*b^5*c^4*d^3*g^3*i^3 + 21*a^4*b^3*c^2*d^5*g^3*i^3 - 7*a^5*b^2*c*d^6*g^3*i^3 + a^6*b*d^7*g^3*i^3)*B^2*x + 6*(20*B^2*b^7*d^7*g^3*i^3*x^7 + 140*B^2*a^3*b^4*c^3*d^4*g^3*i^3*x + 70*(b^7*c*d^6*g^3*i^3 + a*b^6*d^7*g^3*i^3)*B^2*x^6 + 84*(b^7*c^2*d^5*g^3*i^3 + 3*a*b^6*c*d^6*g^3*i^3 + a^2*b^5*d^7*g^3*i^3)*B^2*x^5 + 35*(b^7*c^3*d^4*g^3*i^3 + 9*a*b^6*c^2*d^5*g^3*i^3 + 9*a^2*b^5*c*d^6*g^3*i^3 + a^3*b^4*d^7*g^3*i^3)*B^2*x^4 + 140*(a*b^6*c^3*d^4*g^3*i^3 + 3*a^2*b^5*c^2*d^5*g^3*i^3 + a^3*b^4*c*d^6*g^3*i^3)*B^2*x^3 + 210*(a^2*b^5*c^3*d^4*g^3*i^3 + a^3*b^4*c^2*d^5*g^3*i^3)*B^2*x^2 + (35*a^4*b^3*c^3*d^4*g^3*i^3 - 21*a^5*b^2*c^2*d^5*g^3*i^3 + 7*a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d^4)","B",0
75,1,5196,0,2.862021," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{6} \, A^{2} b^{2} d^{3} g^{2} i^{3} x^{6} + \frac{3}{5} \, A^{2} b^{2} c d^{2} g^{2} i^{3} x^{5} + \frac{2}{5} \, A^{2} a b d^{3} g^{2} i^{3} x^{5} + \frac{3}{4} \, A^{2} b^{2} c^{2} d g^{2} i^{3} x^{4} + \frac{3}{2} \, A^{2} a b c d^{2} g^{2} i^{3} x^{4} + \frac{1}{4} \, A^{2} a^{2} d^{3} g^{2} i^{3} x^{4} + \frac{1}{3} \, A^{2} b^{2} c^{3} g^{2} i^{3} x^{3} + 2 \, A^{2} a b c^{2} d g^{2} i^{3} x^{3} + A^{2} a^{2} c d^{2} g^{2} i^{3} x^{3} + A^{2} a b c^{3} g^{2} i^{3} x^{2} + \frac{3}{2} \, A^{2} a^{2} c^{2} d g^{2} i^{3} x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{2} c^{3} g^{2} i^{3} + 2 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a b c^{3} g^{2} i^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B b^{2} c^{3} g^{2} i^{3} + 3 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a^{2} c^{2} d g^{2} i^{3} + 2 \, {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a b c^{2} d g^{2} i^{3} + \frac{1}{4} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B b^{2} c^{2} d g^{2} i^{3} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a^{2} c d^{2} g^{2} i^{3} + \frac{1}{2} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a b c d^{2} g^{2} i^{3} + \frac{1}{10} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B b^{2} c d^{2} g^{2} i^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a^{2} d^{3} g^{2} i^{3} + \frac{1}{15} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B a b d^{3} g^{2} i^{3} + \frac{1}{180} \, {\left(60 \, x^{6} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} + \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} - \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} A B b^{2} d^{3} g^{2} i^{3} + A^{2} a^{2} c^{3} g^{2} i^{3} x - \frac{{\left(74 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 33 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 6 \, a^{5} c d^{5} g^{2} i^{3} + 2 \, {\left(3 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} b^{5} c^{6} - 18 \, {\left(2 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} a b^{4} c^{5} d + 9 \, {\left(10 \, g^{2} i^{3} \log\left(e\right) - 7 \, g^{2} i^{3}\right)} a^{2} b^{3} c^{4} d^{2}\right)} B^{2} \log\left(d x + c\right)}{180 \, b^{3} d^{3}} - \frac{{\left(b^{6} c^{6} g^{2} i^{3} - 6 \, a b^{5} c^{5} d g^{2} i^{3} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3} - 20 \, a^{3} b^{3} c^{3} d^{3} g^{2} i^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} g^{2} i^{3} - 6 \, a^{5} b c d^{5} g^{2} i^{3} + a^{6} d^{6} g^{2} i^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{30 \, b^{4} d^{3}} + \frac{60 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} \log\left(e\right)^{2} + 24 \, {\left({\left(9 \, g^{2} i^{3} \log\left(e\right)^{2} - g^{2} i^{3} \log\left(e\right)\right)} b^{6} c d^{5} + {\left(6 \, g^{2} i^{3} \log\left(e\right)^{2} + g^{2} i^{3} \log\left(e\right)\right)} a b^{5} d^{6}\right)} B^{2} x^{5} + 6 \, {\left({\left(45 \, g^{2} i^{3} \log\left(e\right)^{2} - 13 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} b^{6} c^{2} d^{4} + 2 \, {\left(45 \, g^{2} i^{3} \log\left(e\right)^{2} + 3 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} a b^{5} c d^{5} + {\left(15 \, g^{2} i^{3} \log\left(e\right)^{2} + 7 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} + 2 \, {\left({\left(60 \, g^{2} i^{3} \log\left(e\right)^{2} - 38 \, g^{2} i^{3} \log\left(e\right) + 9 \, g^{2} i^{3}\right)} b^{6} c^{3} d^{3} + 3 \, {\left(120 \, g^{2} i^{3} \log\left(e\right)^{2} - 14 \, g^{2} i^{3} \log\left(e\right) - 5 \, g^{2} i^{3}\right)} a b^{5} c^{2} d^{4} + 3 \, {\left(60 \, g^{2} i^{3} \log\left(e\right)^{2} + 26 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a^{2} b^{4} c d^{5} + {\left(2 \, g^{2} i^{3} \log\left(e\right) + 3 \, g^{2} i^{3}\right)} a^{3} b^{3} d^{6}\right)} B^{2} x^{3} - {\left({\left(6 \, g^{2} i^{3} \log\left(e\right) - 11 \, g^{2} i^{3}\right)} b^{6} c^{4} d^{2} - 2 \, {\left(180 \, g^{2} i^{3} \log\left(e\right)^{2} - 102 \, g^{2} i^{3} \log\left(e\right) + 5 \, g^{2} i^{3}\right)} a b^{5} c^{3} d^{3} - 60 \, {\left(9 \, g^{2} i^{3} \log\left(e\right)^{2} + 3 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} a^{2} b^{4} c^{2} d^{4} - 2 \, {\left(18 \, g^{2} i^{3} \log\left(e\right) + 23 \, g^{2} i^{3}\right)} a^{3} b^{3} c d^{5} + {\left(6 \, g^{2} i^{3} \log\left(e\right) + 7 \, g^{2} i^{3}\right)} a^{4} b^{2} d^{6}\right)} B^{2} x^{2} + 2 \, {\left(2 \, {\left(3 \, g^{2} i^{3} \log\left(e\right) - 4 \, g^{2} i^{3}\right)} b^{6} c^{5} d - 3 \, {\left(12 \, g^{2} i^{3} \log\left(e\right) - 17 \, g^{2} i^{3}\right)} a b^{5} c^{4} d^{2} + {\left(180 \, g^{2} i^{3} \log\left(e\right)^{2} - 30 \, g^{2} i^{3} \log\left(e\right) - 97 \, g^{2} i^{3}\right)} a^{2} b^{4} c^{3} d^{3} + {\left(90 \, g^{2} i^{3} \log\left(e\right) + 77 \, g^{2} i^{3}\right)} a^{3} b^{3} c^{2} d^{4} - 9 \, {\left(4 \, g^{2} i^{3} \log\left(e\right) + 3 \, g^{2} i^{3}\right)} a^{4} b^{2} c d^{5} + 2 \, {\left(3 \, g^{2} i^{3} \log\left(e\right) + 2 \, g^{2} i^{3}\right)} a^{5} b d^{6}\right)} B^{2} x + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} + 60 \, B^{2} a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} x + 12 \, {\left(3 \, b^{6} c d^{5} g^{2} i^{3} + 2 \, a b^{5} d^{6} g^{2} i^{3}\right)} B^{2} x^{5} + 15 \, {\left(3 \, b^{6} c^{2} d^{4} g^{2} i^{3} + 6 \, a b^{5} c d^{5} g^{2} i^{3} + a^{2} b^{4} d^{6} g^{2} i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{6} c^{3} d^{3} g^{2} i^{3} + 6 \, a b^{5} c^{2} d^{4} g^{2} i^{3} + 3 \, a^{2} b^{4} c d^{5} g^{2} i^{3}\right)} B^{2} x^{3} + 30 \, {\left(2 \, a b^{5} c^{3} d^{3} g^{2} i^{3} + 3 \, a^{2} b^{4} c^{2} d^{4} g^{2} i^{3}\right)} B^{2} x^{2} + {\left(20 \, a^{3} b^{3} c^{3} d^{3} g^{2} i^{3} - 15 \, a^{4} b^{2} c^{2} d^{4} g^{2} i^{3} + 6 \, a^{5} b c d^{5} g^{2} i^{3} - a^{6} d^{6} g^{2} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} + 60 \, B^{2} a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} x + 12 \, {\left(3 \, b^{6} c d^{5} g^{2} i^{3} + 2 \, a b^{5} d^{6} g^{2} i^{3}\right)} B^{2} x^{5} + 15 \, {\left(3 \, b^{6} c^{2} d^{4} g^{2} i^{3} + 6 \, a b^{5} c d^{5} g^{2} i^{3} + a^{2} b^{4} d^{6} g^{2} i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{6} c^{3} d^{3} g^{2} i^{3} + 6 \, a b^{5} c^{2} d^{4} g^{2} i^{3} + 3 \, a^{2} b^{4} c d^{5} g^{2} i^{3}\right)} B^{2} x^{3} + 30 \, {\left(2 \, a b^{5} c^{3} d^{3} g^{2} i^{3} + 3 \, a^{2} b^{4} c^{2} d^{4} g^{2} i^{3}\right)} B^{2} x^{2} + {\left(b^{6} c^{6} g^{2} i^{3} - 6 \, a b^{5} c^{5} d g^{2} i^{3} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(60 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} \log\left(e\right) + 12 \, {\left({\left(18 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} b^{6} c d^{5} + {\left(12 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a b^{5} d^{6}\right)} B^{2} x^{5} + 3 \, {\left({\left(90 \, g^{2} i^{3} \log\left(e\right) - 13 \, g^{2} i^{3}\right)} b^{6} c^{2} d^{4} + 6 \, {\left(30 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a b^{5} c d^{5} + {\left(30 \, g^{2} i^{3} \log\left(e\right) + 7 \, g^{2} i^{3}\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} + 2 \, {\left(a^{3} b^{3} d^{6} g^{2} i^{3} + {\left(60 \, g^{2} i^{3} \log\left(e\right) - 19 \, g^{2} i^{3}\right)} b^{6} c^{3} d^{3} + 3 \, {\left(120 \, g^{2} i^{3} \log\left(e\right) - 7 \, g^{2} i^{3}\right)} a b^{5} c^{2} d^{4} + 3 \, {\left(60 \, g^{2} i^{3} \log\left(e\right) + 13 \, g^{2} i^{3}\right)} a^{2} b^{4} c d^{5}\right)} B^{2} x^{3} - 3 \, {\left(b^{6} c^{4} d^{2} g^{2} i^{3} - 6 \, a^{3} b^{3} c d^{5} g^{2} i^{3} + a^{4} b^{2} d^{6} g^{2} i^{3} - 2 \, {\left(60 \, g^{2} i^{3} \log\left(e\right) - 17 \, g^{2} i^{3}\right)} a b^{5} c^{3} d^{3} - 30 \, {\left(6 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a^{2} b^{4} c^{2} d^{4}\right)} B^{2} x^{2} + 6 \, {\left(b^{6} c^{5} d g^{2} i^{3} - 6 \, a b^{5} c^{4} d^{2} g^{2} i^{3} + 15 \, a^{3} b^{3} c^{2} d^{4} g^{2} i^{3} - 6 \, a^{4} b^{2} c d^{5} g^{2} i^{3} + a^{5} b d^{6} g^{2} i^{3} + 5 \, {\left(12 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} a^{2} b^{4} c^{3} d^{3}\right)} B^{2} x + {\left(6 \, a b^{5} c^{5} d g^{2} i^{3} - 33 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3} + 2 \, {\left(60 \, g^{2} i^{3} \log\left(e\right) + 17 \, g^{2} i^{3}\right)} a^{3} b^{3} c^{3} d^{3} - 3 \, {\left(30 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a^{4} b^{2} c^{2} d^{4} + 6 \, {\left(6 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} a^{5} b c d^{5} - 2 \, {\left(3 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} a^{6} d^{6}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(60 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} \log\left(e\right) + 12 \, {\left({\left(18 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} b^{6} c d^{5} + {\left(12 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a b^{5} d^{6}\right)} B^{2} x^{5} + 3 \, {\left({\left(90 \, g^{2} i^{3} \log\left(e\right) - 13 \, g^{2} i^{3}\right)} b^{6} c^{2} d^{4} + 6 \, {\left(30 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a b^{5} c d^{5} + {\left(30 \, g^{2} i^{3} \log\left(e\right) + 7 \, g^{2} i^{3}\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} + 2 \, {\left(a^{3} b^{3} d^{6} g^{2} i^{3} + {\left(60 \, g^{2} i^{3} \log\left(e\right) - 19 \, g^{2} i^{3}\right)} b^{6} c^{3} d^{3} + 3 \, {\left(120 \, g^{2} i^{3} \log\left(e\right) - 7 \, g^{2} i^{3}\right)} a b^{5} c^{2} d^{4} + 3 \, {\left(60 \, g^{2} i^{3} \log\left(e\right) + 13 \, g^{2} i^{3}\right)} a^{2} b^{4} c d^{5}\right)} B^{2} x^{3} - 3 \, {\left(b^{6} c^{4} d^{2} g^{2} i^{3} - 6 \, a^{3} b^{3} c d^{5} g^{2} i^{3} + a^{4} b^{2} d^{6} g^{2} i^{3} - 2 \, {\left(60 \, g^{2} i^{3} \log\left(e\right) - 17 \, g^{2} i^{3}\right)} a b^{5} c^{3} d^{3} - 30 \, {\left(6 \, g^{2} i^{3} \log\left(e\right) + g^{2} i^{3}\right)} a^{2} b^{4} c^{2} d^{4}\right)} B^{2} x^{2} + 6 \, {\left(b^{6} c^{5} d g^{2} i^{3} - 6 \, a b^{5} c^{4} d^{2} g^{2} i^{3} + 15 \, a^{3} b^{3} c^{2} d^{4} g^{2} i^{3} - 6 \, a^{4} b^{2} c d^{5} g^{2} i^{3} + a^{5} b d^{6} g^{2} i^{3} + 5 \, {\left(12 \, g^{2} i^{3} \log\left(e\right) - g^{2} i^{3}\right)} a^{2} b^{4} c^{3} d^{3}\right)} B^{2} x + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} + 60 \, B^{2} a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} x + 12 \, {\left(3 \, b^{6} c d^{5} g^{2} i^{3} + 2 \, a b^{5} d^{6} g^{2} i^{3}\right)} B^{2} x^{5} + 15 \, {\left(3 \, b^{6} c^{2} d^{4} g^{2} i^{3} + 6 \, a b^{5} c d^{5} g^{2} i^{3} + a^{2} b^{4} d^{6} g^{2} i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{6} c^{3} d^{3} g^{2} i^{3} + 6 \, a b^{5} c^{2} d^{4} g^{2} i^{3} + 3 \, a^{2} b^{4} c d^{5} g^{2} i^{3}\right)} B^{2} x^{3} + 30 \, {\left(2 \, a b^{5} c^{3} d^{3} g^{2} i^{3} + 3 \, a^{2} b^{4} c^{2} d^{4} g^{2} i^{3}\right)} B^{2} x^{2} + {\left(20 \, a^{3} b^{3} c^{3} d^{3} g^{2} i^{3} - 15 \, a^{4} b^{2} c^{2} d^{4} g^{2} i^{3} + 6 \, a^{5} b c d^{5} g^{2} i^{3} - a^{6} d^{6} g^{2} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{360 \, b^{4} d^{3}}"," ",0,"1/6*A^2*b^2*d^3*g^2*i^3*x^6 + 3/5*A^2*b^2*c*d^2*g^2*i^3*x^5 + 2/5*A^2*a*b*d^3*g^2*i^3*x^5 + 3/4*A^2*b^2*c^2*d*g^2*i^3*x^4 + 3/2*A^2*a*b*c*d^2*g^2*i^3*x^4 + 1/4*A^2*a^2*d^3*g^2*i^3*x^4 + 1/3*A^2*b^2*c^3*g^2*i^3*x^3 + 2*A^2*a*b*c^2*d*g^2*i^3*x^3 + A^2*a^2*c*d^2*g^2*i^3*x^3 + A^2*a*b*c^3*g^2*i^3*x^2 + 3/2*A^2*a^2*c^2*d*g^2*i^3*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a^2*c^3*g^2*i^3 + 2*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a*b*c^3*g^2*i^3 + 1/3*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*b^2*c^3*g^2*i^3 + 3*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a^2*c^2*d*g^2*i^3 + 2*(2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a*b*c^2*d*g^2*i^3 + 1/4*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*b^2*c^2*d*g^2*i^3 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a^2*c*d^2*g^2*i^3 + 1/2*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a*b*c*d^2*g^2*i^3 + 1/10*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*b^2*c*d^2*g^2*i^3 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a^2*d^3*g^2*i^3 + 1/15*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*a*b*d^3*g^2*i^3 + 1/180*(60*x^6*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 60*a^6*log(b*x + a)/b^6 + 60*c^6*log(d*x + c)/d^6 - (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5))*A*B*b^2*d^3*g^2*i^3 + A^2*a^2*c^3*g^2*i^3*x - 1/180*(74*a^3*b^2*c^3*d^3*g^2*i^3 - 33*a^4*b*c^2*d^4*g^2*i^3 + 6*a^5*c*d^5*g^2*i^3 + 2*(3*g^2*i^3*log(e) - g^2*i^3)*b^5*c^6 - 18*(2*g^2*i^3*log(e) - g^2*i^3)*a*b^4*c^5*d + 9*(10*g^2*i^3*log(e) - 7*g^2*i^3)*a^2*b^3*c^4*d^2)*B^2*log(d*x + c)/(b^3*d^3) - 1/30*(b^6*c^6*g^2*i^3 - 6*a*b^5*c^5*d*g^2*i^3 + 15*a^2*b^4*c^4*d^2*g^2*i^3 - 20*a^3*b^3*c^3*d^3*g^2*i^3 + 15*a^4*b^2*c^2*d^4*g^2*i^3 - 6*a^5*b*c*d^5*g^2*i^3 + a^6*d^6*g^2*i^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^4*d^3) + 1/360*(60*B^2*b^6*d^6*g^2*i^3*x^6*log(e)^2 + 24*((9*g^2*i^3*log(e)^2 - g^2*i^3*log(e))*b^6*c*d^5 + (6*g^2*i^3*log(e)^2 + g^2*i^3*log(e))*a*b^5*d^6)*B^2*x^5 + 6*((45*g^2*i^3*log(e)^2 - 13*g^2*i^3*log(e) + g^2*i^3)*b^6*c^2*d^4 + 2*(45*g^2*i^3*log(e)^2 + 3*g^2*i^3*log(e) - g^2*i^3)*a*b^5*c*d^5 + (15*g^2*i^3*log(e)^2 + 7*g^2*i^3*log(e) + g^2*i^3)*a^2*b^4*d^6)*B^2*x^4 + 2*((60*g^2*i^3*log(e)^2 - 38*g^2*i^3*log(e) + 9*g^2*i^3)*b^6*c^3*d^3 + 3*(120*g^2*i^3*log(e)^2 - 14*g^2*i^3*log(e) - 5*g^2*i^3)*a*b^5*c^2*d^4 + 3*(60*g^2*i^3*log(e)^2 + 26*g^2*i^3*log(e) + g^2*i^3)*a^2*b^4*c*d^5 + (2*g^2*i^3*log(e) + 3*g^2*i^3)*a^3*b^3*d^6)*B^2*x^3 - ((6*g^2*i^3*log(e) - 11*g^2*i^3)*b^6*c^4*d^2 - 2*(180*g^2*i^3*log(e)^2 - 102*g^2*i^3*log(e) + 5*g^2*i^3)*a*b^5*c^3*d^3 - 60*(9*g^2*i^3*log(e)^2 + 3*g^2*i^3*log(e) - g^2*i^3)*a^2*b^4*c^2*d^4 - 2*(18*g^2*i^3*log(e) + 23*g^2*i^3)*a^3*b^3*c*d^5 + (6*g^2*i^3*log(e) + 7*g^2*i^3)*a^4*b^2*d^6)*B^2*x^2 + 2*(2*(3*g^2*i^3*log(e) - 4*g^2*i^3)*b^6*c^5*d - 3*(12*g^2*i^3*log(e) - 17*g^2*i^3)*a*b^5*c^4*d^2 + (180*g^2*i^3*log(e)^2 - 30*g^2*i^3*log(e) - 97*g^2*i^3)*a^2*b^4*c^3*d^3 + (90*g^2*i^3*log(e) + 77*g^2*i^3)*a^3*b^3*c^2*d^4 - 9*(4*g^2*i^3*log(e) + 3*g^2*i^3)*a^4*b^2*c*d^5 + 2*(3*g^2*i^3*log(e) + 2*g^2*i^3)*a^5*b*d^6)*B^2*x + 6*(10*B^2*b^6*d^6*g^2*i^3*x^6 + 60*B^2*a^2*b^4*c^3*d^3*g^2*i^3*x + 12*(3*b^6*c*d^5*g^2*i^3 + 2*a*b^5*d^6*g^2*i^3)*B^2*x^5 + 15*(3*b^6*c^2*d^4*g^2*i^3 + 6*a*b^5*c*d^5*g^2*i^3 + a^2*b^4*d^6*g^2*i^3)*B^2*x^4 + 20*(b^6*c^3*d^3*g^2*i^3 + 6*a*b^5*c^2*d^4*g^2*i^3 + 3*a^2*b^4*c*d^5*g^2*i^3)*B^2*x^3 + 30*(2*a*b^5*c^3*d^3*g^2*i^3 + 3*a^2*b^4*c^2*d^4*g^2*i^3)*B^2*x^2 + (20*a^3*b^3*c^3*d^3*g^2*i^3 - 15*a^4*b^2*c^2*d^4*g^2*i^3 + 6*a^5*b*c*d^5*g^2*i^3 - a^6*d^6*g^2*i^3)*B^2)*log(b*x + a)^2 + 6*(10*B^2*b^6*d^6*g^2*i^3*x^6 + 60*B^2*a^2*b^4*c^3*d^3*g^2*i^3*x + 12*(3*b^6*c*d^5*g^2*i^3 + 2*a*b^5*d^6*g^2*i^3)*B^2*x^5 + 15*(3*b^6*c^2*d^4*g^2*i^3 + 6*a*b^5*c*d^5*g^2*i^3 + a^2*b^4*d^6*g^2*i^3)*B^2*x^4 + 20*(b^6*c^3*d^3*g^2*i^3 + 6*a*b^5*c^2*d^4*g^2*i^3 + 3*a^2*b^4*c*d^5*g^2*i^3)*B^2*x^3 + 30*(2*a*b^5*c^3*d^3*g^2*i^3 + 3*a^2*b^4*c^2*d^4*g^2*i^3)*B^2*x^2 + (b^6*c^6*g^2*i^3 - 6*a*b^5*c^5*d*g^2*i^3 + 15*a^2*b^4*c^4*d^2*g^2*i^3)*B^2)*log(d*x + c)^2 + 2*(60*B^2*b^6*d^6*g^2*i^3*x^6*log(e) + 12*((18*g^2*i^3*log(e) - g^2*i^3)*b^6*c*d^5 + (12*g^2*i^3*log(e) + g^2*i^3)*a*b^5*d^6)*B^2*x^5 + 3*((90*g^2*i^3*log(e) - 13*g^2*i^3)*b^6*c^2*d^4 + 6*(30*g^2*i^3*log(e) + g^2*i^3)*a*b^5*c*d^5 + (30*g^2*i^3*log(e) + 7*g^2*i^3)*a^2*b^4*d^6)*B^2*x^4 + 2*(a^3*b^3*d^6*g^2*i^3 + (60*g^2*i^3*log(e) - 19*g^2*i^3)*b^6*c^3*d^3 + 3*(120*g^2*i^3*log(e) - 7*g^2*i^3)*a*b^5*c^2*d^4 + 3*(60*g^2*i^3*log(e) + 13*g^2*i^3)*a^2*b^4*c*d^5)*B^2*x^3 - 3*(b^6*c^4*d^2*g^2*i^3 - 6*a^3*b^3*c*d^5*g^2*i^3 + a^4*b^2*d^6*g^2*i^3 - 2*(60*g^2*i^3*log(e) - 17*g^2*i^3)*a*b^5*c^3*d^3 - 30*(6*g^2*i^3*log(e) + g^2*i^3)*a^2*b^4*c^2*d^4)*B^2*x^2 + 6*(b^6*c^5*d*g^2*i^3 - 6*a*b^5*c^4*d^2*g^2*i^3 + 15*a^3*b^3*c^2*d^4*g^2*i^3 - 6*a^4*b^2*c*d^5*g^2*i^3 + a^5*b*d^6*g^2*i^3 + 5*(12*g^2*i^3*log(e) - g^2*i^3)*a^2*b^4*c^3*d^3)*B^2*x + (6*a*b^5*c^5*d*g^2*i^3 - 33*a^2*b^4*c^4*d^2*g^2*i^3 + 2*(60*g^2*i^3*log(e) + 17*g^2*i^3)*a^3*b^3*c^3*d^3 - 3*(30*g^2*i^3*log(e) + g^2*i^3)*a^4*b^2*c^2*d^4 + 6*(6*g^2*i^3*log(e) - g^2*i^3)*a^5*b*c*d^5 - 2*(3*g^2*i^3*log(e) - g^2*i^3)*a^6*d^6)*B^2)*log(b*x + a) - 2*(60*B^2*b^6*d^6*g^2*i^3*x^6*log(e) + 12*((18*g^2*i^3*log(e) - g^2*i^3)*b^6*c*d^5 + (12*g^2*i^3*log(e) + g^2*i^3)*a*b^5*d^6)*B^2*x^5 + 3*((90*g^2*i^3*log(e) - 13*g^2*i^3)*b^6*c^2*d^4 + 6*(30*g^2*i^3*log(e) + g^2*i^3)*a*b^5*c*d^5 + (30*g^2*i^3*log(e) + 7*g^2*i^3)*a^2*b^4*d^6)*B^2*x^4 + 2*(a^3*b^3*d^6*g^2*i^3 + (60*g^2*i^3*log(e) - 19*g^2*i^3)*b^6*c^3*d^3 + 3*(120*g^2*i^3*log(e) - 7*g^2*i^3)*a*b^5*c^2*d^4 + 3*(60*g^2*i^3*log(e) + 13*g^2*i^3)*a^2*b^4*c*d^5)*B^2*x^3 - 3*(b^6*c^4*d^2*g^2*i^3 - 6*a^3*b^3*c*d^5*g^2*i^3 + a^4*b^2*d^6*g^2*i^3 - 2*(60*g^2*i^3*log(e) - 17*g^2*i^3)*a*b^5*c^3*d^3 - 30*(6*g^2*i^3*log(e) + g^2*i^3)*a^2*b^4*c^2*d^4)*B^2*x^2 + 6*(b^6*c^5*d*g^2*i^3 - 6*a*b^5*c^4*d^2*g^2*i^3 + 15*a^3*b^3*c^2*d^4*g^2*i^3 - 6*a^4*b^2*c*d^5*g^2*i^3 + a^5*b*d^6*g^2*i^3 + 5*(12*g^2*i^3*log(e) - g^2*i^3)*a^2*b^4*c^3*d^3)*B^2*x + 6*(10*B^2*b^6*d^6*g^2*i^3*x^6 + 60*B^2*a^2*b^4*c^3*d^3*g^2*i^3*x + 12*(3*b^6*c*d^5*g^2*i^3 + 2*a*b^5*d^6*g^2*i^3)*B^2*x^5 + 15*(3*b^6*c^2*d^4*g^2*i^3 + 6*a*b^5*c*d^5*g^2*i^3 + a^2*b^4*d^6*g^2*i^3)*B^2*x^4 + 20*(b^6*c^3*d^3*g^2*i^3 + 6*a*b^5*c^2*d^4*g^2*i^3 + 3*a^2*b^4*c*d^5*g^2*i^3)*B^2*x^3 + 30*(2*a*b^5*c^3*d^3*g^2*i^3 + 3*a^2*b^4*c^2*d^4*g^2*i^3)*B^2*x^2 + (20*a^3*b^3*c^3*d^3*g^2*i^3 - 15*a^4*b^2*c^2*d^4*g^2*i^3 + 6*a^5*b*c*d^5*g^2*i^3 - a^6*d^6*g^2*i^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d^3)","B",0
76,1,3218,0,2.412472," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{5} \, A^{2} b d^{3} g i^{3} x^{5} + \frac{3}{4} \, A^{2} b c d^{2} g i^{3} x^{4} + \frac{1}{4} \, A^{2} a d^{3} g i^{3} x^{4} + A^{2} b c^{2} d g i^{3} x^{3} + A^{2} a c d^{2} g i^{3} x^{3} + \frac{1}{2} \, A^{2} b c^{3} g i^{3} x^{2} + \frac{3}{2} \, A^{2} a c^{2} d g i^{3} x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B a c^{3} g i^{3} + {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B b c^{3} g i^{3} + 3 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B a c^{2} d g i^{3} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B b c^{2} d g i^{3} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B a c d^{2} g i^{3} + \frac{1}{4} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B b c d^{2} g i^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B a d^{3} g i^{3} + \frac{1}{30} \, {\left(12 \, x^{5} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} A B b d^{3} g i^{3} + A^{2} a c^{3} g i^{3} x - \frac{{\left(47 \, a^{2} b^{2} c^{3} d^{2} g i^{3} - 27 \, a^{3} b c^{2} d^{3} g i^{3} + 6 \, a^{4} c d^{4} g i^{3} - {\left(6 \, g i^{3} \log\left(e\right) - 5 \, g i^{3}\right)} b^{4} c^{5} + {\left(30 \, g i^{3} \log\left(e\right) - 31 \, g i^{3}\right)} a b^{3} c^{4} d\right)} B^{2} \log\left(d x + c\right)}{60 \, b^{3} d^{2}} + \frac{{\left(b^{5} c^{5} g i^{3} - 5 \, a b^{4} c^{4} d g i^{3} + 10 \, a^{2} b^{3} c^{3} d^{2} g i^{3} - 10 \, a^{3} b^{2} c^{2} d^{3} g i^{3} + 5 \, a^{4} b c d^{4} g i^{3} - a^{5} d^{5} g i^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{10 \, b^{4} d^{2}} + \frac{12 \, B^{2} b^{5} d^{5} g i^{3} x^{5} \log\left(e\right)^{2} + 3 \, {\left({\left(15 \, g i^{3} \log\left(e\right)^{2} - 2 \, g i^{3} \log\left(e\right)\right)} b^{5} c d^{4} + {\left(5 \, g i^{3} \log\left(e\right)^{2} + 2 \, g i^{3} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left({\left(30 \, g i^{3} \log\left(e\right)^{2} - 11 \, g i^{3} \log\left(e\right) + g i^{3}\right)} b^{5} c^{2} d^{3} + 2 \, {\left(15 \, g i^{3} \log\left(e\right)^{2} + 5 \, g i^{3} \log\left(e\right) - g i^{3}\right)} a b^{4} c d^{4} + {\left(g i^{3} \log\left(e\right) + g i^{3}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + {\left({\left(30 \, g i^{3} \log\left(e\right)^{2} - 27 \, g i^{3} \log\left(e\right) + 8 \, g i^{3}\right)} b^{5} c^{3} d^{2} + 3 \, {\left(30 \, g i^{3} \log\left(e\right)^{2} + 5 \, g i^{3} \log\left(e\right) - 6 \, g i^{3}\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(5 \, g i^{3} \log\left(e\right) + 4 \, g i^{3}\right)} a^{2} b^{3} c d^{4} - {\left(3 \, g i^{3} \log\left(e\right) + 2 \, g i^{3}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - {\left({\left(6 \, g i^{3} \log\left(e\right) - 11 \, g i^{3}\right)} b^{5} c^{4} d - 2 \, {\left(30 \, g i^{3} \log\left(e\right)^{2} - 15 \, g i^{3} \log\left(e\right) - 14 \, g i^{3}\right)} a b^{4} c^{3} d^{2} - 12 \, {\left(5 \, g i^{3} \log\left(e\right) + 2 \, g i^{3}\right)} a^{2} b^{3} c^{2} d^{3} + 2 \, {\left(15 \, g i^{3} \log\left(e\right) + 4 \, g i^{3}\right)} a^{3} b^{2} c d^{4} - {\left(6 \, g i^{3} \log\left(e\right) + g i^{3}\right)} a^{4} b d^{5}\right)} B^{2} x + 3 \, {\left(4 \, B^{2} b^{5} d^{5} g i^{3} x^{5} + 20 \, B^{2} a b^{4} c^{3} d^{2} g i^{3} x + 5 \, {\left(3 \, b^{5} c d^{4} g i^{3} + a b^{4} d^{5} g i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} g i^{3} + a b^{4} c d^{4} g i^{3}\right)} B^{2} x^{3} + 10 \, {\left(b^{5} c^{3} d^{2} g i^{3} + 3 \, a b^{4} c^{2} d^{3} g i^{3}\right)} B^{2} x^{2} + {\left(10 \, a^{2} b^{3} c^{3} d^{2} g i^{3} - 10 \, a^{3} b^{2} c^{2} d^{3} g i^{3} + 5 \, a^{4} b c d^{4} g i^{3} - a^{5} d^{5} g i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(4 \, B^{2} b^{5} d^{5} g i^{3} x^{5} + 20 \, B^{2} a b^{4} c^{3} d^{2} g i^{3} x + 5 \, {\left(3 \, b^{5} c d^{4} g i^{3} + a b^{4} d^{5} g i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} g i^{3} + a b^{4} c d^{4} g i^{3}\right)} B^{2} x^{3} + 10 \, {\left(b^{5} c^{3} d^{2} g i^{3} + 3 \, a b^{4} c^{2} d^{3} g i^{3}\right)} B^{2} x^{2} - {\left(b^{5} c^{5} g i^{3} - 5 \, a b^{4} c^{4} d g i^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + {\left(24 \, B^{2} b^{5} d^{5} g i^{3} x^{5} \log\left(e\right) + 6 \, {\left({\left(15 \, g i^{3} \log\left(e\right) - g i^{3}\right)} b^{5} c d^{4} + {\left(5 \, g i^{3} \log\left(e\right) + g i^{3}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left(a^{2} b^{3} d^{5} g i^{3} + {\left(60 \, g i^{3} \log\left(e\right) - 11 \, g i^{3}\right)} b^{5} c^{2} d^{3} + 10 \, {\left(6 \, g i^{3} \log\left(e\right) + g i^{3}\right)} a b^{4} c d^{4}\right)} B^{2} x^{3} + 3 \, {\left(5 \, a^{2} b^{3} c d^{4} g i^{3} - a^{3} b^{2} d^{5} g i^{3} + {\left(20 \, g i^{3} \log\left(e\right) - 9 \, g i^{3}\right)} b^{5} c^{3} d^{2} + 5 \, {\left(12 \, g i^{3} \log\left(e\right) + g i^{3}\right)} a b^{4} c^{2} d^{3}\right)} B^{2} x^{2} - 6 \, {\left(b^{5} c^{4} d g i^{3} - 10 \, a^{2} b^{3} c^{2} d^{3} g i^{3} + 5 \, a^{3} b^{2} c d^{4} g i^{3} - a^{4} b d^{5} g i^{3} - 5 \, {\left(4 \, g i^{3} \log\left(e\right) - g i^{3}\right)} a b^{4} c^{3} d^{2}\right)} B^{2} x - {\left(6 \, a b^{4} c^{4} d g i^{3} - 3 \, {\left(20 \, g i^{3} \log\left(e\right) - g i^{3}\right)} a^{2} b^{3} c^{3} d^{2} + {\left(60 \, g i^{3} \log\left(e\right) - 23 \, g i^{3}\right)} a^{3} b^{2} c^{2} d^{3} - {\left(30 \, g i^{3} \log\left(e\right) - 19 \, g i^{3}\right)} a^{4} b c d^{4} + {\left(6 \, g i^{3} \log\left(e\right) - 5 \, g i^{3}\right)} a^{5} d^{5}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(24 \, B^{2} b^{5} d^{5} g i^{3} x^{5} \log\left(e\right) + 6 \, {\left({\left(15 \, g i^{3} \log\left(e\right) - g i^{3}\right)} b^{5} c d^{4} + {\left(5 \, g i^{3} \log\left(e\right) + g i^{3}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left(a^{2} b^{3} d^{5} g i^{3} + {\left(60 \, g i^{3} \log\left(e\right) - 11 \, g i^{3}\right)} b^{5} c^{2} d^{3} + 10 \, {\left(6 \, g i^{3} \log\left(e\right) + g i^{3}\right)} a b^{4} c d^{4}\right)} B^{2} x^{3} + 3 \, {\left(5 \, a^{2} b^{3} c d^{4} g i^{3} - a^{3} b^{2} d^{5} g i^{3} + {\left(20 \, g i^{3} \log\left(e\right) - 9 \, g i^{3}\right)} b^{5} c^{3} d^{2} + 5 \, {\left(12 \, g i^{3} \log\left(e\right) + g i^{3}\right)} a b^{4} c^{2} d^{3}\right)} B^{2} x^{2} - 6 \, {\left(b^{5} c^{4} d g i^{3} - 10 \, a^{2} b^{3} c^{2} d^{3} g i^{3} + 5 \, a^{3} b^{2} c d^{4} g i^{3} - a^{4} b d^{5} g i^{3} - 5 \, {\left(4 \, g i^{3} \log\left(e\right) - g i^{3}\right)} a b^{4} c^{3} d^{2}\right)} B^{2} x + 6 \, {\left(4 \, B^{2} b^{5} d^{5} g i^{3} x^{5} + 20 \, B^{2} a b^{4} c^{3} d^{2} g i^{3} x + 5 \, {\left(3 \, b^{5} c d^{4} g i^{3} + a b^{4} d^{5} g i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} g i^{3} + a b^{4} c d^{4} g i^{3}\right)} B^{2} x^{3} + 10 \, {\left(b^{5} c^{3} d^{2} g i^{3} + 3 \, a b^{4} c^{2} d^{3} g i^{3}\right)} B^{2} x^{2} + {\left(10 \, a^{2} b^{3} c^{3} d^{2} g i^{3} - 10 \, a^{3} b^{2} c^{2} d^{3} g i^{3} + 5 \, a^{4} b c d^{4} g i^{3} - a^{5} d^{5} g i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{60 \, b^{4} d^{2}}"," ",0,"1/5*A^2*b*d^3*g*i^3*x^5 + 3/4*A^2*b*c*d^2*g*i^3*x^4 + 1/4*A^2*a*d^3*g*i^3*x^4 + A^2*b*c^2*d*g*i^3*x^3 + A^2*a*c*d^2*g*i^3*x^3 + 1/2*A^2*b*c^3*g*i^3*x^2 + 3/2*A^2*a*c^2*d*g*i^3*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*a*c^3*g*i^3 + (x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*b*c^3*g*i^3 + 3*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*a*c^2*d*g*i^3 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*b*c^2*d*g*i^3 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*a*c*d^2*g*i^3 + 1/4*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*b*c*d^2*g*i^3 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*a*d^3*g*i^3 + 1/30*(12*x^5*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4))*A*B*b*d^3*g*i^3 + A^2*a*c^3*g*i^3*x - 1/60*(47*a^2*b^2*c^3*d^2*g*i^3 - 27*a^3*b*c^2*d^3*g*i^3 + 6*a^4*c*d^4*g*i^3 - (6*g*i^3*log(e) - 5*g*i^3)*b^4*c^5 + (30*g*i^3*log(e) - 31*g*i^3)*a*b^3*c^4*d)*B^2*log(d*x + c)/(b^3*d^2) + 1/10*(b^5*c^5*g*i^3 - 5*a*b^4*c^4*d*g*i^3 + 10*a^2*b^3*c^3*d^2*g*i^3 - 10*a^3*b^2*c^2*d^3*g*i^3 + 5*a^4*b*c*d^4*g*i^3 - a^5*d^5*g*i^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^4*d^2) + 1/60*(12*B^2*b^5*d^5*g*i^3*x^5*log(e)^2 + 3*((15*g*i^3*log(e)^2 - 2*g*i^3*log(e))*b^5*c*d^4 + (5*g*i^3*log(e)^2 + 2*g*i^3*log(e))*a*b^4*d^5)*B^2*x^4 + 2*((30*g*i^3*log(e)^2 - 11*g*i^3*log(e) + g*i^3)*b^5*c^2*d^3 + 2*(15*g*i^3*log(e)^2 + 5*g*i^3*log(e) - g*i^3)*a*b^4*c*d^4 + (g*i^3*log(e) + g*i^3)*a^2*b^3*d^5)*B^2*x^3 + ((30*g*i^3*log(e)^2 - 27*g*i^3*log(e) + 8*g*i^3)*b^5*c^3*d^2 + 3*(30*g*i^3*log(e)^2 + 5*g*i^3*log(e) - 6*g*i^3)*a*b^4*c^2*d^3 + 3*(5*g*i^3*log(e) + 4*g*i^3)*a^2*b^3*c*d^4 - (3*g*i^3*log(e) + 2*g*i^3)*a^3*b^2*d^5)*B^2*x^2 - ((6*g*i^3*log(e) - 11*g*i^3)*b^5*c^4*d - 2*(30*g*i^3*log(e)^2 - 15*g*i^3*log(e) - 14*g*i^3)*a*b^4*c^3*d^2 - 12*(5*g*i^3*log(e) + 2*g*i^3)*a^2*b^3*c^2*d^3 + 2*(15*g*i^3*log(e) + 4*g*i^3)*a^3*b^2*c*d^4 - (6*g*i^3*log(e) + g*i^3)*a^4*b*d^5)*B^2*x + 3*(4*B^2*b^5*d^5*g*i^3*x^5 + 20*B^2*a*b^4*c^3*d^2*g*i^3*x + 5*(3*b^5*c*d^4*g*i^3 + a*b^4*d^5*g*i^3)*B^2*x^4 + 20*(b^5*c^2*d^3*g*i^3 + a*b^4*c*d^4*g*i^3)*B^2*x^3 + 10*(b^5*c^3*d^2*g*i^3 + 3*a*b^4*c^2*d^3*g*i^3)*B^2*x^2 + (10*a^2*b^3*c^3*d^2*g*i^3 - 10*a^3*b^2*c^2*d^3*g*i^3 + 5*a^4*b*c*d^4*g*i^3 - a^5*d^5*g*i^3)*B^2)*log(b*x + a)^2 + 3*(4*B^2*b^5*d^5*g*i^3*x^5 + 20*B^2*a*b^4*c^3*d^2*g*i^3*x + 5*(3*b^5*c*d^4*g*i^3 + a*b^4*d^5*g*i^3)*B^2*x^4 + 20*(b^5*c^2*d^3*g*i^3 + a*b^4*c*d^4*g*i^3)*B^2*x^3 + 10*(b^5*c^3*d^2*g*i^3 + 3*a*b^4*c^2*d^3*g*i^3)*B^2*x^2 - (b^5*c^5*g*i^3 - 5*a*b^4*c^4*d*g*i^3)*B^2)*log(d*x + c)^2 + (24*B^2*b^5*d^5*g*i^3*x^5*log(e) + 6*((15*g*i^3*log(e) - g*i^3)*b^5*c*d^4 + (5*g*i^3*log(e) + g*i^3)*a*b^4*d^5)*B^2*x^4 + 2*(a^2*b^3*d^5*g*i^3 + (60*g*i^3*log(e) - 11*g*i^3)*b^5*c^2*d^3 + 10*(6*g*i^3*log(e) + g*i^3)*a*b^4*c*d^4)*B^2*x^3 + 3*(5*a^2*b^3*c*d^4*g*i^3 - a^3*b^2*d^5*g*i^3 + (20*g*i^3*log(e) - 9*g*i^3)*b^5*c^3*d^2 + 5*(12*g*i^3*log(e) + g*i^3)*a*b^4*c^2*d^3)*B^2*x^2 - 6*(b^5*c^4*d*g*i^3 - 10*a^2*b^3*c^2*d^3*g*i^3 + 5*a^3*b^2*c*d^4*g*i^3 - a^4*b*d^5*g*i^3 - 5*(4*g*i^3*log(e) - g*i^3)*a*b^4*c^3*d^2)*B^2*x - (6*a*b^4*c^4*d*g*i^3 - 3*(20*g*i^3*log(e) - g*i^3)*a^2*b^3*c^3*d^2 + (60*g*i^3*log(e) - 23*g*i^3)*a^3*b^2*c^2*d^3 - (30*g*i^3*log(e) - 19*g*i^3)*a^4*b*c*d^4 + (6*g*i^3*log(e) - 5*g*i^3)*a^5*d^5)*B^2)*log(b*x + a) - (24*B^2*b^5*d^5*g*i^3*x^5*log(e) + 6*((15*g*i^3*log(e) - g*i^3)*b^5*c*d^4 + (5*g*i^3*log(e) + g*i^3)*a*b^4*d^5)*B^2*x^4 + 2*(a^2*b^3*d^5*g*i^3 + (60*g*i^3*log(e) - 11*g*i^3)*b^5*c^2*d^3 + 10*(6*g*i^3*log(e) + g*i^3)*a*b^4*c*d^4)*B^2*x^3 + 3*(5*a^2*b^3*c*d^4*g*i^3 - a^3*b^2*d^5*g*i^3 + (20*g*i^3*log(e) - 9*g*i^3)*b^5*c^3*d^2 + 5*(12*g*i^3*log(e) + g*i^3)*a*b^4*c^2*d^3)*B^2*x^2 - 6*(b^5*c^4*d*g*i^3 - 10*a^2*b^3*c^2*d^3*g*i^3 + 5*a^3*b^2*c*d^4*g*i^3 - a^4*b*d^5*g*i^3 - 5*(4*g*i^3*log(e) - g*i^3)*a*b^4*c^3*d^2)*B^2*x + 6*(4*B^2*b^5*d^5*g*i^3*x^5 + 20*B^2*a*b^4*c^3*d^2*g*i^3*x + 5*(3*b^5*c*d^4*g*i^3 + a*b^4*d^5*g*i^3)*B^2*x^4 + 20*(b^5*c^2*d^3*g*i^3 + a*b^4*c*d^4*g*i^3)*B^2*x^3 + 10*(b^5*c^3*d^2*g*i^3 + 3*a*b^4*c^2*d^3*g*i^3)*B^2*x^2 + (10*a^2*b^3*c^3*d^2*g*i^3 - 10*a^3*b^2*c^2*d^3*g*i^3 + 5*a^4*b*c*d^4*g*i^3 - a^5*d^5*g*i^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d^2)","B",0
77,1,1789,0,2.185531," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} d^{3} i^{3} x^{4} + A^{2} c d^{2} i^{3} x^{3} + \frac{3}{2} \, A^{2} c^{2} d i^{3} x^{2} + 2 \, {\left(x \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} A B c^{3} i^{3} + 3 \, {\left(x^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{{\left(b c - a d\right)} x}{b d}\right)} A B c^{2} d i^{3} + {\left(2 \, x^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} A B c d^{2} i^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} + \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} - \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} A B d^{3} i^{3} + A^{2} c^{3} i^{3} x - \frac{{\left(26 \, a b^{2} c^{3} d i^{3} - 21 \, a^{2} b c^{2} d^{2} i^{3} + 6 \, a^{3} c d^{3} i^{3} + {\left(6 \, i^{3} \log\left(e\right) - 11 \, i^{3}\right)} b^{3} c^{4}\right)} B^{2} \log\left(d x + c\right)}{12 \, b^{3} d} - \frac{{\left(b^{4} c^{4} i^{3} - 4 \, a b^{3} c^{3} d i^{3} + 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} - 4 \, a^{3} b c d^{3} i^{3} + a^{4} d^{4} i^{3}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{2 \, b^{4} d} + \frac{3 \, B^{2} b^{4} d^{4} i^{3} x^{4} \log\left(e\right)^{2} + 2 \, {\left(a b^{3} d^{4} i^{3} \log\left(e\right) + {\left(6 \, i^{3} \log\left(e\right)^{2} - i^{3} \log\left(e\right)\right)} b^{4} c d^{3}\right)} B^{2} x^{3} + {\left({\left(18 \, i^{3} \log\left(e\right)^{2} - 9 \, i^{3} \log\left(e\right) + i^{3}\right)} b^{4} c^{2} d^{2} + 2 \, {\left(6 \, i^{3} \log\left(e\right) - i^{3}\right)} a b^{3} c d^{3} - {\left(3 \, i^{3} \log\left(e\right) - i^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + {\left({\left(12 \, i^{3} \log\left(e\right)^{2} - 18 \, i^{3} \log\left(e\right) + 7 \, i^{3}\right)} b^{4} c^{3} d + {\left(36 \, i^{3} \log\left(e\right) - 19 \, i^{3}\right)} a b^{3} c^{2} d^{2} - {\left(24 \, i^{3} \log\left(e\right) - 17 \, i^{3}\right)} a^{2} b^{2} c d^{3} + {\left(6 \, i^{3} \log\left(e\right) - 5 \, i^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + {\left(4 \, a b^{3} c^{3} d i^{3} - 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 4 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left(d x + c\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} i^{3} x^{4} \log\left(e\right) + 2 \, {\left(a b^{3} d^{4} i^{3} + {\left(12 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{4} c d^{3}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} c d^{3} i^{3} - a^{2} b^{2} d^{4} i^{3} + 3 \, {\left(4 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{4} c^{2} d^{2}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} c^{2} d^{2} i^{3} - 4 \, a^{2} b^{2} c d^{3} i^{3} + a^{3} b d^{4} i^{3} + {\left(4 \, i^{3} \log\left(e\right) - 3 \, i^{3}\right)} b^{4} c^{3} d\right)} B^{2} x + {\left(6 \, {\left(4 \, i^{3} \log\left(e\right) - 3 \, i^{3}\right)} a b^{3} c^{3} d - 9 \, {\left(4 \, i^{3} \log\left(e\right) - 5 \, i^{3}\right)} a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(12 \, i^{3} \log\left(e\right) - 19 \, i^{3}\right)} a^{3} b c d^{3} - {\left(6 \, i^{3} \log\left(e\right) - 11 \, i^{3}\right)} a^{4} d^{4}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(6 \, B^{2} b^{4} d^{4} i^{3} x^{4} \log\left(e\right) + 2 \, {\left(a b^{3} d^{4} i^{3} + {\left(12 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{4} c d^{3}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} c d^{3} i^{3} - a^{2} b^{2} d^{4} i^{3} + 3 \, {\left(4 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{4} c^{2} d^{2}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} c^{2} d^{2} i^{3} - 4 \, a^{2} b^{2} c d^{3} i^{3} + a^{3} b d^{4} i^{3} + {\left(4 \, i^{3} \log\left(e\right) - 3 \, i^{3}\right)} b^{4} c^{3} d\right)} B^{2} x + 6 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + {\left(4 \, a b^{3} c^{3} d i^{3} - 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 4 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b^{4} d}"," ",0,"1/4*A^2*d^3*i^3*x^4 + A^2*c*d^2*i^3*x^3 + 3/2*A^2*c^2*d*i^3*x^2 + 2*(x*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + a*log(b*x + a)/b - c*log(d*x + c)/d)*A*B*c^3*i^3 + 3*(x^2*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - a^2*log(b*x + a)/b^2 + c^2*log(d*x + c)/d^2 - (b*c - a*d)*x/(b*d))*A*B*c^2*d*i^3 + (2*x^3*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2))*A*B*c*d^2*i^3 + 1/12*(6*x^4*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 6*a^4*log(b*x + a)/b^4 + 6*c^4*log(d*x + c)/d^4 - (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3))*A*B*d^3*i^3 + A^2*c^3*i^3*x - 1/12*(26*a*b^2*c^3*d*i^3 - 21*a^2*b*c^2*d^2*i^3 + 6*a^3*c*d^3*i^3 + (6*i^3*log(e) - 11*i^3)*b^3*c^4)*B^2*log(d*x + c)/(b^3*d) - 1/2*(b^4*c^4*i^3 - 4*a*b^3*c^3*d*i^3 + 6*a^2*b^2*c^2*d^2*i^3 - 4*a^3*b*c*d^3*i^3 + a^4*d^4*i^3)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^4*d) + 1/12*(3*B^2*b^4*d^4*i^3*x^4*log(e)^2 + 2*(a*b^3*d^4*i^3*log(e) + (6*i^3*log(e)^2 - i^3*log(e))*b^4*c*d^3)*B^2*x^3 + ((18*i^3*log(e)^2 - 9*i^3*log(e) + i^3)*b^4*c^2*d^2 + 2*(6*i^3*log(e) - i^3)*a*b^3*c*d^3 - (3*i^3*log(e) - i^3)*a^2*b^2*d^4)*B^2*x^2 + ((12*i^3*log(e)^2 - 18*i^3*log(e) + 7*i^3)*b^4*c^3*d + (36*i^3*log(e) - 19*i^3)*a*b^3*c^2*d^2 - (24*i^3*log(e) - 17*i^3)*a^2*b^2*c*d^3 + (6*i^3*log(e) - 5*i^3)*a^3*b*d^4)*B^2*x + 3*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + (4*a*b^3*c^3*d*i^3 - 6*a^2*b^2*c^2*d^2*i^3 + 4*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B^2)*log(b*x + a)^2 + 3*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log(d*x + c)^2 + (6*B^2*b^4*d^4*i^3*x^4*log(e) + 2*(a*b^3*d^4*i^3 + (12*i^3*log(e) - i^3)*b^4*c*d^3)*B^2*x^3 + 3*(4*a*b^3*c*d^3*i^3 - a^2*b^2*d^4*i^3 + 3*(4*i^3*log(e) - i^3)*b^4*c^2*d^2)*B^2*x^2 + 6*(6*a*b^3*c^2*d^2*i^3 - 4*a^2*b^2*c*d^3*i^3 + a^3*b*d^4*i^3 + (4*i^3*log(e) - 3*i^3)*b^4*c^3*d)*B^2*x + (6*(4*i^3*log(e) - 3*i^3)*a*b^3*c^3*d - 9*(4*i^3*log(e) - 5*i^3)*a^2*b^2*c^2*d^2 + 2*(12*i^3*log(e) - 19*i^3)*a^3*b*c*d^3 - (6*i^3*log(e) - 11*i^3)*a^4*d^4)*B^2)*log(b*x + a) - (6*B^2*b^4*d^4*i^3*x^4*log(e) + 2*(a*b^3*d^4*i^3 + (12*i^3*log(e) - i^3)*b^4*c*d^3)*B^2*x^3 + 3*(4*a*b^3*c*d^3*i^3 - a^2*b^2*d^4*i^3 + 3*(4*i^3*log(e) - i^3)*b^4*c^2*d^2)*B^2*x^2 + 6*(6*a*b^3*c^2*d^2*i^3 - 4*a^2*b^2*c*d^3*i^3 + a^3*b*d^4*i^3 + (4*i^3*log(e) - 3*i^3)*b^4*c^3*d)*B^2*x + 6*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + (4*a*b^3*c^3*d*i^3 - 6*a^2*b^2*c^2*d^2*i^3 + 4*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d)","B",0
78,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g),x, algorithm=""maxima"")","3 \, A^{2} c^{2} d i^{3} {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} - \frac{1}{6} \, A^{2} d^{3} i^{3} {\left(\frac{6 \, a^{3} \log\left(b x + a\right)}{b^{4} g} - \frac{2 \, b^{2} x^{3} - 3 \, a b x^{2} + 6 \, a^{2} x}{b^{3} g}\right)} + \frac{3}{2} \, A^{2} c d^{2} i^{3} {\left(\frac{2 \, a^{2} \log\left(b x + a\right)}{b^{3} g} + \frac{b x^{2} - 2 \, a x}{b^{2} g}\right)} + \frac{A^{2} c^{3} i^{3} \log\left(b g x + a g\right)}{b g} + \frac{{\left(2 \, B^{2} b^{3} d^{3} i^{3} x^{3} + 3 \, {\left(3 \, b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B^{2} x^{2} + 6 \, {\left(3 \, b^{3} c^{2} d i^{3} - 3 \, a b^{2} c d^{2} i^{3} + a^{2} b d^{3} i^{3}\right)} B^{2} x + 6 \, {\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B^{2} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2}}{6 \, b^{4} g} - \int -\frac{3 \, B^{2} b^{4} c^{4} i^{3} \log\left(e\right)^{2} + 6 \, A B b^{4} c^{4} i^{3} \log\left(e\right) + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} d^{4} i^{3} \log\left(e\right)\right)} x^{4} + 12 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c d^{3} i^{3} \log\left(e\right)\right)} x^{3} + 18 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c^{2} d^{2} i^{3} \log\left(e\right)\right)} x^{2} + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(B^{2} b^{4} c^{3} d i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c^{3} d i^{3} \log\left(e\right)\right)} x + 6 \, {\left(B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + A B b^{4} c^{4} i^{3} + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right) + A B b^{4} d^{4} i^{3}\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right) + A B b^{4} c d^{3} i^{3}\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right) + A B b^{4} c^{2} d^{2} i^{3}\right)} x^{2} + 4 \, {\left(B^{2} b^{4} c^{3} d i^{3} \log\left(e\right) + A B b^{4} c^{3} d i^{3}\right)} x\right)} \log\left(b x + a\right) - {\left(6 \, B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + 6 \, A B b^{4} c^{4} i^{3} + 2 \, {\left(3 \, A B b^{4} d^{4} i^{3} + {\left(3 \, i^{3} \log\left(e\right) + i^{3}\right)} B^{2} b^{4} d^{4}\right)} x^{4} + {\left(24 \, A B b^{4} c d^{3} i^{3} - {\left(a b^{3} d^{4} i^{3} - 3 \, {\left(8 \, i^{3} \log\left(e\right) + 3 \, i^{3}\right)} b^{4} c d^{3}\right)} B^{2}\right)} x^{3} + 3 \, {\left(12 \, A B b^{4} c^{2} d^{2} i^{3} - {\left(3 \, a b^{3} c d^{3} i^{3} - a^{2} b^{2} d^{4} i^{3} - 6 \, {\left(2 \, i^{3} \log\left(e\right) + i^{3}\right)} b^{4} c^{2} d^{2}\right)} B^{2}\right)} x^{2} + 6 \, {\left(4 \, A B b^{4} c^{3} d i^{3} + {\left(4 \, b^{4} c^{3} d i^{3} \log\left(e\right) + 3 \, a b^{3} c^{2} d^{2} i^{3} - 3 \, a^{2} b^{2} c d^{3} i^{3} + a^{3} b d^{4} i^{3}\right)} B^{2}\right)} x + 6 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + {\left(5 \, b^{4} c^{3} d i^{3} - 3 \, a b^{3} c^{2} d^{2} i^{3} + 3 \, a^{2} b^{2} c d^{3} i^{3} - a^{3} b d^{4} i^{3}\right)} B^{2} x + {\left(b^{4} c^{4} i^{3} + a b^{3} c^{3} d i^{3} - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 3 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, {\left(b^{5} d g x^{2} + a b^{4} c g + {\left(b^{5} c g + a b^{4} d g\right)} x\right)}}\,{d x}"," ",0,"3*A^2*c^2*d*i^3*(x/(b*g) - a*log(b*x + a)/(b^2*g)) - 1/6*A^2*d^3*i^3*(6*a^3*log(b*x + a)/(b^4*g) - (2*b^2*x^3 - 3*a*b*x^2 + 6*a^2*x)/(b^3*g)) + 3/2*A^2*c*d^2*i^3*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2*g)) + A^2*c^3*i^3*log(b*g*x + a*g)/(b*g) + 1/6*(2*B^2*b^3*d^3*i^3*x^3 + 3*(3*b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B^2*x^2 + 6*(3*b^3*c^2*d*i^3 - 3*a*b^2*c*d^2*i^3 + a^2*b*d^3*i^3)*B^2*x + 6*(b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B^2*log(b*x + a))*log(d*x + c)^2/(b^4*g) - integrate(-1/3*(3*B^2*b^4*c^4*i^3*log(e)^2 + 6*A*B*b^4*c^4*i^3*log(e) + 3*(B^2*b^4*d^4*i^3*log(e)^2 + 2*A*B*b^4*d^4*i^3*log(e))*x^4 + 12*(B^2*b^4*c*d^3*i^3*log(e)^2 + 2*A*B*b^4*c*d^3*i^3*log(e))*x^3 + 18*(B^2*b^4*c^2*d^2*i^3*log(e)^2 + 2*A*B*b^4*c^2*d^2*i^3*log(e))*x^2 + 3*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log(b*x + a)^2 + 12*(B^2*b^4*c^3*d*i^3*log(e)^2 + 2*A*B*b^4*c^3*d*i^3*log(e))*x + 6*(B^2*b^4*c^4*i^3*log(e) + A*B*b^4*c^4*i^3 + (B^2*b^4*d^4*i^3*log(e) + A*B*b^4*d^4*i^3)*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e) + A*B*b^4*c*d^3*i^3)*x^3 + 6*(B^2*b^4*c^2*d^2*i^3*log(e) + A*B*b^4*c^2*d^2*i^3)*x^2 + 4*(B^2*b^4*c^3*d*i^3*log(e) + A*B*b^4*c^3*d*i^3)*x)*log(b*x + a) - (6*B^2*b^4*c^4*i^3*log(e) + 6*A*B*b^4*c^4*i^3 + 2*(3*A*B*b^4*d^4*i^3 + (3*i^3*log(e) + i^3)*B^2*b^4*d^4)*x^4 + (24*A*B*b^4*c*d^3*i^3 - (a*b^3*d^4*i^3 - 3*(8*i^3*log(e) + 3*i^3)*b^4*c*d^3)*B^2)*x^3 + 3*(12*A*B*b^4*c^2*d^2*i^3 - (3*a*b^3*c*d^3*i^3 - a^2*b^2*d^4*i^3 - 6*(2*i^3*log(e) + i^3)*b^4*c^2*d^2)*B^2)*x^2 + 6*(4*A*B*b^4*c^3*d*i^3 + (4*b^4*c^3*d*i^3*log(e) + 3*a*b^3*c^2*d^2*i^3 - 3*a^2*b^2*c*d^3*i^3 + a^3*b*d^4*i^3)*B^2)*x + 6*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + (5*b^4*c^3*d*i^3 - 3*a*b^3*c^2*d^2*i^3 + 3*a^2*b^2*c*d^3*i^3 - a^3*b*d^4*i^3)*B^2*x + (b^4*c^4*i^3 + a*b^3*c^3*d*i^3 - 3*a^2*b^2*c^2*d^2*i^3 + 3*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^5*d*g*x^2 + a*b^4*c*g + (b^5*c*g + a*b^4*d*g)*x), x)","F",0
79,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-3 \, A^{2} {\left(\frac{a^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \frac{x}{b^{2} g^{2}} + \frac{2 \, a \log\left(b x + a\right)}{b^{3} g^{2}}\right)} c d^{2} i^{3} + \frac{1}{2} \, {\left(\frac{2 \, a^{3}}{b^{5} g^{2} x + a b^{4} g^{2}} + \frac{6 \, a^{2} \log\left(b x + a\right)}{b^{4} g^{2}} + \frac{b x^{2} - 4 \, a x}{b^{3} g^{2}}\right)} A^{2} d^{3} i^{3} + 3 \, A^{2} c^{2} d i^{3} {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - 2 \, A B c^{3} i^{3} {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{2} g^{2} x + a b g^{2}} + \frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{A^{2} c^{3} i^{3}}{b^{2} g^{2} x + a b g^{2}} + \frac{{\left(B^{2} b^{3} d^{3} i^{3} x^{3} + 3 \, {\left(2 \, b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} c d^{2} i^{3} - 2 \, a^{2} b d^{3} i^{3}\right)} B^{2} x - 2 \, {\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B^{2} + 6 \, {\left({\left(b^{3} c^{2} d i^{3} - 2 \, a b^{2} c d^{2} i^{3} + a^{2} b d^{3} i^{3}\right)} B^{2} x + {\left(a b^{2} c^{2} d i^{3} - 2 \, a^{2} b c d^{2} i^{3} + a^{3} d^{3} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2}}{2 \, {\left(b^{5} g^{2} x + a b^{4} g^{2}\right)}} - \int -\frac{B^{2} b^{4} c^{4} i^{3} \log\left(e\right)^{2} + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} d^{4} i^{3} \log\left(e\right)\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c d^{3} i^{3} \log\left(e\right)\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c^{2} d^{2} i^{3} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(2 \, B^{2} b^{4} c^{3} d i^{3} \log\left(e\right)^{2} + 3 \, A B b^{4} c^{3} d i^{3} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right) + A B b^{4} d^{4} i^{3}\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right) + A B b^{4} c d^{3} i^{3}\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right) + A B b^{4} c^{2} d^{2} i^{3}\right)} x^{2} + {\left(4 \, B^{2} b^{4} c^{3} d i^{3} \log\left(e\right) + 3 \, A B b^{4} c^{3} d i^{3}\right)} x\right)} \log\left(b x + a\right) - {\left({\left(2 \, A B b^{4} d^{4} i^{3} + {\left(2 \, i^{3} \log\left(e\right) + i^{3}\right)} B^{2} b^{4} d^{4}\right)} x^{4} + 2 \, {\left(4 \, A B b^{4} c d^{3} i^{3} - {\left(a b^{3} d^{4} i^{3} - {\left(4 \, i^{3} \log\left(e\right) + 3 \, i^{3}\right)} b^{4} c d^{3}\right)} B^{2}\right)} x^{3} + 2 \, {\left(b^{4} c^{4} i^{3} \log\left(e\right) - a b^{3} c^{3} d i^{3} + 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} - 3 \, a^{3} b c d^{3} i^{3} + a^{4} d^{4} i^{3}\right)} B^{2} + {\left(12 \, A B b^{4} c^{2} d^{2} i^{3} + {\left(12 \, b^{4} c^{2} d^{2} i^{3} \log\left(e\right) + 12 \, a b^{3} c d^{3} i^{3} - 7 \, a^{2} b^{2} d^{4} i^{3}\right)} B^{2}\right)} x^{2} + 2 \, {\left(3 \, A B b^{4} c^{3} d i^{3} + {\left(3 \, a b^{3} c^{2} d^{2} i^{3} - a^{3} b d^{4} i^{3} + {\left(4 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{4} c^{3} d\right)} B^{2}\right)} x + 2 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 3 \, {\left(3 \, b^{4} c^{2} d^{2} i^{3} - 2 \, a b^{3} c d^{3} i^{3} + a^{2} b^{2} d^{4} i^{3}\right)} B^{2} x^{2} + 2 \, {\left(2 \, b^{4} c^{3} d i^{3} + 3 \, a b^{3} c^{2} d^{2} i^{3} - 6 \, a^{2} b^{2} c d^{3} i^{3} + 3 \, a^{3} b d^{4} i^{3}\right)} B^{2} x + {\left(b^{4} c^{4} i^{3} + 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} - 6 \, a^{3} b c d^{3} i^{3} + 3 \, a^{4} d^{4} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{6} d g^{2} x^{3} + a^{2} b^{4} c g^{2} + {\left(b^{6} c g^{2} + 2 \, a b^{5} d g^{2}\right)} x^{2} + {\left(2 \, a b^{5} c g^{2} + a^{2} b^{4} d g^{2}\right)} x}\,{d x}"," ",0,"-3*A^2*(a^2/(b^4*g^2*x + a*b^3*g^2) - x/(b^2*g^2) + 2*a*log(b*x + a)/(b^3*g^2))*c*d^2*i^3 + 1/2*(2*a^3/(b^5*g^2*x + a*b^4*g^2) + 6*a^2*log(b*x + a)/(b^4*g^2) + (b*x^2 - 4*a*x)/(b^3*g^2))*A^2*d^3*i^3 + 3*A^2*c^2*d*i^3*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - 2*A*B*c^3*i^3*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^2*g^2*x + a*b*g^2) + 1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A^2*c^3*i^3/(b^2*g^2*x + a*b*g^2) + 1/2*(B^2*b^3*d^3*i^3*x^3 + 3*(2*b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B^2*x^2 + 2*(3*a*b^2*c*d^2*i^3 - 2*a^2*b*d^3*i^3)*B^2*x - 2*(b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B^2 + 6*((b^3*c^2*d*i^3 - 2*a*b^2*c*d^2*i^3 + a^2*b*d^3*i^3)*B^2*x + (a*b^2*c^2*d*i^3 - 2*a^2*b*c*d^2*i^3 + a^3*d^3*i^3)*B^2)*log(b*x + a))*log(d*x + c)^2/(b^5*g^2*x + a*b^4*g^2) - integrate(-(B^2*b^4*c^4*i^3*log(e)^2 + (B^2*b^4*d^4*i^3*log(e)^2 + 2*A*B*b^4*d^4*i^3*log(e))*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e)^2 + 2*A*B*b^4*c*d^3*i^3*log(e))*x^3 + 6*(B^2*b^4*c^2*d^2*i^3*log(e)^2 + 2*A*B*b^4*c^2*d^2*i^3*log(e))*x^2 + (B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log(b*x + a)^2 + 2*(2*B^2*b^4*c^3*d*i^3*log(e)^2 + 3*A*B*b^4*c^3*d*i^3*log(e))*x + 2*(B^2*b^4*c^4*i^3*log(e) + (B^2*b^4*d^4*i^3*log(e) + A*B*b^4*d^4*i^3)*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e) + A*B*b^4*c*d^3*i^3)*x^3 + 6*(B^2*b^4*c^2*d^2*i^3*log(e) + A*B*b^4*c^2*d^2*i^3)*x^2 + (4*B^2*b^4*c^3*d*i^3*log(e) + 3*A*B*b^4*c^3*d*i^3)*x)*log(b*x + a) - ((2*A*B*b^4*d^4*i^3 + (2*i^3*log(e) + i^3)*B^2*b^4*d^4)*x^4 + 2*(4*A*B*b^4*c*d^3*i^3 - (a*b^3*d^4*i^3 - (4*i^3*log(e) + 3*i^3)*b^4*c*d^3)*B^2)*x^3 + 2*(b^4*c^4*i^3*log(e) - a*b^3*c^3*d*i^3 + 3*a^2*b^2*c^2*d^2*i^3 - 3*a^3*b*c*d^3*i^3 + a^4*d^4*i^3)*B^2 + (12*A*B*b^4*c^2*d^2*i^3 + (12*b^4*c^2*d^2*i^3*log(e) + 12*a*b^3*c*d^3*i^3 - 7*a^2*b^2*d^4*i^3)*B^2)*x^2 + 2*(3*A*B*b^4*c^3*d*i^3 + (3*a*b^3*c^2*d^2*i^3 - a^3*b*d^4*i^3 + (4*i^3*log(e) - i^3)*b^4*c^3*d)*B^2)*x + 2*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 3*(3*b^4*c^2*d^2*i^3 - 2*a*b^3*c*d^3*i^3 + a^2*b^2*d^4*i^3)*B^2*x^2 + 2*(2*b^4*c^3*d*i^3 + 3*a*b^3*c^2*d^2*i^3 - 6*a^2*b^2*c*d^3*i^3 + 3*a^3*b*d^4*i^3)*B^2*x + (b^4*c^4*i^3 + 3*a^2*b^2*c^2*d^2*i^3 - 6*a^3*b*c*d^3*i^3 + 3*a^4*d^4*i^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^6*d*g^2*x^3 + a^2*b^4*c*g^2 + (b^6*c*g^2 + 2*a*b^5*d*g^2)*x^2 + (2*a*b^5*c*g^2 + a^2*b^4*d*g^2)*x), x)","F",0
80,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{3}{2} \, A B c^{2} d i^{3} {\left(\frac{2 \, {\left(2 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} + \frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} - \frac{1}{2} \, A^{2} d^{3} i^{3} {\left(\frac{6 \, a^{2} b x + 5 \, a^{3}}{b^{6} g^{3} x^{2} + 2 \, a b^{5} g^{3} x + a^{2} b^{4} g^{3}} - \frac{2 \, x}{b^{3} g^{3}} + \frac{6 \, a \log\left(b x + a\right)}{b^{4} g^{3}}\right)} + \frac{3}{2} \, A^{2} c d^{2} i^{3} {\left(\frac{4 \, a b x + 3 \, a^{2}}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + \frac{2 \, \log\left(b x + a\right)}{b^{3} g^{3}}\right)} + \frac{1}{2} \, A B c^{3} i^{3} {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{3 \, {\left(2 \, b x + a\right)} A^{2} c^{2} d i^{3}}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{A^{2} c^{3} i^{3}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} + \frac{{\left(2 \, B^{2} b^{3} d^{3} i^{3} x^{3} + 4 \, B^{2} a b^{2} d^{3} i^{3} x^{2} - 2 \, {\left(3 \, b^{3} c^{2} d i^{3} - 6 \, a b^{2} c d^{2} i^{3} + 2 \, a^{2} b d^{3} i^{3}\right)} B^{2} x - {\left(b^{3} c^{3} i^{3} + 3 \, a b^{2} c^{2} d i^{3} - 9 \, a^{2} b c d^{2} i^{3} + 5 \, a^{3} d^{3} i^{3}\right)} B^{2} + 6 \, {\left({\left(b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c d^{2} i^{3} - a^{2} b d^{3} i^{3}\right)} B^{2} x + {\left(a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2}}{2 \, {\left(b^{6} g^{3} x^{2} + 2 \, a b^{5} g^{3} x + a^{2} b^{4} g^{3}\right)}} - \int -\frac{4 \, B^{2} b^{4} c^{3} d i^{3} x \log\left(e\right)^{2} + B^{2} b^{4} c^{4} i^{3} \log\left(e\right)^{2} + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} d^{4} i^{3} \log\left(e\right)\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c d^{3} i^{3} \log\left(e\right)\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right)^{2} + A B b^{4} c^{2} d^{2} i^{3} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(4 \, B^{2} b^{4} c^{3} d i^{3} x \log\left(e\right) + B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right) + A B b^{4} d^{4} i^{3}\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right) + A B b^{4} c d^{3} i^{3}\right)} x^{3} + 3 \, {\left(2 \, B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right) + A B b^{4} c^{2} d^{2} i^{3}\right)} x^{2}\right)} \log\left(b x + a\right) - {\left(2 \, {\left(A B b^{4} d^{4} i^{3} + {\left(i^{3} \log\left(e\right) + i^{3}\right)} B^{2} b^{4} d^{4}\right)} x^{4} - {\left(9 \, a b^{3} c^{2} d^{2} i^{3} - 21 \, a^{2} b^{2} c d^{3} i^{3} + 9 \, a^{3} b d^{4} i^{3} - {\left(8 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{4} c^{3} d\right)} B^{2} x + 2 \, {\left(4 \, A B b^{4} c d^{3} i^{3} + {\left(4 \, b^{4} c d^{3} i^{3} \log\left(e\right) + 3 \, a b^{3} d^{4} i^{3}\right)} B^{2}\right)} x^{3} + {\left(2 \, b^{4} c^{4} i^{3} \log\left(e\right) - a b^{3} c^{3} d i^{3} - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 9 \, a^{3} b c d^{3} i^{3} - 5 \, a^{4} d^{4} i^{3}\right)} B^{2} + 6 \, {\left(A B b^{4} c^{2} d^{2} i^{3} + {\left(2 \, a b^{3} c d^{3} i^{3} + {\left(2 \, i^{3} \log\left(e\right) - i^{3}\right)} b^{4} c^{2} d^{2}\right)} B^{2}\right)} x^{2} + 2 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + {\left(7 \, b^{4} c d^{3} i^{3} - 3 \, a b^{3} d^{4} i^{3}\right)} B^{2} x^{3} + 3 \, {\left(2 \, b^{4} c^{2} d^{2} i^{3} + 3 \, a b^{3} c d^{3} i^{3} - 3 \, a^{2} b^{2} d^{4} i^{3}\right)} B^{2} x^{2} + {\left(4 \, b^{4} c^{3} d i^{3} + 9 \, a^{2} b^{2} c d^{3} i^{3} - 9 \, a^{3} b d^{4} i^{3}\right)} B^{2} x + {\left(b^{4} c^{4} i^{3} + 3 \, a^{3} b c d^{3} i^{3} - 3 \, a^{4} d^{4} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{7} d g^{3} x^{4} + a^{3} b^{4} c g^{3} + {\left(b^{7} c g^{3} + 3 \, a b^{6} d g^{3}\right)} x^{3} + 3 \, {\left(a b^{6} c g^{3} + a^{2} b^{5} d g^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{5} c g^{3} + a^{3} b^{4} d g^{3}\right)} x}\,{d x}"," ",0,"-3/2*A*B*c^2*d*i^3*(2*(2*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) + (3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) - 1/2*A^2*d^3*i^3*((6*a^2*b*x + 5*a^3)/(b^6*g^3*x^2 + 2*a*b^5*g^3*x + a^2*b^4*g^3) - 2*x/(b^3*g^3) + 6*a*log(b*x + a)/(b^4*g^3)) + 3/2*A^2*c*d^2*i^3*((4*a*b*x + 3*a^2)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*log(b*x + a)/(b^3*g^3)) + 1/2*A*B*c^3*i^3*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - 3/2*(2*b*x + a)*A^2*c^2*d*i^3/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*A^2*c^3*i^3/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) + 1/2*(2*B^2*b^3*d^3*i^3*x^3 + 4*B^2*a*b^2*d^3*i^3*x^2 - 2*(3*b^3*c^2*d*i^3 - 6*a*b^2*c*d^2*i^3 + 2*a^2*b*d^3*i^3)*B^2*x - (b^3*c^3*i^3 + 3*a*b^2*c^2*d*i^3 - 9*a^2*b*c*d^2*i^3 + 5*a^3*d^3*i^3)*B^2 + 6*((b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B^2*x^2 + 2*(a*b^2*c*d^2*i^3 - a^2*b*d^3*i^3)*B^2*x + (a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B^2)*log(b*x + a))*log(d*x + c)^2/(b^6*g^3*x^2 + 2*a*b^5*g^3*x + a^2*b^4*g^3) - integrate(-(4*B^2*b^4*c^3*d*i^3*x*log(e)^2 + B^2*b^4*c^4*i^3*log(e)^2 + (B^2*b^4*d^4*i^3*log(e)^2 + 2*A*B*b^4*d^4*i^3*log(e))*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e)^2 + 2*A*B*b^4*c*d^3*i^3*log(e))*x^3 + 6*(B^2*b^4*c^2*d^2*i^3*log(e)^2 + A*B*b^4*c^2*d^2*i^3*log(e))*x^2 + (B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log(b*x + a)^2 + 2*(4*B^2*b^4*c^3*d*i^3*x*log(e) + B^2*b^4*c^4*i^3*log(e) + (B^2*b^4*d^4*i^3*log(e) + A*B*b^4*d^4*i^3)*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e) + A*B*b^4*c*d^3*i^3)*x^3 + 3*(2*B^2*b^4*c^2*d^2*i^3*log(e) + A*B*b^4*c^2*d^2*i^3)*x^2)*log(b*x + a) - (2*(A*B*b^4*d^4*i^3 + (i^3*log(e) + i^3)*B^2*b^4*d^4)*x^4 - (9*a*b^3*c^2*d^2*i^3 - 21*a^2*b^2*c*d^3*i^3 + 9*a^3*b*d^4*i^3 - (8*i^3*log(e) - i^3)*b^4*c^3*d)*B^2*x + 2*(4*A*B*b^4*c*d^3*i^3 + (4*b^4*c*d^3*i^3*log(e) + 3*a*b^3*d^4*i^3)*B^2)*x^3 + (2*b^4*c^4*i^3*log(e) - a*b^3*c^3*d*i^3 - 3*a^2*b^2*c^2*d^2*i^3 + 9*a^3*b*c*d^3*i^3 - 5*a^4*d^4*i^3)*B^2 + 6*(A*B*b^4*c^2*d^2*i^3 + (2*a*b^3*c*d^3*i^3 + (2*i^3*log(e) - i^3)*b^4*c^2*d^2)*B^2)*x^2 + 2*(B^2*b^4*d^4*i^3*x^4 + (7*b^4*c*d^3*i^3 - 3*a*b^3*d^4*i^3)*B^2*x^3 + 3*(2*b^4*c^2*d^2*i^3 + 3*a*b^3*c*d^3*i^3 - 3*a^2*b^2*d^4*i^3)*B^2*x^2 + (4*b^4*c^3*d*i^3 + 9*a^2*b^2*c*d^3*i^3 - 9*a^3*b*d^4*i^3)*B^2*x + (b^4*c^4*i^3 + 3*a^3*b*c*d^3*i^3 - 3*a^4*d^4*i^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^7*d*g^3*x^4 + a^3*b^4*c*g^3 + (b^7*c*g^3 + 3*a*b^6*d*g^3)*x^3 + 3*(a*b^6*c*g^3 + a^2*b^5*d*g^3)*x^2 + (3*a^2*b^5*c*g^3 + a^3*b^4*d*g^3)*x), x)","F",0
81,1,11688,0,11.335537," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{{\left(4 \, b x + a\right)} B^{2} c^{2} d i^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{4 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} B^{2} c d^{2} i^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{4 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{{\left(4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}\right)} B^{2} d^{3} i^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{4 \, {\left(b^{8} g^{5} x^{4} + 4 \, a b^{7} g^{5} x^{3} + 6 \, a^{2} b^{6} g^{5} x^{2} + 4 \, a^{3} b^{5} g^{5} x + a^{4} b^{4} g^{5}\right)}} + \frac{1}{288} \, {\left(12 \, {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{9 \, b^{4} c^{4} - 64 \, a b^{3} c^{3} d + 216 \, a^{2} b^{2} c^{2} d^{2} - 576 \, a^{3} b c d^{3} + 415 \, a^{4} d^{4} - 300 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(13 \, b^{4} c^{2} d^{2} - 176 \, a b^{3} c d^{3} + 163 \, a^{2} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(7 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 324 \, a^{2} b^{2} c d^{3} - 271 \, a^{3} b d^{4}\right)} x - 300 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(25 \, b^{4} d^{4} x^{4} + 100 \, a b^{3} d^{4} x^{3} + 150 \, a^{2} b^{2} d^{4} x^{2} + 100 \, a^{3} b d^{4} x + 25 \, a^{4} d^{4} - 12 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{5} c^{4} g^{5} - 4 \, a^{5} b^{4} c^{3} d g^{5} + 6 \, a^{6} b^{3} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{2} c d^{3} g^{5} + a^{8} b d^{4} g^{5} + {\left(b^{9} c^{4} g^{5} - 4 \, a b^{8} c^{3} d g^{5} + 6 \, a^{2} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{6} c d^{3} g^{5} + a^{4} b^{5} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} g^{5} - 4 \, a^{2} b^{7} c^{3} d g^{5} + 6 \, a^{3} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{5} c d^{3} g^{5} + a^{5} b^{4} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} g^{5} - 4 \, a^{3} b^{6} c^{3} d g^{5} + 6 \, a^{4} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{4} c d^{3} g^{5} + a^{6} b^{3} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} g^{5} - 4 \, a^{4} b^{5} c^{3} d g^{5} + 6 \, a^{5} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{3} c d^{3} g^{5} + a^{7} b^{2} d^{4} g^{5}\right)} x}\right)} B^{2} c^{3} i^{3} - \frac{1}{288} \, {\left(12 \, {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{37 \, a b^{4} c^{4} - 304 \, a^{2} b^{3} c^{3} d + 1512 \, a^{3} b^{2} c^{2} d^{2} - 1360 \, a^{4} b c d^{3} + 115 \, a^{5} d^{4} + 12 \, {\left(88 \, b^{5} c^{2} d^{2} - 101 \, a b^{4} c d^{3} + 13 \, a^{2} b^{3} d^{4}\right)} x^{3} - 6 \, {\left(40 \, b^{5} c^{3} d - 609 \, a b^{4} c^{2} d^{2} + 648 \, a^{2} b^{3} c d^{3} - 79 \, a^{3} b^{2} d^{4}\right)} x^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(16 \, b^{5} c^{4} - 163 \, a b^{4} c^{3} d + 1068 \, a^{2} b^{3} c^{2} d^{2} - 1036 \, a^{3} b^{2} c d^{3} + 115 \, a^{4} b d^{4}\right)} x + 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x - 12 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{6} c^{4} g^{5} - 4 \, a^{5} b^{5} c^{3} d g^{5} + 6 \, a^{6} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{3} c d^{3} g^{5} + a^{8} b^{2} d^{4} g^{5} + {\left(b^{10} c^{4} g^{5} - 4 \, a b^{9} c^{3} d g^{5} + 6 \, a^{2} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{7} c d^{3} g^{5} + a^{4} b^{6} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{9} c^{4} g^{5} - 4 \, a^{2} b^{8} c^{3} d g^{5} + 6 \, a^{3} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{6} c d^{3} g^{5} + a^{5} b^{5} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} c^{4} g^{5} - 4 \, a^{3} b^{7} c^{3} d g^{5} + 6 \, a^{4} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{5} c d^{3} g^{5} + a^{6} b^{4} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} c^{4} g^{5} - 4 \, a^{4} b^{6} c^{3} d g^{5} + 6 \, a^{5} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{4} c d^{3} g^{5} + a^{7} b^{3} d^{4} g^{5}\right)} x}\right)} B^{2} c^{2} d i^{3} - \frac{1}{288} \, {\left(12 \, {\left(\frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{115 \, a^{2} b^{4} c^{4} - 1360 \, a^{3} b^{3} c^{3} d + 1512 \, a^{4} b^{2} c^{2} d^{2} - 304 \, a^{5} b c d^{3} + 37 \, a^{6} d^{4} - 12 \, {\left(108 \, b^{6} c^{3} d - 148 \, a b^{5} c^{2} d^{2} + 47 \, a^{2} b^{4} c d^{3} - 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(36 \, b^{6} c^{4} - 712 \, a b^{5} c^{3} d + 903 \, a^{2} b^{4} c^{2} d^{2} - 264 \, a^{3} b^{3} c d^{3} + 37 \, a^{4} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(76 \, a b^{5} c^{4} - 1057 \, a^{2} b^{4} c^{3} d + 1248 \, a^{3} b^{3} c^{2} d^{2} - 304 \, a^{4} b^{2} c d^{3} + 37 \, a^{5} b d^{4}\right)} x - 12 \, {\left(108 \, a^{4} b^{2} c^{2} d^{2} - 40 \, a^{5} b c d^{3} + 7 \, a^{6} d^{4} + {\left(108 \, b^{6} c^{2} d^{2} - 40 \, a b^{5} c d^{3} + 7 \, a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(108 \, a b^{5} c^{2} d^{2} - 40 \, a^{2} b^{4} c d^{3} + 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(108 \, a^{2} b^{4} c^{2} d^{2} - 40 \, a^{3} b^{3} c d^{3} + 7 \, a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(108 \, a^{3} b^{3} c^{2} d^{2} - 40 \, a^{4} b^{2} c d^{3} + 7 \, a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(108 \, a^{4} b^{2} c^{2} d^{2} - 40 \, a^{5} b c d^{3} + 7 \, a^{6} d^{4} + {\left(108 \, b^{6} c^{2} d^{2} - 40 \, a b^{5} c d^{3} + 7 \, a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(108 \, a b^{5} c^{2} d^{2} - 40 \, a^{2} b^{4} c d^{3} + 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(108 \, a^{2} b^{4} c^{2} d^{2} - 40 \, a^{3} b^{3} c d^{3} + 7 \, a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(108 \, a^{3} b^{3} c^{2} d^{2} - 40 \, a^{4} b^{2} c d^{3} + 7 \, a^{5} b d^{4}\right)} x - 12 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{7} c^{4} g^{5} - 4 \, a^{5} b^{6} c^{3} d g^{5} + 6 \, a^{6} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{4} c d^{3} g^{5} + a^{8} b^{3} d^{4} g^{5} + {\left(b^{11} c^{4} g^{5} - 4 \, a b^{10} c^{3} d g^{5} + 6 \, a^{2} b^{9} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{8} c d^{3} g^{5} + a^{4} b^{7} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{10} c^{4} g^{5} - 4 \, a^{2} b^{9} c^{3} d g^{5} + 6 \, a^{3} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{7} c d^{3} g^{5} + a^{5} b^{6} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} c^{4} g^{5} - 4 \, a^{3} b^{8} c^{3} d g^{5} + 6 \, a^{4} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{6} c d^{3} g^{5} + a^{6} b^{5} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} c^{4} g^{5} - 4 \, a^{4} b^{7} c^{3} d g^{5} + 6 \, a^{5} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{5} c d^{3} g^{5} + a^{7} b^{4} d^{4} g^{5}\right)} x}\right)} B^{2} c d^{2} i^{3} - \frac{1}{288} \, {\left(12 \, {\left(\frac{25 \, a^{3} b^{3} c^{3} - 23 \, a^{4} b^{2} c^{2} d + 13 \, a^{5} b c d^{2} - 3 \, a^{6} d^{3} + 12 \, {\left(4 \, b^{6} c^{3} - 6 \, a b^{5} c^{2} d + 4 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(18 \, a b^{5} c^{3} - 22 \, a^{2} b^{4} c^{2} d + 13 \, a^{3} b^{3} c d^{2} - 3 \, a^{4} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(22 \, a^{2} b^{4} c^{3} - 23 \, a^{3} b^{3} c^{2} d + 13 \, a^{4} b^{2} c d^{2} - 3 \, a^{5} b d^{3}\right)} x}{{\left(b^{11} c^{3} - 3 \, a b^{10} c^{2} d + 3 \, a^{2} b^{9} c d^{2} - a^{3} b^{8} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{10} c^{3} - 3 \, a^{2} b^{9} c^{2} d + 3 \, a^{3} b^{8} c d^{2} - a^{4} b^{7} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{9} c^{3} - 3 \, a^{3} b^{8} c^{2} d + 3 \, a^{4} b^{7} c d^{2} - a^{5} b^{6} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{8} c^{3} - 3 \, a^{4} b^{7} c^{2} d + 3 \, a^{5} b^{6} c d^{2} - a^{6} b^{5} d^{3}\right)} g^{5} x + {\left(a^{4} b^{7} c^{3} - 3 \, a^{5} b^{6} c^{2} d + 3 \, a^{6} b^{5} c d^{2} - a^{7} b^{4} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{4} - 4 \, a b^{7} c^{3} d + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{3} b^{5} c d^{3} + a^{4} b^{4} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{4} - 4 \, a b^{7} c^{3} d + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{3} b^{5} c d^{3} + a^{4} b^{4} d^{4}\right)} g^{5}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{415 \, a^{3} b^{4} c^{4} - 576 \, a^{4} b^{3} c^{3} d + 216 \, a^{5} b^{2} c^{2} d^{2} - 64 \, a^{6} b c d^{3} + 9 \, a^{7} d^{4} + 12 \, {\left(48 \, b^{7} c^{4} - 84 \, a b^{6} c^{3} d + 52 \, a^{2} b^{5} c^{2} d^{2} - 19 \, a^{3} b^{4} c d^{3} + 3 \, a^{4} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(252 \, a b^{6} c^{4} - 400 \, a^{2} b^{5} c^{3} d + 203 \, a^{3} b^{4} c^{2} d^{2} - 64 \, a^{4} b^{3} c d^{3} + 9 \, a^{5} b^{2} d^{4}\right)} x^{2} - 72 \, {\left(4 \, a^{4} b^{3} c^{3} d - 6 \, a^{5} b^{2} c^{2} d^{2} + 4 \, a^{6} b c d^{3} - a^{7} d^{4} + {\left(4 \, b^{7} c^{3} d - 6 \, a b^{6} c^{2} d^{2} + 4 \, a^{2} b^{5} c d^{3} - a^{3} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{6} c^{3} d - 6 \, a^{2} b^{5} c^{2} d^{2} + 4 \, a^{3} b^{4} c d^{3} - a^{4} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{5} c^{3} d - 6 \, a^{3} b^{4} c^{2} d^{2} + 4 \, a^{4} b^{3} c d^{3} - a^{5} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{4} c^{3} d - 6 \, a^{4} b^{3} c^{2} d^{2} + 4 \, a^{5} b^{2} c d^{3} - a^{6} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 72 \, {\left(4 \, a^{4} b^{3} c^{3} d - 6 \, a^{5} b^{2} c^{2} d^{2} + 4 \, a^{6} b c d^{3} - a^{7} d^{4} + {\left(4 \, b^{7} c^{3} d - 6 \, a b^{6} c^{2} d^{2} + 4 \, a^{2} b^{5} c d^{3} - a^{3} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{6} c^{3} d - 6 \, a^{2} b^{5} c^{2} d^{2} + 4 \, a^{3} b^{4} c d^{3} - a^{4} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{5} c^{3} d - 6 \, a^{3} b^{4} c^{2} d^{2} + 4 \, a^{4} b^{3} c d^{3} - a^{5} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{4} c^{3} d - 6 \, a^{4} b^{3} c^{2} d^{2} + 4 \, a^{5} b^{2} c d^{3} - a^{6} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(340 \, a^{2} b^{5} c^{4} - 501 \, a^{3} b^{4} c^{3} d + 216 \, a^{4} b^{3} c^{2} d^{2} - 64 \, a^{5} b^{2} c d^{3} + 9 \, a^{6} b d^{4}\right)} x + 12 \, {\left(48 \, a^{4} b^{3} c^{3} d - 36 \, a^{5} b^{2} c^{2} d^{2} + 16 \, a^{6} b c d^{3} - 3 \, a^{7} d^{4} + {\left(48 \, b^{7} c^{3} d - 36 \, a b^{6} c^{2} d^{2} + 16 \, a^{2} b^{5} c d^{3} - 3 \, a^{3} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(48 \, a b^{6} c^{3} d - 36 \, a^{2} b^{5} c^{2} d^{2} + 16 \, a^{3} b^{4} c d^{3} - 3 \, a^{4} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(48 \, a^{2} b^{5} c^{3} d - 36 \, a^{3} b^{4} c^{2} d^{2} + 16 \, a^{4} b^{3} c d^{3} - 3 \, a^{5} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(48 \, a^{3} b^{4} c^{3} d - 36 \, a^{4} b^{3} c^{2} d^{2} + 16 \, a^{5} b^{2} c d^{3} - 3 \, a^{6} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(48 \, a^{4} b^{3} c^{3} d - 36 \, a^{5} b^{2} c^{2} d^{2} + 16 \, a^{6} b c d^{3} - 3 \, a^{7} d^{4} + {\left(48 \, b^{7} c^{3} d - 36 \, a b^{6} c^{2} d^{2} + 16 \, a^{2} b^{5} c d^{3} - 3 \, a^{3} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(48 \, a b^{6} c^{3} d - 36 \, a^{2} b^{5} c^{2} d^{2} + 16 \, a^{3} b^{4} c d^{3} - 3 \, a^{4} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(48 \, a^{2} b^{5} c^{3} d - 36 \, a^{3} b^{4} c^{2} d^{2} + 16 \, a^{4} b^{3} c d^{3} - 3 \, a^{5} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(48 \, a^{3} b^{4} c^{3} d - 36 \, a^{4} b^{3} c^{2} d^{2} + 16 \, a^{5} b^{2} c d^{3} - 3 \, a^{6} b d^{4}\right)} x - 12 \, {\left(4 \, a^{4} b^{3} c^{3} d - 6 \, a^{5} b^{2} c^{2} d^{2} + 4 \, a^{6} b c d^{3} - a^{7} d^{4} + {\left(4 \, b^{7} c^{3} d - 6 \, a b^{6} c^{2} d^{2} + 4 \, a^{2} b^{5} c d^{3} - a^{3} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{6} c^{3} d - 6 \, a^{2} b^{5} c^{2} d^{2} + 4 \, a^{3} b^{4} c d^{3} - a^{4} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{5} c^{3} d - 6 \, a^{3} b^{4} c^{2} d^{2} + 4 \, a^{4} b^{3} c d^{3} - a^{5} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{4} c^{3} d - 6 \, a^{4} b^{3} c^{2} d^{2} + 4 \, a^{5} b^{2} c d^{3} - a^{6} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{4} b^{8} c^{4} g^{5} - 4 \, a^{5} b^{7} c^{3} d g^{5} + 6 \, a^{6} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{5} c d^{3} g^{5} + a^{8} b^{4} d^{4} g^{5} + {\left(b^{12} c^{4} g^{5} - 4 \, a b^{11} c^{3} d g^{5} + 6 \, a^{2} b^{10} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{9} c d^{3} g^{5} + a^{4} b^{8} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{11} c^{4} g^{5} - 4 \, a^{2} b^{10} c^{3} d g^{5} + 6 \, a^{3} b^{9} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{8} c d^{3} g^{5} + a^{5} b^{7} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{10} c^{4} g^{5} - 4 \, a^{3} b^{9} c^{3} d g^{5} + 6 \, a^{4} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{7} c d^{3} g^{5} + a^{6} b^{6} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{9} c^{4} g^{5} - 4 \, a^{4} b^{8} c^{3} d g^{5} + 6 \, a^{5} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{6} c d^{3} g^{5} + a^{7} b^{5} d^{4} g^{5}\right)} x}\right)} B^{2} d^{3} i^{3} - \frac{1}{24} \, A B d^{3} i^{3} {\left(\frac{12 \, {\left(4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{8} g^{5} x^{4} + 4 \, a b^{7} g^{5} x^{3} + 6 \, a^{2} b^{6} g^{5} x^{2} + 4 \, a^{3} b^{5} g^{5} x + a^{4} b^{4} g^{5}} + \frac{25 \, a^{3} b^{3} c^{3} - 23 \, a^{4} b^{2} c^{2} d + 13 \, a^{5} b c d^{2} - 3 \, a^{6} d^{3} + 12 \, {\left(4 \, b^{6} c^{3} - 6 \, a b^{5} c^{2} d + 4 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(18 \, a b^{5} c^{3} - 22 \, a^{2} b^{4} c^{2} d + 13 \, a^{3} b^{3} c d^{2} - 3 \, a^{4} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(22 \, a^{2} b^{4} c^{3} - 23 \, a^{3} b^{3} c^{2} d + 13 \, a^{4} b^{2} c d^{2} - 3 \, a^{5} b d^{3}\right)} x}{{\left(b^{11} c^{3} - 3 \, a b^{10} c^{2} d + 3 \, a^{2} b^{9} c d^{2} - a^{3} b^{8} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{10} c^{3} - 3 \, a^{2} b^{9} c^{2} d + 3 \, a^{3} b^{8} c d^{2} - a^{4} b^{7} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{9} c^{3} - 3 \, a^{3} b^{8} c^{2} d + 3 \, a^{4} b^{7} c d^{2} - a^{5} b^{6} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{8} c^{3} - 3 \, a^{4} b^{7} c^{2} d + 3 \, a^{5} b^{6} c d^{2} - a^{6} b^{5} d^{3}\right)} g^{5} x + {\left(a^{4} b^{7} c^{3} - 3 \, a^{5} b^{6} c^{2} d + 3 \, a^{6} b^{5} c d^{2} - a^{7} b^{4} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{4} - 4 \, a b^{7} c^{3} d + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{3} b^{5} c d^{3} + a^{4} b^{4} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 4 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{4} - 4 \, a b^{7} c^{3} d + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{3} b^{5} c d^{3} + a^{4} b^{4} d^{4}\right)} g^{5}}\right)} - \frac{1}{24} \, A B c d^{2} i^{3} {\left(\frac{12 \, {\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}} + \frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} - \frac{1}{24} \, A B c^{2} d i^{3} {\left(\frac{12 \, {\left(4 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}} + \frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} + \frac{1}{24} \, A B c^{3} i^{3} {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} - \frac{12 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{B^{2} c^{3} i^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{{\left(4 \, b x + a\right)} A^{2} c^{2} d i^{3}}{4 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} A^{2} c d^{2} i^{3}}{4 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{{\left(4 \, b^{3} x^{3} + 6 \, a b^{2} x^{2} + 4 \, a^{2} b x + a^{3}\right)} A^{2} d^{3} i^{3}}{4 \, {\left(b^{8} g^{5} x^{4} + 4 \, a b^{7} g^{5} x^{3} + 6 \, a^{2} b^{6} g^{5} x^{2} + 4 \, a^{3} b^{5} g^{5} x + a^{4} b^{4} g^{5}\right)}} - \frac{A^{2} c^{3} i^{3}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"-1/4*(4*b*x + a)*B^2*c^2*d*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/4*(6*b^2*x^2 + 4*a*b*x + a^2)*B^2*c*d^2*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/4*(4*b^3*x^3 + 6*a*b^2*x^2 + 4*a^2*b*x + a^3)*B^2*d^3*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^8*g^5*x^4 + 4*a*b^7*g^5*x^3 + 6*a^2*b^6*g^5*x^2 + 4*a^3*b^5*g^5*x + a^4*b^4*g^5) + 1/288*(12*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - (9*b^4*c^4 - 64*a*b^3*c^3*d + 216*a^2*b^2*c^2*d^2 - 576*a^3*b*c*d^3 + 415*a^4*d^4 - 300*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 6*(13*b^4*c^2*d^2 - 176*a*b^3*c*d^3 + 163*a^2*b^2*d^4)*x^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a)^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(d*x + c)^2 - 4*(7*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 324*a^2*b^2*c*d^3 - 271*a^3*b*d^4)*x - 300*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a) + 12*(25*b^4*d^4*x^4 + 100*a*b^3*d^4*x^3 + 150*a^2*b^2*d^4*x^2 + 100*a^3*b*d^4*x + 25*a^4*d^4 - 12*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a))*log(d*x + c))/(a^4*b^5*c^4*g^5 - 4*a^5*b^4*c^3*d*g^5 + 6*a^6*b^3*c^2*d^2*g^5 - 4*a^7*b^2*c*d^3*g^5 + a^8*b*d^4*g^5 + (b^9*c^4*g^5 - 4*a*b^8*c^3*d*g^5 + 6*a^2*b^7*c^2*d^2*g^5 - 4*a^3*b^6*c*d^3*g^5 + a^4*b^5*d^4*g^5)*x^4 + 4*(a*b^8*c^4*g^5 - 4*a^2*b^7*c^3*d*g^5 + 6*a^3*b^6*c^2*d^2*g^5 - 4*a^4*b^5*c*d^3*g^5 + a^5*b^4*d^4*g^5)*x^3 + 6*(a^2*b^7*c^4*g^5 - 4*a^3*b^6*c^3*d*g^5 + 6*a^4*b^5*c^2*d^2*g^5 - 4*a^5*b^4*c*d^3*g^5 + a^6*b^3*d^4*g^5)*x^2 + 4*(a^3*b^6*c^4*g^5 - 4*a^4*b^5*c^3*d*g^5 + 6*a^5*b^4*c^2*d^2*g^5 - 4*a^6*b^3*c*d^3*g^5 + a^7*b^2*d^4*g^5)*x))*B^2*c^3*i^3 - 1/288*(12*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (37*a*b^4*c^4 - 304*a^2*b^3*c^3*d + 1512*a^3*b^2*c^2*d^2 - 1360*a^4*b*c*d^3 + 115*a^5*d^4 + 12*(88*b^5*c^2*d^2 - 101*a*b^4*c*d^3 + 13*a^2*b^3*d^4)*x^3 - 6*(40*b^5*c^3*d - 609*a*b^4*c^2*d^2 + 648*a^2*b^3*c*d^3 - 79*a^3*b^2*d^4)*x^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a)^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(d*x + c)^2 + 4*(16*b^5*c^4 - 163*a*b^4*c^3*d + 1068*a^2*b^3*c^2*d^2 - 1036*a^3*b^2*c*d^3 + 115*a^4*b*d^4)*x + 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x)*log(b*x + a) - 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x - 12*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a))*log(d*x + c))/(a^4*b^6*c^4*g^5 - 4*a^5*b^5*c^3*d*g^5 + 6*a^6*b^4*c^2*d^2*g^5 - 4*a^7*b^3*c*d^3*g^5 + a^8*b^2*d^4*g^5 + (b^10*c^4*g^5 - 4*a*b^9*c^3*d*g^5 + 6*a^2*b^8*c^2*d^2*g^5 - 4*a^3*b^7*c*d^3*g^5 + a^4*b^6*d^4*g^5)*x^4 + 4*(a*b^9*c^4*g^5 - 4*a^2*b^8*c^3*d*g^5 + 6*a^3*b^7*c^2*d^2*g^5 - 4*a^4*b^6*c*d^3*g^5 + a^5*b^5*d^4*g^5)*x^3 + 6*(a^2*b^8*c^4*g^5 - 4*a^3*b^7*c^3*d*g^5 + 6*a^4*b^6*c^2*d^2*g^5 - 4*a^5*b^5*c*d^3*g^5 + a^6*b^4*d^4*g^5)*x^2 + 4*(a^3*b^7*c^4*g^5 - 4*a^4*b^6*c^3*d*g^5 + 6*a^5*b^5*c^2*d^2*g^5 - 4*a^6*b^4*c*d^3*g^5 + a^7*b^3*d^4*g^5)*x))*B^2*c^2*d*i^3 - 1/288*(12*((13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (115*a^2*b^4*c^4 - 1360*a^3*b^3*c^3*d + 1512*a^4*b^2*c^2*d^2 - 304*a^5*b*c*d^3 + 37*a^6*d^4 - 12*(108*b^6*c^3*d - 148*a*b^5*c^2*d^2 + 47*a^2*b^4*c*d^3 - 7*a^3*b^3*d^4)*x^3 + 6*(36*b^6*c^4 - 712*a*b^5*c^3*d + 903*a^2*b^4*c^2*d^2 - 264*a^3*b^3*c*d^3 + 37*a^4*b^2*d^4)*x^2 + 72*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(b*x + a)^2 + 72*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(d*x + c)^2 + 4*(76*a*b^5*c^4 - 1057*a^2*b^4*c^3*d + 1248*a^3*b^3*c^2*d^2 - 304*a^4*b^2*c*d^3 + 37*a^5*b*d^4)*x - 12*(108*a^4*b^2*c^2*d^2 - 40*a^5*b*c*d^3 + 7*a^6*d^4 + (108*b^6*c^2*d^2 - 40*a*b^5*c*d^3 + 7*a^2*b^4*d^4)*x^4 + 4*(108*a*b^5*c^2*d^2 - 40*a^2*b^4*c*d^3 + 7*a^3*b^3*d^4)*x^3 + 6*(108*a^2*b^4*c^2*d^2 - 40*a^3*b^3*c*d^3 + 7*a^4*b^2*d^4)*x^2 + 4*(108*a^3*b^3*c^2*d^2 - 40*a^4*b^2*c*d^3 + 7*a^5*b*d^4)*x)*log(b*x + a) + 12*(108*a^4*b^2*c^2*d^2 - 40*a^5*b*c*d^3 + 7*a^6*d^4 + (108*b^6*c^2*d^2 - 40*a*b^5*c*d^3 + 7*a^2*b^4*d^4)*x^4 + 4*(108*a*b^5*c^2*d^2 - 40*a^2*b^4*c*d^3 + 7*a^3*b^3*d^4)*x^3 + 6*(108*a^2*b^4*c^2*d^2 - 40*a^3*b^3*c*d^3 + 7*a^4*b^2*d^4)*x^2 + 4*(108*a^3*b^3*c^2*d^2 - 40*a^4*b^2*c*d^3 + 7*a^5*b*d^4)*x - 12*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(b*x + a))*log(d*x + c))/(a^4*b^7*c^4*g^5 - 4*a^5*b^6*c^3*d*g^5 + 6*a^6*b^5*c^2*d^2*g^5 - 4*a^7*b^4*c*d^3*g^5 + a^8*b^3*d^4*g^5 + (b^11*c^4*g^5 - 4*a*b^10*c^3*d*g^5 + 6*a^2*b^9*c^2*d^2*g^5 - 4*a^3*b^8*c*d^3*g^5 + a^4*b^7*d^4*g^5)*x^4 + 4*(a*b^10*c^4*g^5 - 4*a^2*b^9*c^3*d*g^5 + 6*a^3*b^8*c^2*d^2*g^5 - 4*a^4*b^7*c*d^3*g^5 + a^5*b^6*d^4*g^5)*x^3 + 6*(a^2*b^9*c^4*g^5 - 4*a^3*b^8*c^3*d*g^5 + 6*a^4*b^7*c^2*d^2*g^5 - 4*a^5*b^6*c*d^3*g^5 + a^6*b^5*d^4*g^5)*x^2 + 4*(a^3*b^8*c^4*g^5 - 4*a^4*b^7*c^3*d*g^5 + 6*a^5*b^6*c^2*d^2*g^5 - 4*a^6*b^5*c*d^3*g^5 + a^7*b^4*d^4*g^5)*x))*B^2*c*d^2*i^3 - 1/288*(12*((25*a^3*b^3*c^3 - 23*a^4*b^2*c^2*d + 13*a^5*b*c*d^2 - 3*a^6*d^3 + 12*(4*b^6*c^3 - 6*a*b^5*c^2*d + 4*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^3 + 6*(18*a*b^5*c^3 - 22*a^2*b^4*c^2*d + 13*a^3*b^3*c*d^2 - 3*a^4*b^2*d^3)*x^2 + 4*(22*a^2*b^4*c^3 - 23*a^3*b^3*c^2*d + 13*a^4*b^2*c*d^2 - 3*a^5*b*d^3)*x)/((b^11*c^3 - 3*a*b^10*c^2*d + 3*a^2*b^9*c*d^2 - a^3*b^8*d^3)*g^5*x^4 + 4*(a*b^10*c^3 - 3*a^2*b^9*c^2*d + 3*a^3*b^8*c*d^2 - a^4*b^7*d^3)*g^5*x^3 + 6*(a^2*b^9*c^3 - 3*a^3*b^8*c^2*d + 3*a^4*b^7*c*d^2 - a^5*b^6*d^3)*g^5*x^2 + 4*(a^3*b^8*c^3 - 3*a^4*b^7*c^2*d + 3*a^5*b^6*c*d^2 - a^6*b^5*d^3)*g^5*x + (a^4*b^7*c^3 - 3*a^5*b^6*c^2*d + 3*a^6*b^5*c*d^2 - a^7*b^4*d^3)*g^5) + 12*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*log(b*x + a)/((b^8*c^4 - 4*a*b^7*c^3*d + 6*a^2*b^6*c^2*d^2 - 4*a^3*b^5*c*d^3 + a^4*b^4*d^4)*g^5) - 12*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*log(d*x + c)/((b^8*c^4 - 4*a*b^7*c^3*d + 6*a^2*b^6*c^2*d^2 - 4*a^3*b^5*c*d^3 + a^4*b^4*d^4)*g^5))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (415*a^3*b^4*c^4 - 576*a^4*b^3*c^3*d + 216*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3 + 9*a^7*d^4 + 12*(48*b^7*c^4 - 84*a*b^6*c^3*d + 52*a^2*b^5*c^2*d^2 - 19*a^3*b^4*c*d^3 + 3*a^4*b^3*d^4)*x^3 + 6*(252*a*b^6*c^4 - 400*a^2*b^5*c^3*d + 203*a^3*b^4*c^2*d^2 - 64*a^4*b^3*c*d^3 + 9*a^5*b^2*d^4)*x^2 - 72*(4*a^4*b^3*c^3*d - 6*a^5*b^2*c^2*d^2 + 4*a^6*b*c*d^3 - a^7*d^4 + (4*b^7*c^3*d - 6*a*b^6*c^2*d^2 + 4*a^2*b^5*c*d^3 - a^3*b^4*d^4)*x^4 + 4*(4*a*b^6*c^3*d - 6*a^2*b^5*c^2*d^2 + 4*a^3*b^4*c*d^3 - a^4*b^3*d^4)*x^3 + 6*(4*a^2*b^5*c^3*d - 6*a^3*b^4*c^2*d^2 + 4*a^4*b^3*c*d^3 - a^5*b^2*d^4)*x^2 + 4*(4*a^3*b^4*c^3*d - 6*a^4*b^3*c^2*d^2 + 4*a^5*b^2*c*d^3 - a^6*b*d^4)*x)*log(b*x + a)^2 - 72*(4*a^4*b^3*c^3*d - 6*a^5*b^2*c^2*d^2 + 4*a^6*b*c*d^3 - a^7*d^4 + (4*b^7*c^3*d - 6*a*b^6*c^2*d^2 + 4*a^2*b^5*c*d^3 - a^3*b^4*d^4)*x^4 + 4*(4*a*b^6*c^3*d - 6*a^2*b^5*c^2*d^2 + 4*a^3*b^4*c*d^3 - a^4*b^3*d^4)*x^3 + 6*(4*a^2*b^5*c^3*d - 6*a^3*b^4*c^2*d^2 + 4*a^4*b^3*c*d^3 - a^5*b^2*d^4)*x^2 + 4*(4*a^3*b^4*c^3*d - 6*a^4*b^3*c^2*d^2 + 4*a^5*b^2*c*d^3 - a^6*b*d^4)*x)*log(d*x + c)^2 + 4*(340*a^2*b^5*c^4 - 501*a^3*b^4*c^3*d + 216*a^4*b^3*c^2*d^2 - 64*a^5*b^2*c*d^3 + 9*a^6*b*d^4)*x + 12*(48*a^4*b^3*c^3*d - 36*a^5*b^2*c^2*d^2 + 16*a^6*b*c*d^3 - 3*a^7*d^4 + (48*b^7*c^3*d - 36*a*b^6*c^2*d^2 + 16*a^2*b^5*c*d^3 - 3*a^3*b^4*d^4)*x^4 + 4*(48*a*b^6*c^3*d - 36*a^2*b^5*c^2*d^2 + 16*a^3*b^4*c*d^3 - 3*a^4*b^3*d^4)*x^3 + 6*(48*a^2*b^5*c^3*d - 36*a^3*b^4*c^2*d^2 + 16*a^4*b^3*c*d^3 - 3*a^5*b^2*d^4)*x^2 + 4*(48*a^3*b^4*c^3*d - 36*a^4*b^3*c^2*d^2 + 16*a^5*b^2*c*d^3 - 3*a^6*b*d^4)*x)*log(b*x + a) - 12*(48*a^4*b^3*c^3*d - 36*a^5*b^2*c^2*d^2 + 16*a^6*b*c*d^3 - 3*a^7*d^4 + (48*b^7*c^3*d - 36*a*b^6*c^2*d^2 + 16*a^2*b^5*c*d^3 - 3*a^3*b^4*d^4)*x^4 + 4*(48*a*b^6*c^3*d - 36*a^2*b^5*c^2*d^2 + 16*a^3*b^4*c*d^3 - 3*a^4*b^3*d^4)*x^3 + 6*(48*a^2*b^5*c^3*d - 36*a^3*b^4*c^2*d^2 + 16*a^4*b^3*c*d^3 - 3*a^5*b^2*d^4)*x^2 + 4*(48*a^3*b^4*c^3*d - 36*a^4*b^3*c^2*d^2 + 16*a^5*b^2*c*d^3 - 3*a^6*b*d^4)*x - 12*(4*a^4*b^3*c^3*d - 6*a^5*b^2*c^2*d^2 + 4*a^6*b*c*d^3 - a^7*d^4 + (4*b^7*c^3*d - 6*a*b^6*c^2*d^2 + 4*a^2*b^5*c*d^3 - a^3*b^4*d^4)*x^4 + 4*(4*a*b^6*c^3*d - 6*a^2*b^5*c^2*d^2 + 4*a^3*b^4*c*d^3 - a^4*b^3*d^4)*x^3 + 6*(4*a^2*b^5*c^3*d - 6*a^3*b^4*c^2*d^2 + 4*a^4*b^3*c*d^3 - a^5*b^2*d^4)*x^2 + 4*(4*a^3*b^4*c^3*d - 6*a^4*b^3*c^2*d^2 + 4*a^5*b^2*c*d^3 - a^6*b*d^4)*x)*log(b*x + a))*log(d*x + c))/(a^4*b^8*c^4*g^5 - 4*a^5*b^7*c^3*d*g^5 + 6*a^6*b^6*c^2*d^2*g^5 - 4*a^7*b^5*c*d^3*g^5 + a^8*b^4*d^4*g^5 + (b^12*c^4*g^5 - 4*a*b^11*c^3*d*g^5 + 6*a^2*b^10*c^2*d^2*g^5 - 4*a^3*b^9*c*d^3*g^5 + a^4*b^8*d^4*g^5)*x^4 + 4*(a*b^11*c^4*g^5 - 4*a^2*b^10*c^3*d*g^5 + 6*a^3*b^9*c^2*d^2*g^5 - 4*a^4*b^8*c*d^3*g^5 + a^5*b^7*d^4*g^5)*x^3 + 6*(a^2*b^10*c^4*g^5 - 4*a^3*b^9*c^3*d*g^5 + 6*a^4*b^8*c^2*d^2*g^5 - 4*a^5*b^7*c*d^3*g^5 + a^6*b^6*d^4*g^5)*x^2 + 4*(a^3*b^9*c^4*g^5 - 4*a^4*b^8*c^3*d*g^5 + 6*a^5*b^7*c^2*d^2*g^5 - 4*a^6*b^6*c*d^3*g^5 + a^7*b^5*d^4*g^5)*x))*B^2*d^3*i^3 - 1/24*A*B*d^3*i^3*(12*(4*b^3*x^3 + 6*a*b^2*x^2 + 4*a^2*b*x + a^3)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^8*g^5*x^4 + 4*a*b^7*g^5*x^3 + 6*a^2*b^6*g^5*x^2 + 4*a^3*b^5*g^5*x + a^4*b^4*g^5) + (25*a^3*b^3*c^3 - 23*a^4*b^2*c^2*d + 13*a^5*b*c*d^2 - 3*a^6*d^3 + 12*(4*b^6*c^3 - 6*a*b^5*c^2*d + 4*a^2*b^4*c*d^2 - a^3*b^3*d^3)*x^3 + 6*(18*a*b^5*c^3 - 22*a^2*b^4*c^2*d + 13*a^3*b^3*c*d^2 - 3*a^4*b^2*d^3)*x^2 + 4*(22*a^2*b^4*c^3 - 23*a^3*b^3*c^2*d + 13*a^4*b^2*c*d^2 - 3*a^5*b*d^3)*x)/((b^11*c^3 - 3*a*b^10*c^2*d + 3*a^2*b^9*c*d^2 - a^3*b^8*d^3)*g^5*x^4 + 4*(a*b^10*c^3 - 3*a^2*b^9*c^2*d + 3*a^3*b^8*c*d^2 - a^4*b^7*d^3)*g^5*x^3 + 6*(a^2*b^9*c^3 - 3*a^3*b^8*c^2*d + 3*a^4*b^7*c*d^2 - a^5*b^6*d^3)*g^5*x^2 + 4*(a^3*b^8*c^3 - 3*a^4*b^7*c^2*d + 3*a^5*b^6*c*d^2 - a^6*b^5*d^3)*g^5*x + (a^4*b^7*c^3 - 3*a^5*b^6*c^2*d + 3*a^6*b^5*c*d^2 - a^7*b^4*d^3)*g^5) + 12*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*log(b*x + a)/((b^8*c^4 - 4*a*b^7*c^3*d + 6*a^2*b^6*c^2*d^2 - 4*a^3*b^5*c*d^3 + a^4*b^4*d^4)*g^5) - 12*(4*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 4*a^2*b*c*d^3 - a^3*d^4)*log(d*x + c)/((b^8*c^4 - 4*a*b^7*c^3*d + 6*a^2*b^6*c^2*d^2 - 4*a^3*b^5*c*d^3 + a^4*b^4*d^4)*g^5)) - 1/24*A*B*c*d^2*i^3*(12*(6*b^2*x^2 + 4*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) + (13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5)) - 1/24*A*B*c^2*d*i^3*(12*(4*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) + (7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) + 1/24*A*B*c^3*i^3*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) - 12*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/4*B^2*c^3*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/4*(4*b*x + a)*A^2*c^2*d*i^3/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/4*(6*b^2*x^2 + 4*a*b*x + a^2)*A^2*c*d^2*i^3/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/4*(4*b^3*x^3 + 6*a*b^2*x^2 + 4*a^2*b*x + a^3)*A^2*d^3*i^3/(b^8*g^5*x^4 + 4*a*b^7*g^5*x^3 + 6*a^2*b^6*g^5*x^2 + 4*a^3*b^5*g^5*x + a^4*b^4*g^5) - 1/4*A^2*c^3*i^3/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
82,1,15765,0,16.437549," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^6,x, algorithm=""maxima"")","-\frac{3 \, {\left(5 \, b x + a\right)} B^{2} c^{2} d i^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{20 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} B^{2} c d^{2} i^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{10 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{{\left(10 \, b^{3} x^{3} + 10 \, a b^{2} x^{2} + 5 \, a^{2} b x + a^{3}\right)} B^{2} d^{3} i^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{20 \, {\left(b^{9} g^{6} x^{5} + 5 \, a b^{8} g^{6} x^{4} + 10 \, a^{2} b^{7} g^{6} x^{3} + 10 \, a^{3} b^{6} g^{6} x^{2} + 5 \, a^{4} b^{5} g^{6} x + a^{5} b^{4} g^{6}\right)}} - \frac{1}{9000} \, {\left(60 \, {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{144 \, b^{5} c^{5} - 1125 \, a b^{4} c^{4} d + 4000 \, a^{2} b^{3} c^{3} d^{2} - 9000 \, a^{3} b^{2} c^{2} d^{3} + 18000 \, a^{4} b c d^{4} - 12019 \, a^{5} d^{5} + 8220 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} - 30 \, {\left(77 \, b^{5} c^{2} d^{3} - 1250 \, a b^{4} c d^{4} + 1173 \, a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(94 \, b^{5} c^{3} d^{2} - 975 \, a b^{4} c^{2} d^{3} + 6600 \, a^{2} b^{3} c d^{4} - 5719 \, a^{3} b^{2} d^{5}\right)} x^{2} - 1800 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right)^{2} - 1800 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(81 \, b^{5} c^{4} d - 700 \, a b^{4} c^{3} d^{2} + 3000 \, a^{2} b^{3} c^{2} d^{3} - 10800 \, a^{3} b^{2} c d^{4} + 8419 \, a^{4} b d^{5}\right)} x + 8220 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right) - 60 \, {\left(137 \, b^{5} d^{5} x^{5} + 685 \, a b^{4} d^{5} x^{4} + 1370 \, a^{2} b^{3} d^{5} x^{3} + 1370 \, a^{3} b^{2} d^{5} x^{2} + 685 \, a^{4} b d^{5} x + 137 \, a^{5} d^{5} - 60 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{5} b^{6} c^{5} g^{6} - 5 \, a^{6} b^{5} c^{4} d g^{6} + 10 \, a^{7} b^{4} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{3} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{2} c d^{4} g^{6} - a^{10} b d^{5} g^{6} + {\left(b^{11} c^{5} g^{6} - 5 \, a b^{10} c^{4} d g^{6} + 10 \, a^{2} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{7} c d^{4} g^{6} - a^{5} b^{6} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{10} c^{5} g^{6} - 5 \, a^{2} b^{9} c^{4} d g^{6} + 10 \, a^{3} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{6} c d^{4} g^{6} - a^{6} b^{5} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{9} c^{5} g^{6} - 5 \, a^{3} b^{8} c^{4} d g^{6} + 10 \, a^{4} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{5} c d^{4} g^{6} - a^{7} b^{4} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{8} c^{5} g^{6} - 5 \, a^{4} b^{7} c^{4} d g^{6} + 10 \, a^{5} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{4} c d^{4} g^{6} - a^{8} b^{3} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{7} c^{5} g^{6} - 5 \, a^{5} b^{6} c^{4} d g^{6} + 10 \, a^{6} b^{5} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{4} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{3} c d^{4} g^{6} - a^{9} b^{2} d^{5} g^{6}\right)} x}\right)} B^{2} c^{3} i^{3} - \frac{1}{12000} \, {\left(60 \, {\left(\frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{549 \, a b^{5} c^{5} - 4625 \, a^{2} b^{4} c^{4} d + 19000 \, a^{3} b^{3} c^{3} d^{2} - 63000 \, a^{4} b^{2} c^{2} d^{3} + 51875 \, a^{5} b c d^{4} - 3799 \, a^{6} d^{5} - 60 \, {\left(625 \, b^{6} c^{2} d^{3} - 702 \, a b^{5} c d^{4} + 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 30 \, {\left(325 \, b^{6} c^{3} d^{2} - 5667 \, a b^{5} c^{2} d^{3} + 5975 \, a^{2} b^{4} c d^{4} - 633 \, a^{3} b^{3} d^{5}\right)} x^{3} - 10 \, {\left(350 \, b^{6} c^{4} d - 3949 \, a b^{5} c^{3} d^{2} + 29475 \, a^{2} b^{4} c^{2} d^{3} - 28775 \, a^{3} b^{3} c d^{4} + 2899 \, a^{4} b^{2} d^{5}\right)} x^{2} + 1800 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right)^{2} + 1800 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(d x + c\right)^{2} + 5 \, {\left(225 \, b^{6} c^{5} - 2201 \, a b^{5} c^{4} d + 10900 \, a^{2} b^{4} c^{3} d^{2} - 46200 \, a^{3} b^{3} c^{2} d^{3} + 41075 \, a^{4} b^{2} c d^{4} - 3799 \, a^{5} b d^{5}\right)} x - 60 \, {\left(625 \, a^{5} b c d^{4} - 77 \, a^{6} d^{5} + {\left(625 \, b^{6} c d^{4} - 77 \, a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(625 \, a b^{5} c d^{4} - 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(625 \, a^{2} b^{4} c d^{4} - 77 \, a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(625 \, a^{3} b^{3} c d^{4} - 77 \, a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(625 \, a^{4} b^{2} c d^{4} - 77 \, a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(625 \, a^{5} b c d^{4} - 77 \, a^{6} d^{5} + {\left(625 \, b^{6} c d^{4} - 77 \, a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(625 \, a b^{5} c d^{4} - 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(625 \, a^{2} b^{4} c d^{4} - 77 \, a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(625 \, a^{3} b^{3} c d^{4} - 77 \, a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(625 \, a^{4} b^{2} c d^{4} - 77 \, a^{5} b d^{5}\right)} x - 60 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{5} b^{7} c^{5} g^{6} - 5 \, a^{6} b^{6} c^{4} d g^{6} + 10 \, a^{7} b^{5} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{4} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{3} c d^{4} g^{6} - a^{10} b^{2} d^{5} g^{6} + {\left(b^{12} c^{5} g^{6} - 5 \, a b^{11} c^{4} d g^{6} + 10 \, a^{2} b^{10} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{9} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{8} c d^{4} g^{6} - a^{5} b^{7} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{11} c^{5} g^{6} - 5 \, a^{2} b^{10} c^{4} d g^{6} + 10 \, a^{3} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{7} c d^{4} g^{6} - a^{6} b^{6} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} c^{5} g^{6} - 5 \, a^{3} b^{9} c^{4} d g^{6} + 10 \, a^{4} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{6} c d^{4} g^{6} - a^{7} b^{5} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} c^{5} g^{6} - 5 \, a^{4} b^{8} c^{4} d g^{6} + 10 \, a^{5} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{5} c d^{4} g^{6} - a^{8} b^{4} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} c^{5} g^{6} - 5 \, a^{5} b^{7} c^{4} d g^{6} + 10 \, a^{6} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{4} c d^{4} g^{6} - a^{9} b^{3} d^{5} g^{6}\right)} x}\right)} B^{2} c^{2} d i^{3} - \frac{1}{18000} \, {\left(60 \, {\left(\frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{1489 \, a^{2} b^{5} c^{5} - 14375 \, a^{3} b^{4} c^{4} d + 85000 \, a^{4} b^{3} c^{3} d^{2} - 85000 \, a^{5} b^{2} c^{2} d^{3} + 14375 \, a^{6} b c d^{4} - 1489 \, a^{7} d^{5} + 60 \, {\left(1100 \, b^{7} c^{3} d^{2} - 1425 \, a b^{6} c^{2} d^{3} + 372 \, a^{2} b^{5} c d^{4} - 47 \, a^{3} b^{4} d^{5}\right)} x^{4} - 30 \, {\left(500 \, b^{7} c^{4} d - 9825 \, a b^{6} c^{3} d^{2} + 11937 \, a^{2} b^{5} c^{2} d^{3} - 2975 \, a^{3} b^{4} c d^{4} + 363 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(400 \, b^{7} c^{5} - 5450 \, a b^{6} c^{4} d + 49189 \, a^{2} b^{5} c^{3} d^{2} - 55525 \, a^{3} b^{4} c^{2} d^{3} + 12875 \, a^{4} b^{3} c d^{4} - 1489 \, a^{5} b^{2} d^{5}\right)} x^{2} - 1800 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right)^{2} - 1800 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(d x + c\right)^{2} + 5 \, {\left(925 \, a b^{6} c^{5} - 9911 \, a^{2} b^{5} c^{4} d + 67900 \, a^{3} b^{4} c^{3} d^{2} - 71800 \, a^{4} b^{3} c^{2} d^{3} + 14375 \, a^{5} b^{2} c d^{4} - 1489 \, a^{6} b d^{5}\right)} x + 60 \, {\left(1100 \, a^{5} b^{2} c^{2} d^{3} - 325 \, a^{6} b c d^{4} + 47 \, a^{7} d^{5} + {\left(1100 \, b^{7} c^{2} d^{3} - 325 \, a b^{6} c d^{4} + 47 \, a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(1100 \, a b^{6} c^{2} d^{3} - 325 \, a^{2} b^{5} c d^{4} + 47 \, a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(1100 \, a^{2} b^{5} c^{2} d^{3} - 325 \, a^{3} b^{4} c d^{4} + 47 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(1100 \, a^{3} b^{4} c^{2} d^{3} - 325 \, a^{4} b^{3} c d^{4} + 47 \, a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(1100 \, a^{4} b^{3} c^{2} d^{3} - 325 \, a^{5} b^{2} c d^{4} + 47 \, a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(1100 \, a^{5} b^{2} c^{2} d^{3} - 325 \, a^{6} b c d^{4} + 47 \, a^{7} d^{5} + {\left(1100 \, b^{7} c^{2} d^{3} - 325 \, a b^{6} c d^{4} + 47 \, a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(1100 \, a b^{6} c^{2} d^{3} - 325 \, a^{2} b^{5} c d^{4} + 47 \, a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(1100 \, a^{2} b^{5} c^{2} d^{3} - 325 \, a^{3} b^{4} c d^{4} + 47 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(1100 \, a^{3} b^{4} c^{2} d^{3} - 325 \, a^{4} b^{3} c d^{4} + 47 \, a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(1100 \, a^{4} b^{3} c^{2} d^{3} - 325 \, a^{5} b^{2} c d^{4} + 47 \, a^{6} b d^{5}\right)} x - 60 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{5} b^{8} c^{5} g^{6} - 5 \, a^{6} b^{7} c^{4} d g^{6} + 10 \, a^{7} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{4} c d^{4} g^{6} - a^{10} b^{3} d^{5} g^{6} + {\left(b^{13} c^{5} g^{6} - 5 \, a b^{12} c^{4} d g^{6} + 10 \, a^{2} b^{11} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{10} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{9} c d^{4} g^{6} - a^{5} b^{8} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{12} c^{5} g^{6} - 5 \, a^{2} b^{11} c^{4} d g^{6} + 10 \, a^{3} b^{10} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{9} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{8} c d^{4} g^{6} - a^{6} b^{7} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} c^{5} g^{6} - 5 \, a^{3} b^{10} c^{4} d g^{6} + 10 \, a^{4} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{7} c d^{4} g^{6} - a^{7} b^{6} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} c^{5} g^{6} - 5 \, a^{4} b^{9} c^{4} d g^{6} + 10 \, a^{5} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{6} c d^{4} g^{6} - a^{8} b^{5} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} c^{5} g^{6} - 5 \, a^{5} b^{8} c^{4} d g^{6} + 10 \, a^{6} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{5} c d^{4} g^{6} - a^{9} b^{4} d^{5} g^{6}\right)} x}\right)} B^{2} c d^{2} i^{3} - \frac{1}{36000} \, {\left(60 \, {\left(\frac{77 \, a^{3} b^{4} c^{4} - 548 \, a^{4} b^{3} c^{3} d + 352 \, a^{5} b^{2} c^{2} d^{2} - 148 \, a^{6} b c d^{3} + 27 \, a^{7} d^{4} - 60 \, {\left(10 \, b^{7} c^{3} d - 10 \, a b^{6} c^{2} d^{2} + 5 \, a^{2} b^{5} c d^{3} - a^{3} b^{4} d^{4}\right)} x^{4} + 30 \, {\left(10 \, b^{7} c^{4} - 100 \, a b^{6} c^{3} d + 95 \, a^{2} b^{5} c^{2} d^{2} - 46 \, a^{3} b^{4} c d^{3} + 9 \, a^{4} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(50 \, a b^{6} c^{4} - 410 \, a^{2} b^{5} c^{3} d + 337 \, a^{3} b^{4} c^{2} d^{2} - 148 \, a^{4} b^{3} c d^{3} + 27 \, a^{5} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(65 \, a^{2} b^{5} c^{4} - 488 \, a^{3} b^{4} c^{3} d + 352 \, a^{4} b^{3} c^{2} d^{2} - 148 \, a^{5} b^{2} c d^{3} + 27 \, a^{6} b d^{4}\right)} x}{{\left(b^{13} c^{4} - 4 \, a b^{12} c^{3} d + 6 \, a^{2} b^{11} c^{2} d^{2} - 4 \, a^{3} b^{10} c d^{3} + a^{4} b^{9} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{12} c^{4} - 4 \, a^{2} b^{11} c^{3} d + 6 \, a^{3} b^{10} c^{2} d^{2} - 4 \, a^{4} b^{9} c d^{3} + a^{5} b^{8} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{11} c^{4} - 4 \, a^{3} b^{10} c^{3} d + 6 \, a^{4} b^{9} c^{2} d^{2} - 4 \, a^{5} b^{8} c d^{3} + a^{6} b^{7} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{10} c^{4} - 4 \, a^{4} b^{9} c^{3} d + 6 \, a^{5} b^{8} c^{2} d^{2} - 4 \, a^{6} b^{7} c d^{3} + a^{7} b^{6} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{9} c^{4} - 4 \, a^{5} b^{8} c^{3} d + 6 \, a^{6} b^{7} c^{2} d^{2} - 4 \, a^{7} b^{6} c d^{3} + a^{8} b^{5} d^{4}\right)} g^{6} x + {\left(a^{5} b^{8} c^{4} - 4 \, a^{6} b^{7} c^{3} d + 6 \, a^{7} b^{6} c^{2} d^{2} - 4 \, a^{8} b^{5} c d^{3} + a^{9} b^{4} d^{4}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{3} c^{3} d^{2} - 10 \, a b^{2} c^{2} d^{3} + 5 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{9} c^{5} - 5 \, a b^{8} c^{4} d + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{4} b^{5} c d^{4} - a^{5} b^{4} d^{5}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{3} c^{3} d^{2} - 10 \, a b^{2} c^{2} d^{3} + 5 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{9} c^{5} - 5 \, a b^{8} c^{4} d + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{4} b^{5} c d^{4} - a^{5} b^{4} d^{5}\right)} g^{6}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{3799 \, a^{3} b^{5} c^{5} - 51875 \, a^{4} b^{4} c^{4} d + 63000 \, a^{5} b^{3} c^{3} d^{2} - 19000 \, a^{6} b^{2} c^{2} d^{3} + 4625 \, a^{7} b c d^{4} - 549 \, a^{8} d^{5} - 60 \, {\left(900 \, b^{8} c^{4} d - 1400 \, a b^{7} c^{3} d^{2} + 675 \, a^{2} b^{6} c^{2} d^{3} - 202 \, a^{3} b^{5} c d^{4} + 27 \, a^{4} b^{4} d^{5}\right)} x^{4} + 30 \, {\left(300 \, b^{8} c^{5} - 7700 \, a b^{7} c^{4} d + 11175 \, a^{2} b^{6} c^{3} d^{2} - 5017 \, a^{3} b^{5} c^{2} d^{3} + 1425 \, a^{4} b^{4} c d^{4} - 183 \, a^{5} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(1900 \, a b^{7} c^{5} - 33950 \, a^{2} b^{6} c^{4} d + 45999 \, a^{3} b^{5} c^{3} d^{2} - 18025 \, a^{4} b^{4} c^{2} d^{3} + 4625 \, a^{5} b^{3} c d^{4} - 549 \, a^{6} b^{2} d^{5}\right)} x^{2} + 1800 \, {\left(10 \, a^{5} b^{3} c^{3} d^{2} - 10 \, a^{6} b^{2} c^{2} d^{3} + 5 \, a^{7} b c d^{4} - a^{8} d^{5} + {\left(10 \, b^{8} c^{3} d^{2} - 10 \, a b^{7} c^{2} d^{3} + 5 \, a^{2} b^{6} c d^{4} - a^{3} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{7} c^{3} d^{2} - 10 \, a^{2} b^{6} c^{2} d^{3} + 5 \, a^{3} b^{5} c d^{4} - a^{4} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{5} c^{3} d^{2} - 10 \, a^{4} b^{4} c^{2} d^{3} + 5 \, a^{5} b^{3} c d^{4} - a^{6} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{4} c^{3} d^{2} - 10 \, a^{5} b^{3} c^{2} d^{3} + 5 \, a^{6} b^{2} c d^{4} - a^{7} b d^{5}\right)} x\right)} \log\left(b x + a\right)^{2} + 1800 \, {\left(10 \, a^{5} b^{3} c^{3} d^{2} - 10 \, a^{6} b^{2} c^{2} d^{3} + 5 \, a^{7} b c d^{4} - a^{8} d^{5} + {\left(10 \, b^{8} c^{3} d^{2} - 10 \, a b^{7} c^{2} d^{3} + 5 \, a^{2} b^{6} c d^{4} - a^{3} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{7} c^{3} d^{2} - 10 \, a^{2} b^{6} c^{2} d^{3} + 5 \, a^{3} b^{5} c d^{4} - a^{4} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{5} c^{3} d^{2} - 10 \, a^{4} b^{4} c^{2} d^{3} + 5 \, a^{5} b^{3} c d^{4} - a^{6} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{4} c^{3} d^{2} - 10 \, a^{5} b^{3} c^{2} d^{3} + 5 \, a^{6} b^{2} c d^{4} - a^{7} b d^{5}\right)} x\right)} \log\left(d x + c\right)^{2} + 5 \, {\left(2875 \, a^{2} b^{6} c^{5} - 43451 \, a^{3} b^{5} c^{4} d + 55500 \, a^{4} b^{4} c^{3} d^{2} - 19000 \, a^{5} b^{3} c^{2} d^{3} + 4625 \, a^{6} b^{2} c d^{4} - 549 \, a^{7} b d^{5}\right)} x - 60 \, {\left(900 \, a^{5} b^{3} c^{3} d^{2} - 500 \, a^{6} b^{2} c^{2} d^{3} + 175 \, a^{7} b c d^{4} - 27 \, a^{8} d^{5} + {\left(900 \, b^{8} c^{3} d^{2} - 500 \, a b^{7} c^{2} d^{3} + 175 \, a^{2} b^{6} c d^{4} - 27 \, a^{3} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(900 \, a b^{7} c^{3} d^{2} - 500 \, a^{2} b^{6} c^{2} d^{3} + 175 \, a^{3} b^{5} c d^{4} - 27 \, a^{4} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(900 \, a^{2} b^{6} c^{3} d^{2} - 500 \, a^{3} b^{5} c^{2} d^{3} + 175 \, a^{4} b^{4} c d^{4} - 27 \, a^{5} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(900 \, a^{3} b^{5} c^{3} d^{2} - 500 \, a^{4} b^{4} c^{2} d^{3} + 175 \, a^{5} b^{3} c d^{4} - 27 \, a^{6} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(900 \, a^{4} b^{4} c^{3} d^{2} - 500 \, a^{5} b^{3} c^{2} d^{3} + 175 \, a^{6} b^{2} c d^{4} - 27 \, a^{7} b d^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(900 \, a^{5} b^{3} c^{3} d^{2} - 500 \, a^{6} b^{2} c^{2} d^{3} + 175 \, a^{7} b c d^{4} - 27 \, a^{8} d^{5} + {\left(900 \, b^{8} c^{3} d^{2} - 500 \, a b^{7} c^{2} d^{3} + 175 \, a^{2} b^{6} c d^{4} - 27 \, a^{3} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(900 \, a b^{7} c^{3} d^{2} - 500 \, a^{2} b^{6} c^{2} d^{3} + 175 \, a^{3} b^{5} c d^{4} - 27 \, a^{4} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(900 \, a^{2} b^{6} c^{3} d^{2} - 500 \, a^{3} b^{5} c^{2} d^{3} + 175 \, a^{4} b^{4} c d^{4} - 27 \, a^{5} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(900 \, a^{3} b^{5} c^{3} d^{2} - 500 \, a^{4} b^{4} c^{2} d^{3} + 175 \, a^{5} b^{3} c d^{4} - 27 \, a^{6} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(900 \, a^{4} b^{4} c^{3} d^{2} - 500 \, a^{5} b^{3} c^{2} d^{3} + 175 \, a^{6} b^{2} c d^{4} - 27 \, a^{7} b d^{5}\right)} x - 60 \, {\left(10 \, a^{5} b^{3} c^{3} d^{2} - 10 \, a^{6} b^{2} c^{2} d^{3} + 5 \, a^{7} b c d^{4} - a^{8} d^{5} + {\left(10 \, b^{8} c^{3} d^{2} - 10 \, a b^{7} c^{2} d^{3} + 5 \, a^{2} b^{6} c d^{4} - a^{3} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{7} c^{3} d^{2} - 10 \, a^{2} b^{6} c^{2} d^{3} + 5 \, a^{3} b^{5} c d^{4} - a^{4} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{5} c^{3} d^{2} - 10 \, a^{4} b^{4} c^{2} d^{3} + 5 \, a^{5} b^{3} c d^{4} - a^{6} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{4} c^{3} d^{2} - 10 \, a^{5} b^{3} c^{2} d^{3} + 5 \, a^{6} b^{2} c d^{4} - a^{7} b d^{5}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{5} b^{9} c^{5} g^{6} - 5 \, a^{6} b^{8} c^{4} d g^{6} + 10 \, a^{7} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{5} c d^{4} g^{6} - a^{10} b^{4} d^{5} g^{6} + {\left(b^{14} c^{5} g^{6} - 5 \, a b^{13} c^{4} d g^{6} + 10 \, a^{2} b^{12} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{11} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{10} c d^{4} g^{6} - a^{5} b^{9} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{13} c^{5} g^{6} - 5 \, a^{2} b^{12} c^{4} d g^{6} + 10 \, a^{3} b^{11} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{10} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{9} c d^{4} g^{6} - a^{6} b^{8} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{12} c^{5} g^{6} - 5 \, a^{3} b^{11} c^{4} d g^{6} + 10 \, a^{4} b^{10} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{9} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{8} c d^{4} g^{6} - a^{7} b^{7} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{11} c^{5} g^{6} - 5 \, a^{4} b^{10} c^{4} d g^{6} + 10 \, a^{5} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{7} c d^{4} g^{6} - a^{8} b^{6} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{10} c^{5} g^{6} - 5 \, a^{5} b^{9} c^{4} d g^{6} + 10 \, a^{6} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{6} c d^{4} g^{6} - a^{9} b^{5} d^{5} g^{6}\right)} x}\right)} B^{2} d^{3} i^{3} - \frac{1}{600} \, A B d^{3} i^{3} {\left(\frac{60 \, {\left(10 \, b^{3} x^{3} + 10 \, a b^{2} x^{2} + 5 \, a^{2} b x + a^{3}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{9} g^{6} x^{5} + 5 \, a b^{8} g^{6} x^{4} + 10 \, a^{2} b^{7} g^{6} x^{3} + 10 \, a^{3} b^{6} g^{6} x^{2} + 5 \, a^{4} b^{5} g^{6} x + a^{5} b^{4} g^{6}} + \frac{77 \, a^{3} b^{4} c^{4} - 548 \, a^{4} b^{3} c^{3} d + 352 \, a^{5} b^{2} c^{2} d^{2} - 148 \, a^{6} b c d^{3} + 27 \, a^{7} d^{4} - 60 \, {\left(10 \, b^{7} c^{3} d - 10 \, a b^{6} c^{2} d^{2} + 5 \, a^{2} b^{5} c d^{3} - a^{3} b^{4} d^{4}\right)} x^{4} + 30 \, {\left(10 \, b^{7} c^{4} - 100 \, a b^{6} c^{3} d + 95 \, a^{2} b^{5} c^{2} d^{2} - 46 \, a^{3} b^{4} c d^{3} + 9 \, a^{4} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(50 \, a b^{6} c^{4} - 410 \, a^{2} b^{5} c^{3} d + 337 \, a^{3} b^{4} c^{2} d^{2} - 148 \, a^{4} b^{3} c d^{3} + 27 \, a^{5} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(65 \, a^{2} b^{5} c^{4} - 488 \, a^{3} b^{4} c^{3} d + 352 \, a^{4} b^{3} c^{2} d^{2} - 148 \, a^{5} b^{2} c d^{3} + 27 \, a^{6} b d^{4}\right)} x}{{\left(b^{13} c^{4} - 4 \, a b^{12} c^{3} d + 6 \, a^{2} b^{11} c^{2} d^{2} - 4 \, a^{3} b^{10} c d^{3} + a^{4} b^{9} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{12} c^{4} - 4 \, a^{2} b^{11} c^{3} d + 6 \, a^{3} b^{10} c^{2} d^{2} - 4 \, a^{4} b^{9} c d^{3} + a^{5} b^{8} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{11} c^{4} - 4 \, a^{3} b^{10} c^{3} d + 6 \, a^{4} b^{9} c^{2} d^{2} - 4 \, a^{5} b^{8} c d^{3} + a^{6} b^{7} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{10} c^{4} - 4 \, a^{4} b^{9} c^{3} d + 6 \, a^{5} b^{8} c^{2} d^{2} - 4 \, a^{6} b^{7} c d^{3} + a^{7} b^{6} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{9} c^{4} - 4 \, a^{5} b^{8} c^{3} d + 6 \, a^{6} b^{7} c^{2} d^{2} - 4 \, a^{7} b^{6} c d^{3} + a^{8} b^{5} d^{4}\right)} g^{6} x + {\left(a^{5} b^{8} c^{4} - 4 \, a^{6} b^{7} c^{3} d + 6 \, a^{7} b^{6} c^{2} d^{2} - 4 \, a^{8} b^{5} c d^{3} + a^{9} b^{4} d^{4}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{3} c^{3} d^{2} - 10 \, a b^{2} c^{2} d^{3} + 5 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{9} c^{5} - 5 \, a b^{8} c^{4} d + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{4} b^{5} c d^{4} - a^{5} b^{4} d^{5}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{3} c^{3} d^{2} - 10 \, a b^{2} c^{2} d^{3} + 5 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{9} c^{5} - 5 \, a b^{8} c^{4} d + 10 \, a^{2} b^{7} c^{3} d^{2} - 10 \, a^{3} b^{6} c^{2} d^{3} + 5 \, a^{4} b^{5} c d^{4} - a^{5} b^{4} d^{5}\right)} g^{6}}\right)} - \frac{1}{300} \, A B c d^{2} i^{3} {\left(\frac{60 \, {\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}} + \frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} - \frac{1}{200} \, A B c^{2} d i^{3} {\left(\frac{60 \, {\left(5 \, b x + a\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}} + \frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} - \frac{1}{150} \, A B c^{3} i^{3} {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} - \frac{B^{2} c^{3} i^{3} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}} - \frac{3 \, {\left(5 \, b x + a\right)} A^{2} c^{2} d i^{3}}{20 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} A^{2} c d^{2} i^{3}}{10 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{{\left(10 \, b^{3} x^{3} + 10 \, a b^{2} x^{2} + 5 \, a^{2} b x + a^{3}\right)} A^{2} d^{3} i^{3}}{20 \, {\left(b^{9} g^{6} x^{5} + 5 \, a b^{8} g^{6} x^{4} + 10 \, a^{2} b^{7} g^{6} x^{3} + 10 \, a^{3} b^{6} g^{6} x^{2} + 5 \, a^{4} b^{5} g^{6} x + a^{5} b^{4} g^{6}\right)}} - \frac{A^{2} c^{3} i^{3}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}}"," ",0,"-3/20*(5*b*x + a)*B^2*c^2*d*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/10*(10*b^2*x^2 + 5*a*b*x + a^2)*B^2*c*d^2*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/20*(10*b^3*x^3 + 10*a*b^2*x^2 + 5*a^2*b*x + a^3)*B^2*d^3*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^9*g^6*x^5 + 5*a*b^8*g^6*x^4 + 10*a^2*b^7*g^6*x^3 + 10*a^3*b^6*g^6*x^2 + 5*a^4*b^5*g^6*x + a^5*b^4*g^6) - 1/9000*(60*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (144*b^5*c^5 - 1125*a*b^4*c^4*d + 4000*a^2*b^3*c^3*d^2 - 9000*a^3*b^2*c^2*d^3 + 18000*a^4*b*c*d^4 - 12019*a^5*d^5 + 8220*(b^5*c*d^4 - a*b^4*d^5)*x^4 - 30*(77*b^5*c^2*d^3 - 1250*a*b^4*c*d^4 + 1173*a^2*b^3*d^5)*x^3 + 10*(94*b^5*c^3*d^2 - 975*a*b^4*c^2*d^3 + 6600*a^2*b^3*c*d^4 - 5719*a^3*b^2*d^5)*x^2 - 1800*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a)^2 - 1800*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(d*x + c)^2 - 5*(81*b^5*c^4*d - 700*a*b^4*c^3*d^2 + 3000*a^2*b^3*c^2*d^3 - 10800*a^3*b^2*c*d^4 + 8419*a^4*b*d^5)*x + 8220*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a) - 60*(137*b^5*d^5*x^5 + 685*a*b^4*d^5*x^4 + 1370*a^2*b^3*d^5*x^3 + 1370*a^3*b^2*d^5*x^2 + 685*a^4*b*d^5*x + 137*a^5*d^5 - 60*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a))*log(d*x + c))/(a^5*b^6*c^5*g^6 - 5*a^6*b^5*c^4*d*g^6 + 10*a^7*b^4*c^3*d^2*g^6 - 10*a^8*b^3*c^2*d^3*g^6 + 5*a^9*b^2*c*d^4*g^6 - a^10*b*d^5*g^6 + (b^11*c^5*g^6 - 5*a*b^10*c^4*d*g^6 + 10*a^2*b^9*c^3*d^2*g^6 - 10*a^3*b^8*c^2*d^3*g^6 + 5*a^4*b^7*c*d^4*g^6 - a^5*b^6*d^5*g^6)*x^5 + 5*(a*b^10*c^5*g^6 - 5*a^2*b^9*c^4*d*g^6 + 10*a^3*b^8*c^3*d^2*g^6 - 10*a^4*b^7*c^2*d^3*g^6 + 5*a^5*b^6*c*d^4*g^6 - a^6*b^5*d^5*g^6)*x^4 + 10*(a^2*b^9*c^5*g^6 - 5*a^3*b^8*c^4*d*g^6 + 10*a^4*b^7*c^3*d^2*g^6 - 10*a^5*b^6*c^2*d^3*g^6 + 5*a^6*b^5*c*d^4*g^6 - a^7*b^4*d^5*g^6)*x^3 + 10*(a^3*b^8*c^5*g^6 - 5*a^4*b^7*c^4*d*g^6 + 10*a^5*b^6*c^3*d^2*g^6 - 10*a^6*b^5*c^2*d^3*g^6 + 5*a^7*b^4*c*d^4*g^6 - a^8*b^3*d^5*g^6)*x^2 + 5*(a^4*b^7*c^5*g^6 - 5*a^5*b^6*c^4*d*g^6 + 10*a^6*b^5*c^3*d^2*g^6 - 10*a^7*b^4*c^2*d^3*g^6 + 5*a^8*b^3*c*d^4*g^6 - a^9*b^2*d^5*g^6)*x))*B^2*c^3*i^3 - 1/12000*(60*((27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (549*a*b^5*c^5 - 4625*a^2*b^4*c^4*d + 19000*a^3*b^3*c^3*d^2 - 63000*a^4*b^2*c^2*d^3 + 51875*a^5*b*c*d^4 - 3799*a^6*d^5 - 60*(625*b^6*c^2*d^3 - 702*a*b^5*c*d^4 + 77*a^2*b^4*d^5)*x^4 + 30*(325*b^6*c^3*d^2 - 5667*a*b^5*c^2*d^3 + 5975*a^2*b^4*c*d^4 - 633*a^3*b^3*d^5)*x^3 - 10*(350*b^6*c^4*d - 3949*a*b^5*c^3*d^2 + 29475*a^2*b^4*c^2*d^3 - 28775*a^3*b^3*c*d^4 + 2899*a^4*b^2*d^5)*x^2 + 1800*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(b*x + a)^2 + 1800*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(d*x + c)^2 + 5*(225*b^6*c^5 - 2201*a*b^5*c^4*d + 10900*a^2*b^4*c^3*d^2 - 46200*a^3*b^3*c^2*d^3 + 41075*a^4*b^2*c*d^4 - 3799*a^5*b*d^5)*x - 60*(625*a^5*b*c*d^4 - 77*a^6*d^5 + (625*b^6*c*d^4 - 77*a*b^5*d^5)*x^5 + 5*(625*a*b^5*c*d^4 - 77*a^2*b^4*d^5)*x^4 + 10*(625*a^2*b^4*c*d^4 - 77*a^3*b^3*d^5)*x^3 + 10*(625*a^3*b^3*c*d^4 - 77*a^4*b^2*d^5)*x^2 + 5*(625*a^4*b^2*c*d^4 - 77*a^5*b*d^5)*x)*log(b*x + a) + 60*(625*a^5*b*c*d^4 - 77*a^6*d^5 + (625*b^6*c*d^4 - 77*a*b^5*d^5)*x^5 + 5*(625*a*b^5*c*d^4 - 77*a^2*b^4*d^5)*x^4 + 10*(625*a^2*b^4*c*d^4 - 77*a^3*b^3*d^5)*x^3 + 10*(625*a^3*b^3*c*d^4 - 77*a^4*b^2*d^5)*x^2 + 5*(625*a^4*b^2*c*d^4 - 77*a^5*b*d^5)*x - 60*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(b*x + a))*log(d*x + c))/(a^5*b^7*c^5*g^6 - 5*a^6*b^6*c^4*d*g^6 + 10*a^7*b^5*c^3*d^2*g^6 - 10*a^8*b^4*c^2*d^3*g^6 + 5*a^9*b^3*c*d^4*g^6 - a^10*b^2*d^5*g^6 + (b^12*c^5*g^6 - 5*a*b^11*c^4*d*g^6 + 10*a^2*b^10*c^3*d^2*g^6 - 10*a^3*b^9*c^2*d^3*g^6 + 5*a^4*b^8*c*d^4*g^6 - a^5*b^7*d^5*g^6)*x^5 + 5*(a*b^11*c^5*g^6 - 5*a^2*b^10*c^4*d*g^6 + 10*a^3*b^9*c^3*d^2*g^6 - 10*a^4*b^8*c^2*d^3*g^6 + 5*a^5*b^7*c*d^4*g^6 - a^6*b^6*d^5*g^6)*x^4 + 10*(a^2*b^10*c^5*g^6 - 5*a^3*b^9*c^4*d*g^6 + 10*a^4*b^8*c^3*d^2*g^6 - 10*a^5*b^7*c^2*d^3*g^6 + 5*a^6*b^6*c*d^4*g^6 - a^7*b^5*d^5*g^6)*x^3 + 10*(a^3*b^9*c^5*g^6 - 5*a^4*b^8*c^4*d*g^6 + 10*a^5*b^7*c^3*d^2*g^6 - 10*a^6*b^6*c^2*d^3*g^6 + 5*a^7*b^5*c*d^4*g^6 - a^8*b^4*d^5*g^6)*x^2 + 5*(a^4*b^8*c^5*g^6 - 5*a^5*b^7*c^4*d*g^6 + 10*a^6*b^6*c^3*d^2*g^6 - 10*a^7*b^5*c^2*d^3*g^6 + 5*a^8*b^4*c*d^4*g^6 - a^9*b^3*d^5*g^6)*x))*B^2*c^2*d*i^3 - 1/18000*(60*((47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (1489*a^2*b^5*c^5 - 14375*a^3*b^4*c^4*d + 85000*a^4*b^3*c^3*d^2 - 85000*a^5*b^2*c^2*d^3 + 14375*a^6*b*c*d^4 - 1489*a^7*d^5 + 60*(1100*b^7*c^3*d^2 - 1425*a*b^6*c^2*d^3 + 372*a^2*b^5*c*d^4 - 47*a^3*b^4*d^5)*x^4 - 30*(500*b^7*c^4*d - 9825*a*b^6*c^3*d^2 + 11937*a^2*b^5*c^2*d^3 - 2975*a^3*b^4*c*d^4 + 363*a^4*b^3*d^5)*x^3 + 10*(400*b^7*c^5 - 5450*a*b^6*c^4*d + 49189*a^2*b^5*c^3*d^2 - 55525*a^3*b^4*c^2*d^3 + 12875*a^4*b^3*c*d^4 - 1489*a^5*b^2*d^5)*x^2 - 1800*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(b*x + a)^2 - 1800*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(d*x + c)^2 + 5*(925*a*b^6*c^5 - 9911*a^2*b^5*c^4*d + 67900*a^3*b^4*c^3*d^2 - 71800*a^4*b^3*c^2*d^3 + 14375*a^5*b^2*c*d^4 - 1489*a^6*b*d^5)*x + 60*(1100*a^5*b^2*c^2*d^3 - 325*a^6*b*c*d^4 + 47*a^7*d^5 + (1100*b^7*c^2*d^3 - 325*a*b^6*c*d^4 + 47*a^2*b^5*d^5)*x^5 + 5*(1100*a*b^6*c^2*d^3 - 325*a^2*b^5*c*d^4 + 47*a^3*b^4*d^5)*x^4 + 10*(1100*a^2*b^5*c^2*d^3 - 325*a^3*b^4*c*d^4 + 47*a^4*b^3*d^5)*x^3 + 10*(1100*a^3*b^4*c^2*d^3 - 325*a^4*b^3*c*d^4 + 47*a^5*b^2*d^5)*x^2 + 5*(1100*a^4*b^3*c^2*d^3 - 325*a^5*b^2*c*d^4 + 47*a^6*b*d^5)*x)*log(b*x + a) - 60*(1100*a^5*b^2*c^2*d^3 - 325*a^6*b*c*d^4 + 47*a^7*d^5 + (1100*b^7*c^2*d^3 - 325*a*b^6*c*d^4 + 47*a^2*b^5*d^5)*x^5 + 5*(1100*a*b^6*c^2*d^3 - 325*a^2*b^5*c*d^4 + 47*a^3*b^4*d^5)*x^4 + 10*(1100*a^2*b^5*c^2*d^3 - 325*a^3*b^4*c*d^4 + 47*a^4*b^3*d^5)*x^3 + 10*(1100*a^3*b^4*c^2*d^3 - 325*a^4*b^3*c*d^4 + 47*a^5*b^2*d^5)*x^2 + 5*(1100*a^4*b^3*c^2*d^3 - 325*a^5*b^2*c*d^4 + 47*a^6*b*d^5)*x - 60*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(b*x + a))*log(d*x + c))/(a^5*b^8*c^5*g^6 - 5*a^6*b^7*c^4*d*g^6 + 10*a^7*b^6*c^3*d^2*g^6 - 10*a^8*b^5*c^2*d^3*g^6 + 5*a^9*b^4*c*d^4*g^6 - a^10*b^3*d^5*g^6 + (b^13*c^5*g^6 - 5*a*b^12*c^4*d*g^6 + 10*a^2*b^11*c^3*d^2*g^6 - 10*a^3*b^10*c^2*d^3*g^6 + 5*a^4*b^9*c*d^4*g^6 - a^5*b^8*d^5*g^6)*x^5 + 5*(a*b^12*c^5*g^6 - 5*a^2*b^11*c^4*d*g^6 + 10*a^3*b^10*c^3*d^2*g^6 - 10*a^4*b^9*c^2*d^3*g^6 + 5*a^5*b^8*c*d^4*g^6 - a^6*b^7*d^5*g^6)*x^4 + 10*(a^2*b^11*c^5*g^6 - 5*a^3*b^10*c^4*d*g^6 + 10*a^4*b^9*c^3*d^2*g^6 - 10*a^5*b^8*c^2*d^3*g^6 + 5*a^6*b^7*c*d^4*g^6 - a^7*b^6*d^5*g^6)*x^3 + 10*(a^3*b^10*c^5*g^6 - 5*a^4*b^9*c^4*d*g^6 + 10*a^5*b^8*c^3*d^2*g^6 - 10*a^6*b^7*c^2*d^3*g^6 + 5*a^7*b^6*c*d^4*g^6 - a^8*b^5*d^5*g^6)*x^2 + 5*(a^4*b^9*c^5*g^6 - 5*a^5*b^8*c^4*d*g^6 + 10*a^6*b^7*c^3*d^2*g^6 - 10*a^7*b^6*c^2*d^3*g^6 + 5*a^8*b^5*c*d^4*g^6 - a^9*b^4*d^5*g^6)*x))*B^2*c*d^2*i^3 - 1/36000*(60*((77*a^3*b^4*c^4 - 548*a^4*b^3*c^3*d + 352*a^5*b^2*c^2*d^2 - 148*a^6*b*c*d^3 + 27*a^7*d^4 - 60*(10*b^7*c^3*d - 10*a*b^6*c^2*d^2 + 5*a^2*b^5*c*d^3 - a^3*b^4*d^4)*x^4 + 30*(10*b^7*c^4 - 100*a*b^6*c^3*d + 95*a^2*b^5*c^2*d^2 - 46*a^3*b^4*c*d^3 + 9*a^4*b^3*d^4)*x^3 + 10*(50*a*b^6*c^4 - 410*a^2*b^5*c^3*d + 337*a^3*b^4*c^2*d^2 - 148*a^4*b^3*c*d^3 + 27*a^5*b^2*d^4)*x^2 + 5*(65*a^2*b^5*c^4 - 488*a^3*b^4*c^3*d + 352*a^4*b^3*c^2*d^2 - 148*a^5*b^2*c*d^3 + 27*a^6*b*d^4)*x)/((b^13*c^4 - 4*a*b^12*c^3*d + 6*a^2*b^11*c^2*d^2 - 4*a^3*b^10*c*d^3 + a^4*b^9*d^4)*g^6*x^5 + 5*(a*b^12*c^4 - 4*a^2*b^11*c^3*d + 6*a^3*b^10*c^2*d^2 - 4*a^4*b^9*c*d^3 + a^5*b^8*d^4)*g^6*x^4 + 10*(a^2*b^11*c^4 - 4*a^3*b^10*c^3*d + 6*a^4*b^9*c^2*d^2 - 4*a^5*b^8*c*d^3 + a^6*b^7*d^4)*g^6*x^3 + 10*(a^3*b^10*c^4 - 4*a^4*b^9*c^3*d + 6*a^5*b^8*c^2*d^2 - 4*a^6*b^7*c*d^3 + a^7*b^6*d^4)*g^6*x^2 + 5*(a^4*b^9*c^4 - 4*a^5*b^8*c^3*d + 6*a^6*b^7*c^2*d^2 - 4*a^7*b^6*c*d^3 + a^8*b^5*d^4)*g^6*x + (a^5*b^8*c^4 - 4*a^6*b^7*c^3*d + 6*a^7*b^6*c^2*d^2 - 4*a^8*b^5*c*d^3 + a^9*b^4*d^4)*g^6) - 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(b*x + a)/((b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6) + 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(d*x + c)/((b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + (3799*a^3*b^5*c^5 - 51875*a^4*b^4*c^4*d + 63000*a^5*b^3*c^3*d^2 - 19000*a^6*b^2*c^2*d^3 + 4625*a^7*b*c*d^4 - 549*a^8*d^5 - 60*(900*b^8*c^4*d - 1400*a*b^7*c^3*d^2 + 675*a^2*b^6*c^2*d^3 - 202*a^3*b^5*c*d^4 + 27*a^4*b^4*d^5)*x^4 + 30*(300*b^8*c^5 - 7700*a*b^7*c^4*d + 11175*a^2*b^6*c^3*d^2 - 5017*a^3*b^5*c^2*d^3 + 1425*a^4*b^4*c*d^4 - 183*a^5*b^3*d^5)*x^3 + 10*(1900*a*b^7*c^5 - 33950*a^2*b^6*c^4*d + 45999*a^3*b^5*c^3*d^2 - 18025*a^4*b^4*c^2*d^3 + 4625*a^5*b^3*c*d^4 - 549*a^6*b^2*d^5)*x^2 + 1800*(10*a^5*b^3*c^3*d^2 - 10*a^6*b^2*c^2*d^3 + 5*a^7*b*c*d^4 - a^8*d^5 + (10*b^8*c^3*d^2 - 10*a*b^7*c^2*d^3 + 5*a^2*b^6*c*d^4 - a^3*b^5*d^5)*x^5 + 5*(10*a*b^7*c^3*d^2 - 10*a^2*b^6*c^2*d^3 + 5*a^3*b^5*c*d^4 - a^4*b^4*d^5)*x^4 + 10*(10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*x^3 + 10*(10*a^3*b^5*c^3*d^2 - 10*a^4*b^4*c^2*d^3 + 5*a^5*b^3*c*d^4 - a^6*b^2*d^5)*x^2 + 5*(10*a^4*b^4*c^3*d^2 - 10*a^5*b^3*c^2*d^3 + 5*a^6*b^2*c*d^4 - a^7*b*d^5)*x)*log(b*x + a)^2 + 1800*(10*a^5*b^3*c^3*d^2 - 10*a^6*b^2*c^2*d^3 + 5*a^7*b*c*d^4 - a^8*d^5 + (10*b^8*c^3*d^2 - 10*a*b^7*c^2*d^3 + 5*a^2*b^6*c*d^4 - a^3*b^5*d^5)*x^5 + 5*(10*a*b^7*c^3*d^2 - 10*a^2*b^6*c^2*d^3 + 5*a^3*b^5*c*d^4 - a^4*b^4*d^5)*x^4 + 10*(10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*x^3 + 10*(10*a^3*b^5*c^3*d^2 - 10*a^4*b^4*c^2*d^3 + 5*a^5*b^3*c*d^4 - a^6*b^2*d^5)*x^2 + 5*(10*a^4*b^4*c^3*d^2 - 10*a^5*b^3*c^2*d^3 + 5*a^6*b^2*c*d^4 - a^7*b*d^5)*x)*log(d*x + c)^2 + 5*(2875*a^2*b^6*c^5 - 43451*a^3*b^5*c^4*d + 55500*a^4*b^4*c^3*d^2 - 19000*a^5*b^3*c^2*d^3 + 4625*a^6*b^2*c*d^4 - 549*a^7*b*d^5)*x - 60*(900*a^5*b^3*c^3*d^2 - 500*a^6*b^2*c^2*d^3 + 175*a^7*b*c*d^4 - 27*a^8*d^5 + (900*b^8*c^3*d^2 - 500*a*b^7*c^2*d^3 + 175*a^2*b^6*c*d^4 - 27*a^3*b^5*d^5)*x^5 + 5*(900*a*b^7*c^3*d^2 - 500*a^2*b^6*c^2*d^3 + 175*a^3*b^5*c*d^4 - 27*a^4*b^4*d^5)*x^4 + 10*(900*a^2*b^6*c^3*d^2 - 500*a^3*b^5*c^2*d^3 + 175*a^4*b^4*c*d^4 - 27*a^5*b^3*d^5)*x^3 + 10*(900*a^3*b^5*c^3*d^2 - 500*a^4*b^4*c^2*d^3 + 175*a^5*b^3*c*d^4 - 27*a^6*b^2*d^5)*x^2 + 5*(900*a^4*b^4*c^3*d^2 - 500*a^5*b^3*c^2*d^3 + 175*a^6*b^2*c*d^4 - 27*a^7*b*d^5)*x)*log(b*x + a) + 60*(900*a^5*b^3*c^3*d^2 - 500*a^6*b^2*c^2*d^3 + 175*a^7*b*c*d^4 - 27*a^8*d^5 + (900*b^8*c^3*d^2 - 500*a*b^7*c^2*d^3 + 175*a^2*b^6*c*d^4 - 27*a^3*b^5*d^5)*x^5 + 5*(900*a*b^7*c^3*d^2 - 500*a^2*b^6*c^2*d^3 + 175*a^3*b^5*c*d^4 - 27*a^4*b^4*d^5)*x^4 + 10*(900*a^2*b^6*c^3*d^2 - 500*a^3*b^5*c^2*d^3 + 175*a^4*b^4*c*d^4 - 27*a^5*b^3*d^5)*x^3 + 10*(900*a^3*b^5*c^3*d^2 - 500*a^4*b^4*c^2*d^3 + 175*a^5*b^3*c*d^4 - 27*a^6*b^2*d^5)*x^2 + 5*(900*a^4*b^4*c^3*d^2 - 500*a^5*b^3*c^2*d^3 + 175*a^6*b^2*c*d^4 - 27*a^7*b*d^5)*x - 60*(10*a^5*b^3*c^3*d^2 - 10*a^6*b^2*c^2*d^3 + 5*a^7*b*c*d^4 - a^8*d^5 + (10*b^8*c^3*d^2 - 10*a*b^7*c^2*d^3 + 5*a^2*b^6*c*d^4 - a^3*b^5*d^5)*x^5 + 5*(10*a*b^7*c^3*d^2 - 10*a^2*b^6*c^2*d^3 + 5*a^3*b^5*c*d^4 - a^4*b^4*d^5)*x^4 + 10*(10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*x^3 + 10*(10*a^3*b^5*c^3*d^2 - 10*a^4*b^4*c^2*d^3 + 5*a^5*b^3*c*d^4 - a^6*b^2*d^5)*x^2 + 5*(10*a^4*b^4*c^3*d^2 - 10*a^5*b^3*c^2*d^3 + 5*a^6*b^2*c*d^4 - a^7*b*d^5)*x)*log(b*x + a))*log(d*x + c))/(a^5*b^9*c^5*g^6 - 5*a^6*b^8*c^4*d*g^6 + 10*a^7*b^7*c^3*d^2*g^6 - 10*a^8*b^6*c^2*d^3*g^6 + 5*a^9*b^5*c*d^4*g^6 - a^10*b^4*d^5*g^6 + (b^14*c^5*g^6 - 5*a*b^13*c^4*d*g^6 + 10*a^2*b^12*c^3*d^2*g^6 - 10*a^3*b^11*c^2*d^3*g^6 + 5*a^4*b^10*c*d^4*g^6 - a^5*b^9*d^5*g^6)*x^5 + 5*(a*b^13*c^5*g^6 - 5*a^2*b^12*c^4*d*g^6 + 10*a^3*b^11*c^3*d^2*g^6 - 10*a^4*b^10*c^2*d^3*g^6 + 5*a^5*b^9*c*d^4*g^6 - a^6*b^8*d^5*g^6)*x^4 + 10*(a^2*b^12*c^5*g^6 - 5*a^3*b^11*c^4*d*g^6 + 10*a^4*b^10*c^3*d^2*g^6 - 10*a^5*b^9*c^2*d^3*g^6 + 5*a^6*b^8*c*d^4*g^6 - a^7*b^7*d^5*g^6)*x^3 + 10*(a^3*b^11*c^5*g^6 - 5*a^4*b^10*c^4*d*g^6 + 10*a^5*b^9*c^3*d^2*g^6 - 10*a^6*b^8*c^2*d^3*g^6 + 5*a^7*b^7*c*d^4*g^6 - a^8*b^6*d^5*g^6)*x^2 + 5*(a^4*b^10*c^5*g^6 - 5*a^5*b^9*c^4*d*g^6 + 10*a^6*b^8*c^3*d^2*g^6 - 10*a^7*b^7*c^2*d^3*g^6 + 5*a^8*b^6*c*d^4*g^6 - a^9*b^5*d^5*g^6)*x))*B^2*d^3*i^3 - 1/600*A*B*d^3*i^3*(60*(10*b^3*x^3 + 10*a*b^2*x^2 + 5*a^2*b*x + a^3)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^9*g^6*x^5 + 5*a*b^8*g^6*x^4 + 10*a^2*b^7*g^6*x^3 + 10*a^3*b^6*g^6*x^2 + 5*a^4*b^5*g^6*x + a^5*b^4*g^6) + (77*a^3*b^4*c^4 - 548*a^4*b^3*c^3*d + 352*a^5*b^2*c^2*d^2 - 148*a^6*b*c*d^3 + 27*a^7*d^4 - 60*(10*b^7*c^3*d - 10*a*b^6*c^2*d^2 + 5*a^2*b^5*c*d^3 - a^3*b^4*d^4)*x^4 + 30*(10*b^7*c^4 - 100*a*b^6*c^3*d + 95*a^2*b^5*c^2*d^2 - 46*a^3*b^4*c*d^3 + 9*a^4*b^3*d^4)*x^3 + 10*(50*a*b^6*c^4 - 410*a^2*b^5*c^3*d + 337*a^3*b^4*c^2*d^2 - 148*a^4*b^3*c*d^3 + 27*a^5*b^2*d^4)*x^2 + 5*(65*a^2*b^5*c^4 - 488*a^3*b^4*c^3*d + 352*a^4*b^3*c^2*d^2 - 148*a^5*b^2*c*d^3 + 27*a^6*b*d^4)*x)/((b^13*c^4 - 4*a*b^12*c^3*d + 6*a^2*b^11*c^2*d^2 - 4*a^3*b^10*c*d^3 + a^4*b^9*d^4)*g^6*x^5 + 5*(a*b^12*c^4 - 4*a^2*b^11*c^3*d + 6*a^3*b^10*c^2*d^2 - 4*a^4*b^9*c*d^3 + a^5*b^8*d^4)*g^6*x^4 + 10*(a^2*b^11*c^4 - 4*a^3*b^10*c^3*d + 6*a^4*b^9*c^2*d^2 - 4*a^5*b^8*c*d^3 + a^6*b^7*d^4)*g^6*x^3 + 10*(a^3*b^10*c^4 - 4*a^4*b^9*c^3*d + 6*a^5*b^8*c^2*d^2 - 4*a^6*b^7*c*d^3 + a^7*b^6*d^4)*g^6*x^2 + 5*(a^4*b^9*c^4 - 4*a^5*b^8*c^3*d + 6*a^6*b^7*c^2*d^2 - 4*a^7*b^6*c*d^3 + a^8*b^5*d^4)*g^6*x + (a^5*b^8*c^4 - 4*a^6*b^7*c^3*d + 6*a^7*b^6*c^2*d^2 - 4*a^8*b^5*c*d^3 + a^9*b^4*d^4)*g^6) - 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(b*x + a)/((b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6) + 60*(10*b^3*c^3*d^2 - 10*a*b^2*c^2*d^3 + 5*a^2*b*c*d^4 - a^3*d^5)*log(d*x + c)/((b^9*c^5 - 5*a*b^8*c^4*d + 10*a^2*b^7*c^3*d^2 - 10*a^3*b^6*c^2*d^3 + 5*a^4*b^5*c*d^4 - a^5*b^4*d^5)*g^6)) - 1/300*A*B*c*d^2*i^3*(60*(10*b^2*x^2 + 5*a*b*x + a^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) + (47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6)) - 1/200*A*B*c^2*d*i^3*(60*(5*b*x + a)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) + (27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6)) - 1/150*A*B*c^3*i^3*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6)) - 1/5*B^2*c^3*i^3*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) - 3/20*(5*b*x + a)*A^2*c^2*d*i^3/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/10*(10*b^2*x^2 + 5*a*b*x + a^2)*A^2*c*d^2*i^3/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/20*(10*b^3*x^3 + 10*a*b^2*x^2 + 5*a^2*b*x + a^3)*A^2*d^3*i^3/(b^9*g^6*x^5 + 5*a*b^8*g^6*x^4 + 10*a^2*b^7*g^6*x^3 + 10*a^3*b^6*g^6*x^2 + 5*a^4*b^5*g^6*x + a^5*b^4*g^6) - 1/5*A^2*c^3*i^3/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6)","B",0
83,-1,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^7,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,0,0,0,0.000000," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i),x, algorithm=""maxima"")","3 \, A^{2} a^{2} b g^{3} {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} - \frac{1}{6} \, A^{2} b^{3} g^{3} {\left(\frac{6 \, c^{3} \log\left(d x + c\right)}{d^{4} i} - \frac{2 \, d^{2} x^{3} - 3 \, c d x^{2} + 6 \, c^{2} x}{d^{3} i}\right)} + \frac{3}{2} \, A^{2} a b^{2} g^{3} {\left(\frac{2 \, c^{2} \log\left(d x + c\right)}{d^{3} i} + \frac{d x^{2} - 2 \, c x}{d^{2} i}\right)} + \frac{A^{2} a^{3} g^{3} \log\left(d i x + c i\right)}{d i} - \frac{2 \, {\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - a^{3} d^{3} g^{3}\right)} B^{2} \log\left(d x + c\right)^{3} - {\left(2 \, B^{2} b^{3} d^{3} g^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} g^{3} - 3 \, a b^{2} d^{3} g^{3}\right)} B^{2} x^{2} + 6 \, {\left(b^{3} c^{2} d g^{3} - 3 \, a b^{2} c d^{2} g^{3} + 3 \, a^{2} b d^{3} g^{3}\right)} B^{2} x\right)} \log\left(d x + c\right)^{2}}{6 \, d^{4} i} - \int -\frac{3 \, B^{2} a^{3} d^{2} g^{3} \log\left(e\right)^{2} + 6 \, A B a^{3} d^{2} g^{3} \log\left(e\right) + 3 \, {\left(B^{2} b^{3} d^{2} g^{3} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{2} g^{3} \log\left(e\right)\right)} x^{3} + 9 \, {\left(B^{2} a b^{2} d^{2} g^{3} \log\left(e\right)^{2} + 2 \, A B a b^{2} d^{2} g^{3} \log\left(e\right)\right)} x^{2} + 3 \, {\left(B^{2} b^{3} d^{2} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{2} g^{3} x + B^{2} a^{3} d^{2} g^{3}\right)} \log\left(b x + a\right)^{2} + 9 \, {\left(B^{2} a^{2} b d^{2} g^{3} \log\left(e\right)^{2} + 2 \, A B a^{2} b d^{2} g^{3} \log\left(e\right)\right)} x + 6 \, {\left(B^{2} a^{3} d^{2} g^{3} \log\left(e\right) + A B a^{3} d^{2} g^{3} + {\left(B^{2} b^{3} d^{2} g^{3} \log\left(e\right) + A B b^{3} d^{2} g^{3}\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{2} g^{3} \log\left(e\right) + A B a b^{2} d^{2} g^{3}\right)} x^{2} + 3 \, {\left(B^{2} a^{2} b d^{2} g^{3} \log\left(e\right) + A B a^{2} b d^{2} g^{3}\right)} x\right)} \log\left(b x + a\right) - {\left(6 \, B^{2} a^{3} d^{2} g^{3} \log\left(e\right) + 6 \, A B a^{3} d^{2} g^{3} + 2 \, {\left(3 \, A B b^{3} d^{2} g^{3} + {\left(3 \, g^{3} \log\left(e\right) + g^{3}\right)} B^{2} b^{3} d^{2}\right)} x^{3} + 3 \, {\left(6 \, A B a b^{2} d^{2} g^{3} - {\left(b^{3} c d g^{3} - 3 \, {\left(2 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{2} d^{2}\right)} B^{2}\right)} x^{2} + 6 \, {\left(3 \, A B a^{2} b d^{2} g^{3} + {\left(b^{3} c^{2} g^{3} - 3 \, a b^{2} c d g^{3} + 3 \, {\left(g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b d^{2}\right)} B^{2}\right)} x + 6 \, {\left(B^{2} b^{3} d^{2} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{2} g^{3} x + B^{2} a^{3} d^{2} g^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, {\left(d^{3} i x + c d^{2} i\right)}}\,{d x}"," ",0,"3*A^2*a^2*b*g^3*(x/(d*i) - c*log(d*x + c)/(d^2*i)) - 1/6*A^2*b^3*g^3*(6*c^3*log(d*x + c)/(d^4*i) - (2*d^2*x^3 - 3*c*d*x^2 + 6*c^2*x)/(d^3*i)) + 3/2*A^2*a*b^2*g^3*(2*c^2*log(d*x + c)/(d^3*i) + (d*x^2 - 2*c*x)/(d^2*i)) + A^2*a^3*g^3*log(d*i*x + c*i)/(d*i) - 1/6*(2*(b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - a^3*d^3*g^3)*B^2*log(d*x + c)^3 - (2*B^2*b^3*d^3*g^3*x^3 - 3*(b^3*c*d^2*g^3 - 3*a*b^2*d^3*g^3)*B^2*x^2 + 6*(b^3*c^2*d*g^3 - 3*a*b^2*c*d^2*g^3 + 3*a^2*b*d^3*g^3)*B^2*x)*log(d*x + c)^2)/(d^4*i) - integrate(-1/3*(3*B^2*a^3*d^2*g^3*log(e)^2 + 6*A*B*a^3*d^2*g^3*log(e) + 3*(B^2*b^3*d^2*g^3*log(e)^2 + 2*A*B*b^3*d^2*g^3*log(e))*x^3 + 9*(B^2*a*b^2*d^2*g^3*log(e)^2 + 2*A*B*a*b^2*d^2*g^3*log(e))*x^2 + 3*(B^2*b^3*d^2*g^3*x^3 + 3*B^2*a*b^2*d^2*g^3*x^2 + 3*B^2*a^2*b*d^2*g^3*x + B^2*a^3*d^2*g^3)*log(b*x + a)^2 + 9*(B^2*a^2*b*d^2*g^3*log(e)^2 + 2*A*B*a^2*b*d^2*g^3*log(e))*x + 6*(B^2*a^3*d^2*g^3*log(e) + A*B*a^3*d^2*g^3 + (B^2*b^3*d^2*g^3*log(e) + A*B*b^3*d^2*g^3)*x^3 + 3*(B^2*a*b^2*d^2*g^3*log(e) + A*B*a*b^2*d^2*g^3)*x^2 + 3*(B^2*a^2*b*d^2*g^3*log(e) + A*B*a^2*b*d^2*g^3)*x)*log(b*x + a) - (6*B^2*a^3*d^2*g^3*log(e) + 6*A*B*a^3*d^2*g^3 + 2*(3*A*B*b^3*d^2*g^3 + (3*g^3*log(e) + g^3)*B^2*b^3*d^2)*x^3 + 3*(6*A*B*a*b^2*d^2*g^3 - (b^3*c*d*g^3 - 3*(2*g^3*log(e) + g^3)*a*b^2*d^2)*B^2)*x^2 + 6*(3*A*B*a^2*b*d^2*g^3 + (b^3*c^2*g^3 - 3*a*b^2*c*d*g^3 + 3*(g^3*log(e) + g^3)*a^2*b*d^2)*B^2)*x + 6*(B^2*b^3*d^2*g^3*x^3 + 3*B^2*a*b^2*d^2*g^3*x^2 + 3*B^2*a^2*b*d^2*g^3*x + B^2*a^3*d^2*g^3)*log(b*x + a))*log(d*x + c))/(d^3*i*x + c*d^2*i), x)","F",0
85,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i),x, algorithm=""maxima"")","2 \, A^{2} a b g^{2} {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} + \frac{1}{2} \, A^{2} b^{2} g^{2} {\left(\frac{2 \, c^{2} \log\left(d x + c\right)}{d^{3} i} + \frac{d x^{2} - 2 \, c x}{d^{2} i}\right)} + \frac{A^{2} a^{2} g^{2} \log\left(d i x + c i\right)}{d i} + \frac{2 \, {\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + a^{2} d^{2} g^{2}\right)} B^{2} \log\left(d x + c\right)^{3} + 3 \, {\left(B^{2} b^{2} d^{2} g^{2} x^{2} - 2 \, {\left(b^{2} c d g^{2} - 2 \, a b d^{2} g^{2}\right)} B^{2} x\right)} \log\left(d x + c\right)^{2}}{6 \, d^{3} i} - \int -\frac{B^{2} a^{2} d g^{2} \log\left(e\right)^{2} + 2 \, A B a^{2} d g^{2} \log\left(e\right) + {\left(B^{2} b^{2} d g^{2} \log\left(e\right)^{2} + 2 \, A B b^{2} d g^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d g^{2} x^{2} + 2 \, B^{2} a b d g^{2} x + B^{2} a^{2} d g^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(B^{2} a b d g^{2} \log\left(e\right)^{2} + 2 \, A B a b d g^{2} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a^{2} d g^{2} \log\left(e\right) + A B a^{2} d g^{2} + {\left(B^{2} b^{2} d g^{2} \log\left(e\right) + A B b^{2} d g^{2}\right)} x^{2} + 2 \, {\left(B^{2} a b d g^{2} \log\left(e\right) + A B a b d g^{2}\right)} x\right)} \log\left(b x + a\right) - {\left(2 \, B^{2} a^{2} d g^{2} \log\left(e\right) + 2 \, A B a^{2} d g^{2} + {\left(2 \, A B b^{2} d g^{2} + {\left(2 \, g^{2} \log\left(e\right) + g^{2}\right)} B^{2} b^{2} d\right)} x^{2} + 2 \, {\left(2 \, A B a b d g^{2} - {\left(b^{2} c g^{2} - 2 \, {\left(g^{2} \log\left(e\right) + g^{2}\right)} a b d\right)} B^{2}\right)} x + 2 \, {\left(B^{2} b^{2} d g^{2} x^{2} + 2 \, B^{2} a b d g^{2} x + B^{2} a^{2} d g^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d^{2} i x + c d i}\,{d x}"," ",0,"2*A^2*a*b*g^2*(x/(d*i) - c*log(d*x + c)/(d^2*i)) + 1/2*A^2*b^2*g^2*(2*c^2*log(d*x + c)/(d^3*i) + (d*x^2 - 2*c*x)/(d^2*i)) + A^2*a^2*g^2*log(d*i*x + c*i)/(d*i) + 1/6*(2*(b^2*c^2*g^2 - 2*a*b*c*d*g^2 + a^2*d^2*g^2)*B^2*log(d*x + c)^3 + 3*(B^2*b^2*d^2*g^2*x^2 - 2*(b^2*c*d*g^2 - 2*a*b*d^2*g^2)*B^2*x)*log(d*x + c)^2)/(d^3*i) - integrate(-(B^2*a^2*d*g^2*log(e)^2 + 2*A*B*a^2*d*g^2*log(e) + (B^2*b^2*d*g^2*log(e)^2 + 2*A*B*b^2*d*g^2*log(e))*x^2 + (B^2*b^2*d*g^2*x^2 + 2*B^2*a*b*d*g^2*x + B^2*a^2*d*g^2)*log(b*x + a)^2 + 2*(B^2*a*b*d*g^2*log(e)^2 + 2*A*B*a*b*d*g^2*log(e))*x + 2*(B^2*a^2*d*g^2*log(e) + A*B*a^2*d*g^2 + (B^2*b^2*d*g^2*log(e) + A*B*b^2*d*g^2)*x^2 + 2*(B^2*a*b*d*g^2*log(e) + A*B*a*b*d*g^2)*x)*log(b*x + a) - (2*B^2*a^2*d*g^2*log(e) + 2*A*B*a^2*d*g^2 + (2*A*B*b^2*d*g^2 + (2*g^2*log(e) + g^2)*B^2*b^2*d)*x^2 + 2*(2*A*B*a*b*d*g^2 - (b^2*c*g^2 - 2*(g^2*log(e) + g^2)*a*b*d)*B^2)*x + 2*(B^2*b^2*d*g^2*x^2 + 2*B^2*a*b*d*g^2*x + B^2*a^2*d*g^2)*log(b*x + a))*log(d*x + c))/(d^2*i*x + c*d*i), x)","F",0
86,0,0,0,0.000000," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i),x, algorithm=""maxima"")","A^{2} b g {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} + \frac{A^{2} a g \log\left(d i x + c i\right)}{d i} + \frac{3 \, B^{2} b d g x \log\left(d x + c\right)^{2} - {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right)^{3}}{3 \, d^{2} i} - \int -\frac{B^{2} a g \log\left(e\right)^{2} + 2 \, A B a g \log\left(e\right) + {\left(B^{2} b g x + B^{2} a g\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b g \log\left(e\right)^{2} + 2 \, A B b g \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a g \log\left(e\right) + A B a g + {\left(B^{2} b g \log\left(e\right) + A B b g\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} a g \log\left(e\right) + A B a g + {\left({\left(g \log\left(e\right) + g\right)} B^{2} b + A B b g\right)} x + {\left(B^{2} b g x + B^{2} a g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d i x + c i}\,{d x}"," ",0,"A^2*b*g*(x/(d*i) - c*log(d*x + c)/(d^2*i)) + A^2*a*g*log(d*i*x + c*i)/(d*i) + 1/3*(3*B^2*b*d*g*x*log(d*x + c)^2 - (b*c*g - a*d*g)*B^2*log(d*x + c)^3)/(d^2*i) - integrate(-(B^2*a*g*log(e)^2 + 2*A*B*a*g*log(e) + (B^2*b*g*x + B^2*a*g)*log(b*x + a)^2 + (B^2*b*g*log(e)^2 + 2*A*B*b*g*log(e))*x + 2*(B^2*a*g*log(e) + A*B*a*g + (B^2*b*g*log(e) + A*B*b*g)*x)*log(b*x + a) - 2*(B^2*a*g*log(e) + A*B*a*g + ((g*log(e) + g)*B^2*b + A*B*b*g)*x + (B^2*b*g*x + B^2*a*g)*log(b*x + a))*log(d*x + c))/(d*i*x + c*i), x)","F",0
87,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i),x, algorithm=""maxima"")","\frac{B^{2} \log\left(d x + c\right)^{3}}{3 \, d i} + \frac{A^{2} \log\left(d i x + c i\right)}{d i} - \int -\frac{B^{2} \log\left(b x + a\right)^{2} + B^{2} \log\left(e\right)^{2} + 2 \, A B \log\left(e\right) + 2 \, {\left(B^{2} \log\left(e\right) + A B\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} \log\left(b x + a\right) + B^{2} \log\left(e\right) + A B\right)} \log\left(d x + c\right)}{d i x + c i}\,{d x}"," ",0,"1/3*B^2*log(d*x + c)^3/(d*i) + A^2*log(d*i*x + c*i)/(d*i) - integrate(-(B^2*log(b*x + a)^2 + B^2*log(e)^2 + 2*A*B*log(e) + 2*(B^2*log(e) + A*B)*log(b*x + a) - 2*(B^2*log(b*x + a) + B^2*log(e) + A*B)*log(d*x + c))/(d*i*x + c*i), x)","F",0
88,1,397,0,1.352868," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)/(d*i*x+c*i),x, algorithm=""maxima"")","B^{2} {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} + 2 \, A B {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{3} \, B^{2} {\left(\frac{3 \, {\left(\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right) + \log\left(d x + c\right)^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b c g i - a d g i} - \frac{\log\left(b x + a\right)^{3} - 3 \, \log\left(b x + a\right)^{2} \log\left(d x + c\right) + 3 \, \log\left(b x + a\right) \log\left(d x + c\right)^{2} - \log\left(d x + c\right)^{3}}{b c g i - a d g i}\right)} + A^{2} {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)} - \frac{{\left(\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right) + \log\left(d x + c\right)^{2}\right)} A B}{b c g i - a d g i}"," ",0,"B^2*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 + 2*A*B*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/3*B^2*(3*(log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c) + log(d*x + c)^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b*c*g*i - a*d*g*i) - (log(b*x + a)^3 - 3*log(b*x + a)^2*log(d*x + c) + 3*log(b*x + a)*log(d*x + c)^2 - log(d*x + c)^3)/(b*c*g*i - a*d*g*i)) + A^2*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i)) - (log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c) + log(d*x + c)^2)*A*B/(b*c*g*i - a*d*g*i)","B",0
89,1,1008,0,1.986752," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2/(d*i*x+c*i),x, algorithm=""maxima"")","-B^{2} {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} - 2 \, A B {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) + \frac{1}{3} \, B^{2} {\left(\frac{3 \, {\left({\left(b d x + a d\right)} \log\left(b x + a\right)^{2} + {\left(b d x + a d\right)} \log\left(d x + c\right)^{2} - 2 \, b c + 2 \, a d - 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right) + 2 \, {\left(b d x + a d - {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a b^{2} c^{2} g^{2} i - 2 \, a^{2} b c d g^{2} i + a^{3} d^{2} g^{2} i + {\left(b^{3} c^{2} g^{2} i - 2 \, a b^{2} c d g^{2} i + a^{2} b d^{2} g^{2} i\right)} x} - \frac{{\left(b d x + a d\right)} \log\left(b x + a\right)^{3} - {\left(b d x + a d\right)} \log\left(d x + c\right)^{3} - 3 \, {\left(b d x + a d\right)} \log\left(b x + a\right)^{2} - 3 \, {\left(b d x + a d - {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 6 \, b c - 6 \, a d + 6 \, {\left(b d x + a d\right)} \log\left(b x + a\right) - 3 \, {\left(2 \, b d x + {\left(b d x + a d\right)} \log\left(b x + a\right)^{2} + 2 \, a d - 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a b^{2} c^{2} g^{2} i - 2 \, a^{2} b c d g^{2} i + a^{3} d^{2} g^{2} i + {\left(b^{3} c^{2} g^{2} i - 2 \, a b^{2} c d g^{2} i + a^{2} b d^{2} g^{2} i\right)} x}\right)} - A^{2} {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)} + \frac{{\left({\left(b d x + a d\right)} \log\left(b x + a\right)^{2} + {\left(b d x + a d\right)} \log\left(d x + c\right)^{2} - 2 \, b c + 2 \, a d - 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right) + 2 \, {\left(b d x + a d - {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{a b^{2} c^{2} g^{2} i - 2 \, a^{2} b c d g^{2} i + a^{3} d^{2} g^{2} i + {\left(b^{3} c^{2} g^{2} i - 2 \, a b^{2} c d g^{2} i + a^{2} b d^{2} g^{2} i\right)} x}"," ",0,"-B^2*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 - 2*A*B*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) + 1/3*B^2*(3*((b*d*x + a*d)*log(b*x + a)^2 + (b*d*x + a*d)*log(d*x + c)^2 - 2*b*c + 2*a*d - 2*(b*d*x + a*d)*log(b*x + a) + 2*(b*d*x + a*d - (b*d*x + a*d)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a*b^2*c^2*g^2*i - 2*a^2*b*c*d*g^2*i + a^3*d^2*g^2*i + (b^3*c^2*g^2*i - 2*a*b^2*c*d*g^2*i + a^2*b*d^2*g^2*i)*x) - ((b*d*x + a*d)*log(b*x + a)^3 - (b*d*x + a*d)*log(d*x + c)^3 - 3*(b*d*x + a*d)*log(b*x + a)^2 - 3*(b*d*x + a*d - (b*d*x + a*d)*log(b*x + a))*log(d*x + c)^2 + 6*b*c - 6*a*d + 6*(b*d*x + a*d)*log(b*x + a) - 3*(2*b*d*x + (b*d*x + a*d)*log(b*x + a)^2 + 2*a*d - 2*(b*d*x + a*d)*log(b*x + a))*log(d*x + c))/(a*b^2*c^2*g^2*i - 2*a^2*b*c*d*g^2*i + a^3*d^2*g^2*i + (b^3*c^2*g^2*i - 2*a*b^2*c*d*g^2*i + a^2*b*d^2*g^2*i)*x)) - A^2*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i)) + ((b*d*x + a*d)*log(b*x + a)^2 + (b*d*x + a*d)*log(d*x + c)^2 - 2*b*c + 2*a*d - 2*(b*d*x + a*d)*log(b*x + a) + 2*(b*d*x + a*d - (b*d*x + a*d)*log(b*x + a))*log(d*x + c))*A*B/(a*b^2*c^2*g^2*i - 2*a^2*b*c*d*g^2*i + a^3*d^2*g^2*i + (b^3*c^2*g^2*i - 2*a*b^2*c*d*g^2*i + a^2*b*d^2*g^2*i)*x)","B",0
90,1,2115,0,3.114199," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3/(d*i*x+c*i),x, algorithm=""maxima"")","\frac{1}{2} \, B^{2} {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} + A B {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{12} \, B^{2} {\left(\frac{6 \, {\left(b^{2} c^{2} - 8 \, a b c d + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d - a b d^{2}\right)} x - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a^{2} b^{3} c^{3} g^{3} i - 3 \, a^{3} b^{2} c^{2} d g^{3} i + 3 \, a^{4} b c d^{2} g^{3} i - a^{5} d^{3} g^{3} i + {\left(b^{5} c^{3} g^{3} i - 3 \, a b^{4} c^{2} d g^{3} i + 3 \, a^{2} b^{3} c d^{2} g^{3} i - a^{3} b^{2} d^{3} g^{3} i\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} g^{3} i - 3 \, a^{2} b^{3} c^{2} d g^{3} i + 3 \, a^{3} b^{2} c d^{2} g^{3} i - a^{4} b d^{3} g^{3} i\right)} x} + \frac{3 \, b^{2} c^{2} - 48 \, a b c d + 45 \, a^{2} d^{2} - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{3} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{3} + 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 42 \, {\left(b^{2} c d - a b d^{2}\right)} x - 42 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 6 \, {\left(7 \, b^{2} d^{2} x^{2} + 14 \, a b d^{2} x + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{2} b^{3} c^{3} g^{3} i - 3 \, a^{3} b^{2} c^{2} d g^{3} i + 3 \, a^{4} b c d^{2} g^{3} i - a^{5} d^{3} g^{3} i + {\left(b^{5} c^{3} g^{3} i - 3 \, a b^{4} c^{2} d g^{3} i + 3 \, a^{2} b^{3} c d^{2} g^{3} i - a^{3} b^{2} d^{3} g^{3} i\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} g^{3} i - 3 \, a^{2} b^{3} c^{2} d g^{3} i + 3 \, a^{3} b^{2} c d^{2} g^{3} i - a^{4} b d^{3} g^{3} i\right)} x}\right)} + \frac{1}{2} \, A^{2} {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)} - \frac{{\left(b^{2} c^{2} - 8 \, a b c d + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d - a b d^{2}\right)} x - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{2 \, {\left(a^{2} b^{3} c^{3} g^{3} i - 3 \, a^{3} b^{2} c^{2} d g^{3} i + 3 \, a^{4} b c d^{2} g^{3} i - a^{5} d^{3} g^{3} i + {\left(b^{5} c^{3} g^{3} i - 3 \, a b^{4} c^{2} d g^{3} i + 3 \, a^{2} b^{3} c d^{2} g^{3} i - a^{3} b^{2} d^{3} g^{3} i\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} g^{3} i - 3 \, a^{2} b^{3} c^{2} d g^{3} i + 3 \, a^{3} b^{2} c d^{2} g^{3} i - a^{4} b d^{3} g^{3} i\right)} x\right)}}"," ",0,"1/2*B^2*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 + A*B*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/12*B^2*(6*(b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^2 - 6*(b^2*c*d - a*b*d^2)*x - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a^2*b^3*c^3*g^3*i - 3*a^3*b^2*c^2*d*g^3*i + 3*a^4*b*c*d^2*g^3*i - a^5*d^3*g^3*i + (b^5*c^3*g^3*i - 3*a*b^4*c^2*d*g^3*i + 3*a^2*b^3*c*d^2*g^3*i - a^3*b^2*d^3*g^3*i)*x^2 + 2*(a*b^4*c^3*g^3*i - 3*a^2*b^3*c^2*d*g^3*i + 3*a^3*b^2*c*d^2*g^3*i - a^4*b*d^3*g^3*i)*x) + (3*b^2*c^2 - 48*a*b*c*d + 45*a^2*d^2 - 4*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^3 + 4*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^3 + 18*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 6*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c)^2 - 42*(b^2*c*d - a*b*d^2)*x - 42*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 6*(7*b^2*d^2*x^2 + 14*a*b*d^2*x + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))/(a^2*b^3*c^3*g^3*i - 3*a^3*b^2*c^2*d*g^3*i + 3*a^4*b*c*d^2*g^3*i - a^5*d^3*g^3*i + (b^5*c^3*g^3*i - 3*a*b^4*c^2*d*g^3*i + 3*a^2*b^3*c*d^2*g^3*i - a^3*b^2*d^3*g^3*i)*x^2 + 2*(a*b^4*c^3*g^3*i - 3*a^2*b^3*c^2*d*g^3*i + 3*a^3*b^2*c*d^2*g^3*i - a^4*b*d^3*g^3*i)*x)) + 1/2*A^2*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i)) - 1/2*(b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^2 - 6*(b^2*c*d - a*b*d^2)*x - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))*A*B/(a^2*b^3*c^3*g^3*i - 3*a^3*b^2*c^2*d*g^3*i + 3*a^4*b*c*d^2*g^3*i - a^5*d^3*g^3*i + (b^5*c^3*g^3*i - 3*a*b^4*c^2*d*g^3*i + 3*a^2*b^3*c*d^2*g^3*i - a^3*b^2*d^3*g^3*i)*x^2 + 2*(a*b^4*c^3*g^3*i - 3*a^2*b^3*c^2*d*g^3*i + 3*a^3*b^2*c*d^2*g^3*i - a^4*b*d^3*g^3*i)*x)","B",0
91,1,3434,0,4.370926," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4/(d*i*x+c*i),x, algorithm=""maxima"")","-\frac{1}{6} \, B^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} - \frac{1}{3} \, A B {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{108} \, B^{2} {\left(\frac{6 \, {\left(4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a^{3} b^{4} c^{4} g^{4} i - 4 \, a^{4} b^{3} c^{3} d g^{4} i + 6 \, a^{5} b^{2} c^{2} d^{2} g^{4} i - 4 \, a^{6} b c d^{3} g^{4} i + a^{7} d^{4} g^{4} i + {\left(b^{7} c^{4} g^{4} i - 4 \, a b^{6} c^{3} d g^{4} i + 6 \, a^{2} b^{5} c^{2} d^{2} g^{4} i - 4 \, a^{3} b^{4} c d^{3} g^{4} i + a^{4} b^{3} d^{4} g^{4} i\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} g^{4} i - 4 \, a^{2} b^{5} c^{3} d g^{4} i + 6 \, a^{3} b^{4} c^{2} d^{2} g^{4} i - 4 \, a^{4} b^{3} c d^{3} g^{4} i + a^{5} b^{2} d^{4} g^{4} i\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} g^{4} i - 4 \, a^{3} b^{4} c^{3} d g^{4} i + 6 \, a^{4} b^{3} c^{2} d^{2} g^{4} i - 4 \, a^{5} b^{2} c d^{3} g^{4} i + a^{6} b d^{4} g^{4} i\right)} x} + \frac{8 \, b^{3} c^{3} - 81 \, a b^{2} c^{2} d + 648 \, a^{2} b c d^{2} - 575 \, a^{3} d^{3} + 36 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{3} - 36 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{3} + 510 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 198 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(19 \, b^{3} c^{2} d - 378 \, a b^{2} c d^{2} + 359 \, a^{2} b d^{3}\right)} x + 510 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(85 \, b^{3} d^{3} x^{3} + 255 \, a b^{2} d^{3} x^{2} + 255 \, a^{2} b d^{3} x + 85 \, a^{3} d^{3} + 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{3} b^{4} c^{4} g^{4} i - 4 \, a^{4} b^{3} c^{3} d g^{4} i + 6 \, a^{5} b^{2} c^{2} d^{2} g^{4} i - 4 \, a^{6} b c d^{3} g^{4} i + a^{7} d^{4} g^{4} i + {\left(b^{7} c^{4} g^{4} i - 4 \, a b^{6} c^{3} d g^{4} i + 6 \, a^{2} b^{5} c^{2} d^{2} g^{4} i - 4 \, a^{3} b^{4} c d^{3} g^{4} i + a^{4} b^{3} d^{4} g^{4} i\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} g^{4} i - 4 \, a^{2} b^{5} c^{3} d g^{4} i + 6 \, a^{3} b^{4} c^{2} d^{2} g^{4} i - 4 \, a^{4} b^{3} c d^{3} g^{4} i + a^{5} b^{2} d^{4} g^{4} i\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} g^{4} i - 4 \, a^{3} b^{4} c^{3} d g^{4} i + 6 \, a^{4} b^{3} c^{2} d^{2} g^{4} i - 4 \, a^{5} b^{2} c d^{3} g^{4} i + a^{6} b d^{4} g^{4} i\right)} x}\right)} - \frac{1}{6} \, A^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)} - \frac{{\left(4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{18 \, {\left(a^{3} b^{4} c^{4} g^{4} i - 4 \, a^{4} b^{3} c^{3} d g^{4} i + 6 \, a^{5} b^{2} c^{2} d^{2} g^{4} i - 4 \, a^{6} b c d^{3} g^{4} i + a^{7} d^{4} g^{4} i + {\left(b^{7} c^{4} g^{4} i - 4 \, a b^{6} c^{3} d g^{4} i + 6 \, a^{2} b^{5} c^{2} d^{2} g^{4} i - 4 \, a^{3} b^{4} c d^{3} g^{4} i + a^{4} b^{3} d^{4} g^{4} i\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} g^{4} i - 4 \, a^{2} b^{5} c^{3} d g^{4} i + 6 \, a^{3} b^{4} c^{2} d^{2} g^{4} i - 4 \, a^{4} b^{3} c d^{3} g^{4} i + a^{5} b^{2} d^{4} g^{4} i\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} g^{4} i - 4 \, a^{3} b^{4} c^{3} d g^{4} i + 6 \, a^{4} b^{3} c^{2} d^{2} g^{4} i - 4 \, a^{5} b^{2} c d^{3} g^{4} i + a^{6} b d^{4} g^{4} i\right)} x\right)}}"," ",0,"-1/6*B^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 - 1/3*A*B*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/108*B^2*(6*(4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a^3*b^4*c^4*g^4*i - 4*a^4*b^3*c^3*d*g^4*i + 6*a^5*b^2*c^2*d^2*g^4*i - 4*a^6*b*c*d^3*g^4*i + a^7*d^4*g^4*i + (b^7*c^4*g^4*i - 4*a*b^6*c^3*d*g^4*i + 6*a^2*b^5*c^2*d^2*g^4*i - 4*a^3*b^4*c*d^3*g^4*i + a^4*b^3*d^4*g^4*i)*x^3 + 3*(a*b^6*c^4*g^4*i - 4*a^2*b^5*c^3*d*g^4*i + 6*a^3*b^4*c^2*d^2*g^4*i - 4*a^4*b^3*c*d^3*g^4*i + a^5*b^2*d^4*g^4*i)*x^2 + 3*(a^2*b^5*c^4*g^4*i - 4*a^3*b^4*c^3*d*g^4*i + 6*a^4*b^3*c^2*d^2*g^4*i - 4*a^5*b^2*c*d^3*g^4*i + a^6*b*d^4*g^4*i)*x) + (8*b^3*c^3 - 81*a*b^2*c^2*d + 648*a^2*b*c*d^2 - 575*a^3*d^3 + 36*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^3 - 36*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^3 + 510*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 198*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c)^2 - 3*(19*b^3*c^2*d - 378*a*b^2*c*d^2 + 359*a^2*b*d^3)*x + 510*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(85*b^3*d^3*x^3 + 255*a*b^2*d^3*x^2 + 255*a^2*b*d^3*x + 85*a^3*d^3 + 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))/(a^3*b^4*c^4*g^4*i - 4*a^4*b^3*c^3*d*g^4*i + 6*a^5*b^2*c^2*d^2*g^4*i - 4*a^6*b*c*d^3*g^4*i + a^7*d^4*g^4*i + (b^7*c^4*g^4*i - 4*a*b^6*c^3*d*g^4*i + 6*a^2*b^5*c^2*d^2*g^4*i - 4*a^3*b^4*c*d^3*g^4*i + a^4*b^3*d^4*g^4*i)*x^3 + 3*(a*b^6*c^4*g^4*i - 4*a^2*b^5*c^3*d*g^4*i + 6*a^3*b^4*c^2*d^2*g^4*i - 4*a^4*b^3*c*d^3*g^4*i + a^5*b^2*d^4*g^4*i)*x^2 + 3*(a^2*b^5*c^4*g^4*i - 4*a^3*b^4*c^3*d*g^4*i + 6*a^4*b^3*c^2*d^2*g^4*i - 4*a^5*b^2*c*d^3*g^4*i + a^6*b*d^4*g^4*i)*x)) - 1/6*A^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i)) - 1/18*(4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*A*B/(a^3*b^4*c^4*g^4*i - 4*a^4*b^3*c^3*d*g^4*i + 6*a^5*b^2*c^2*d^2*g^4*i - 4*a^6*b*c*d^3*g^4*i + a^7*d^4*g^4*i + (b^7*c^4*g^4*i - 4*a*b^6*c^3*d*g^4*i + 6*a^2*b^5*c^2*d^2*g^4*i - 4*a^3*b^4*c*d^3*g^4*i + a^4*b^3*d^4*g^4*i)*x^3 + 3*(a*b^6*c^4*g^4*i - 4*a^2*b^5*c^3*d*g^4*i + 6*a^3*b^4*c^2*d^2*g^4*i - 4*a^4*b^3*c*d^3*g^4*i + a^5*b^2*d^4*g^4*i)*x^2 + 3*(a^2*b^5*c^4*g^4*i - 4*a^3*b^4*c^3*d*g^4*i + 6*a^4*b^3*c^2*d^2*g^4*i - 4*a^5*b^2*c*d^3*g^4*i + a^6*b*d^4*g^4*i)*x)","B",0
92,0,0,0,0.000000," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{2 \, c^{3}}{d^{5} i^{2} x + c d^{4} i^{2}} + \frac{6 \, c^{2} \log\left(d x + c\right)}{d^{4} i^{2}} + \frac{d x^{2} - 4 \, c x}{d^{3} i^{2}}\right)} A^{2} b^{3} g^{3} - 3 \, A^{2} a b^{2} {\left(\frac{c^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \frac{x}{d^{2} i^{2}} + \frac{2 \, c \log\left(d x + c\right)}{d^{3} i^{2}}\right)} g^{3} + 3 \, A^{2} a^{2} b g^{3} {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - 2 \, A B a^{3} g^{3} {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{1}{d^{2} i^{2} x + c d i^{2}} - \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} + \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{A^{2} a^{3} g^{3}}{d^{2} i^{2} x + c d i^{2}} + \frac{2 \, {\left({\left(b^{3} c^{2} d g^{3} - 2 \, a b^{2} c d^{2} g^{3} + a^{2} b d^{3} g^{3}\right)} B^{2} x + {\left(b^{3} c^{3} g^{3} - 2 \, a b^{2} c^{2} d g^{3} + a^{2} b c d^{2} g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{3} + {\left(B^{2} b^{3} d^{3} g^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} g^{3} - 2 \, a b^{2} d^{3} g^{3}\right)} B^{2} x^{2} - 2 \, {\left(2 \, b^{3} c^{2} d g^{3} - 3 \, a b^{2} c d^{2} g^{3}\right)} B^{2} x + 2 \, {\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - a^{3} d^{3} g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2}}{2 \, {\left(d^{5} i^{2} x + c d^{4} i^{2}\right)}} - \int -\frac{B^{2} a^{3} d^{3} g^{3} \log\left(e\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} g^{3} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B a b^{2} d^{3} g^{3} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(B^{2} a^{2} b d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B a^{2} b d^{3} g^{3} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a^{3} d^{3} g^{3} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right) + A B b^{3} d^{3} g^{3}\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right) + A B a b^{2} d^{3} g^{3}\right)} x^{2} + 3 \, {\left(B^{2} a^{2} b d^{3} g^{3} \log\left(e\right) + A B a^{2} b d^{3} g^{3}\right)} x\right)} \log\left(b x + a\right) - {\left({\left(2 \, A B b^{3} d^{3} g^{3} + {\left(2 \, g^{3} \log\left(e\right) + g^{3}\right)} B^{2} b^{3} d^{3}\right)} x^{3} + 2 \, {\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} + {\left(g^{3} \log\left(e\right) - g^{3}\right)} a^{3} d^{3}\right)} B^{2} + 3 \, {\left(2 \, A B a b^{2} d^{3} g^{3} - {\left(b^{3} c d^{2} g^{3} - 2 \, {\left(g^{3} \log\left(e\right) + g^{3}\right)} a b^{2} d^{3}\right)} B^{2}\right)} x^{2} + 2 \, {\left(3 \, A B a^{2} b d^{3} g^{3} + {\left(3 \, a^{2} b d^{3} g^{3} \log\left(e\right) - 2 \, b^{3} c^{2} d g^{3} + 3 \, a b^{2} c d^{2} g^{3}\right)} B^{2}\right)} x + 2 \, {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d^{5} i^{2} x^{2} + 2 \, c d^{4} i^{2} x + c^{2} d^{3} i^{2}}\,{d x}"," ",0,"1/2*(2*c^3/(d^5*i^2*x + c*d^4*i^2) + 6*c^2*log(d*x + c)/(d^4*i^2) + (d*x^2 - 4*c*x)/(d^3*i^2))*A^2*b^3*g^3 - 3*A^2*a*b^2*(c^2/(d^4*i^2*x + c*d^3*i^2) - x/(d^2*i^2) + 2*c*log(d*x + c)/(d^3*i^2))*g^3 + 3*A^2*a^2*b*g^3*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - 2*A*B*a^3*g^3*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^2*i^2*x + c*d*i^2) - 1/(d^2*i^2*x + c*d*i^2) - b*log(b*x + a)/((b*c*d - a*d^2)*i^2) + b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A^2*a^3*g^3/(d^2*i^2*x + c*d*i^2) + 1/2*(2*((b^3*c^2*d*g^3 - 2*a*b^2*c*d^2*g^3 + a^2*b*d^3*g^3)*B^2*x + (b^3*c^3*g^3 - 2*a*b^2*c^2*d*g^3 + a^2*b*c*d^2*g^3)*B^2)*log(d*x + c)^3 + (B^2*b^3*d^3*g^3*x^3 - 3*(b^3*c*d^2*g^3 - 2*a*b^2*d^3*g^3)*B^2*x^2 - 2*(2*b^3*c^2*d*g^3 - 3*a*b^2*c*d^2*g^3)*B^2*x + 2*(b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - a^3*d^3*g^3)*B^2)*log(d*x + c)^2)/(d^5*i^2*x + c*d^4*i^2) - integrate(-(B^2*a^3*d^3*g^3*log(e)^2 + (B^2*b^3*d^3*g^3*log(e)^2 + 2*A*B*b^3*d^3*g^3*log(e))*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e)^2 + 2*A*B*a*b^2*d^3*g^3*log(e))*x^2 + (B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log(b*x + a)^2 + 3*(B^2*a^2*b*d^3*g^3*log(e)^2 + 2*A*B*a^2*b*d^3*g^3*log(e))*x + 2*(B^2*a^3*d^3*g^3*log(e) + (B^2*b^3*d^3*g^3*log(e) + A*B*b^3*d^3*g^3)*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e) + A*B*a*b^2*d^3*g^3)*x^2 + 3*(B^2*a^2*b*d^3*g^3*log(e) + A*B*a^2*b*d^3*g^3)*x)*log(b*x + a) - ((2*A*B*b^3*d^3*g^3 + (2*g^3*log(e) + g^3)*B^2*b^3*d^3)*x^3 + 2*(b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 + (g^3*log(e) - g^3)*a^3*d^3)*B^2 + 3*(2*A*B*a*b^2*d^3*g^3 - (b^3*c*d^2*g^3 - 2*(g^3*log(e) + g^3)*a*b^2*d^3)*B^2)*x^2 + 2*(3*A*B*a^2*b*d^3*g^3 + (3*a^2*b*d^3*g^3*log(e) - 2*b^3*c^2*d*g^3 + 3*a*b^2*c*d^2*g^3)*B^2)*x + 2*(B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log(b*x + a))*log(d*x + c))/(d^5*i^2*x^2 + 2*c*d^4*i^2*x + c^2*d^3*i^2), x)","F",0
93,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-A^{2} b^{2} {\left(\frac{c^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \frac{x}{d^{2} i^{2}} + \frac{2 \, c \log\left(d x + c\right)}{d^{3} i^{2}}\right)} g^{2} + 2 \, A^{2} a b g^{2} {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - 2 \, A B a^{2} g^{2} {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{1}{d^{2} i^{2} x + c d i^{2}} - \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} + \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{A^{2} a^{2} g^{2}}{d^{2} i^{2} x + c d i^{2}} - \frac{2 \, {\left({\left(b^{2} c d g^{2} - a b d^{2} g^{2}\right)} B^{2} x + {\left(b^{2} c^{2} g^{2} - a b c d g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{3} - 3 \, {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + B^{2} b^{2} c d g^{2} x - {\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + a^{2} d^{2} g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2}}{3 \, {\left(d^{4} i^{2} x + c d^{3} i^{2}\right)}} - \int -\frac{B^{2} a^{2} d^{2} g^{2} \log\left(e\right)^{2} + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} g^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(B^{2} a b d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B a b d^{2} g^{2} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a^{2} d^{2} g^{2} \log\left(e\right) + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right) + A B b^{2} d^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} a b d^{2} g^{2} \log\left(e\right) + A B a b d^{2} g^{2}\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left({\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} - {\left(g^{2} \log\left(e\right) - g^{2}\right)} a^{2} d^{2}\right)} B^{2} - {\left(A B b^{2} d^{2} g^{2} + {\left(g^{2} \log\left(e\right) + g^{2}\right)} B^{2} b^{2} d^{2}\right)} x^{2} - {\left(2 \, A B a b d^{2} g^{2} + {\left(2 \, a b d^{2} g^{2} \log\left(e\right) + b^{2} c d g^{2}\right)} B^{2}\right)} x - {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d^{4} i^{2} x^{2} + 2 \, c d^{3} i^{2} x + c^{2} d^{2} i^{2}}\,{d x}"," ",0,"-A^2*b^2*(c^2/(d^4*i^2*x + c*d^3*i^2) - x/(d^2*i^2) + 2*c*log(d*x + c)/(d^3*i^2))*g^2 + 2*A^2*a*b*g^2*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - 2*A*B*a^2*g^2*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^2*i^2*x + c*d*i^2) - 1/(d^2*i^2*x + c*d*i^2) - b*log(b*x + a)/((b*c*d - a*d^2)*i^2) + b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A^2*a^2*g^2/(d^2*i^2*x + c*d*i^2) - 1/3*(2*((b^2*c*d*g^2 - a*b*d^2*g^2)*B^2*x + (b^2*c^2*g^2 - a*b*c*d*g^2)*B^2)*log(d*x + c)^3 - 3*(B^2*b^2*d^2*g^2*x^2 + B^2*b^2*c*d*g^2*x - (b^2*c^2*g^2 - 2*a*b*c*d*g^2 + a^2*d^2*g^2)*B^2)*log(d*x + c)^2)/(d^4*i^2*x + c*d^3*i^2) - integrate(-(B^2*a^2*d^2*g^2*log(e)^2 + (B^2*b^2*d^2*g^2*log(e)^2 + 2*A*B*b^2*d^2*g^2*log(e))*x^2 + (B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log(b*x + a)^2 + 2*(B^2*a*b*d^2*g^2*log(e)^2 + 2*A*B*a*b*d^2*g^2*log(e))*x + 2*(B^2*a^2*d^2*g^2*log(e) + (B^2*b^2*d^2*g^2*log(e) + A*B*b^2*d^2*g^2)*x^2 + 2*(B^2*a*b*d^2*g^2*log(e) + A*B*a*b*d^2*g^2)*x)*log(b*x + a) + 2*((b^2*c^2*g^2 - 2*a*b*c*d*g^2 - (g^2*log(e) - g^2)*a^2*d^2)*B^2 - (A*B*b^2*d^2*g^2 + (g^2*log(e) + g^2)*B^2*b^2*d^2)*x^2 - (2*A*B*a*b*d^2*g^2 + (2*a*b*d^2*g^2*log(e) + b^2*c*d*g^2)*B^2)*x - (B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log(b*x + a))*log(d*x + c))/(d^4*i^2*x^2 + 2*c*d^3*i^2*x + c^2*d^2*i^2), x)","F",0
94,0,0,0,0.000000," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","A^{2} b g {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - 2 \, A B a g {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{1}{d^{2} i^{2} x + c d i^{2}} - \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} + \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{A^{2} a g}{d^{2} i^{2} x + c d i^{2}} + \frac{3 \, {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right)^{2} + {\left(B^{2} b d g x + B^{2} b c g\right)} \log\left(d x + c\right)^{3}}{3 \, {\left(d^{3} i^{2} x + c d^{2} i^{2}\right)}} - \int -\frac{B^{2} a d g \log\left(e\right)^{2} + {\left(B^{2} b d g x + B^{2} a d g\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b d g \log\left(e\right)^{2} + 2 \, A B b d g \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a d g \log\left(e\right) + {\left(B^{2} b d g \log\left(e\right) + A B b d g\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left({\left({\left(g \log\left(e\right) - g\right)} a d + b c g\right)} B^{2} + {\left(B^{2} b d g \log\left(e\right) + A B b d g\right)} x + {\left(B^{2} b d g x + B^{2} a d g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d^{3} i^{2} x^{2} + 2 \, c d^{2} i^{2} x + c^{2} d i^{2}}\,{d x}"," ",0,"A^2*b*g*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - 2*A*B*a*g*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^2*i^2*x + c*d*i^2) - 1/(d^2*i^2*x + c*d*i^2) - b*log(b*x + a)/((b*c*d - a*d^2)*i^2) + b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A^2*a*g/(d^2*i^2*x + c*d*i^2) + 1/3*(3*(b*c*g - a*d*g)*B^2*log(d*x + c)^2 + (B^2*b*d*g*x + B^2*b*c*g)*log(d*x + c)^3)/(d^3*i^2*x + c*d^2*i^2) - integrate(-(B^2*a*d*g*log(e)^2 + (B^2*b*d*g*x + B^2*a*d*g)*log(b*x + a)^2 + (B^2*b*d*g*log(e)^2 + 2*A*B*b*d*g*log(e))*x + 2*(B^2*a*d*g*log(e) + (B^2*b*d*g*log(e) + A*B*b*d*g)*x)*log(b*x + a) - 2*(((g*log(e) - g)*a*d + b*c*g)*B^2 + (B^2*b*d*g*log(e) + A*B*b*d*g)*x + (B^2*b*d*g*x + B^2*a*d*g)*log(b*x + a))*log(d*x + c))/(d^3*i^2*x^2 + 2*c*d^2*i^2*x + c^2*d*i^2), x)","F",0
95,1,416,0,1.304489," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","{\left(2 \, {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{{\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} + 2 \, b c - 2 \, a d + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 2 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b c^{2} d i^{2} - a c d^{2} i^{2} + {\left(b c d^{2} i^{2} - a d^{3} i^{2}\right)} x}\right)} B^{2} - 2 \, A B {\left(\frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{1}{d^{2} i^{2} x + c d i^{2}} - \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} + \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{B^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{d^{2} i^{2} x + c d i^{2}} - \frac{A^{2}}{d^{2} i^{2} x + c d i^{2}}"," ",0,"(2*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - ((b*d*x + b*c)*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 + 2*b*c - 2*a*d + 2*(b*d*x + b*c)*log(b*x + a) - 2*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c))/(b*c^2*d*i^2 - a*c*d^2*i^2 + (b*c*d^2*i^2 - a*d^3*i^2)*x))*B^2 - 2*A*B*(log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^2*i^2*x + c*d*i^2) - 1/(d^2*i^2*x + c*d*i^2) - b*log(b*x + a)/((b*c*d - a*d^2)*i^2) + b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - B^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(d^2*i^2*x + c*d*i^2) - A^2/(d^2*i^2*x + c*d*i^2)","B",0
96,1,1004,0,1.921983," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)/(d*i*x+c*i)^2,x, algorithm=""maxima"")","B^{2} {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} + 2 \, A B {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{3} \, B^{2} {\left(\frac{3 \, {\left({\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} + 2 \, b c - 2 \, a d + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 2 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{2} c^{3} g i^{2} - 2 \, a b c^{2} d g i^{2} + a^{2} c d^{2} g i^{2} + {\left(b^{2} c^{2} d g i^{2} - 2 \, a b c d^{2} g i^{2} + a^{2} d^{3} g i^{2}\right)} x} - \frac{{\left(b d x + b c\right)} \log\left(b x + a\right)^{3} - {\left(b d x + b c\right)} \log\left(d x + c\right)^{3} + 3 \, {\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 6 \, b c - 6 \, a d + 6 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 3 \, {\left(2 \, b d x + {\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + 2 \, b c + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{2} c^{3} g i^{2} - 2 \, a b c^{2} d g i^{2} + a^{2} c d^{2} g i^{2} + {\left(b^{2} c^{2} d g i^{2} - 2 \, a b c d^{2} g i^{2} + a^{2} d^{3} g i^{2}\right)} x}\right)} + A^{2} {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)} - \frac{{\left({\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} + 2 \, b c - 2 \, a d + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 2 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{b^{2} c^{3} g i^{2} - 2 \, a b c^{2} d g i^{2} + a^{2} c d^{2} g i^{2} + {\left(b^{2} c^{2} d g i^{2} - 2 \, a b c d^{2} g i^{2} + a^{2} d^{3} g i^{2}\right)} x}"," ",0,"B^2*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 + 2*A*B*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/3*B^2*(3*((b*d*x + b*c)*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 + 2*b*c - 2*a*d + 2*(b*d*x + b*c)*log(b*x + a) - 2*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^2*c^3*g*i^2 - 2*a*b*c^2*d*g*i^2 + a^2*c*d^2*g*i^2 + (b^2*c^2*d*g*i^2 - 2*a*b*c*d^2*g*i^2 + a^2*d^3*g*i^2)*x) - ((b*d*x + b*c)*log(b*x + a)^3 - (b*d*x + b*c)*log(d*x + c)^3 + 3*(b*d*x + b*c)*log(b*x + a)^2 + 3*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c)^2 + 6*b*c - 6*a*d + 6*(b*d*x + b*c)*log(b*x + a) - 3*(2*b*d*x + (b*d*x + b*c)*log(b*x + a)^2 + 2*b*c + 2*(b*d*x + b*c)*log(b*x + a))*log(d*x + c))/(b^2*c^3*g*i^2 - 2*a*b*c^2*d*g*i^2 + a^2*c*d^2*g*i^2 + (b^2*c^2*d*g*i^2 - 2*a*b*c*d^2*g*i^2 + a^2*d^3*g*i^2)*x)) + A^2*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2)) - ((b*d*x + b*c)*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 + 2*b*c - 2*a*d + 2*(b*d*x + b*c)*log(b*x + a) - 2*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c))*A*B/(b^2*c^3*g*i^2 - 2*a*b*c^2*d*g*i^2 + a^2*c*d^2*g*i^2 + (b^2*c^2*d*g*i^2 - 2*a*b*c*d^2*g*i^2 + a^2*d^3*g*i^2)*x)","B",0
97,1,1995,0,2.614765," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-B^{2} {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} - 2 \, A B {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{2}{3} \, B^{2} {\left(\frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)^{2}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a b^{3} c^{4} g^{2} i^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} i^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} i^{2} - a^{4} c d^{3} g^{2} i^{2} + {\left(b^{4} c^{3} d g^{2} i^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} i^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} i^{2} - a^{3} b d^{4} g^{2} i^{2}\right)} x^{2} + {\left(b^{4} c^{4} g^{2} i^{2} - 2 \, a b^{3} c^{3} d g^{2} i^{2} + 2 \, a^{3} b c d^{3} g^{2} i^{2} - a^{4} d^{4} g^{2} i^{2}\right)} x} + \frac{3 \, b^{2} c^{2} - 3 \, a^{2} d^{2} + {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{3} + 3 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right)^{2} - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)^{3} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) - 3 \, {\left(2 \, b^{2} d^{2} x^{2} + 2 \, a b c d + {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)}{a b^{3} c^{4} g^{2} i^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} i^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} i^{2} - a^{4} c d^{3} g^{2} i^{2} + {\left(b^{4} c^{3} d g^{2} i^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} i^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} i^{2} - a^{3} b d^{4} g^{2} i^{2}\right)} x^{2} + {\left(b^{4} c^{4} g^{2} i^{2} - 2 \, a b^{3} c^{3} d g^{2} i^{2} + 2 \, a^{3} b c d^{3} g^{2} i^{2} - a^{4} d^{4} g^{2} i^{2}\right)} x}\right)} - A^{2} {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)} - \frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)^{2}\right)} A B}{a b^{3} c^{4} g^{2} i^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} i^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} i^{2} - a^{4} c d^{3} g^{2} i^{2} + {\left(b^{4} c^{3} d g^{2} i^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} i^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} i^{2} - a^{3} b d^{4} g^{2} i^{2}\right)} x^{2} + {\left(b^{4} c^{4} g^{2} i^{2} - 2 \, a b^{3} c^{3} d g^{2} i^{2} + 2 \, a^{3} b c d^{3} g^{2} i^{2} - a^{4} d^{4} g^{2} i^{2}\right)} x}"," ",0,"-B^2*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 - 2*A*B*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 2/3*B^2*(3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)*log(d*x + c) - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c)^2)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a*b^3*c^4*g^2*i^2 - 3*a^2*b^2*c^3*d*g^2*i^2 + 3*a^3*b*c^2*d^2*g^2*i^2 - a^4*c*d^3*g^2*i^2 + (b^4*c^3*d*g^2*i^2 - 3*a*b^3*c^2*d^2*g^2*i^2 + 3*a^2*b^2*c*d^3*g^2*i^2 - a^3*b*d^4*g^2*i^2)*x^2 + (b^4*c^4*g^2*i^2 - 2*a*b^3*c^3*d*g^2*i^2 + 2*a^3*b*c*d^3*g^2*i^2 - a^4*d^4*g^2*i^2)*x) + (3*b^2*c^2 - 3*a^2*d^2 + (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^3 + 3*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)*log(d*x + c)^2 - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c)^3 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a) - 3*(2*b^2*d^2*x^2 + 2*a*b*c*d + (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^2 + 2*(b^2*c*d + a*b*d^2)*x)*log(d*x + c))/(a*b^3*c^4*g^2*i^2 - 3*a^2*b^2*c^3*d*g^2*i^2 + 3*a^3*b*c^2*d^2*g^2*i^2 - a^4*c*d^3*g^2*i^2 + (b^4*c^3*d*g^2*i^2 - 3*a*b^3*c^2*d^2*g^2*i^2 + 3*a^2*b^2*c*d^3*g^2*i^2 - a^3*b*d^4*g^2*i^2)*x^2 + (b^4*c^4*g^2*i^2 - 2*a*b^3*c^3*d*g^2*i^2 + 2*a^3*b*c*d^3*g^2*i^2 - a^4*d^4*g^2*i^2)*x)) - A^2*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2)) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)*log(d*x + c) - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c)^2)*A*B/(a*b^3*c^4*g^2*i^2 - 3*a^2*b^2*c^3*d*g^2*i^2 + 3*a^3*b*c^2*d^2*g^2*i^2 - a^4*c*d^3*g^2*i^2 + (b^4*c^3*d*g^2*i^2 - 3*a*b^3*c^2*d^2*g^2*i^2 + 3*a^2*b^2*c*d^3*g^2*i^2 - a^3*b*d^4*g^2*i^2)*x^2 + (b^4*c^4*g^2*i^2 - 2*a*b^3*c^3*d*g^2*i^2 + 2*a^3*b*c*d^3*g^2*i^2 - a^4*d^4*g^2*i^2)*x)","B",0
98,1,4187,0,4.887989," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3/(d*i*x+c*i)^2,x, algorithm=""maxima"")","\frac{1}{2} \, B^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} + A B {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{4} \, B^{2} {\left(\frac{2 \, {\left(b^{3} c^{3} - 12 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a^{2} b^{4} c^{5} g^{3} i^{2} - 4 \, a^{3} b^{3} c^{4} d g^{3} i^{2} + 6 \, a^{4} b^{2} c^{3} d^{2} g^{3} i^{2} - 4 \, a^{5} b c^{2} d^{3} g^{3} i^{2} + a^{6} c d^{4} g^{3} i^{2} + {\left(b^{6} c^{4} d g^{3} i^{2} - 4 \, a b^{5} c^{3} d^{2} g^{3} i^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} g^{3} i^{2} - 4 \, a^{3} b^{3} c d^{4} g^{3} i^{2} + a^{4} b^{2} d^{5} g^{3} i^{2}\right)} x^{3} + {\left(b^{6} c^{5} g^{3} i^{2} - 2 \, a b^{5} c^{4} d g^{3} i^{2} - 2 \, a^{2} b^{4} c^{3} d^{2} g^{3} i^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} g^{3} i^{2} - 7 \, a^{4} b^{2} c d^{4} g^{3} i^{2} + 2 \, a^{5} b d^{5} g^{3} i^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} g^{3} i^{2} - 7 \, a^{2} b^{4} c^{4} d g^{3} i^{2} + 8 \, a^{3} b^{3} c^{3} d^{2} g^{3} i^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} g^{3} i^{2} - 2 \, a^{5} b c d^{4} g^{3} i^{2} + a^{6} d^{5} g^{3} i^{2}\right)} x} + \frac{b^{3} c^{3} - 24 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 8 \, a^{3} d^{3} - 4 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{3} + 4 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{3} - 30 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(7 \, b^{3} c^{2} d + 6 \, a b^{2} c d^{2} - 13 \, a^{2} b d^{3}\right)} x - 30 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(5 \, b^{3} d^{3} x^{3} + 5 \, a^{2} b c d^{2} + 5 \, {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 5 \, {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{2} b^{4} c^{5} g^{3} i^{2} - 4 \, a^{3} b^{3} c^{4} d g^{3} i^{2} + 6 \, a^{4} b^{2} c^{3} d^{2} g^{3} i^{2} - 4 \, a^{5} b c^{2} d^{3} g^{3} i^{2} + a^{6} c d^{4} g^{3} i^{2} + {\left(b^{6} c^{4} d g^{3} i^{2} - 4 \, a b^{5} c^{3} d^{2} g^{3} i^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} g^{3} i^{2} - 4 \, a^{3} b^{3} c d^{4} g^{3} i^{2} + a^{4} b^{2} d^{5} g^{3} i^{2}\right)} x^{3} + {\left(b^{6} c^{5} g^{3} i^{2} - 2 \, a b^{5} c^{4} d g^{3} i^{2} - 2 \, a^{2} b^{4} c^{3} d^{2} g^{3} i^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} g^{3} i^{2} - 7 \, a^{4} b^{2} c d^{4} g^{3} i^{2} + 2 \, a^{5} b d^{5} g^{3} i^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} g^{3} i^{2} - 7 \, a^{2} b^{4} c^{4} d g^{3} i^{2} + 8 \, a^{3} b^{3} c^{3} d^{2} g^{3} i^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} g^{3} i^{2} - 2 \, a^{5} b c d^{4} g^{3} i^{2} + a^{6} d^{5} g^{3} i^{2}\right)} x}\right)} + \frac{1}{2} \, A^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)} - \frac{{\left(b^{3} c^{3} - 12 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{2 \, {\left(a^{2} b^{4} c^{5} g^{3} i^{2} - 4 \, a^{3} b^{3} c^{4} d g^{3} i^{2} + 6 \, a^{4} b^{2} c^{3} d^{2} g^{3} i^{2} - 4 \, a^{5} b c^{2} d^{3} g^{3} i^{2} + a^{6} c d^{4} g^{3} i^{2} + {\left(b^{6} c^{4} d g^{3} i^{2} - 4 \, a b^{5} c^{3} d^{2} g^{3} i^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} g^{3} i^{2} - 4 \, a^{3} b^{3} c d^{4} g^{3} i^{2} + a^{4} b^{2} d^{5} g^{3} i^{2}\right)} x^{3} + {\left(b^{6} c^{5} g^{3} i^{2} - 2 \, a b^{5} c^{4} d g^{3} i^{2} - 2 \, a^{2} b^{4} c^{3} d^{2} g^{3} i^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} g^{3} i^{2} - 7 \, a^{4} b^{2} c d^{4} g^{3} i^{2} + 2 \, a^{5} b d^{5} g^{3} i^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} g^{3} i^{2} - 7 \, a^{2} b^{4} c^{4} d g^{3} i^{2} + 8 \, a^{3} b^{3} c^{3} d^{2} g^{3} i^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} g^{3} i^{2} - 2 \, a^{5} b c d^{4} g^{3} i^{2} + a^{6} d^{5} g^{3} i^{2}\right)} x\right)}}"," ",0,"1/2*B^2*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 + A*B*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/4*B^2*(2*(b^3*c^3 - 12*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c)^2 - 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a^2*b^4*c^5*g^3*i^2 - 4*a^3*b^3*c^4*d*g^3*i^2 + 6*a^4*b^2*c^3*d^2*g^3*i^2 - 4*a^5*b*c^2*d^3*g^3*i^2 + a^6*c*d^4*g^3*i^2 + (b^6*c^4*d*g^3*i^2 - 4*a*b^5*c^3*d^2*g^3*i^2 + 6*a^2*b^4*c^2*d^3*g^3*i^2 - 4*a^3*b^3*c*d^4*g^3*i^2 + a^4*b^2*d^5*g^3*i^2)*x^3 + (b^6*c^5*g^3*i^2 - 2*a*b^5*c^4*d*g^3*i^2 - 2*a^2*b^4*c^3*d^2*g^3*i^2 + 8*a^3*b^3*c^2*d^3*g^3*i^2 - 7*a^4*b^2*c*d^4*g^3*i^2 + 2*a^5*b*d^5*g^3*i^2)*x^2 + (2*a*b^5*c^5*g^3*i^2 - 7*a^2*b^4*c^4*d*g^3*i^2 + 8*a^3*b^3*c^3*d^2*g^3*i^2 - 2*a^4*b^2*c^2*d^3*g^3*i^2 - 2*a^5*b*c*d^4*g^3*i^2 + a^6*d^5*g^3*i^2)*x) + (b^3*c^3 - 24*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 8*a^3*d^3 - 4*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^3 + 4*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c)^3 - 30*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c)^2 - 3*(7*b^3*c^2*d + 6*a*b^2*c*d^2 - 13*a^2*b*d^3)*x - 30*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(5*b^3*d^3*x^3 + 5*a^2*b*c*d^2 + 5*(b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 5*(2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c))/(a^2*b^4*c^5*g^3*i^2 - 4*a^3*b^3*c^4*d*g^3*i^2 + 6*a^4*b^2*c^3*d^2*g^3*i^2 - 4*a^5*b*c^2*d^3*g^3*i^2 + a^6*c*d^4*g^3*i^2 + (b^6*c^4*d*g^3*i^2 - 4*a*b^5*c^3*d^2*g^3*i^2 + 6*a^2*b^4*c^2*d^3*g^3*i^2 - 4*a^3*b^3*c*d^4*g^3*i^2 + a^4*b^2*d^5*g^3*i^2)*x^3 + (b^6*c^5*g^3*i^2 - 2*a*b^5*c^4*d*g^3*i^2 - 2*a^2*b^4*c^3*d^2*g^3*i^2 + 8*a^3*b^3*c^2*d^3*g^3*i^2 - 7*a^4*b^2*c*d^4*g^3*i^2 + 2*a^5*b*d^5*g^3*i^2)*x^2 + (2*a*b^5*c^5*g^3*i^2 - 7*a^2*b^4*c^4*d*g^3*i^2 + 8*a^3*b^3*c^3*d^2*g^3*i^2 - 2*a^4*b^2*c^2*d^3*g^3*i^2 - 2*a^5*b*c*d^4*g^3*i^2 + a^6*d^5*g^3*i^2)*x)) + 1/2*A^2*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2)) - 1/2*(b^3*c^3 - 12*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c)^2 - 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c))*A*B/(a^2*b^4*c^5*g^3*i^2 - 4*a^3*b^3*c^4*d*g^3*i^2 + 6*a^4*b^2*c^3*d^2*g^3*i^2 - 4*a^5*b*c^2*d^3*g^3*i^2 + a^6*c*d^4*g^3*i^2 + (b^6*c^4*d*g^3*i^2 - 4*a*b^5*c^3*d^2*g^3*i^2 + 6*a^2*b^4*c^2*d^3*g^3*i^2 - 4*a^3*b^3*c*d^4*g^3*i^2 + a^4*b^2*d^5*g^3*i^2)*x^3 + (b^6*c^5*g^3*i^2 - 2*a*b^5*c^4*d*g^3*i^2 - 2*a^2*b^4*c^3*d^2*g^3*i^2 + 8*a^3*b^3*c^2*d^3*g^3*i^2 - 7*a^4*b^2*c*d^4*g^3*i^2 + 2*a^5*b*d^5*g^3*i^2)*x^2 + (2*a*b^5*c^5*g^3*i^2 - 7*a^2*b^4*c^4*d*g^3*i^2 + 8*a^3*b^3*c^3*d^2*g^3*i^2 - 2*a^4*b^2*c^2*d^3*g^3*i^2 - 2*a^5*b*c*d^4*g^3*i^2 + a^6*d^5*g^3*i^2)*x)","B",0
99,1,6160,0,7.923067," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, B^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} - \frac{2}{3} \, A B {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{27} \, B^{2} {\left(\frac{6 \, {\left(b^{4} c^{4} - 9 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} - 55 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4} + 30 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(11 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} - 19 \, a^{2} b^{2} d^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - {\left(5 \, b^{4} c^{3} d - 81 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} + 19 \, a^{3} b d^{4}\right)} x + 30 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{3} b c d^{3} + 5 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 15 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 6 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a^{3} b^{5} c^{6} g^{4} i^{2} - 5 \, a^{4} b^{4} c^{5} d g^{4} i^{2} + 10 \, a^{5} b^{3} c^{4} d^{2} g^{4} i^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{7} b c^{2} d^{4} g^{4} i^{2} - a^{8} c d^{5} g^{4} i^{2} + {\left(b^{8} c^{5} d g^{4} i^{2} - 5 \, a b^{7} c^{4} d^{2} g^{4} i^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} g^{4} i^{2} - 10 \, a^{3} b^{5} c^{2} d^{4} g^{4} i^{2} + 5 \, a^{4} b^{4} c d^{5} g^{4} i^{2} - a^{5} b^{3} d^{6} g^{4} i^{2}\right)} x^{4} + {\left(b^{8} c^{6} g^{4} i^{2} - 2 \, a b^{7} c^{5} d g^{4} i^{2} - 5 \, a^{2} b^{6} c^{4} d^{2} g^{4} i^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} g^{4} i^{2} - 25 \, a^{4} b^{4} c^{2} d^{4} g^{4} i^{2} + 14 \, a^{5} b^{3} c d^{5} g^{4} i^{2} - 3 \, a^{6} b^{2} d^{6} g^{4} i^{2}\right)} x^{3} + 3 \, {\left(a b^{7} c^{6} g^{4} i^{2} - 4 \, a^{2} b^{6} c^{5} d g^{4} i^{2} + 5 \, a^{3} b^{5} c^{4} d^{2} g^{4} i^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} g^{4} i^{2} + 4 \, a^{6} b^{2} c d^{5} g^{4} i^{2} - a^{7} b d^{6} g^{4} i^{2}\right)} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} g^{4} i^{2} - 14 \, a^{3} b^{5} c^{5} d g^{4} i^{2} + 25 \, a^{4} b^{4} c^{4} d^{2} g^{4} i^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{6} b^{2} c^{2} d^{4} g^{4} i^{2} + 2 \, a^{7} b c d^{5} g^{4} i^{2} - a^{8} d^{6} g^{4} i^{2}\right)} x} + \frac{2 \, b^{4} c^{4} - 27 \, a b^{3} c^{3} d + 324 \, a^{2} b^{2} c^{2} d^{2} - 245 \, a^{3} b c d^{3} - 54 \, a^{4} d^{4} + 330 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 36 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{3} - 36 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{3} + 15 \, {\left(17 \, b^{4} c^{2} d^{2} + 32 \, a b^{3} c d^{3} - 49 \, a^{2} b^{2} d^{4}\right)} x^{2} - 90 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{3} b c d^{3} + 5 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 15 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 6 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - {\left(19 \, b^{4} c^{3} d - 567 \, a b^{3} c^{2} d^{2} + 87 \, a^{2} b^{2} c d^{3} + 461 \, a^{3} b d^{4}\right)} x + 330 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(55 \, b^{4} d^{4} x^{4} + 55 \, a^{3} b c d^{3} + 55 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 165 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} + 55 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 30 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{3} b^{5} c^{6} g^{4} i^{2} - 5 \, a^{4} b^{4} c^{5} d g^{4} i^{2} + 10 \, a^{5} b^{3} c^{4} d^{2} g^{4} i^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{7} b c^{2} d^{4} g^{4} i^{2} - a^{8} c d^{5} g^{4} i^{2} + {\left(b^{8} c^{5} d g^{4} i^{2} - 5 \, a b^{7} c^{4} d^{2} g^{4} i^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} g^{4} i^{2} - 10 \, a^{3} b^{5} c^{2} d^{4} g^{4} i^{2} + 5 \, a^{4} b^{4} c d^{5} g^{4} i^{2} - a^{5} b^{3} d^{6} g^{4} i^{2}\right)} x^{4} + {\left(b^{8} c^{6} g^{4} i^{2} - 2 \, a b^{7} c^{5} d g^{4} i^{2} - 5 \, a^{2} b^{6} c^{4} d^{2} g^{4} i^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} g^{4} i^{2} - 25 \, a^{4} b^{4} c^{2} d^{4} g^{4} i^{2} + 14 \, a^{5} b^{3} c d^{5} g^{4} i^{2} - 3 \, a^{6} b^{2} d^{6} g^{4} i^{2}\right)} x^{3} + 3 \, {\left(a b^{7} c^{6} g^{4} i^{2} - 4 \, a^{2} b^{6} c^{5} d g^{4} i^{2} + 5 \, a^{3} b^{5} c^{4} d^{2} g^{4} i^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} g^{4} i^{2} + 4 \, a^{6} b^{2} c d^{5} g^{4} i^{2} - a^{7} b d^{6} g^{4} i^{2}\right)} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} g^{4} i^{2} - 14 \, a^{3} b^{5} c^{5} d g^{4} i^{2} + 25 \, a^{4} b^{4} c^{4} d^{2} g^{4} i^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{6} b^{2} c^{2} d^{4} g^{4} i^{2} + 2 \, a^{7} b c d^{5} g^{4} i^{2} - a^{8} d^{6} g^{4} i^{2}\right)} x}\right)} - \frac{1}{3} \, A^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)} - \frac{2 \, {\left(b^{4} c^{4} - 9 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} - 55 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4} + 30 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(11 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} - 19 \, a^{2} b^{2} d^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - {\left(5 \, b^{4} c^{3} d - 81 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} + 19 \, a^{3} b d^{4}\right)} x + 30 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{3} b c d^{3} + 5 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 15 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 6 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{9 \, {\left(a^{3} b^{5} c^{6} g^{4} i^{2} - 5 \, a^{4} b^{4} c^{5} d g^{4} i^{2} + 10 \, a^{5} b^{3} c^{4} d^{2} g^{4} i^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{7} b c^{2} d^{4} g^{4} i^{2} - a^{8} c d^{5} g^{4} i^{2} + {\left(b^{8} c^{5} d g^{4} i^{2} - 5 \, a b^{7} c^{4} d^{2} g^{4} i^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} g^{4} i^{2} - 10 \, a^{3} b^{5} c^{2} d^{4} g^{4} i^{2} + 5 \, a^{4} b^{4} c d^{5} g^{4} i^{2} - a^{5} b^{3} d^{6} g^{4} i^{2}\right)} x^{4} + {\left(b^{8} c^{6} g^{4} i^{2} - 2 \, a b^{7} c^{5} d g^{4} i^{2} - 5 \, a^{2} b^{6} c^{4} d^{2} g^{4} i^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} g^{4} i^{2} - 25 \, a^{4} b^{4} c^{2} d^{4} g^{4} i^{2} + 14 \, a^{5} b^{3} c d^{5} g^{4} i^{2} - 3 \, a^{6} b^{2} d^{6} g^{4} i^{2}\right)} x^{3} + 3 \, {\left(a b^{7} c^{6} g^{4} i^{2} - 4 \, a^{2} b^{6} c^{5} d g^{4} i^{2} + 5 \, a^{3} b^{5} c^{4} d^{2} g^{4} i^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} g^{4} i^{2} + 4 \, a^{6} b^{2} c d^{5} g^{4} i^{2} - a^{7} b d^{6} g^{4} i^{2}\right)} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} g^{4} i^{2} - 14 \, a^{3} b^{5} c^{5} d g^{4} i^{2} + 25 \, a^{4} b^{4} c^{4} d^{2} g^{4} i^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{6} b^{2} c^{2} d^{4} g^{4} i^{2} + 2 \, a^{7} b c d^{5} g^{4} i^{2} - a^{8} d^{6} g^{4} i^{2}\right)} x\right)}}"," ",0,"-1/3*B^2*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 - 2/3*A*B*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/27*B^2*(6*(b^4*c^4 - 9*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 - 55*a^3*b*c*d^3 + 9*a^4*d^4 + 30*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 3*(11*b^4*c^2*d^2 + 8*a*b^3*c*d^3 - 19*a^2*b^2*d^4)*x^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(d*x + c)^2 - (5*b^4*c^3*d - 81*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 + 19*a^3*b*d^4)*x + 30*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a) - 6*(5*b^4*d^4*x^4 + 5*a^3*b*c*d^3 + 5*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 15*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 5*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 6*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a^3*b^5*c^6*g^4*i^2 - 5*a^4*b^4*c^5*d*g^4*i^2 + 10*a^5*b^3*c^4*d^2*g^4*i^2 - 10*a^6*b^2*c^3*d^3*g^4*i^2 + 5*a^7*b*c^2*d^4*g^4*i^2 - a^8*c*d^5*g^4*i^2 + (b^8*c^5*d*g^4*i^2 - 5*a*b^7*c^4*d^2*g^4*i^2 + 10*a^2*b^6*c^3*d^3*g^4*i^2 - 10*a^3*b^5*c^2*d^4*g^4*i^2 + 5*a^4*b^4*c*d^5*g^4*i^2 - a^5*b^3*d^6*g^4*i^2)*x^4 + (b^8*c^6*g^4*i^2 - 2*a*b^7*c^5*d*g^4*i^2 - 5*a^2*b^6*c^4*d^2*g^4*i^2 + 20*a^3*b^5*c^3*d^3*g^4*i^2 - 25*a^4*b^4*c^2*d^4*g^4*i^2 + 14*a^5*b^3*c*d^5*g^4*i^2 - 3*a^6*b^2*d^6*g^4*i^2)*x^3 + 3*(a*b^7*c^6*g^4*i^2 - 4*a^2*b^6*c^5*d*g^4*i^2 + 5*a^3*b^5*c^4*d^2*g^4*i^2 - 5*a^5*b^3*c^2*d^4*g^4*i^2 + 4*a^6*b^2*c*d^5*g^4*i^2 - a^7*b*d^6*g^4*i^2)*x^2 + (3*a^2*b^6*c^6*g^4*i^2 - 14*a^3*b^5*c^5*d*g^4*i^2 + 25*a^4*b^4*c^4*d^2*g^4*i^2 - 20*a^5*b^3*c^3*d^3*g^4*i^2 + 5*a^6*b^2*c^2*d^4*g^4*i^2 + 2*a^7*b*c*d^5*g^4*i^2 - a^8*d^6*g^4*i^2)*x) + (2*b^4*c^4 - 27*a*b^3*c^3*d + 324*a^2*b^2*c^2*d^2 - 245*a^3*b*c*d^3 - 54*a^4*d^4 + 330*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 36*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^3 - 36*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(d*x + c)^3 + 15*(17*b^4*c^2*d^2 + 32*a*b^3*c*d^3 - 49*a^2*b^2*d^4)*x^2 - 90*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 - 18*(5*b^4*d^4*x^4 + 5*a^3*b*c*d^3 + 5*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 15*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 5*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 6*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c)^2 - (19*b^4*c^3*d - 567*a*b^3*c^2*d^2 + 87*a^2*b^2*c*d^3 + 461*a^3*b*d^4)*x + 330*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a) - 6*(55*b^4*d^4*x^4 + 55*a^3*b*c*d^3 + 55*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 165*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 + 55*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 30*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c))/(a^3*b^5*c^6*g^4*i^2 - 5*a^4*b^4*c^5*d*g^4*i^2 + 10*a^5*b^3*c^4*d^2*g^4*i^2 - 10*a^6*b^2*c^3*d^3*g^4*i^2 + 5*a^7*b*c^2*d^4*g^4*i^2 - a^8*c*d^5*g^4*i^2 + (b^8*c^5*d*g^4*i^2 - 5*a*b^7*c^4*d^2*g^4*i^2 + 10*a^2*b^6*c^3*d^3*g^4*i^2 - 10*a^3*b^5*c^2*d^4*g^4*i^2 + 5*a^4*b^4*c*d^5*g^4*i^2 - a^5*b^3*d^6*g^4*i^2)*x^4 + (b^8*c^6*g^4*i^2 - 2*a*b^7*c^5*d*g^4*i^2 - 5*a^2*b^6*c^4*d^2*g^4*i^2 + 20*a^3*b^5*c^3*d^3*g^4*i^2 - 25*a^4*b^4*c^2*d^4*g^4*i^2 + 14*a^5*b^3*c*d^5*g^4*i^2 - 3*a^6*b^2*d^6*g^4*i^2)*x^3 + 3*(a*b^7*c^6*g^4*i^2 - 4*a^2*b^6*c^5*d*g^4*i^2 + 5*a^3*b^5*c^4*d^2*g^4*i^2 - 5*a^5*b^3*c^2*d^4*g^4*i^2 + 4*a^6*b^2*c*d^5*g^4*i^2 - a^7*b*d^6*g^4*i^2)*x^2 + (3*a^2*b^6*c^6*g^4*i^2 - 14*a^3*b^5*c^5*d*g^4*i^2 + 25*a^4*b^4*c^4*d^2*g^4*i^2 - 20*a^5*b^3*c^3*d^3*g^4*i^2 + 5*a^6*b^2*c^2*d^4*g^4*i^2 + 2*a^7*b*c*d^5*g^4*i^2 - a^8*d^6*g^4*i^2)*x)) - 1/3*A^2*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2)) - 2/9*(b^4*c^4 - 9*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 - 55*a^3*b*c*d^3 + 9*a^4*d^4 + 30*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 3*(11*b^4*c^2*d^2 + 8*a*b^3*c*d^3 - 19*a^2*b^2*d^4)*x^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(d*x + c)^2 - (5*b^4*c^3*d - 81*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 + 19*a^3*b*d^4)*x + 30*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a) - 6*(5*b^4*d^4*x^4 + 5*a^3*b*c*d^3 + 5*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 15*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 5*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 6*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c))*A*B/(a^3*b^5*c^6*g^4*i^2 - 5*a^4*b^4*c^5*d*g^4*i^2 + 10*a^5*b^3*c^4*d^2*g^4*i^2 - 10*a^6*b^2*c^3*d^3*g^4*i^2 + 5*a^7*b*c^2*d^4*g^4*i^2 - a^8*c*d^5*g^4*i^2 + (b^8*c^5*d*g^4*i^2 - 5*a*b^7*c^4*d^2*g^4*i^2 + 10*a^2*b^6*c^3*d^3*g^4*i^2 - 10*a^3*b^5*c^2*d^4*g^4*i^2 + 5*a^4*b^4*c*d^5*g^4*i^2 - a^5*b^3*d^6*g^4*i^2)*x^4 + (b^8*c^6*g^4*i^2 - 2*a*b^7*c^5*d*g^4*i^2 - 5*a^2*b^6*c^4*d^2*g^4*i^2 + 20*a^3*b^5*c^3*d^3*g^4*i^2 - 25*a^4*b^4*c^2*d^4*g^4*i^2 + 14*a^5*b^3*c*d^5*g^4*i^2 - 3*a^6*b^2*d^6*g^4*i^2)*x^3 + 3*(a*b^7*c^6*g^4*i^2 - 4*a^2*b^6*c^5*d*g^4*i^2 + 5*a^3*b^5*c^4*d^2*g^4*i^2 - 5*a^5*b^3*c^2*d^4*g^4*i^2 + 4*a^6*b^2*c*d^5*g^4*i^2 - a^7*b*d^6*g^4*i^2)*x^2 + (3*a^2*b^6*c^6*g^4*i^2 - 14*a^3*b^5*c^5*d*g^4*i^2 + 25*a^4*b^4*c^4*d^2*g^4*i^2 - 20*a^5*b^3*c^3*d^3*g^4*i^2 + 5*a^6*b^2*c^2*d^4*g^4*i^2 + 2*a^7*b*c*d^5*g^4*i^2 - a^8*d^6*g^4*i^2)*x)","B",0
100,0,0,0,0.000000," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{3}{2} \, A B a^{2} b g^{3} {\left(\frac{2 \, {\left(2 \, d x + c\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} - \frac{1}{2} \, A^{2} b^{3} g^{3} {\left(\frac{6 \, c^{2} d x + 5 \, c^{3}}{d^{6} i^{3} x^{2} + 2 \, c d^{5} i^{3} x + c^{2} d^{4} i^{3}} - \frac{2 \, x}{d^{3} i^{3}} + \frac{6 \, c \log\left(d x + c\right)}{d^{4} i^{3}}\right)} + \frac{1}{2} \, A B a^{3} g^{3} {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} + \frac{3}{2} \, A^{2} a b^{2} g^{3} {\left(\frac{4 \, c d x + 3 \, c^{2}}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} + \frac{2 \, \log\left(d x + c\right)}{d^{3} i^{3}}\right)} - \frac{3 \, {\left(2 \, d x + c\right)} A^{2} a^{2} b g^{3}}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{A^{2} a^{3} g^{3}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{2 \, {\left({\left(b^{3} c d^{2} g^{3} - a b^{2} d^{3} g^{3}\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{2} d g^{3} - a b^{2} c d^{2} g^{3}\right)} B^{2} x + {\left(b^{3} c^{3} g^{3} - a b^{2} c^{2} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{3} - {\left(2 \, B^{2} b^{3} d^{3} g^{3} x^{3} + 4 \, B^{2} b^{3} c d^{2} g^{3} x^{2} - 2 \, {\left(2 \, b^{3} c^{2} d g^{3} - 6 \, a b^{2} c d^{2} g^{3} + 3 \, a^{2} b d^{3} g^{3}\right)} B^{2} x - {\left(5 \, b^{3} c^{3} g^{3} - 9 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} + a^{3} d^{3} g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2}}{2 \, {\left(d^{6} i^{3} x^{2} + 2 \, c d^{5} i^{3} x + c^{2} d^{4} i^{3}\right)}} - \int -\frac{3 \, B^{2} a^{2} b d^{3} g^{3} x \log\left(e\right)^{2} + B^{2} a^{3} d^{3} g^{3} \log\left(e\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} g^{3} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B a b^{2} d^{3} g^{3} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(3 \, B^{2} a^{2} b d^{3} g^{3} x \log\left(e\right) + B^{2} a^{3} d^{3} g^{3} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right) + A B b^{3} d^{3} g^{3}\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right) + A B a b^{2} d^{3} g^{3}\right)} x^{2}\right)} \log\left(b x + a\right) + {\left(2 \, {\left(2 \, b^{3} c^{2} d g^{3} - 6 \, a b^{2} c d^{2} g^{3} - 3 \, {\left(g^{3} \log\left(e\right) - g^{3}\right)} a^{2} b d^{3}\right)} B^{2} x - 2 \, {\left(A B b^{3} d^{3} g^{3} + {\left(g^{3} \log\left(e\right) + g^{3}\right)} B^{2} b^{3} d^{3}\right)} x^{3} + {\left(5 \, b^{3} c^{3} g^{3} - 9 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - {\left(2 \, g^{3} \log\left(e\right) - g^{3}\right)} a^{3} d^{3}\right)} B^{2} - 2 \, {\left(3 \, A B a b^{2} d^{3} g^{3} + {\left(3 \, a b^{2} d^{3} g^{3} \log\left(e\right) + 2 \, b^{3} c d^{2} g^{3}\right)} B^{2}\right)} x^{2} - 2 \, {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d^{6} i^{3} x^{3} + 3 \, c d^{5} i^{3} x^{2} + 3 \, c^{2} d^{4} i^{3} x + c^{3} d^{3} i^{3}}\,{d x}"," ",0,"-3/2*A*B*a^2*b*g^3*(2*(2*d*x + c)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - (b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) - 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) + 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) - 1/2*A^2*b^3*g^3*((6*c^2*d*x + 5*c^3)/(d^6*i^3*x^2 + 2*c*d^5*i^3*x + c^2*d^4*i^3) - 2*x/(d^3*i^3) + 6*c*log(d*x + c)/(d^4*i^3)) + 1/2*A*B*a^3*g^3*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) + 3/2*A^2*a*b^2*g^3*((4*c*d*x + 3*c^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) + 2*log(d*x + c)/(d^3*i^3)) - 3/2*(2*d*x + c)*A^2*a^2*b*g^3/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*A^2*a^3*g^3/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*(2*((b^3*c*d^2*g^3 - a*b^2*d^3*g^3)*B^2*x^2 + 2*(b^3*c^2*d*g^3 - a*b^2*c*d^2*g^3)*B^2*x + (b^3*c^3*g^3 - a*b^2*c^2*d*g^3)*B^2)*log(d*x + c)^3 - (2*B^2*b^3*d^3*g^3*x^3 + 4*B^2*b^3*c*d^2*g^3*x^2 - 2*(2*b^3*c^2*d*g^3 - 6*a*b^2*c*d^2*g^3 + 3*a^2*b*d^3*g^3)*B^2*x - (5*b^3*c^3*g^3 - 9*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 + a^3*d^3*g^3)*B^2)*log(d*x + c)^2)/(d^6*i^3*x^2 + 2*c*d^5*i^3*x + c^2*d^4*i^3) - integrate(-(3*B^2*a^2*b*d^3*g^3*x*log(e)^2 + B^2*a^3*d^3*g^3*log(e)^2 + (B^2*b^3*d^3*g^3*log(e)^2 + 2*A*B*b^3*d^3*g^3*log(e))*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e)^2 + 2*A*B*a*b^2*d^3*g^3*log(e))*x^2 + (B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log(b*x + a)^2 + 2*(3*B^2*a^2*b*d^3*g^3*x*log(e) + B^2*a^3*d^3*g^3*log(e) + (B^2*b^3*d^3*g^3*log(e) + A*B*b^3*d^3*g^3)*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e) + A*B*a*b^2*d^3*g^3)*x^2)*log(b*x + a) + (2*(2*b^3*c^2*d*g^3 - 6*a*b^2*c*d^2*g^3 - 3*(g^3*log(e) - g^3)*a^2*b*d^3)*B^2*x - 2*(A*B*b^3*d^3*g^3 + (g^3*log(e) + g^3)*B^2*b^3*d^3)*x^3 + (5*b^3*c^3*g^3 - 9*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - (2*g^3*log(e) - g^3)*a^3*d^3)*B^2 - 2*(3*A*B*a*b^2*d^3*g^3 + (3*a*b^2*d^3*g^3*log(e) + 2*b^3*c*d^2*g^3)*B^2)*x^2 - 2*(B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log(b*x + a))*log(d*x + c))/(d^6*i^3*x^3 + 3*c*d^5*i^3*x^2 + 3*c^2*d^4*i^3*x + c^3*d^3*i^3), x)","F",0
101,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-A B a b g^{2} {\left(\frac{2 \, {\left(2 \, d x + c\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{2} \, A B a^{2} g^{2} {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} + \frac{1}{2} \, A^{2} b^{2} g^{2} {\left(\frac{4 \, c d x + 3 \, c^{2}}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} + \frac{2 \, \log\left(d x + c\right)}{d^{3} i^{3}}\right)} - \frac{{\left(2 \, d x + c\right)} A^{2} a b g^{2}}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{A^{2} a^{2} g^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} + \frac{2 \, {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} b^{2} c d g^{2} x + B^{2} b^{2} c^{2} g^{2}\right)} \log\left(d x + c\right)^{3} + 3 \, {\left(4 \, {\left(b^{2} c d g^{2} - a b d^{2} g^{2}\right)} B^{2} x + {\left(3 \, b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} - a^{2} d^{2} g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2}}{6 \, {\left(d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}\right)}} - \int -\frac{2 \, B^{2} a b d^{2} g^{2} x \log\left(e\right)^{2} + B^{2} a^{2} d^{2} g^{2} \log\left(e\right)^{2} + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} g^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(2 \, B^{2} a b d^{2} g^{2} x \log\left(e\right) + B^{2} a^{2} d^{2} g^{2} \log\left(e\right) + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right) + A B b^{2} d^{2} g^{2}\right)} x^{2}\right)} \log\left(b x + a\right) - {\left(4 \, {\left(b^{2} c d g^{2} + {\left(g^{2} \log\left(e\right) - g^{2}\right)} a b d^{2}\right)} B^{2} x + {\left(3 \, b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + {\left(2 \, g^{2} \log\left(e\right) - g^{2}\right)} a^{2} d^{2}\right)} B^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right) + A B b^{2} d^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d^{5} i^{3} x^{3} + 3 \, c d^{4} i^{3} x^{2} + 3 \, c^{2} d^{3} i^{3} x + c^{3} d^{2} i^{3}}\,{d x}"," ",0,"-A*B*a*b*g^2*(2*(2*d*x + c)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - (b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) - 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) + 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/2*A*B*a^2*g^2*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) + 1/2*A^2*b^2*g^2*((4*c*d*x + 3*c^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) + 2*log(d*x + c)/(d^3*i^3)) - (2*d*x + c)*A^2*a*b*g^2/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*A^2*a^2*g^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 1/6*(2*(B^2*b^2*d^2*g^2*x^2 + 2*B^2*b^2*c*d*g^2*x + B^2*b^2*c^2*g^2)*log(d*x + c)^3 + 3*(4*(b^2*c*d*g^2 - a*b*d^2*g^2)*B^2*x + (3*b^2*c^2*g^2 - 2*a*b*c*d*g^2 - a^2*d^2*g^2)*B^2)*log(d*x + c)^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) - integrate(-(2*B^2*a*b*d^2*g^2*x*log(e)^2 + B^2*a^2*d^2*g^2*log(e)^2 + (B^2*b^2*d^2*g^2*log(e)^2 + 2*A*B*b^2*d^2*g^2*log(e))*x^2 + (B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log(b*x + a)^2 + 2*(2*B^2*a*b*d^2*g^2*x*log(e) + B^2*a^2*d^2*g^2*log(e) + (B^2*b^2*d^2*g^2*log(e) + A*B*b^2*d^2*g^2)*x^2)*log(b*x + a) - (4*(b^2*c*d*g^2 + (g^2*log(e) - g^2)*a*b*d^2)*B^2*x + (3*b^2*c^2*g^2 - 2*a*b*c*d*g^2 + (2*g^2*log(e) - g^2)*a^2*d^2)*B^2 + 2*(B^2*b^2*d^2*g^2*log(e) + A*B*b^2*d^2*g^2)*x^2 + 2*(B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log(b*x + a))*log(d*x + c))/(d^5*i^3*x^3 + 3*c*d^4*i^3*x^2 + 3*c^2*d^3*i^3*x + c^3*d^2*i^3), x)","F",0
102,1,1966,0,2.519800," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, d x + c\right)} B^{2} b g \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} + \frac{1}{4} \, {\left(2 \, {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{2} c^{4} d i^{3} - 2 \, a b c^{3} d^{2} i^{3} + a^{2} c^{2} d^{3} i^{3} + {\left(b^{2} c^{2} d^{3} i^{3} - 2 \, a b c d^{4} i^{3} + a^{2} d^{5} i^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} i^{3} - 2 \, a b c^{2} d^{3} i^{3} + a^{2} c d^{4} i^{3}\right)} x}\right)} B^{2} a g + \frac{1}{4} \, {\left(2 \, {\left(\frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2} + 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(b^{2} c^{2} d - 5 \, a b c d^{2} + 4 \, a^{2} d^{3}\right)} x + 2 \, {\left(b^{2} c^{3} - 4 \, a b c^{2} d + {\left(b^{2} c d^{2} - 4 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} c^{3} - 4 \, a b c^{2} d + {\left(b^{2} c d^{2} - 4 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x + 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{2} c^{4} d^{2} i^{3} - 2 \, a b c^{3} d^{3} i^{3} + a^{2} c^{2} d^{4} i^{3} + {\left(b^{2} c^{2} d^{4} i^{3} - 2 \, a b c d^{5} i^{3} + a^{2} d^{6} i^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{3} i^{3} - 2 \, a b c^{2} d^{4} i^{3} + a^{2} c d^{5} i^{3}\right)} x}\right)} B^{2} b g - \frac{1}{2} \, A B b g {\left(\frac{2 \, {\left(2 \, d x + c\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{2} \, A B a g {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{B^{2} a g \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{{\left(2 \, d x + c\right)} A^{2} b g}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{A^{2} a g}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"-1/2*(2*d*x + c)*B^2*b*g*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) + 1/4*(2*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - (7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))/(b^2*c^4*d*i^3 - 2*a*b*c^3*d^2*i^3 + a^2*c^2*d^3*i^3 + (b^2*c^2*d^3*i^3 - 2*a*b*c*d^4*i^3 + a^2*d^5*i^3)*x^2 + 2*(b^2*c^3*d^2*i^3 - 2*a*b*c^2*d^3*i^3 + a^2*c*d^4*i^3)*x))*B^2*a*g + 1/4*(2*((b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) + 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) - 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2 + 2*(b^2*c^3 - 2*a*b*c^2*d + (b^2*c*d^2 - 2*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 2*a*b*c*d^2)*x)*log(b*x + a)^2 + 2*(b^2*c^3 - 2*a*b*c^2*d + (b^2*c*d^2 - 2*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 2*a*b*c*d^2)*x)*log(d*x + c)^2 + 2*(b^2*c^2*d - 5*a*b*c*d^2 + 4*a^2*d^3)*x + 2*(b^2*c^3 - 4*a*b*c^2*d + (b^2*c*d^2 - 4*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 4*a*b*c*d^2)*x)*log(b*x + a) - 2*(b^2*c^3 - 4*a*b*c^2*d + (b^2*c*d^2 - 4*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 4*a*b*c*d^2)*x + 2*(b^2*c^3 - 2*a*b*c^2*d + (b^2*c*d^2 - 2*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 2*a*b*c*d^2)*x)*log(b*x + a))*log(d*x + c))/(b^2*c^4*d^2*i^3 - 2*a*b*c^3*d^3*i^3 + a^2*c^2*d^4*i^3 + (b^2*c^2*d^4*i^3 - 2*a*b*c*d^5*i^3 + a^2*d^6*i^3)*x^2 + 2*(b^2*c^3*d^3*i^3 - 2*a*b*c^2*d^4*i^3 + a^2*c*d^5*i^3)*x))*B^2*b*g - 1/2*A*B*b*g*(2*(2*d*x + c)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - (b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) - 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) + 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/2*A*B*a*g*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*B^2*a*g*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*(2*d*x + c)*A^2*b*g/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*A^2*a*g/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","B",0
103,1,848,0,1.456792," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(2 \, {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{2} c^{4} d i^{3} - 2 \, a b c^{3} d^{2} i^{3} + a^{2} c^{2} d^{3} i^{3} + {\left(b^{2} c^{2} d^{3} i^{3} - 2 \, a b c d^{4} i^{3} + a^{2} d^{5} i^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} i^{3} - 2 \, a b c^{2} d^{3} i^{3} + a^{2} c d^{4} i^{3}\right)} x}\right)} B^{2} + \frac{1}{2} \, A B {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{B^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{A^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"1/4*(2*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - (7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))/(b^2*c^4*d*i^3 - 2*a*b*c^3*d^2*i^3 + a^2*c^2*d^3*i^3 + (b^2*c^2*d^3*i^3 - 2*a*b*c*d^4*i^3 + a^2*d^5*i^3)*x^2 + 2*(b^2*c^3*d^2*i^3 - 2*a*b*c^2*d^3*i^3 + a^2*c*d^4*i^3)*x))*B^2 + 1/2*A*B*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*B^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","B",0
104,1,2116,0,3.062871," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B^{2} {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} + A B {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{12} \, B^{2} {\left(\frac{6 \, {\left(7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{b^{3} c^{5} g i^{3} - 3 \, a b^{2} c^{4} d g i^{3} + 3 \, a^{2} b c^{3} d^{2} g i^{3} - a^{3} c^{2} d^{3} g i^{3} + {\left(b^{3} c^{3} d^{2} g i^{3} - 3 \, a b^{2} c^{2} d^{3} g i^{3} + 3 \, a^{2} b c d^{4} g i^{3} - a^{3} d^{5} g i^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d g i^{3} - 3 \, a b^{2} c^{3} d^{2} g i^{3} + 3 \, a^{2} b c^{2} d^{3} g i^{3} - a^{3} c d^{4} g i^{3}\right)} x} - \frac{45 \, b^{2} c^{2} - 48 \, a b c d + 3 \, a^{2} d^{2} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{3} - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{3} + 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 42 \, {\left(b^{2} c d - a b d^{2}\right)} x + 42 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 6 \, {\left(7 \, b^{2} d^{2} x^{2} + 14 \, b^{2} c d x + 7 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{3} c^{5} g i^{3} - 3 \, a b^{2} c^{4} d g i^{3} + 3 \, a^{2} b c^{3} d^{2} g i^{3} - a^{3} c^{2} d^{3} g i^{3} + {\left(b^{3} c^{3} d^{2} g i^{3} - 3 \, a b^{2} c^{2} d^{3} g i^{3} + 3 \, a^{2} b c d^{4} g i^{3} - a^{3} d^{5} g i^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d g i^{3} - 3 \, a b^{2} c^{3} d^{2} g i^{3} + 3 \, a^{2} b c^{2} d^{3} g i^{3} - a^{3} c d^{4} g i^{3}\right)} x}\right)} + \frac{1}{2} \, A^{2} {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)} - \frac{{\left(7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{2 \, {\left(b^{3} c^{5} g i^{3} - 3 \, a b^{2} c^{4} d g i^{3} + 3 \, a^{2} b c^{3} d^{2} g i^{3} - a^{3} c^{2} d^{3} g i^{3} + {\left(b^{3} c^{3} d^{2} g i^{3} - 3 \, a b^{2} c^{2} d^{3} g i^{3} + 3 \, a^{2} b c d^{4} g i^{3} - a^{3} d^{5} g i^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d g i^{3} - 3 \, a b^{2} c^{3} d^{2} g i^{3} + 3 \, a^{2} b c^{2} d^{3} g i^{3} - a^{3} c d^{4} g i^{3}\right)} x\right)}}"," ",0,"1/2*B^2*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 + A*B*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/12*B^2*(6*(7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(b^3*c^5*g*i^3 - 3*a*b^2*c^4*d*g*i^3 + 3*a^2*b*c^3*d^2*g*i^3 - a^3*c^2*d^3*g*i^3 + (b^3*c^3*d^2*g*i^3 - 3*a*b^2*c^2*d^3*g*i^3 + 3*a^2*b*c*d^4*g*i^3 - a^3*d^5*g*i^3)*x^2 + 2*(b^3*c^4*d*g*i^3 - 3*a*b^2*c^3*d^2*g*i^3 + 3*a^2*b*c^2*d^3*g*i^3 - a^3*c*d^4*g*i^3)*x) - (45*b^2*c^2 - 48*a*b*c*d + 3*a^2*d^2 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^3 - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^3 + 18*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 6*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c)^2 + 42*(b^2*c*d - a*b*d^2)*x + 42*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 6*(7*b^2*d^2*x^2 + 14*b^2*c*d*x + 7*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))/(b^3*c^5*g*i^3 - 3*a*b^2*c^4*d*g*i^3 + 3*a^2*b*c^3*d^2*g*i^3 - a^3*c^2*d^3*g*i^3 + (b^3*c^3*d^2*g*i^3 - 3*a*b^2*c^2*d^3*g*i^3 + 3*a^2*b*c*d^4*g*i^3 - a^3*d^5*g*i^3)*x^2 + 2*(b^3*c^4*d*g*i^3 - 3*a*b^2*c^3*d^2*g*i^3 + 3*a^2*b*c^2*d^3*g*i^3 - a^3*c*d^4*g*i^3)*x)) + 1/2*A^2*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3)) - 1/2*(7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*A*B/(b^3*c^5*g*i^3 - 3*a*b^2*c^4*d*g*i^3 + 3*a^2*b*c^3*d^2*g*i^3 - a^3*c^2*d^3*g*i^3 + (b^3*c^3*d^2*g*i^3 - 3*a*b^2*c^2*d^3*g*i^3 + 3*a^2*b*c*d^4*g*i^3 - a^3*d^5*g*i^3)*x^2 + 2*(b^3*c^4*d*g*i^3 - 3*a*b^2*c^3*d^2*g*i^3 + 3*a^2*b*c^2*d^3*g*i^3 - a^3*c*d^4*g*i^3)*x)","B",0
105,1,4188,0,4.819777," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} - A B {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{4} \, B^{2} {\left(\frac{2 \, {\left(4 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} - a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a b^{4} c^{6} g^{2} i^{3} - 4 \, a^{2} b^{3} c^{5} d g^{2} i^{3} + 6 \, a^{3} b^{2} c^{4} d^{2} g^{2} i^{3} - 4 \, a^{4} b c^{3} d^{3} g^{2} i^{3} + a^{5} c^{2} d^{4} g^{2} i^{3} + {\left(b^{5} c^{4} d^{2} g^{2} i^{3} - 4 \, a b^{4} c^{3} d^{3} g^{2} i^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} g^{2} i^{3} - 4 \, a^{3} b^{2} c d^{5} g^{2} i^{3} + a^{4} b d^{6} g^{2} i^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d g^{2} i^{3} - 7 \, a b^{4} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{2} b^{3} c^{3} d^{3} g^{2} i^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} g^{2} i^{3} - 2 \, a^{4} b c d^{5} g^{2} i^{3} + a^{5} d^{6} g^{2} i^{3}\right)} x^{2} + {\left(b^{5} c^{6} g^{2} i^{3} - 2 \, a b^{4} c^{5} d g^{2} i^{3} - 2 \, a^{2} b^{3} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 7 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 2 \, a^{5} c d^{5} g^{2} i^{3}\right)} x} + \frac{8 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 24 \, a^{2} b c d^{2} + a^{3} d^{3} + 4 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{3} - 4 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)^{3} + 30 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(13 \, b^{3} c^{2} d - 6 \, a b^{2} c d^{2} - 7 \, a^{2} b d^{3}\right)} x + 30 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(5 \, b^{3} d^{3} x^{3} + 5 \, a b^{2} c^{2} d + 5 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 5 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a b^{4} c^{6} g^{2} i^{3} - 4 \, a^{2} b^{3} c^{5} d g^{2} i^{3} + 6 \, a^{3} b^{2} c^{4} d^{2} g^{2} i^{3} - 4 \, a^{4} b c^{3} d^{3} g^{2} i^{3} + a^{5} c^{2} d^{4} g^{2} i^{3} + {\left(b^{5} c^{4} d^{2} g^{2} i^{3} - 4 \, a b^{4} c^{3} d^{3} g^{2} i^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} g^{2} i^{3} - 4 \, a^{3} b^{2} c d^{5} g^{2} i^{3} + a^{4} b d^{6} g^{2} i^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d g^{2} i^{3} - 7 \, a b^{4} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{2} b^{3} c^{3} d^{3} g^{2} i^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} g^{2} i^{3} - 2 \, a^{4} b c d^{5} g^{2} i^{3} + a^{5} d^{6} g^{2} i^{3}\right)} x^{2} + {\left(b^{5} c^{6} g^{2} i^{3} - 2 \, a b^{4} c^{5} d g^{2} i^{3} - 2 \, a^{2} b^{3} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 7 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 2 \, a^{5} c d^{5} g^{2} i^{3}\right)} x}\right)} - \frac{1}{2} \, A^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)} - \frac{{\left(4 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} - a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{2 \, {\left(a b^{4} c^{6} g^{2} i^{3} - 4 \, a^{2} b^{3} c^{5} d g^{2} i^{3} + 6 \, a^{3} b^{2} c^{4} d^{2} g^{2} i^{3} - 4 \, a^{4} b c^{3} d^{3} g^{2} i^{3} + a^{5} c^{2} d^{4} g^{2} i^{3} + {\left(b^{5} c^{4} d^{2} g^{2} i^{3} - 4 \, a b^{4} c^{3} d^{3} g^{2} i^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} g^{2} i^{3} - 4 \, a^{3} b^{2} c d^{5} g^{2} i^{3} + a^{4} b d^{6} g^{2} i^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d g^{2} i^{3} - 7 \, a b^{4} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{2} b^{3} c^{3} d^{3} g^{2} i^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} g^{2} i^{3} - 2 \, a^{4} b c d^{5} g^{2} i^{3} + a^{5} d^{6} g^{2} i^{3}\right)} x^{2} + {\left(b^{5} c^{6} g^{2} i^{3} - 2 \, a b^{4} c^{5} d g^{2} i^{3} - 2 \, a^{2} b^{3} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 7 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 2 \, a^{5} c d^{5} g^{2} i^{3}\right)} x\right)}}"," ",0,"-1/2*B^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 - A*B*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/4*B^2*(2*(4*b^3*c^3 - 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 - a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c)^2 - 3*(b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a*b^4*c^6*g^2*i^3 - 4*a^2*b^3*c^5*d*g^2*i^3 + 6*a^3*b^2*c^4*d^2*g^2*i^3 - 4*a^4*b*c^3*d^3*g^2*i^3 + a^5*c^2*d^4*g^2*i^3 + (b^5*c^4*d^2*g^2*i^3 - 4*a*b^4*c^3*d^3*g^2*i^3 + 6*a^2*b^3*c^2*d^4*g^2*i^3 - 4*a^3*b^2*c*d^5*g^2*i^3 + a^4*b*d^6*g^2*i^3)*x^3 + (2*b^5*c^5*d*g^2*i^3 - 7*a*b^4*c^4*d^2*g^2*i^3 + 8*a^2*b^3*c^3*d^3*g^2*i^3 - 2*a^3*b^2*c^2*d^4*g^2*i^3 - 2*a^4*b*c*d^5*g^2*i^3 + a^5*d^6*g^2*i^3)*x^2 + (b^5*c^6*g^2*i^3 - 2*a*b^4*c^5*d*g^2*i^3 - 2*a^2*b^3*c^4*d^2*g^2*i^3 + 8*a^3*b^2*c^3*d^3*g^2*i^3 - 7*a^4*b*c^2*d^4*g^2*i^3 + 2*a^5*c*d^5*g^2*i^3)*x) + (8*b^3*c^3 + 15*a*b^2*c^2*d - 24*a^2*b*c*d^2 + a^3*d^3 + 4*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^3 - 4*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c)^3 + 30*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c)^2 + 3*(13*b^3*c^2*d - 6*a*b^2*c*d^2 - 7*a^2*b*d^3)*x + 30*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) - 6*(5*b^3*d^3*x^3 + 5*a*b^2*c^2*d + 5*(2*b^3*c*d^2 + a*b^2*d^3)*x^2 + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 + 5*(b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c))/(a*b^4*c^6*g^2*i^3 - 4*a^2*b^3*c^5*d*g^2*i^3 + 6*a^3*b^2*c^4*d^2*g^2*i^3 - 4*a^4*b*c^3*d^3*g^2*i^3 + a^5*c^2*d^4*g^2*i^3 + (b^5*c^4*d^2*g^2*i^3 - 4*a*b^4*c^3*d^3*g^2*i^3 + 6*a^2*b^3*c^2*d^4*g^2*i^3 - 4*a^3*b^2*c*d^5*g^2*i^3 + a^4*b*d^6*g^2*i^3)*x^3 + (2*b^5*c^5*d*g^2*i^3 - 7*a*b^4*c^4*d^2*g^2*i^3 + 8*a^2*b^3*c^3*d^3*g^2*i^3 - 2*a^3*b^2*c^2*d^4*g^2*i^3 - 2*a^4*b*c*d^5*g^2*i^3 + a^5*d^6*g^2*i^3)*x^2 + (b^5*c^6*g^2*i^3 - 2*a*b^4*c^5*d*g^2*i^3 - 2*a^2*b^3*c^4*d^2*g^2*i^3 + 8*a^3*b^2*c^3*d^3*g^2*i^3 - 7*a^4*b*c^2*d^4*g^2*i^3 + 2*a^5*c*d^5*g^2*i^3)*x)) - 1/2*A^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3)) - 1/2*(4*b^3*c^3 - 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 - a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c)^2 - 3*(b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c))*A*B/(a*b^4*c^6*g^2*i^3 - 4*a^2*b^3*c^5*d*g^2*i^3 + 6*a^3*b^2*c^4*d^2*g^2*i^3 - 4*a^4*b*c^3*d^3*g^2*i^3 + a^5*c^2*d^4*g^2*i^3 + (b^5*c^4*d^2*g^2*i^3 - 4*a*b^4*c^3*d^3*g^2*i^3 + 6*a^2*b^3*c^2*d^4*g^2*i^3 - 4*a^3*b^2*c*d^5*g^2*i^3 + a^4*b*d^6*g^2*i^3)*x^3 + (2*b^5*c^5*d*g^2*i^3 - 7*a*b^4*c^4*d^2*g^2*i^3 + 8*a^2*b^3*c^3*d^3*g^2*i^3 - 2*a^3*b^2*c^2*d^4*g^2*i^3 - 2*a^4*b*c*d^5*g^2*i^3 + a^5*d^6*g^2*i^3)*x^2 + (b^5*c^6*g^2*i^3 - 2*a*b^4*c^5*d*g^2*i^3 - 2*a^2*b^3*c^4*d^2*g^2*i^3 + 8*a^3*b^2*c^3*d^3*g^2*i^3 - 7*a^4*b*c^2*d^4*g^2*i^3 + 2*a^5*c*d^5*g^2*i^3)*x)","B",0
106,1,5583,0,5.717414," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} + A B {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{4} \, B^{2} {\left(\frac{2 \, {\left(b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} - 16 \, a^{3} b c d^{3} + a^{4} d^{4} - 12 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} - 24 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 12 \, {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a^{2} b^{5} c^{7} g^{3} i^{3} - 5 \, a^{3} b^{4} c^{6} d g^{3} i^{3} + 10 \, a^{4} b^{3} c^{5} d^{2} g^{3} i^{3} - 10 \, a^{5} b^{2} c^{4} d^{3} g^{3} i^{3} + 5 \, a^{6} b c^{3} d^{4} g^{3} i^{3} - a^{7} c^{2} d^{5} g^{3} i^{3} + {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 5 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} - 10 \, a^{3} b^{4} c^{2} d^{5} g^{3} i^{3} + 5 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d g^{3} i^{3} - 4 \, a b^{6} c^{5} d^{2} g^{3} i^{3} + 5 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} + 4 \, a^{5} b^{2} c d^{6} g^{3} i^{3} - a^{6} b d^{7} g^{3} i^{3}\right)} x^{3} + {\left(b^{7} c^{7} g^{3} i^{3} - a b^{6} c^{6} d g^{3} i^{3} - 9 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 25 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} + 9 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} g^{3} i^{3} - 4 \, a^{2} b^{5} c^{6} d g^{3} i^{3} + 5 \, a^{3} b^{4} c^{5} d^{2} g^{3} i^{3} - 5 \, a^{5} b^{2} c^{3} d^{4} g^{3} i^{3} + 4 \, a^{6} b c^{2} d^{5} g^{3} i^{3} - a^{7} c d^{6} g^{3} i^{3}\right)} x} + \frac{b^{4} c^{4} - 32 \, a b^{3} c^{3} d + 32 \, a^{3} b c d^{3} - a^{4} d^{4} - 60 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} - 8 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{3} - 24 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right)^{2} + 8 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)^{3} - 90 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{2} - 4 \, {\left(7 \, b^{4} c^{3} d + 24 \, a b^{3} c^{2} d^{2} - 24 \, a^{2} b^{2} c d^{3} - 7 \, a^{3} b d^{4}\right)} x - 60 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{2} b^{2} c^{2} d^{2} + 10 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + 5 \, {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 10 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)}{a^{2} b^{5} c^{7} g^{3} i^{3} - 5 \, a^{3} b^{4} c^{6} d g^{3} i^{3} + 10 \, a^{4} b^{3} c^{5} d^{2} g^{3} i^{3} - 10 \, a^{5} b^{2} c^{4} d^{3} g^{3} i^{3} + 5 \, a^{6} b c^{3} d^{4} g^{3} i^{3} - a^{7} c^{2} d^{5} g^{3} i^{3} + {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 5 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} - 10 \, a^{3} b^{4} c^{2} d^{5} g^{3} i^{3} + 5 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d g^{3} i^{3} - 4 \, a b^{6} c^{5} d^{2} g^{3} i^{3} + 5 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} + 4 \, a^{5} b^{2} c d^{6} g^{3} i^{3} - a^{6} b d^{7} g^{3} i^{3}\right)} x^{3} + {\left(b^{7} c^{7} g^{3} i^{3} - a b^{6} c^{6} d g^{3} i^{3} - 9 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 25 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} + 9 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} g^{3} i^{3} - 4 \, a^{2} b^{5} c^{6} d g^{3} i^{3} + 5 \, a^{3} b^{4} c^{5} d^{2} g^{3} i^{3} - 5 \, a^{5} b^{2} c^{3} d^{4} g^{3} i^{3} + 4 \, a^{6} b c^{2} d^{5} g^{3} i^{3} - a^{7} c d^{6} g^{3} i^{3}\right)} x}\right)} + \frac{1}{2} \, A^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)} - \frac{{\left(b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} - 16 \, a^{3} b c d^{3} + a^{4} d^{4} - 12 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} - 24 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 12 \, {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} A B}{2 \, {\left(a^{2} b^{5} c^{7} g^{3} i^{3} - 5 \, a^{3} b^{4} c^{6} d g^{3} i^{3} + 10 \, a^{4} b^{3} c^{5} d^{2} g^{3} i^{3} - 10 \, a^{5} b^{2} c^{4} d^{3} g^{3} i^{3} + 5 \, a^{6} b c^{3} d^{4} g^{3} i^{3} - a^{7} c^{2} d^{5} g^{3} i^{3} + {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 5 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} - 10 \, a^{3} b^{4} c^{2} d^{5} g^{3} i^{3} + 5 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d g^{3} i^{3} - 4 \, a b^{6} c^{5} d^{2} g^{3} i^{3} + 5 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} + 4 \, a^{5} b^{2} c d^{6} g^{3} i^{3} - a^{6} b d^{7} g^{3} i^{3}\right)} x^{3} + {\left(b^{7} c^{7} g^{3} i^{3} - a b^{6} c^{6} d g^{3} i^{3} - 9 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 25 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} + 9 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} g^{3} i^{3} - 4 \, a^{2} b^{5} c^{6} d g^{3} i^{3} + 5 \, a^{3} b^{4} c^{5} d^{2} g^{3} i^{3} - 5 \, a^{5} b^{2} c^{3} d^{4} g^{3} i^{3} + 4 \, a^{6} b c^{2} d^{5} g^{3} i^{3} - a^{7} c d^{6} g^{3} i^{3}\right)} x\right)}}"," ",0,"1/2*B^2*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 + A*B*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/4*B^2*(2*(b^4*c^4 - 16*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 - 16*a^3*b*c*d^3 + a^4*d^4 - 12*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^2 - 24*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)*log(d*x + c) + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c)^2 - 12*(b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a^2*b^5*c^7*g^3*i^3 - 5*a^3*b^4*c^6*d*g^3*i^3 + 10*a^4*b^3*c^5*d^2*g^3*i^3 - 10*a^5*b^2*c^4*d^3*g^3*i^3 + 5*a^6*b*c^3*d^4*g^3*i^3 - a^7*c^2*d^5*g^3*i^3 + (b^7*c^5*d^2*g^3*i^3 - 5*a*b^6*c^4*d^3*g^3*i^3 + 10*a^2*b^5*c^3*d^4*g^3*i^3 - 10*a^3*b^4*c^2*d^5*g^3*i^3 + 5*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3)*x^4 + 2*(b^7*c^6*d*g^3*i^3 - 4*a*b^6*c^5*d^2*g^3*i^3 + 5*a^2*b^5*c^4*d^3*g^3*i^3 - 5*a^4*b^3*c^2*d^5*g^3*i^3 + 4*a^5*b^2*c*d^6*g^3*i^3 - a^6*b*d^7*g^3*i^3)*x^3 + (b^7*c^7*g^3*i^3 - a*b^6*c^6*d*g^3*i^3 - 9*a^2*b^5*c^5*d^2*g^3*i^3 + 25*a^3*b^4*c^4*d^3*g^3*i^3 - 25*a^4*b^3*c^3*d^4*g^3*i^3 + 9*a^5*b^2*c^2*d^5*g^3*i^3 + a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*x^2 + 2*(a*b^6*c^7*g^3*i^3 - 4*a^2*b^5*c^6*d*g^3*i^3 + 5*a^3*b^4*c^5*d^2*g^3*i^3 - 5*a^5*b^2*c^3*d^4*g^3*i^3 + 4*a^6*b*c^2*d^5*g^3*i^3 - a^7*c*d^6*g^3*i^3)*x) + (b^4*c^4 - 32*a*b^3*c^3*d + 32*a^3*b*c*d^3 - a^4*d^4 - 60*(b^4*c*d^3 - a*b^3*d^4)*x^3 - 8*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^3 - 24*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)*log(d*x + c)^2 + 8*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c)^3 - 90*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^2 - 4*(7*b^4*c^3*d + 24*a*b^3*c^2*d^2 - 24*a^2*b^2*c*d^3 - 7*a^3*b*d^4)*x - 60*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a) + 12*(5*b^4*d^4*x^4 + 5*a^2*b^2*c^2*d^2 + 10*(b^4*c*d^3 + a*b^3*d^4)*x^3 + 5*(b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^2 + 10*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c))/(a^2*b^5*c^7*g^3*i^3 - 5*a^3*b^4*c^6*d*g^3*i^3 + 10*a^4*b^3*c^5*d^2*g^3*i^3 - 10*a^5*b^2*c^4*d^3*g^3*i^3 + 5*a^6*b*c^3*d^4*g^3*i^3 - a^7*c^2*d^5*g^3*i^3 + (b^7*c^5*d^2*g^3*i^3 - 5*a*b^6*c^4*d^3*g^3*i^3 + 10*a^2*b^5*c^3*d^4*g^3*i^3 - 10*a^3*b^4*c^2*d^5*g^3*i^3 + 5*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3)*x^4 + 2*(b^7*c^6*d*g^3*i^3 - 4*a*b^6*c^5*d^2*g^3*i^3 + 5*a^2*b^5*c^4*d^3*g^3*i^3 - 5*a^4*b^3*c^2*d^5*g^3*i^3 + 4*a^5*b^2*c*d^6*g^3*i^3 - a^6*b*d^7*g^3*i^3)*x^3 + (b^7*c^7*g^3*i^3 - a*b^6*c^6*d*g^3*i^3 - 9*a^2*b^5*c^5*d^2*g^3*i^3 + 25*a^3*b^4*c^4*d^3*g^3*i^3 - 25*a^4*b^3*c^3*d^4*g^3*i^3 + 9*a^5*b^2*c^2*d^5*g^3*i^3 + a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*x^2 + 2*(a*b^6*c^7*g^3*i^3 - 4*a^2*b^5*c^6*d*g^3*i^3 + 5*a^3*b^4*c^5*d^2*g^3*i^3 - 5*a^5*b^2*c^3*d^4*g^3*i^3 + 4*a^6*b*c^2*d^5*g^3*i^3 - a^7*c*d^6*g^3*i^3)*x)) + 1/2*A^2*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3)) - 1/2*(b^4*c^4 - 16*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 - 16*a^3*b*c*d^3 + a^4*d^4 - 12*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^2 - 24*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)*log(d*x + c) + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c)^2 - 12*(b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x)*A*B/(a^2*b^5*c^7*g^3*i^3 - 5*a^3*b^4*c^6*d*g^3*i^3 + 10*a^4*b^3*c^5*d^2*g^3*i^3 - 10*a^5*b^2*c^4*d^3*g^3*i^3 + 5*a^6*b*c^3*d^4*g^3*i^3 - a^7*c^2*d^5*g^3*i^3 + (b^7*c^5*d^2*g^3*i^3 - 5*a*b^6*c^4*d^3*g^3*i^3 + 10*a^2*b^5*c^3*d^4*g^3*i^3 - 10*a^3*b^4*c^2*d^5*g^3*i^3 + 5*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3)*x^4 + 2*(b^7*c^6*d*g^3*i^3 - 4*a*b^6*c^5*d^2*g^3*i^3 + 5*a^2*b^5*c^4*d^3*g^3*i^3 - 5*a^4*b^3*c^2*d^5*g^3*i^3 + 4*a^5*b^2*c*d^6*g^3*i^3 - a^6*b*d^7*g^3*i^3)*x^3 + (b^7*c^7*g^3*i^3 - a*b^6*c^6*d*g^3*i^3 - 9*a^2*b^5*c^5*d^2*g^3*i^3 + 25*a^3*b^4*c^4*d^3*g^3*i^3 - 25*a^4*b^3*c^3*d^4*g^3*i^3 + 9*a^5*b^2*c^2*d^5*g^3*i^3 + a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*x^2 + 2*(a*b^6*c^7*g^3*i^3 - 4*a^2*b^5*c^6*d*g^3*i^3 + 5*a^3*b^4*c^5*d^2*g^3*i^3 - 5*a^5*b^2*c^3*d^4*g^3*i^3 + 4*a^6*b*c^2*d^5*g^3*i^3 - a^7*c*d^6*g^3*i^3)*x)","B",0
107,1,9282,0,12.471539," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{6} \, B^{2} {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2} - \frac{1}{3} \, A B {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{1}{108} \, B^{2} {\left(\frac{6 \, {\left(4 \, b^{5} c^{5} - 45 \, a b^{4} c^{4} d + 360 \, a^{2} b^{3} c^{3} d^{2} - 490 \, a^{3} b^{2} c^{2} d^{3} + 180 \, a^{4} b c d^{4} - 9 \, a^{5} d^{5} + 120 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 120 \, {\left(3 \, b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} - a^{2} b^{3} d^{5}\right)} x^{3} + 20 \, {\left(11 \, b^{5} c^{3} d^{2} + 21 \, a b^{4} c^{2} d^{3} - 39 \, a^{2} b^{3} c d^{4} + 7 \, a^{3} b^{2} d^{5}\right)} x^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(5 \, b^{5} c^{4} d - 108 \, a b^{4} c^{3} d^{2} + 78 \, a^{2} b^{3} c^{2} d^{3} + 52 \, a^{3} b^{2} c d^{4} - 27 \, a^{4} b d^{5}\right)} x + 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 3 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{a^{3} b^{6} c^{8} g^{4} i^{3} - 6 \, a^{4} b^{5} c^{7} d g^{4} i^{3} + 15 \, a^{5} b^{4} c^{6} d^{2} g^{4} i^{3} - 20 \, a^{6} b^{3} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} g^{4} i^{3} - 6 \, a^{8} b c^{3} d^{5} g^{4} i^{3} + a^{9} c^{2} d^{6} g^{4} i^{3} + {\left(b^{9} c^{6} d^{2} g^{4} i^{3} - 6 \, a b^{8} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} g^{4} i^{3} - 20 \, a^{3} b^{6} c^{3} d^{5} g^{4} i^{3} + 15 \, a^{4} b^{5} c^{2} d^{6} g^{4} i^{3} - 6 \, a^{5} b^{4} c d^{7} g^{4} i^{3} + a^{6} b^{3} d^{8} g^{4} i^{3}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d g^{4} i^{3} - 9 \, a b^{8} c^{6} d^{2} g^{4} i^{3} + 12 \, a^{2} b^{7} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} g^{4} i^{3} - 30 \, a^{4} b^{5} c^{3} d^{5} g^{4} i^{3} + 33 \, a^{5} b^{4} c^{2} d^{6} g^{4} i^{3} - 16 \, a^{6} b^{3} c d^{7} g^{4} i^{3} + 3 \, a^{7} b^{2} d^{8} g^{4} i^{3}\right)} x^{4} + {\left(b^{9} c^{8} g^{4} i^{3} - 18 \, a^{2} b^{7} c^{6} d^{2} g^{4} i^{3} + 52 \, a^{3} b^{6} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} g^{4} i^{3} + 24 \, a^{5} b^{4} c^{3} d^{5} g^{4} i^{3} + 10 \, a^{6} b^{3} c^{2} d^{6} g^{4} i^{3} - 12 \, a^{7} b^{2} c d^{7} g^{4} i^{3} + 3 \, a^{8} b d^{8} g^{4} i^{3}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} g^{4} i^{3} - 12 \, a^{2} b^{7} c^{7} d g^{4} i^{3} + 10 \, a^{3} b^{6} c^{6} d^{2} g^{4} i^{3} + 24 \, a^{4} b^{5} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} g^{4} i^{3} + 52 \, a^{6} b^{3} c^{3} d^{5} g^{4} i^{3} - 18 \, a^{7} b^{2} c^{2} d^{6} g^{4} i^{3} + a^{9} d^{8} g^{4} i^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} g^{4} i^{3} - 16 \, a^{3} b^{6} c^{7} d g^{4} i^{3} + 33 \, a^{4} b^{5} c^{6} d^{2} g^{4} i^{3} - 30 \, a^{5} b^{4} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} g^{4} i^{3} + 12 \, a^{7} b^{2} c^{3} d^{5} g^{4} i^{3} - 9 \, a^{8} b c^{2} d^{6} g^{4} i^{3} + 2 \, a^{9} c d^{7} g^{4} i^{3}\right)} x} + \frac{8 \, b^{5} c^{5} - 135 \, a b^{4} c^{4} d + 2160 \, a^{2} b^{3} c^{3} d^{2} - 980 \, a^{3} b^{2} c^{2} d^{3} - 1080 \, a^{4} b c d^{4} + 27 \, a^{5} d^{5} + 2940 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 30 \, {\left(159 \, b^{5} c^{2} d^{3} + 74 \, a b^{4} c d^{4} - 233 \, a^{2} b^{3} d^{5}\right)} x^{3} + 360 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{3} - 360 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)^{3} + 10 \, {\left(170 \, b^{5} c^{3} d^{2} + 921 \, a b^{4} c^{2} d^{3} - 588 \, a^{2} b^{3} c d^{4} - 503 \, a^{3} b^{2} d^{5}\right)} x^{2} - 360 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 360 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 3 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(19 \, b^{5} c^{4} d - 756 \, a b^{4} c^{3} d^{2} - 708 \, a^{2} b^{3} c^{2} d^{3} + 1256 \, a^{3} b^{2} c d^{4} + 189 \, a^{4} b d^{5}\right)} x + 2940 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(49 \, b^{5} d^{5} x^{5} + 49 \, a^{3} b^{2} c^{2} d^{3} + 49 \, {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + 49 \, {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + 49 \, {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + 18 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} + 49 \, {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 12 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{a^{3} b^{6} c^{8} g^{4} i^{3} - 6 \, a^{4} b^{5} c^{7} d g^{4} i^{3} + 15 \, a^{5} b^{4} c^{6} d^{2} g^{4} i^{3} - 20 \, a^{6} b^{3} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} g^{4} i^{3} - 6 \, a^{8} b c^{3} d^{5} g^{4} i^{3} + a^{9} c^{2} d^{6} g^{4} i^{3} + {\left(b^{9} c^{6} d^{2} g^{4} i^{3} - 6 \, a b^{8} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} g^{4} i^{3} - 20 \, a^{3} b^{6} c^{3} d^{5} g^{4} i^{3} + 15 \, a^{4} b^{5} c^{2} d^{6} g^{4} i^{3} - 6 \, a^{5} b^{4} c d^{7} g^{4} i^{3} + a^{6} b^{3} d^{8} g^{4} i^{3}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d g^{4} i^{3} - 9 \, a b^{8} c^{6} d^{2} g^{4} i^{3} + 12 \, a^{2} b^{7} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} g^{4} i^{3} - 30 \, a^{4} b^{5} c^{3} d^{5} g^{4} i^{3} + 33 \, a^{5} b^{4} c^{2} d^{6} g^{4} i^{3} - 16 \, a^{6} b^{3} c d^{7} g^{4} i^{3} + 3 \, a^{7} b^{2} d^{8} g^{4} i^{3}\right)} x^{4} + {\left(b^{9} c^{8} g^{4} i^{3} - 18 \, a^{2} b^{7} c^{6} d^{2} g^{4} i^{3} + 52 \, a^{3} b^{6} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} g^{4} i^{3} + 24 \, a^{5} b^{4} c^{3} d^{5} g^{4} i^{3} + 10 \, a^{6} b^{3} c^{2} d^{6} g^{4} i^{3} - 12 \, a^{7} b^{2} c d^{7} g^{4} i^{3} + 3 \, a^{8} b d^{8} g^{4} i^{3}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} g^{4} i^{3} - 12 \, a^{2} b^{7} c^{7} d g^{4} i^{3} + 10 \, a^{3} b^{6} c^{6} d^{2} g^{4} i^{3} + 24 \, a^{4} b^{5} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} g^{4} i^{3} + 52 \, a^{6} b^{3} c^{3} d^{5} g^{4} i^{3} - 18 \, a^{7} b^{2} c^{2} d^{6} g^{4} i^{3} + a^{9} d^{8} g^{4} i^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} g^{4} i^{3} - 16 \, a^{3} b^{6} c^{7} d g^{4} i^{3} + 33 \, a^{4} b^{5} c^{6} d^{2} g^{4} i^{3} - 30 \, a^{5} b^{4} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} g^{4} i^{3} + 12 \, a^{7} b^{2} c^{3} d^{5} g^{4} i^{3} - 9 \, a^{8} b c^{2} d^{6} g^{4} i^{3} + 2 \, a^{9} c d^{7} g^{4} i^{3}\right)} x}\right)} - \frac{1}{6} \, A^{2} {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)} - \frac{{\left(4 \, b^{5} c^{5} - 45 \, a b^{4} c^{4} d + 360 \, a^{2} b^{3} c^{3} d^{2} - 490 \, a^{3} b^{2} c^{2} d^{3} + 180 \, a^{4} b c d^{4} - 9 \, a^{5} d^{5} + 120 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 120 \, {\left(3 \, b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} - a^{2} b^{3} d^{5}\right)} x^{3} + 20 \, {\left(11 \, b^{5} c^{3} d^{2} + 21 \, a b^{4} c^{2} d^{3} - 39 \, a^{2} b^{3} c d^{4} + 7 \, a^{3} b^{2} d^{5}\right)} x^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(5 \, b^{5} c^{4} d - 108 \, a b^{4} c^{3} d^{2} + 78 \, a^{2} b^{3} c^{2} d^{3} + 52 \, a^{3} b^{2} c d^{4} - 27 \, a^{4} b d^{5}\right)} x + 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 3 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B}{18 \, {\left(a^{3} b^{6} c^{8} g^{4} i^{3} - 6 \, a^{4} b^{5} c^{7} d g^{4} i^{3} + 15 \, a^{5} b^{4} c^{6} d^{2} g^{4} i^{3} - 20 \, a^{6} b^{3} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} g^{4} i^{3} - 6 \, a^{8} b c^{3} d^{5} g^{4} i^{3} + a^{9} c^{2} d^{6} g^{4} i^{3} + {\left(b^{9} c^{6} d^{2} g^{4} i^{3} - 6 \, a b^{8} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} g^{4} i^{3} - 20 \, a^{3} b^{6} c^{3} d^{5} g^{4} i^{3} + 15 \, a^{4} b^{5} c^{2} d^{6} g^{4} i^{3} - 6 \, a^{5} b^{4} c d^{7} g^{4} i^{3} + a^{6} b^{3} d^{8} g^{4} i^{3}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d g^{4} i^{3} - 9 \, a b^{8} c^{6} d^{2} g^{4} i^{3} + 12 \, a^{2} b^{7} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} g^{4} i^{3} - 30 \, a^{4} b^{5} c^{3} d^{5} g^{4} i^{3} + 33 \, a^{5} b^{4} c^{2} d^{6} g^{4} i^{3} - 16 \, a^{6} b^{3} c d^{7} g^{4} i^{3} + 3 \, a^{7} b^{2} d^{8} g^{4} i^{3}\right)} x^{4} + {\left(b^{9} c^{8} g^{4} i^{3} - 18 \, a^{2} b^{7} c^{6} d^{2} g^{4} i^{3} + 52 \, a^{3} b^{6} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} g^{4} i^{3} + 24 \, a^{5} b^{4} c^{3} d^{5} g^{4} i^{3} + 10 \, a^{6} b^{3} c^{2} d^{6} g^{4} i^{3} - 12 \, a^{7} b^{2} c d^{7} g^{4} i^{3} + 3 \, a^{8} b d^{8} g^{4} i^{3}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} g^{4} i^{3} - 12 \, a^{2} b^{7} c^{7} d g^{4} i^{3} + 10 \, a^{3} b^{6} c^{6} d^{2} g^{4} i^{3} + 24 \, a^{4} b^{5} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} g^{4} i^{3} + 52 \, a^{6} b^{3} c^{3} d^{5} g^{4} i^{3} - 18 \, a^{7} b^{2} c^{2} d^{6} g^{4} i^{3} + a^{9} d^{8} g^{4} i^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} g^{4} i^{3} - 16 \, a^{3} b^{6} c^{7} d g^{4} i^{3} + 33 \, a^{4} b^{5} c^{6} d^{2} g^{4} i^{3} - 30 \, a^{5} b^{4} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} g^{4} i^{3} + 12 \, a^{7} b^{2} c^{3} d^{5} g^{4} i^{3} - 9 \, a^{8} b c^{2} d^{6} g^{4} i^{3} + 2 \, a^{9} c d^{7} g^{4} i^{3}\right)} x\right)}}"," ",0,"-1/6*B^2*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2 - 1/3*A*B*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - 1/108*B^2*(6*(4*b^5*c^5 - 45*a*b^4*c^4*d + 360*a^2*b^3*c^3*d^2 - 490*a^3*b^2*c^2*d^3 + 180*a^4*b*c*d^4 - 9*a^5*d^5 + 120*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 120*(3*b^5*c^2*d^3 - 2*a*b^4*c*d^4 - a^2*b^3*d^5)*x^3 + 20*(11*b^5*c^3*d^2 + 21*a*b^4*c^2*d^3 - 39*a^2*b^3*c*d^4 + 7*a^3*b^2*d^5)*x^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c)^2 - 5*(5*b^5*c^4*d - 108*a*b^4*c^3*d^2 + 78*a^2*b^3*c^2*d^3 + 52*a^3*b^2*c*d^4 - 27*a^4*b*d^5)*x + 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 3*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c))*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(a^3*b^6*c^8*g^4*i^3 - 6*a^4*b^5*c^7*d*g^4*i^3 + 15*a^5*b^4*c^6*d^2*g^4*i^3 - 20*a^6*b^3*c^5*d^3*g^4*i^3 + 15*a^7*b^2*c^4*d^4*g^4*i^3 - 6*a^8*b*c^3*d^5*g^4*i^3 + a^9*c^2*d^6*g^4*i^3 + (b^9*c^6*d^2*g^4*i^3 - 6*a*b^8*c^5*d^3*g^4*i^3 + 15*a^2*b^7*c^4*d^4*g^4*i^3 - 20*a^3*b^6*c^3*d^5*g^4*i^3 + 15*a^4*b^5*c^2*d^6*g^4*i^3 - 6*a^5*b^4*c*d^7*g^4*i^3 + a^6*b^3*d^8*g^4*i^3)*x^5 + (2*b^9*c^7*d*g^4*i^3 - 9*a*b^8*c^6*d^2*g^4*i^3 + 12*a^2*b^7*c^5*d^3*g^4*i^3 + 5*a^3*b^6*c^4*d^4*g^4*i^3 - 30*a^4*b^5*c^3*d^5*g^4*i^3 + 33*a^5*b^4*c^2*d^6*g^4*i^3 - 16*a^6*b^3*c*d^7*g^4*i^3 + 3*a^7*b^2*d^8*g^4*i^3)*x^4 + (b^9*c^8*g^4*i^3 - 18*a^2*b^7*c^6*d^2*g^4*i^3 + 52*a^3*b^6*c^5*d^3*g^4*i^3 - 60*a^4*b^5*c^4*d^4*g^4*i^3 + 24*a^5*b^4*c^3*d^5*g^4*i^3 + 10*a^6*b^3*c^2*d^6*g^4*i^3 - 12*a^7*b^2*c*d^7*g^4*i^3 + 3*a^8*b*d^8*g^4*i^3)*x^3 + (3*a*b^8*c^8*g^4*i^3 - 12*a^2*b^7*c^7*d*g^4*i^3 + 10*a^3*b^6*c^6*d^2*g^4*i^3 + 24*a^4*b^5*c^5*d^3*g^4*i^3 - 60*a^5*b^4*c^4*d^4*g^4*i^3 + 52*a^6*b^3*c^3*d^5*g^4*i^3 - 18*a^7*b^2*c^2*d^6*g^4*i^3 + a^9*d^8*g^4*i^3)*x^2 + (3*a^2*b^7*c^8*g^4*i^3 - 16*a^3*b^6*c^7*d*g^4*i^3 + 33*a^4*b^5*c^6*d^2*g^4*i^3 - 30*a^5*b^4*c^5*d^3*g^4*i^3 + 5*a^6*b^3*c^4*d^4*g^4*i^3 + 12*a^7*b^2*c^3*d^5*g^4*i^3 - 9*a^8*b*c^2*d^6*g^4*i^3 + 2*a^9*c*d^7*g^4*i^3)*x) + (8*b^5*c^5 - 135*a*b^4*c^4*d + 2160*a^2*b^3*c^3*d^2 - 980*a^3*b^2*c^2*d^3 - 1080*a^4*b*c*d^4 + 27*a^5*d^5 + 2940*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 30*(159*b^5*c^2*d^3 + 74*a*b^4*c*d^4 - 233*a^2*b^3*d^5)*x^3 + 360*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^3 - 360*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c)^3 + 10*(170*b^5*c^3*d^2 + 921*a*b^4*c^2*d^3 - 588*a^2*b^3*c*d^4 - 503*a^3*b^2*d^5)*x^2 - 360*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 - 360*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 3*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c)^2 - 5*(19*b^5*c^4*d - 756*a*b^4*c^3*d^2 - 708*a^2*b^3*c^2*d^3 + 1256*a^3*b^2*c*d^4 + 189*a^4*b*d^5)*x + 2940*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 60*(49*b^5*d^5*x^5 + 49*a^3*b^2*c^2*d^3 + 49*(2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + 49*(b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + 49*(3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + 18*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 + 49*(3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 12*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c))/(a^3*b^6*c^8*g^4*i^3 - 6*a^4*b^5*c^7*d*g^4*i^3 + 15*a^5*b^4*c^6*d^2*g^4*i^3 - 20*a^6*b^3*c^5*d^3*g^4*i^3 + 15*a^7*b^2*c^4*d^4*g^4*i^3 - 6*a^8*b*c^3*d^5*g^4*i^3 + a^9*c^2*d^6*g^4*i^3 + (b^9*c^6*d^2*g^4*i^3 - 6*a*b^8*c^5*d^3*g^4*i^3 + 15*a^2*b^7*c^4*d^4*g^4*i^3 - 20*a^3*b^6*c^3*d^5*g^4*i^3 + 15*a^4*b^5*c^2*d^6*g^4*i^3 - 6*a^5*b^4*c*d^7*g^4*i^3 + a^6*b^3*d^8*g^4*i^3)*x^5 + (2*b^9*c^7*d*g^4*i^3 - 9*a*b^8*c^6*d^2*g^4*i^3 + 12*a^2*b^7*c^5*d^3*g^4*i^3 + 5*a^3*b^6*c^4*d^4*g^4*i^3 - 30*a^4*b^5*c^3*d^5*g^4*i^3 + 33*a^5*b^4*c^2*d^6*g^4*i^3 - 16*a^6*b^3*c*d^7*g^4*i^3 + 3*a^7*b^2*d^8*g^4*i^3)*x^4 + (b^9*c^8*g^4*i^3 - 18*a^2*b^7*c^6*d^2*g^4*i^3 + 52*a^3*b^6*c^5*d^3*g^4*i^3 - 60*a^4*b^5*c^4*d^4*g^4*i^3 + 24*a^5*b^4*c^3*d^5*g^4*i^3 + 10*a^6*b^3*c^2*d^6*g^4*i^3 - 12*a^7*b^2*c*d^7*g^4*i^3 + 3*a^8*b*d^8*g^4*i^3)*x^3 + (3*a*b^8*c^8*g^4*i^3 - 12*a^2*b^7*c^7*d*g^4*i^3 + 10*a^3*b^6*c^6*d^2*g^4*i^3 + 24*a^4*b^5*c^5*d^3*g^4*i^3 - 60*a^5*b^4*c^4*d^4*g^4*i^3 + 52*a^6*b^3*c^3*d^5*g^4*i^3 - 18*a^7*b^2*c^2*d^6*g^4*i^3 + a^9*d^8*g^4*i^3)*x^2 + (3*a^2*b^7*c^8*g^4*i^3 - 16*a^3*b^6*c^7*d*g^4*i^3 + 33*a^4*b^5*c^6*d^2*g^4*i^3 - 30*a^5*b^4*c^5*d^3*g^4*i^3 + 5*a^6*b^3*c^4*d^4*g^4*i^3 + 12*a^7*b^2*c^3*d^5*g^4*i^3 - 9*a^8*b*c^2*d^6*g^4*i^3 + 2*a^9*c*d^7*g^4*i^3)*x)) - 1/6*A^2*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3)) - 1/18*(4*b^5*c^5 - 45*a*b^4*c^4*d + 360*a^2*b^3*c^3*d^2 - 490*a^3*b^2*c^2*d^3 + 180*a^4*b*c*d^4 - 9*a^5*d^5 + 120*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 120*(3*b^5*c^2*d^3 - 2*a*b^4*c*d^4 - a^2*b^3*d^5)*x^3 + 20*(11*b^5*c^3*d^2 + 21*a*b^4*c^2*d^3 - 39*a^2*b^3*c*d^4 + 7*a^3*b^2*d^5)*x^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c)^2 - 5*(5*b^5*c^4*d - 108*a*b^4*c^3*d^2 + 78*a^2*b^3*c^2*d^3 + 52*a^3*b^2*c*d^4 - 27*a^4*b*d^5)*x + 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 3*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c))*A*B/(a^3*b^6*c^8*g^4*i^3 - 6*a^4*b^5*c^7*d*g^4*i^3 + 15*a^5*b^4*c^6*d^2*g^4*i^3 - 20*a^6*b^3*c^5*d^3*g^4*i^3 + 15*a^7*b^2*c^4*d^4*g^4*i^3 - 6*a^8*b*c^3*d^5*g^4*i^3 + a^9*c^2*d^6*g^4*i^3 + (b^9*c^6*d^2*g^4*i^3 - 6*a*b^8*c^5*d^3*g^4*i^3 + 15*a^2*b^7*c^4*d^4*g^4*i^3 - 20*a^3*b^6*c^3*d^5*g^4*i^3 + 15*a^4*b^5*c^2*d^6*g^4*i^3 - 6*a^5*b^4*c*d^7*g^4*i^3 + a^6*b^3*d^8*g^4*i^3)*x^5 + (2*b^9*c^7*d*g^4*i^3 - 9*a*b^8*c^6*d^2*g^4*i^3 + 12*a^2*b^7*c^5*d^3*g^4*i^3 + 5*a^3*b^6*c^4*d^4*g^4*i^3 - 30*a^4*b^5*c^3*d^5*g^4*i^3 + 33*a^5*b^4*c^2*d^6*g^4*i^3 - 16*a^6*b^3*c*d^7*g^4*i^3 + 3*a^7*b^2*d^8*g^4*i^3)*x^4 + (b^9*c^8*g^4*i^3 - 18*a^2*b^7*c^6*d^2*g^4*i^3 + 52*a^3*b^6*c^5*d^3*g^4*i^3 - 60*a^4*b^5*c^4*d^4*g^4*i^3 + 24*a^5*b^4*c^3*d^5*g^4*i^3 + 10*a^6*b^3*c^2*d^6*g^4*i^3 - 12*a^7*b^2*c*d^7*g^4*i^3 + 3*a^8*b*d^8*g^4*i^3)*x^3 + (3*a*b^8*c^8*g^4*i^3 - 12*a^2*b^7*c^7*d*g^4*i^3 + 10*a^3*b^6*c^6*d^2*g^4*i^3 + 24*a^4*b^5*c^5*d^3*g^4*i^3 - 60*a^5*b^4*c^4*d^4*g^4*i^3 + 52*a^6*b^3*c^3*d^5*g^4*i^3 - 18*a^7*b^2*c^2*d^6*g^4*i^3 + a^9*d^8*g^4*i^3)*x^2 + (3*a^2*b^7*c^8*g^4*i^3 - 16*a^3*b^6*c^7*d*g^4*i^3 + 33*a^4*b^5*c^6*d^2*g^4*i^3 - 30*a^5*b^4*c^5*d^3*g^4*i^3 + 5*a^6*b^3*c^4*d^4*g^4*i^3 + 12*a^7*b^2*c^3*d^5*g^4*i^3 - 9*a^8*b*c^2*d^6*g^4*i^3 + 2*a^9*c*d^7*g^4*i^3)*x)","B",0
108,1,1118,0,1.508514," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{5} \, B b^{3} d g^{3} i x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{5} \, A b^{3} d g^{3} i x^{5} + \frac{1}{4} \, B b^{3} c g^{3} i x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{4} \, B a b^{2} d g^{3} i x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A b^{3} c g^{3} i x^{4} + \frac{3}{4} \, A a b^{2} d g^{3} i x^{4} + B a b^{2} c g^{3} i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + B a^{2} b d g^{3} i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a b^{2} c g^{3} i x^{3} + A a^{2} b d g^{3} i x^{3} + \frac{3}{2} \, B a^{2} b c g^{3} i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, B a^{3} d g^{3} i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A a^{2} b c g^{3} i x^{2} + \frac{1}{2} \, A a^{3} d g^{3} i x^{2} + \frac{1}{60} \, B b^{3} d g^{3} i n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{24} \, B b^{3} c g^{3} i n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{8} \, B a b^{2} d g^{3} i n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{2} \, B a b^{2} c g^{3} i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{2} \, B a^{2} b d g^{3} i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - \frac{3}{2} \, B a^{2} b c g^{3} i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - \frac{1}{2} \, B a^{3} d g^{3} i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a^{3} c g^{3} i n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a^{3} c g^{3} i x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{3} c g^{3} i x"," ",0,"1/5*B*b^3*d*g^3*i*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A*b^3*d*g^3*i*x^5 + 1/4*B*b^3*c*g^3*i*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/4*B*a*b^2*d*g^3*i*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*b^3*c*g^3*i*x^4 + 3/4*A*a*b^2*d*g^3*i*x^4 + B*a*b^2*c*g^3*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + B*a^2*b*d*g^3*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b^2*c*g^3*i*x^3 + A*a^2*b*d*g^3*i*x^3 + 3/2*B*a^2*b*c*g^3*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*B*a^3*d*g^3*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*a^2*b*c*g^3*i*x^2 + 1/2*A*a^3*d*g^3*i*x^2 + 1/60*B*b^3*d*g^3*i*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/24*B*b^3*c*g^3*i*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/8*B*a*b^2*d*g^3*i*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/2*B*a*b^2*c*g^3*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/2*B*a^2*b*d*g^3*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 3/2*B*a^2*b*c*g^3*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 1/2*B*a^3*d*g^3*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a^3*c*g^3*i*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^3*c*g^3*i*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^3*c*g^3*i*x","B",0
109,1,740,0,1.376688," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, B b^{2} d g^{2} i x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A b^{2} d g^{2} i x^{4} + \frac{1}{3} \, B b^{2} c g^{2} i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{3} \, B a b d g^{2} i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A b^{2} c g^{2} i x^{3} + \frac{2}{3} \, A a b d g^{2} i x^{3} + B a b c g^{2} i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, B a^{2} d g^{2} i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a b c g^{2} i x^{2} + \frac{1}{2} \, A a^{2} d g^{2} i x^{2} - \frac{1}{24} \, B b^{2} d g^{2} i n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{6} \, B b^{2} c g^{2} i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{3} \, B a b d g^{2} i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - B a b c g^{2} i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - \frac{1}{2} \, B a^{2} d g^{2} i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a^{2} c g^{2} i n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a^{2} c g^{2} i x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{2} c g^{2} i x"," ",0,"1/4*B*b^2*d*g^2*i*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*b^2*d*g^2*i*x^4 + 1/3*B*b^2*c*g^2*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/3*B*a*b*d*g^2*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A*b^2*c*g^2*i*x^3 + 2/3*A*a*b*d*g^2*i*x^3 + B*a*b*c*g^2*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*B*a^2*d*g^2*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b*c*g^2*i*x^2 + 1/2*A*a^2*d*g^2*i*x^2 - 1/24*B*b^2*d*g^2*i*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/6*B*b^2*c*g^2*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/3*B*a*b*d*g^2*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - B*a*b*c*g^2*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 1/2*B*a^2*d*g^2*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a^2*c*g^2*i*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^2*c*g^2*i*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^2*c*g^2*i*x","B",0
110,1,393,0,1.205478," ","integrate((b*g*x+a*g)*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, B b d g i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A b d g i x^{3} + \frac{1}{2} \, B b c g i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, B a d g i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A b c g i x^{2} + \frac{1}{2} \, A a d g i x^{2} + \frac{1}{6} \, B b d g i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - \frac{1}{2} \, B b c g i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - \frac{1}{2} \, B a d g i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a c g i n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a c g i x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a c g i x"," ",0,"1/3*B*b*d*g*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A*b*d*g*i*x^3 + 1/2*B*b*c*g*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*B*a*d*g*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*b*c*g*i*x^2 + 1/2*A*a*d*g*i*x^2 + 1/6*B*b*d*g*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 1/2*B*b*c*g*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 1/2*B*a*d*g*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a*c*g*i*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a*c*g*i*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*c*g*i*x","B",0
111,1,156,0,1.200744," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{2} \, B d i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A d i x^{2} - \frac{1}{2} \, B d i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B c i n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B c i x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c i x"," ",0,"1/2*B*d*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*d*i*x^2 - 1/2*B*d*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*c*i*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*c*i*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c*i*x","A",0
112,1,276,0,4.575388," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g),x, algorithm=""maxima"")","A d i {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} - \frac{B c i n \log\left(d x + c\right)}{b g} + \frac{A c i \log\left(b g x + a g\right)}{b g} + \frac{{\left(b c i n - a d i n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{2} g} + \frac{2 \, B b d i x \log\left(e\right) - {\left(b c i n - a d i n\right)} B \log\left(b x + a\right)^{2} + 2 \, {\left(b c i \log\left(e\right) + {\left(i n - i \log\left(e\right)\right)} a d\right)} B \log\left(b x + a\right) + 2 \, {\left(B b d i x + {\left(b c i - a d i\right)} B \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B b d i x + {\left(b c i - a d i\right)} B \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, b^{2} g}"," ",0,"A*d*i*(x/(b*g) - a*log(b*x + a)/(b^2*g)) - B*c*i*n*log(d*x + c)/(b*g) + A*c*i*log(b*g*x + a*g)/(b*g) + (b*c*i*n - a*d*i*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^2*g) + 1/2*(2*B*b*d*i*x*log(e) - (b*c*i*n - a*d*i*n)*B*log(b*x + a)^2 + 2*(b*c*i*log(e) + (i*n - i*log(e))*a*d)*B*log(b*x + a) + 2*(B*b*d*i*x + (b*c*i - a*d*i)*B*log(b*x + a))*log((b*x + a)^n) - 2*(B*b*d*i*x + (b*c*i - a*d*i)*B*log(b*x + a))*log((d*x + c)^n))/(b^2*g)","A",0
113,0,0,0,0.000000," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B c i n {\left(\frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} + B d i {\left(\frac{{\left({\left(b x + a\right)} \log\left(b x + a\right) + a\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b x + a\right)} \log\left(b x + a\right) + a\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{3} g^{2} x + a b^{2} g^{2}} + \int \frac{b^{2} d x^{2} \log\left(e\right) + b^{2} c x \log\left(e\right) - a b c n + a^{2} d n - {\left(a b c n - a^{2} d n + {\left(b^{2} c n - a b d n\right)} x\right)} \log\left(b x + a\right)}{b^{4} d g^{2} x^{3} + a^{2} b^{2} c g^{2} + {\left(b^{4} c g^{2} + 2 \, a b^{3} d g^{2}\right)} x^{2} + {\left(2 \, a b^{3} c g^{2} + a^{2} b^{2} d g^{2}\right)} x}\,{d x}\right)} + A d i {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - \frac{B c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{2} g^{2} x + a b g^{2}} - \frac{A c i}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-B*c*i*n*(1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) + B*d*i*((((b*x + a)*log(b*x + a) + a)*log((b*x + a)^n) - ((b*x + a)*log(b*x + a) + a)*log((d*x + c)^n))/(b^3*g^2*x + a*b^2*g^2) + integrate((b^2*d*x^2*log(e) + b^2*c*x*log(e) - a*b*c*n + a^2*d*n - (a*b*c*n - a^2*d*n + (b^2*c*n - a*b*d*n)*x)*log(b*x + a))/(b^4*d*g^2*x^3 + a^2*b^2*c*g^2 + (b^4*c*g^2 + 2*a*b^3*d*g^2)*x^2 + (2*a*b^3*c*g^2 + a^2*b^2*d*g^2)*x), x)) + A*d*i*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - B*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*g^2*x + a*b*g^2) - A*c*i/(b^2*g^2*x + a*b*g^2)","F",0
114,1,582,0,1.254845," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, B d i n {\left(\frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{4} \, B c i n {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{{\left(2 \, b x + a\right)} B d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{{\left(2 \, b x + a\right)} A d i}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{B c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{A c i}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"-1/4*B*d*i*n*((3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/4*B*c*i*n*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - 1/2*(2*b*x + a)*B*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*(2*b*x + a)*A*d*i/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*B*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A*c*i/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
115,1,945,0,2.116256," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{18} \, B c i n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{1}{36} \, B d i n {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{{\left(3 \, b x + a\right)} B d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{6 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b x + a\right)} A d i}{6 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{B c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{A c i}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/18*B*c*i*n*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/36*B*d*i*n*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/6*(3*b*x + a)*B*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/6*(3*b*x + a)*A*d*i/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*B*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/3*A*c*i/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","B",0
116,1,1398,0,1.888457," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\frac{1}{48} \, B c i n {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{1}{144} \, B d i n {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} - \frac{{\left(4 \, b x + a\right)} B d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{12 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(4 \, b x + a\right)} A d i}{12 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{B c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{A c i}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"1/48*B*c*i*n*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/144*B*d*i*n*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) - 1/12*(4*b*x + a)*B*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/12*(4*b*x + a)*A*d*i/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/4*B*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/4*A*c*i/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
117,1,1978,0,1.655130," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{6} \, B b^{3} d^{2} g^{3} i^{2} x^{6} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{6} \, A b^{3} d^{2} g^{3} i^{2} x^{6} + \frac{2}{5} \, B b^{3} c d g^{3} i^{2} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{5} \, B a b^{2} d^{2} g^{3} i^{2} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{5} \, A b^{3} c d g^{3} i^{2} x^{5} + \frac{3}{5} \, A a b^{2} d^{2} g^{3} i^{2} x^{5} + \frac{1}{4} \, B b^{3} c^{2} g^{3} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, B a b^{2} c d g^{3} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{4} \, B a^{2} b d^{2} g^{3} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A b^{3} c^{2} g^{3} i^{2} x^{4} + \frac{3}{2} \, A a b^{2} c d g^{3} i^{2} x^{4} + \frac{3}{4} \, A a^{2} b d^{2} g^{3} i^{2} x^{4} + B a b^{2} c^{2} g^{3} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, B a^{2} b c d g^{3} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, B a^{3} d^{2} g^{3} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a b^{2} c^{2} g^{3} i^{2} x^{3} + 2 \, A a^{2} b c d g^{3} i^{2} x^{3} + \frac{1}{3} \, A a^{3} d^{2} g^{3} i^{2} x^{3} + \frac{3}{2} \, B a^{2} b c^{2} g^{3} i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + B a^{3} c d g^{3} i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A a^{2} b c^{2} g^{3} i^{2} x^{2} + A a^{3} c d g^{3} i^{2} x^{2} - \frac{1}{360} \, B b^{3} d^{2} g^{3} i^{2} n {\left(\frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} - \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} + \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} + \frac{1}{30} \, B b^{3} c d g^{3} i^{2} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} + \frac{1}{20} \, B a b^{2} d^{2} g^{3} i^{2} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{24} \, B b^{3} c^{2} g^{3} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{4} \, B a b^{2} c d g^{3} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{8} \, B a^{2} b d^{2} g^{3} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{2} \, B a b^{2} c^{2} g^{3} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + B a^{2} b c d g^{3} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{6} \, B a^{3} d^{2} g^{3} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - \frac{3}{2} \, B a^{2} b c^{2} g^{3} i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - B a^{3} c d g^{3} i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a^{3} c^{2} g^{3} i^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a^{3} c^{2} g^{3} i^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{3} c^{2} g^{3} i^{2} x"," ",0,"1/6*B*b^3*d^2*g^3*i^2*x^6*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/6*A*b^3*d^2*g^3*i^2*x^6 + 2/5*B*b^3*c*d*g^3*i^2*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/5*B*a*b^2*d^2*g^3*i^2*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/5*A*b^3*c*d*g^3*i^2*x^5 + 3/5*A*a*b^2*d^2*g^3*i^2*x^5 + 1/4*B*b^3*c^2*g^3*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*B*a*b^2*c*d*g^3*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/4*B*a^2*b*d^2*g^3*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*b^3*c^2*g^3*i^2*x^4 + 3/2*A*a*b^2*c*d*g^3*i^2*x^4 + 3/4*A*a^2*b*d^2*g^3*i^2*x^4 + B*a*b^2*c^2*g^3*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*B*a^2*b*c*d*g^3*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*B*a^3*d^2*g^3*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b^2*c^2*g^3*i^2*x^3 + 2*A*a^2*b*c*d*g^3*i^2*x^3 + 1/3*A*a^3*d^2*g^3*i^2*x^3 + 3/2*B*a^2*b*c^2*g^3*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + B*a^3*c*d*g^3*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*a^2*b*c^2*g^3*i^2*x^2 + A*a^3*c*d*g^3*i^2*x^2 - 1/360*B*b^3*d^2*g^3*i^2*n*(60*a^6*log(b*x + a)/b^6 - 60*c^6*log(d*x + c)/d^6 + (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5)) + 1/30*B*b^3*c*d*g^3*i^2*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) + 1/20*B*a*b^2*d^2*g^3*i^2*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/24*B*b^3*c^2*g^3*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/4*B*a*b^2*c*d*g^3*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/8*B*a^2*b*d^2*g^3*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/2*B*a*b^2*c^2*g^3*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + B*a^2*b*c*d*g^3*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/6*B*a^3*d^2*g^3*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 3/2*B*a^2*b*c^2*g^3*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - B*a^3*c*d*g^3*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a^3*c^2*g^3*i^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^3*c^2*g^3*i^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^3*c^2*g^3*i^2*x","B",0
118,1,1336,0,1.426060," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{5} \, B b^{2} d^{2} g^{2} i^{2} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{5} \, A b^{2} d^{2} g^{2} i^{2} x^{5} + \frac{1}{2} \, B b^{2} c d g^{2} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, B a b d^{2} g^{2} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A b^{2} c d g^{2} i^{2} x^{4} + \frac{1}{2} \, A a b d^{2} g^{2} i^{2} x^{4} + \frac{1}{3} \, B b^{2} c^{2} g^{2} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{4}{3} \, B a b c d g^{2} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, B a^{2} d^{2} g^{2} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A b^{2} c^{2} g^{2} i^{2} x^{3} + \frac{4}{3} \, A a b c d g^{2} i^{2} x^{3} + \frac{1}{3} \, A a^{2} d^{2} g^{2} i^{2} x^{3} + B a b c^{2} g^{2} i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + B a^{2} c d g^{2} i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a b c^{2} g^{2} i^{2} x^{2} + A a^{2} c d g^{2} i^{2} x^{2} + \frac{1}{60} \, B b^{2} d^{2} g^{2} i^{2} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{12} \, B b^{2} c d g^{2} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{12} \, B a b d^{2} g^{2} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{6} \, B b^{2} c^{2} g^{2} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{2}{3} \, B a b c d g^{2} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{6} \, B a^{2} d^{2} g^{2} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - B a b c^{2} g^{2} i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - B a^{2} c d g^{2} i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a^{2} c^{2} g^{2} i^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a^{2} c^{2} g^{2} i^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{2} c^{2} g^{2} i^{2} x"," ",0,"1/5*B*b^2*d^2*g^2*i^2*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A*b^2*d^2*g^2*i^2*x^5 + 1/2*B*b^2*c*d*g^2*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*B*a*b*d^2*g^2*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*b^2*c*d*g^2*i^2*x^4 + 1/2*A*a*b*d^2*g^2*i^2*x^4 + 1/3*B*b^2*c^2*g^2*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 4/3*B*a*b*c*d*g^2*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*B*a^2*d^2*g^2*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A*b^2*c^2*g^2*i^2*x^3 + 4/3*A*a*b*c*d*g^2*i^2*x^3 + 1/3*A*a^2*d^2*g^2*i^2*x^3 + B*a*b*c^2*g^2*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + B*a^2*c*d*g^2*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b*c^2*g^2*i^2*x^2 + A*a^2*c*d*g^2*i^2*x^2 + 1/60*B*b^2*d^2*g^2*i^2*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/12*B*b^2*c*d*g^2*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/12*B*a*b*d^2*g^2*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/6*B*b^2*c^2*g^2*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 2/3*B*a*b*c*d*g^2*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/6*B*a^2*d^2*g^2*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - B*a*b*c^2*g^2*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - B*a^2*c*d*g^2*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a^2*c^2*g^2*i^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^2*c^2*g^2*i^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^2*c^2*g^2*i^2*x","B",0
119,1,740,0,1.367890," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, B b d^{2} g i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A b d^{2} g i^{2} x^{4} + \frac{2}{3} \, B b c d g i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, B a d^{2} g i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{3} \, A b c d g i^{2} x^{3} + \frac{1}{3} \, A a d^{2} g i^{2} x^{3} + \frac{1}{2} \, B b c^{2} g i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + B a c d g i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A b c^{2} g i^{2} x^{2} + A a c d g i^{2} x^{2} - \frac{1}{24} \, B b d^{2} g i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{3} \, B b c d g i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{6} \, B a d^{2} g i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - \frac{1}{2} \, B b c^{2} g i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - B a c d g i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a c^{2} g i^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a c^{2} g i^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a c^{2} g i^{2} x"," ",0,"1/4*B*b*d^2*g*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*b*d^2*g*i^2*x^4 + 2/3*B*b*c*d*g*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*B*a*d^2*g*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/3*A*b*c*d*g*i^2*x^3 + 1/3*A*a*d^2*g*i^2*x^3 + 1/2*B*b*c^2*g*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + B*a*c*d*g*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*b*c^2*g*i^2*x^2 + A*a*c*d*g*i^2*x^2 - 1/24*B*b*d^2*g*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/3*B*b*c*d*g*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/6*B*a*d^2*g*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 1/2*B*b*c^2*g*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - B*a*c*d*g*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a*c^2*g*i^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a*c^2*g*i^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*c^2*g*i^2*x","B",0
120,1,309,0,1.183217," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, B d^{2} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A d^{2} i^{2} x^{3} + B c d i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c d i^{2} x^{2} + \frac{1}{6} \, B d^{2} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - B c d i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B c^{2} i^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B c^{2} i^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c^{2} i^{2} x"," ",0,"1/3*B*d^2*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A*d^2*i^2*x^3 + B*c*d*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c*d*i^2*x^2 + 1/6*B*d^2*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - B*c*d*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*c^2*i^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*c^2*i^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c^2*i^2*x","B",0
121,1,580,0,5.312938," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g),x, algorithm=""maxima"")","2 \, A c d i^{2} {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} + \frac{1}{2} \, A d^{2} i^{2} {\left(\frac{2 \, a^{2} \log\left(b x + a\right)}{b^{3} g} + \frac{b x^{2} - 2 \, a x}{b^{2} g}\right)} + \frac{A c^{2} i^{2} \log\left(b g x + a g\right)}{b g} - \frac{{\left(3 \, b c^{2} i^{2} n - 2 \, a c d i^{2} n\right)} B \log\left(d x + c\right)}{2 \, b^{2} g} + \frac{{\left(b^{2} c^{2} i^{2} n - 2 \, a b c d i^{2} n + a^{2} d^{2} i^{2} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{3} g} + \frac{B b^{2} d^{2} i^{2} x^{2} \log\left(e\right) - {\left(b^{2} c^{2} i^{2} n - 2 \, a b c d i^{2} n + a^{2} d^{2} i^{2} n\right)} B \log\left(b x + a\right)^{2} - {\left({\left(i^{2} n - 4 \, i^{2} \log\left(e\right)\right)} b^{2} c d - {\left(i^{2} n - 2 \, i^{2} \log\left(e\right)\right)} a b d^{2}\right)} B x + {\left(2 \, b^{2} c^{2} i^{2} \log\left(e\right) + 4 \, {\left(i^{2} n - i^{2} \log\left(e\right)\right)} a b c d - {\left(3 \, i^{2} n - 2 \, i^{2} \log\left(e\right)\right)} a^{2} d^{2}\right)} B \log\left(b x + a\right) + {\left(B b^{2} d^{2} i^{2} x^{2} + 2 \, {\left(2 \, b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B x + 2 \, {\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} B \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B b^{2} d^{2} i^{2} x^{2} + 2 \, {\left(2 \, b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B x + 2 \, {\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} B \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, b^{3} g}"," ",0,"2*A*c*d*i^2*(x/(b*g) - a*log(b*x + a)/(b^2*g)) + 1/2*A*d^2*i^2*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2*g)) + A*c^2*i^2*log(b*g*x + a*g)/(b*g) - 1/2*(3*b*c^2*i^2*n - 2*a*c*d*i^2*n)*B*log(d*x + c)/(b^2*g) + (b^2*c^2*i^2*n - 2*a*b*c*d*i^2*n + a^2*d^2*i^2*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^3*g) + 1/2*(B*b^2*d^2*i^2*x^2*log(e) - (b^2*c^2*i^2*n - 2*a*b*c*d*i^2*n + a^2*d^2*i^2*n)*B*log(b*x + a)^2 - ((i^2*n - 4*i^2*log(e))*b^2*c*d - (i^2*n - 2*i^2*log(e))*a*b*d^2)*B*x + (2*b^2*c^2*i^2*log(e) + 4*(i^2*n - i^2*log(e))*a*b*c*d - (3*i^2*n - 2*i^2*log(e))*a^2*d^2)*B*log(b*x + a) + (B*b^2*d^2*i^2*x^2 + 2*(2*b^2*c*d*i^2 - a*b*d^2*i^2)*B*x + 2*(b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*B*log(b*x + a))*log((b*x + a)^n) - (B*b^2*d^2*i^2*x^2 + 2*(2*b^2*c*d*i^2 - a*b*d^2*i^2)*B*x + 2*(b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*B*log(b*x + a))*log((d*x + c)^n))/(b^3*g)","B",0
122,1,1190,0,4.348669," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B c^{2} i^{2} n {\left(\frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - A {\left(\frac{a^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \frac{x}{b^{2} g^{2}} + \frac{2 \, a \log\left(b x + a\right)}{b^{3} g^{2}}\right)} d^{2} i^{2} + 2 \, A c d i^{2} {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - \frac{B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{2} g^{2} x + a b g^{2}} - \frac{A c^{2} i^{2}}{b^{2} g^{2} x + a b g^{2}} - \frac{{\left(b^{2} c^{2} d i^{2} n + a b c d^{2} i^{2} n - a^{2} d^{3} i^{2} n\right)} B \log\left(d x + c\right)}{b^{4} c g^{2} - a b^{3} d g^{2}} + \frac{{\left(b^{3} c d^{2} i^{2} \log\left(e\right) - a b^{2} d^{3} i^{2} \log\left(e\right)\right)} B x^{2} + {\left(a b^{2} c d^{2} i^{2} \log\left(e\right) - a^{2} b d^{3} i^{2} \log\left(e\right)\right)} B x - {\left({\left(b^{3} c^{2} d i^{2} n - 2 \, a b^{2} c d^{2} i^{2} n + a^{2} b d^{3} i^{2} n\right)} B x + {\left(a b^{2} c^{2} d i^{2} n - 2 \, a^{2} b c d^{2} i^{2} n + a^{3} d^{3} i^{2} n\right)} B\right)} \log\left(b x + a\right)^{2} + {\left(2 \, {\left(i^{2} n + i^{2} \log\left(e\right)\right)} a b^{2} c^{2} d - 3 \, {\left(i^{2} n + i^{2} \log\left(e\right)\right)} a^{2} b c d^{2} + {\left(i^{2} n + i^{2} \log\left(e\right)\right)} a^{3} d^{3}\right)} B + {\left({\left(2 \, b^{3} c^{2} d i^{2} \log\left(e\right) + {\left(3 \, i^{2} n - 4 \, i^{2} \log\left(e\right)\right)} a b^{2} c d^{2} - 2 \, {\left(i^{2} n - i^{2} \log\left(e\right)\right)} a^{2} b d^{3}\right)} B x + {\left(2 \, a b^{2} c^{2} d i^{2} \log\left(e\right) + {\left(3 \, i^{2} n - 4 \, i^{2} \log\left(e\right)\right)} a^{2} b c d^{2} - 2 \, {\left(i^{2} n - i^{2} \log\left(e\right)\right)} a^{3} d^{3}\right)} B\right)} \log\left(b x + a\right) + {\left({\left(b^{3} c d^{2} i^{2} - a b^{2} d^{3} i^{2}\right)} B x^{2} + {\left(a b^{2} c d^{2} i^{2} - a^{2} b d^{3} i^{2}\right)} B x + {\left(2 \, a b^{2} c^{2} d i^{2} - 3 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B + 2 \, {\left({\left(b^{3} c^{2} d i^{2} - 2 \, a b^{2} c d^{2} i^{2} + a^{2} b d^{3} i^{2}\right)} B x + {\left(a b^{2} c^{2} d i^{2} - 2 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b^{3} c d^{2} i^{2} - a b^{2} d^{3} i^{2}\right)} B x^{2} + {\left(a b^{2} c d^{2} i^{2} - a^{2} b d^{3} i^{2}\right)} B x + {\left(2 \, a b^{2} c^{2} d i^{2} - 3 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B + 2 \, {\left({\left(b^{3} c^{2} d i^{2} - 2 \, a b^{2} c d^{2} i^{2} + a^{2} b d^{3} i^{2}\right)} B x + {\left(a b^{2} c^{2} d i^{2} - 2 \, a^{2} b c d^{2} i^{2} + a^{3} d^{3} i^{2}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{a b^{4} c g^{2} - a^{2} b^{3} d g^{2} + {\left(b^{5} c g^{2} - a b^{4} d g^{2}\right)} x} + \frac{2 \, {\left(b c d i^{2} n - a d^{2} i^{2} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{3} g^{2}}"," ",0,"-B*c^2*i^2*n*(1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A*(a^2/(b^4*g^2*x + a*b^3*g^2) - x/(b^2*g^2) + 2*a*log(b*x + a)/(b^3*g^2))*d^2*i^2 + 2*A*c*d*i^2*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*g^2*x + a*b*g^2) - A*c^2*i^2/(b^2*g^2*x + a*b*g^2) - (b^2*c^2*d*i^2*n + a*b*c*d^2*i^2*n - a^2*d^3*i^2*n)*B*log(d*x + c)/(b^4*c*g^2 - a*b^3*d*g^2) + ((b^3*c*d^2*i^2*log(e) - a*b^2*d^3*i^2*log(e))*B*x^2 + (a*b^2*c*d^2*i^2*log(e) - a^2*b*d^3*i^2*log(e))*B*x - ((b^3*c^2*d*i^2*n - 2*a*b^2*c*d^2*i^2*n + a^2*b*d^3*i^2*n)*B*x + (a*b^2*c^2*d*i^2*n - 2*a^2*b*c*d^2*i^2*n + a^3*d^3*i^2*n)*B)*log(b*x + a)^2 + (2*(i^2*n + i^2*log(e))*a*b^2*c^2*d - 3*(i^2*n + i^2*log(e))*a^2*b*c*d^2 + (i^2*n + i^2*log(e))*a^3*d^3)*B + ((2*b^3*c^2*d*i^2*log(e) + (3*i^2*n - 4*i^2*log(e))*a*b^2*c*d^2 - 2*(i^2*n - i^2*log(e))*a^2*b*d^3)*B*x + (2*a*b^2*c^2*d*i^2*log(e) + (3*i^2*n - 4*i^2*log(e))*a^2*b*c*d^2 - 2*(i^2*n - i^2*log(e))*a^3*d^3)*B)*log(b*x + a) + ((b^3*c*d^2*i^2 - a*b^2*d^3*i^2)*B*x^2 + (a*b^2*c*d^2*i^2 - a^2*b*d^3*i^2)*B*x + (2*a*b^2*c^2*d*i^2 - 3*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B + 2*((b^3*c^2*d*i^2 - 2*a*b^2*c*d^2*i^2 + a^2*b*d^3*i^2)*B*x + (a*b^2*c^2*d*i^2 - 2*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B)*log(b*x + a))*log((b*x + a)^n) - ((b^3*c*d^2*i^2 - a*b^2*d^3*i^2)*B*x^2 + (a*b^2*c*d^2*i^2 - a^2*b*d^3*i^2)*B*x + (2*a*b^2*c^2*d*i^2 - 3*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B + 2*((b^3*c^2*d*i^2 - 2*a*b^2*c*d^2*i^2 + a^2*b*d^3*i^2)*B*x + (a*b^2*c^2*d*i^2 - 2*a^2*b*c*d^2*i^2 + a^3*d^3*i^2)*B)*log(b*x + a))*log((d*x + c)^n))/(a*b^4*c*g^2 - a^2*b^3*d*g^2 + (b^5*c*g^2 - a*b^4*d*g^2)*x) + 2*(b*c*d*i^2*n - a*d^2*i^2*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^3*g^2)","B",0
123,0,0,0,0.000000," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B c d i^{2} n {\left(\frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{4} \, B c^{2} i^{2} n {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} + \frac{1}{2} \, A d^{2} i^{2} {\left(\frac{4 \, a b x + 3 \, a^{2}}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + \frac{2 \, \log\left(b x + a\right)}{b^{3} g^{3}}\right)} + \frac{1}{2} \, B d^{2} i^{2} {\left(\frac{{\left(4 \, a b x + 3 \, a^{2} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(4 \, a b x + 3 \, a^{2} + 2 \, {\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + 2 \, \int \frac{2 \, b^{3} d x^{3} \log\left(e\right) + 2 \, b^{3} c x^{2} \log\left(e\right) - 3 \, a^{2} b c n + 3 \, a^{3} d n - 4 \, {\left(a b^{2} c n - a^{2} b d n\right)} x - 2 \, {\left(a^{2} b c n - a^{3} d n + {\left(b^{3} c n - a b^{2} d n\right)} x^{2} + 2 \, {\left(a b^{2} c n - a^{2} b d n\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b^{6} d g^{3} x^{4} + a^{3} b^{3} c g^{3} + {\left(b^{6} c g^{3} + 3 \, a b^{5} d g^{3}\right)} x^{3} + 3 \, {\left(a b^{5} c g^{3} + a^{2} b^{4} d g^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{4} c g^{3} + a^{3} b^{3} d g^{3}\right)} x\right)}}\,{d x}\right)} - \frac{{\left(2 \, b x + a\right)} B c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} - \frac{{\left(2 \, b x + a\right)} A c d i^{2}}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} - \frac{B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{A c^{2} i^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"-1/2*B*c*d*i^2*n*((3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/4*B*c^2*i^2*n*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) + 1/2*A*d^2*i^2*((4*a*b*x + 3*a^2)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*log(b*x + a)/(b^3*g^3)) + 1/2*B*d^2*i^2*(((4*a*b*x + 3*a^2 + 2*(b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a))*log((b*x + a)^n) - (4*a*b*x + 3*a^2 + 2*(b^2*x^2 + 2*a*b*x + a^2)*log(b*x + a))*log((d*x + c)^n))/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*integrate(1/2*(2*b^3*d*x^3*log(e) + 2*b^3*c*x^2*log(e) - 3*a^2*b*c*n + 3*a^3*d*n - 4*(a*b^2*c*n - a^2*b*d*n)*x - 2*(a^2*b*c*n - a^3*d*n + (b^3*c*n - a*b^2*d*n)*x^2 + 2*(a*b^2*c*n - a^2*b*d*n)*x)*log(b*x + a))/(b^6*d*g^3*x^4 + a^3*b^3*c*g^3 + (b^6*c*g^3 + 3*a*b^5*d*g^3)*x^3 + 3*(a*b^5*c*g^3 + a^2*b^4*d*g^3)*x^2 + (3*a^2*b^4*c*g^3 + a^3*b^3*d*g^3)*x), x)) - (2*b*x + a)*B*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - (2*b*x + a)*A*c*d*i^2/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A*c^2*i^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","F",0
124,1,1544,0,1.936757," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{18} \, B d^{2} i^{2} n {\left(\frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} - \frac{1}{18} \, B c^{2} i^{2} n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{1}{18} \, B c d i^{2} n {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{{\left(3 \, b x + a\right)} B c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} B d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}\right)}} - \frac{{\left(3 \, b x + a\right)} A c d i^{2}}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A d^{2} i^{2}}{3 \, {\left(b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}\right)}} - \frac{B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{A c^{2} i^{2}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/18*B*d^2*i^2*n*((11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4)) - 1/18*B*c^2*i^2*n*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/18*B*c*d*i^2*n*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/3*(3*b*x + a)*B*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*(3*b^2*x^2 + 3*a*b*x + a^2)*B*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/3*(3*b*x + a)*A*c*d*i^2/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*(3*b^2*x^2 + 3*a*b*x + a^2)*A*d^2*i^2/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/3*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/3*A*c^2*i^2/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","B",0
125,1,2247,0,2.862375," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\frac{1}{48} \, B c^{2} i^{2} n {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{1}{144} \, B d^{2} i^{2} n {\left(\frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} - \frac{1}{72} \, B c d i^{2} n {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} - \frac{{\left(4 \, b x + a\right)} B c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{6 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} B d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{12 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{{\left(4 \, b x + a\right)} A c d i^{2}}{6 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} A d^{2} i^{2}}{12 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{A c^{2} i^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"1/48*B*c^2*i^2*n*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/144*B*d^2*i^2*n*((13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5)) - 1/72*B*c*d*i^2*n*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) - 1/6*(4*b*x + a)*B*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/12*(6*b^2*x^2 + 4*a*b*x + a^2)*B*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/6*(4*b*x + a)*A*c*d*i^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/12*(6*b^2*x^2 + 4*a*b*x + a^2)*A*d^2*i^2/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/4*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/4*A*c^2*i^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
126,1,3058,0,3.175613," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^6,x, algorithm=""maxima"")","-\frac{1}{300} \, B c^{2} i^{2} n {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} - \frac{1}{1800} \, B d^{2} i^{2} n {\left(\frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} - \frac{1}{600} \, B c d i^{2} n {\left(\frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} - \frac{{\left(5 \, b x + a\right)} B c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{10 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} B d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{30 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{{\left(5 \, b x + a\right)} A c d i^{2}}{10 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} A d^{2} i^{2}}{30 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}} - \frac{A c^{2} i^{2}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}}"," ",0,"-1/300*B*c^2*i^2*n*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6)) - 1/1800*B*d^2*i^2*n*((47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6)) - 1/600*B*c*d*i^2*n*((27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6)) - 1/10*(5*b*x + a)*B*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/30*(10*b^2*x^2 + 5*a*b*x + a^2)*B*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/10*(5*b*x + a)*A*c*d*i^2/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/30*(10*b^2*x^2 + 5*a*b*x + a^2)*A*d^2*i^2/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/5*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) - 1/5*A*c^2*i^2/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6)","B",0
127,1,2901,0,1.888944," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{7} \, B b^{3} d^{3} g^{3} i^{3} x^{7} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{7} \, A b^{3} d^{3} g^{3} i^{3} x^{7} + \frac{1}{2} \, B b^{3} c d^{2} g^{3} i^{3} x^{6} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, B a b^{2} d^{3} g^{3} i^{3} x^{6} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A b^{3} c d^{2} g^{3} i^{3} x^{6} + \frac{1}{2} \, A a b^{2} d^{3} g^{3} i^{3} x^{6} + \frac{3}{5} \, B b^{3} c^{2} d g^{3} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{9}{5} \, B a b^{2} c d^{2} g^{3} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{5} \, B a^{2} b d^{3} g^{3} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{5} \, A b^{3} c^{2} d g^{3} i^{3} x^{5} + \frac{9}{5} \, A a b^{2} c d^{2} g^{3} i^{3} x^{5} + \frac{3}{5} \, A a^{2} b d^{3} g^{3} i^{3} x^{5} + \frac{1}{4} \, B b^{3} c^{3} g^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{9}{4} \, B a b^{2} c^{2} d g^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{9}{4} \, B a^{2} b c d^{2} g^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, B a^{3} d^{3} g^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A b^{3} c^{3} g^{3} i^{3} x^{4} + \frac{9}{4} \, A a b^{2} c^{2} d g^{3} i^{3} x^{4} + \frac{9}{4} \, A a^{2} b c d^{2} g^{3} i^{3} x^{4} + \frac{1}{4} \, A a^{3} d^{3} g^{3} i^{3} x^{4} + B a b^{2} c^{3} g^{3} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 3 \, B a^{2} b c^{2} d g^{3} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + B a^{3} c d^{2} g^{3} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a b^{2} c^{3} g^{3} i^{3} x^{3} + 3 \, A a^{2} b c^{2} d g^{3} i^{3} x^{3} + A a^{3} c d^{2} g^{3} i^{3} x^{3} + \frac{3}{2} \, B a^{2} b c^{3} g^{3} i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, B a^{3} c^{2} d g^{3} i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A a^{2} b c^{3} g^{3} i^{3} x^{2} + \frac{3}{2} \, A a^{3} c^{2} d g^{3} i^{3} x^{2} + \frac{1}{420} \, B b^{3} d^{3} g^{3} i^{3} n {\left(\frac{60 \, a^{7} \log\left(b x + a\right)}{b^{7}} - \frac{60 \, c^{7} \log\left(d x + c\right)}{d^{7}} - \frac{10 \, {\left(b^{6} c d^{5} - a b^{5} d^{6}\right)} x^{6} - 12 \, {\left(b^{6} c^{2} d^{4} - a^{2} b^{4} d^{6}\right)} x^{5} + 15 \, {\left(b^{6} c^{3} d^{3} - a^{3} b^{3} d^{6}\right)} x^{4} - 20 \, {\left(b^{6} c^{4} d^{2} - a^{4} b^{2} d^{6}\right)} x^{3} + 30 \, {\left(b^{6} c^{5} d - a^{5} b d^{6}\right)} x^{2} - 60 \, {\left(b^{6} c^{6} - a^{6} d^{6}\right)} x}{b^{6} d^{6}}\right)} - \frac{1}{120} \, B b^{3} c d^{2} g^{3} i^{3} n {\left(\frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} - \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} + \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} - \frac{1}{120} \, B a b^{2} d^{3} g^{3} i^{3} n {\left(\frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} - \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} + \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} + \frac{1}{20} \, B b^{3} c^{2} d g^{3} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} + \frac{3}{20} \, B a b^{2} c d^{2} g^{3} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} + \frac{1}{20} \, B a^{2} b d^{3} g^{3} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{24} \, B b^{3} c^{3} g^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{3}{8} \, B a b^{2} c^{2} d g^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{3}{8} \, B a^{2} b c d^{2} g^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{24} \, B a^{3} d^{3} g^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{2} \, B a b^{2} c^{3} g^{3} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{3}{2} \, B a^{2} b c^{2} d g^{3} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{2} \, B a^{3} c d^{2} g^{3} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - \frac{3}{2} \, B a^{2} b c^{3} g^{3} i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - \frac{3}{2} \, B a^{3} c^{2} d g^{3} i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a^{3} c^{3} g^{3} i^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a^{3} c^{3} g^{3} i^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{3} c^{3} g^{3} i^{3} x"," ",0,"1/7*B*b^3*d^3*g^3*i^3*x^7*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/7*A*b^3*d^3*g^3*i^3*x^7 + 1/2*B*b^3*c*d^2*g^3*i^3*x^6*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*B*a*b^2*d^3*g^3*i^3*x^6*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*b^3*c*d^2*g^3*i^3*x^6 + 1/2*A*a*b^2*d^3*g^3*i^3*x^6 + 3/5*B*b^3*c^2*d*g^3*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 9/5*B*a*b^2*c*d^2*g^3*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/5*B*a^2*b*d^3*g^3*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/5*A*b^3*c^2*d*g^3*i^3*x^5 + 9/5*A*a*b^2*c*d^2*g^3*i^3*x^5 + 3/5*A*a^2*b*d^3*g^3*i^3*x^5 + 1/4*B*b^3*c^3*g^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 9/4*B*a*b^2*c^2*d*g^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 9/4*B*a^2*b*c*d^2*g^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*B*a^3*d^3*g^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*b^3*c^3*g^3*i^3*x^4 + 9/4*A*a*b^2*c^2*d*g^3*i^3*x^4 + 9/4*A*a^2*b*c*d^2*g^3*i^3*x^4 + 1/4*A*a^3*d^3*g^3*i^3*x^4 + B*a*b^2*c^3*g^3*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3*B*a^2*b*c^2*d*g^3*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + B*a^3*c*d^2*g^3*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b^2*c^3*g^3*i^3*x^3 + 3*A*a^2*b*c^2*d*g^3*i^3*x^3 + A*a^3*c*d^2*g^3*i^3*x^3 + 3/2*B*a^2*b*c^3*g^3*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*B*a^3*c^2*d*g^3*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*a^2*b*c^3*g^3*i^3*x^2 + 3/2*A*a^3*c^2*d*g^3*i^3*x^2 + 1/420*B*b^3*d^3*g^3*i^3*n*(60*a^7*log(b*x + a)/b^7 - 60*c^7*log(d*x + c)/d^7 - (10*(b^6*c*d^5 - a*b^5*d^6)*x^6 - 12*(b^6*c^2*d^4 - a^2*b^4*d^6)*x^5 + 15*(b^6*c^3*d^3 - a^3*b^3*d^6)*x^4 - 20*(b^6*c^4*d^2 - a^4*b^2*d^6)*x^3 + 30*(b^6*c^5*d - a^5*b*d^6)*x^2 - 60*(b^6*c^6 - a^6*d^6)*x)/(b^6*d^6)) - 1/120*B*b^3*c*d^2*g^3*i^3*n*(60*a^6*log(b*x + a)/b^6 - 60*c^6*log(d*x + c)/d^6 + (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5)) - 1/120*B*a*b^2*d^3*g^3*i^3*n*(60*a^6*log(b*x + a)/b^6 - 60*c^6*log(d*x + c)/d^6 + (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5)) + 1/20*B*b^3*c^2*d*g^3*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) + 3/20*B*a*b^2*c*d^2*g^3*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) + 1/20*B*a^2*b*d^3*g^3*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/24*B*b^3*c^3*g^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 3/8*B*a*b^2*c^2*d*g^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 3/8*B*a^2*b*c*d^2*g^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/24*B*a^3*d^3*g^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/2*B*a*b^2*c^3*g^3*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 3/2*B*a^2*b*c^2*d*g^3*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/2*B*a^3*c*d^2*g^3*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 3/2*B*a^2*b*c^3*g^3*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 3/2*B*a^3*c^2*d*g^3*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a^3*c^3*g^3*i^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^3*c^3*g^3*i^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^3*c^3*g^3*i^3*x","B",0
128,1,1978,0,1.684172," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{6} \, B b^{2} d^{3} g^{2} i^{3} x^{6} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{6} \, A b^{2} d^{3} g^{2} i^{3} x^{6} + \frac{3}{5} \, B b^{2} c d^{2} g^{2} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{5} \, B a b d^{3} g^{2} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{5} \, A b^{2} c d^{2} g^{2} i^{3} x^{5} + \frac{2}{5} \, A a b d^{3} g^{2} i^{3} x^{5} + \frac{3}{4} \, B b^{2} c^{2} d g^{2} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, B a b c d^{2} g^{2} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, B a^{2} d^{3} g^{2} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{4} \, A b^{2} c^{2} d g^{2} i^{3} x^{4} + \frac{3}{2} \, A a b c d^{2} g^{2} i^{3} x^{4} + \frac{1}{4} \, A a^{2} d^{3} g^{2} i^{3} x^{4} + \frac{1}{3} \, B b^{2} c^{3} g^{2} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, B a b c^{2} d g^{2} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + B a^{2} c d^{2} g^{2} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A b^{2} c^{3} g^{2} i^{3} x^{3} + 2 \, A a b c^{2} d g^{2} i^{3} x^{3} + A a^{2} c d^{2} g^{2} i^{3} x^{3} + B a b c^{3} g^{2} i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, B a^{2} c^{2} d g^{2} i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a b c^{3} g^{2} i^{3} x^{2} + \frac{3}{2} \, A a^{2} c^{2} d g^{2} i^{3} x^{2} - \frac{1}{360} \, B b^{2} d^{3} g^{2} i^{3} n {\left(\frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} - \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} + \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} + \frac{1}{20} \, B b^{2} c d^{2} g^{2} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} + \frac{1}{30} \, B a b d^{3} g^{2} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{8} \, B b^{2} c^{2} d g^{2} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{4} \, B a b c d^{2} g^{2} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{24} \, B a^{2} d^{3} g^{2} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{6} \, B b^{2} c^{3} g^{2} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + B a b c^{2} d g^{2} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{2} \, B a^{2} c d^{2} g^{2} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - B a b c^{3} g^{2} i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - \frac{3}{2} \, B a^{2} c^{2} d g^{2} i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a^{2} c^{3} g^{2} i^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a^{2} c^{3} g^{2} i^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{2} c^{3} g^{2} i^{3} x"," ",0,"1/6*B*b^2*d^3*g^2*i^3*x^6*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/6*A*b^2*d^3*g^2*i^3*x^6 + 3/5*B*b^2*c*d^2*g^2*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/5*B*a*b*d^3*g^2*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/5*A*b^2*c*d^2*g^2*i^3*x^5 + 2/5*A*a*b*d^3*g^2*i^3*x^5 + 3/4*B*b^2*c^2*d*g^2*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*B*a*b*c*d^2*g^2*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*B*a^2*d^3*g^2*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/4*A*b^2*c^2*d*g^2*i^3*x^4 + 3/2*A*a*b*c*d^2*g^2*i^3*x^4 + 1/4*A*a^2*d^3*g^2*i^3*x^4 + 1/3*B*b^2*c^3*g^2*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*B*a*b*c^2*d*g^2*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + B*a^2*c*d^2*g^2*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A*b^2*c^3*g^2*i^3*x^3 + 2*A*a*b*c^2*d*g^2*i^3*x^3 + A*a^2*c*d^2*g^2*i^3*x^3 + B*a*b*c^3*g^2*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*B*a^2*c^2*d*g^2*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b*c^3*g^2*i^3*x^2 + 3/2*A*a^2*c^2*d*g^2*i^3*x^2 - 1/360*B*b^2*d^3*g^2*i^3*n*(60*a^6*log(b*x + a)/b^6 - 60*c^6*log(d*x + c)/d^6 + (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5)) + 1/20*B*b^2*c*d^2*g^2*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) + 1/30*B*a*b*d^3*g^2*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/8*B*b^2*c^2*d*g^2*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/4*B*a*b*c*d^2*g^2*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/24*B*a^2*d^3*g^2*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/6*B*b^2*c^3*g^2*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + B*a*b*c^2*d*g^2*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/2*B*a^2*c*d^2*g^2*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - B*a*b*c^3*g^2*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 3/2*B*a^2*c^2*d*g^2*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a^2*c^3*g^2*i^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^2*c^3*g^2*i^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^2*c^3*g^2*i^3*x","B",0
129,1,1118,0,1.402239," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{5} \, B b d^{3} g i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{5} \, A b d^{3} g i^{3} x^{5} + \frac{3}{4} \, B b c d^{2} g i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, B a d^{3} g i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{4} \, A b c d^{2} g i^{3} x^{4} + \frac{1}{4} \, A a d^{3} g i^{3} x^{4} + B b c^{2} d g i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + B a c d^{2} g i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A b c^{2} d g i^{3} x^{3} + A a c d^{2} g i^{3} x^{3} + \frac{1}{2} \, B b c^{3} g i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, B a c^{2} d g i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A b c^{3} g i^{3} x^{2} + \frac{3}{2} \, A a c^{2} d g i^{3} x^{2} + \frac{1}{60} \, B b d^{3} g i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{8} \, B b c d^{2} g i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{24} \, B a d^{3} g i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{2} \, B b c^{2} d g i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{2} \, B a c d^{2} g i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - \frac{1}{2} \, B b c^{3} g i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - \frac{3}{2} \, B a c^{2} d g i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B a c^{3} g i^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a c^{3} g i^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a c^{3} g i^{3} x"," ",0,"1/5*B*b*d^3*g*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A*b*d^3*g*i^3*x^5 + 3/4*B*b*c*d^2*g*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*B*a*d^3*g*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/4*A*b*c*d^2*g*i^3*x^4 + 1/4*A*a*d^3*g*i^3*x^4 + B*b*c^2*d*g*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + B*a*c*d^2*g*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*b*c^2*d*g*i^3*x^3 + A*a*c*d^2*g*i^3*x^3 + 1/2*B*b*c^3*g*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*B*a*c^2*d*g*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*b*c^3*g*i^3*x^2 + 3/2*A*a*c^2*d*g*i^3*x^2 + 1/60*B*b*d^3*g*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/8*B*b*c*d^2*g*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/24*B*a*d^3*g*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/2*B*b*c^2*d*g*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/2*B*a*c*d^2*g*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 1/2*B*b*c^3*g*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 3/2*B*a*c^2*d*g*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*a*c^3*g*i^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a*c^3*g*i^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*c^3*g*i^3*x","B",0
130,1,479,0,1.185299," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, B d^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A d^{3} i^{3} x^{4} + B c d^{2} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c d^{2} i^{3} x^{3} + \frac{3}{2} \, B c^{2} d i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A c^{2} d i^{3} x^{2} - \frac{1}{24} \, B d^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{2} \, B c d^{2} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - \frac{3}{2} \, B c^{2} d i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + B c^{3} i^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B c^{3} i^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c^{3} i^{3} x"," ",0,"1/4*B*d^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*d^3*i^3*x^4 + B*c*d^2*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c*d^2*i^3*x^3 + 3/2*B*c^2*d*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*c^2*d*i^3*x^2 - 1/24*B*d^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/2*B*c*d^2*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 3/2*B*c^2*d*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + B*c^3*i^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*c^3*i^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c^3*i^3*x","B",0
131,1,935,0,4.613473," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g),x, algorithm=""maxima"")","3 \, A c^{2} d i^{3} {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} - \frac{1}{6} \, A d^{3} i^{3} {\left(\frac{6 \, a^{3} \log\left(b x + a\right)}{b^{4} g} - \frac{2 \, b^{2} x^{3} - 3 \, a b x^{2} + 6 \, a^{2} x}{b^{3} g}\right)} + \frac{3}{2} \, A c d^{2} i^{3} {\left(\frac{2 \, a^{2} \log\left(b x + a\right)}{b^{3} g} + \frac{b x^{2} - 2 \, a x}{b^{2} g}\right)} + \frac{A c^{3} i^{3} \log\left(b g x + a g\right)}{b g} - \frac{{\left(11 \, b^{2} c^{3} i^{3} n - 15 \, a b c^{2} d i^{3} n + 6 \, a^{2} c d^{2} i^{3} n\right)} B \log\left(d x + c\right)}{6 \, b^{3} g} + \frac{{\left(b^{3} c^{3} i^{3} n - 3 \, a b^{2} c^{2} d i^{3} n + 3 \, a^{2} b c d^{2} i^{3} n - a^{3} d^{3} i^{3} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{4} g} + \frac{2 \, B b^{3} d^{3} i^{3} x^{3} \log\left(e\right) - {\left({\left(i^{3} n - 9 \, i^{3} \log\left(e\right)\right)} b^{3} c d^{2} - {\left(i^{3} n - 3 \, i^{3} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B x^{2} - 3 \, {\left(b^{3} c^{3} i^{3} n - 3 \, a b^{2} c^{2} d i^{3} n + 3 \, a^{2} b c d^{2} i^{3} n - a^{3} d^{3} i^{3} n\right)} B \log\left(b x + a\right)^{2} - {\left({\left(7 \, i^{3} n - 18 \, i^{3} \log\left(e\right)\right)} b^{3} c^{2} d - 6 \, {\left(2 \, i^{3} n - 3 \, i^{3} \log\left(e\right)\right)} a b^{2} c d^{2} + {\left(5 \, i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} a^{2} b d^{3}\right)} B x + {\left(6 \, b^{3} c^{3} i^{3} \log\left(e\right) + 18 \, {\left(i^{3} n - i^{3} \log\left(e\right)\right)} a b^{2} c^{2} d - 9 \, {\left(3 \, i^{3} n - 2 \, i^{3} \log\left(e\right)\right)} a^{2} b c d^{2} + {\left(11 \, i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} a^{3} d^{3}\right)} B \log\left(b x + a\right) + {\left(2 \, B b^{3} d^{3} i^{3} x^{3} + 3 \, {\left(3 \, b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B x^{2} + 6 \, {\left(3 \, b^{3} c^{2} d i^{3} - 3 \, a b^{2} c d^{2} i^{3} + a^{2} b d^{3} i^{3}\right)} B x + 6 \, {\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, B b^{3} d^{3} i^{3} x^{3} + 3 \, {\left(3 \, b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B x^{2} + 6 \, {\left(3 \, b^{3} c^{2} d i^{3} - 3 \, a b^{2} c d^{2} i^{3} + a^{2} b d^{3} i^{3}\right)} B x + 6 \, {\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{6 \, b^{4} g}"," ",0,"3*A*c^2*d*i^3*(x/(b*g) - a*log(b*x + a)/(b^2*g)) - 1/6*A*d^3*i^3*(6*a^3*log(b*x + a)/(b^4*g) - (2*b^2*x^3 - 3*a*b*x^2 + 6*a^2*x)/(b^3*g)) + 3/2*A*c*d^2*i^3*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2*g)) + A*c^3*i^3*log(b*g*x + a*g)/(b*g) - 1/6*(11*b^2*c^3*i^3*n - 15*a*b*c^2*d*i^3*n + 6*a^2*c*d^2*i^3*n)*B*log(d*x + c)/(b^3*g) + (b^3*c^3*i^3*n - 3*a*b^2*c^2*d*i^3*n + 3*a^2*b*c*d^2*i^3*n - a^3*d^3*i^3*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^4*g) + 1/6*(2*B*b^3*d^3*i^3*x^3*log(e) - ((i^3*n - 9*i^3*log(e))*b^3*c*d^2 - (i^3*n - 3*i^3*log(e))*a*b^2*d^3)*B*x^2 - 3*(b^3*c^3*i^3*n - 3*a*b^2*c^2*d*i^3*n + 3*a^2*b*c*d^2*i^3*n - a^3*d^3*i^3*n)*B*log(b*x + a)^2 - ((7*i^3*n - 18*i^3*log(e))*b^3*c^2*d - 6*(2*i^3*n - 3*i^3*log(e))*a*b^2*c*d^2 + (5*i^3*n - 6*i^3*log(e))*a^2*b*d^3)*B*x + (6*b^3*c^3*i^3*log(e) + 18*(i^3*n - i^3*log(e))*a*b^2*c^2*d - 9*(3*i^3*n - 2*i^3*log(e))*a^2*b*c*d^2 + (11*i^3*n - 6*i^3*log(e))*a^3*d^3)*B*log(b*x + a) + (2*B*b^3*d^3*i^3*x^3 + 3*(3*b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B*x^2 + 6*(3*b^3*c^2*d*i^3 - 3*a*b^2*c*d^2*i^3 + a^2*b*d^3*i^3)*B*x + 6*(b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B*log(b*x + a))*log((b*x + a)^n) - (2*B*b^3*d^3*i^3*x^3 + 3*(3*b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B*x^2 + 6*(3*b^3*c^2*d*i^3 - 3*a*b^2*c*d^2*i^3 + a^2*b*d^3*i^3)*B*x + 6*(b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B*log(b*x + a))*log((d*x + c)^n))/(b^4*g)","B",0
132,1,1785,0,4.411802," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B c^{3} i^{3} n {\left(\frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - 3 \, A {\left(\frac{a^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \frac{x}{b^{2} g^{2}} + \frac{2 \, a \log\left(b x + a\right)}{b^{3} g^{2}}\right)} c d^{2} i^{3} + \frac{1}{2} \, {\left(\frac{2 \, a^{3}}{b^{5} g^{2} x + a b^{4} g^{2}} + \frac{6 \, a^{2} \log\left(b x + a\right)}{b^{4} g^{2}} + \frac{b x^{2} - 4 \, a x}{b^{3} g^{2}}\right)} A d^{3} i^{3} + 3 \, A c^{2} d i^{3} {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - \frac{B c^{3} i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{2} g^{2} x + a b g^{2}} - \frac{A c^{3} i^{3}}{b^{2} g^{2} x + a b g^{2}} - \frac{{\left(5 \, b^{3} c^{3} d i^{3} n - 3 \, a b^{2} c^{2} d^{2} i^{3} n - 2 \, a^{2} b c d^{3} i^{3} n + 2 \, a^{3} d^{4} i^{3} n\right)} B \log\left(d x + c\right)}{2 \, {\left(b^{5} c g^{2} - a b^{4} d g^{2}\right)}} + \frac{{\left(b^{4} c d^{3} i^{3} \log\left(e\right) - a b^{3} d^{4} i^{3} \log\left(e\right)\right)} B x^{3} - {\left({\left(i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} b^{4} c^{2} d^{2} - {\left(2 \, i^{3} n - 9 \, i^{3} \log\left(e\right)\right)} a b^{3} c d^{3} + {\left(i^{3} n - 3 \, i^{3} \log\left(e\right)\right)} a^{2} b^{2} d^{4}\right)} B x^{2} - {\left({\left(i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} a b^{3} c^{2} d^{2} - 2 \, {\left(i^{3} n - 5 \, i^{3} \log\left(e\right)\right)} a^{2} b^{2} c d^{3} + {\left(i^{3} n - 4 \, i^{3} \log\left(e\right)\right)} a^{3} b d^{4}\right)} B x - 3 \, {\left({\left(b^{4} c^{3} d i^{3} n - 3 \, a b^{3} c^{2} d^{2} i^{3} n + 3 \, a^{2} b^{2} c d^{3} i^{3} n - a^{3} b d^{4} i^{3} n\right)} B x + {\left(a b^{3} c^{3} d i^{3} n - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} n + 3 \, a^{3} b c d^{3} i^{3} n - a^{4} d^{4} i^{3} n\right)} B\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(3 \, {\left(i^{3} n + i^{3} \log\left(e\right)\right)} a b^{3} c^{3} d - 6 \, {\left(i^{3} n + i^{3} \log\left(e\right)\right)} a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(i^{3} n + i^{3} \log\left(e\right)\right)} a^{3} b c d^{3} - {\left(i^{3} n + i^{3} \log\left(e\right)\right)} a^{4} d^{4}\right)} B + {\left({\left(6 \, b^{4} c^{3} d i^{3} \log\left(e\right) + 6 \, {\left(2 \, i^{3} n - 3 \, i^{3} \log\left(e\right)\right)} a b^{3} c^{2} d^{2} - {\left(17 \, i^{3} n - 18 \, i^{3} \log\left(e\right)\right)} a^{2} b^{2} c d^{3} + {\left(7 \, i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} a^{3} b d^{4}\right)} B x + {\left(6 \, a b^{3} c^{3} d i^{3} \log\left(e\right) + 6 \, {\left(2 \, i^{3} n - 3 \, i^{3} \log\left(e\right)\right)} a^{2} b^{2} c^{2} d^{2} - {\left(17 \, i^{3} n - 18 \, i^{3} \log\left(e\right)\right)} a^{3} b c d^{3} + {\left(7 \, i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} a^{4} d^{4}\right)} B\right)} \log\left(b x + a\right) + {\left({\left(b^{4} c d^{3} i^{3} - a b^{3} d^{4} i^{3}\right)} B x^{3} + 3 \, {\left(2 \, b^{4} c^{2} d^{2} i^{3} - 3 \, a b^{3} c d^{3} i^{3} + a^{2} b^{2} d^{4} i^{3}\right)} B x^{2} + 2 \, {\left(3 \, a b^{3} c^{2} d^{2} i^{3} - 5 \, a^{2} b^{2} c d^{3} i^{3} + 2 \, a^{3} b d^{4} i^{3}\right)} B x + 2 \, {\left(3 \, a b^{3} c^{3} d i^{3} - 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 4 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B + 6 \, {\left({\left(b^{4} c^{3} d i^{3} - 3 \, a b^{3} c^{2} d^{2} i^{3} + 3 \, a^{2} b^{2} c d^{3} i^{3} - a^{3} b d^{4} i^{3}\right)} B x + {\left(a b^{3} c^{3} d i^{3} - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 3 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b^{4} c d^{3} i^{3} - a b^{3} d^{4} i^{3}\right)} B x^{3} + 3 \, {\left(2 \, b^{4} c^{2} d^{2} i^{3} - 3 \, a b^{3} c d^{3} i^{3} + a^{2} b^{2} d^{4} i^{3}\right)} B x^{2} + 2 \, {\left(3 \, a b^{3} c^{2} d^{2} i^{3} - 5 \, a^{2} b^{2} c d^{3} i^{3} + 2 \, a^{3} b d^{4} i^{3}\right)} B x + 2 \, {\left(3 \, a b^{3} c^{3} d i^{3} - 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 4 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B + 6 \, {\left({\left(b^{4} c^{3} d i^{3} - 3 \, a b^{3} c^{2} d^{2} i^{3} + 3 \, a^{2} b^{2} c d^{3} i^{3} - a^{3} b d^{4} i^{3}\right)} B x + {\left(a b^{3} c^{3} d i^{3} - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} + 3 \, a^{3} b c d^{3} i^{3} - a^{4} d^{4} i^{3}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, {\left(a b^{5} c g^{2} - a^{2} b^{4} d g^{2} + {\left(b^{6} c g^{2} - a b^{5} d g^{2}\right)} x\right)}} + \frac{3 \, {\left(b^{2} c^{2} d i^{3} n - 2 \, a b c d^{2} i^{3} n + a^{2} d^{3} i^{3} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{4} g^{2}}"," ",0,"-B*c^3*i^3*n*(1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - 3*A*(a^2/(b^4*g^2*x + a*b^3*g^2) - x/(b^2*g^2) + 2*a*log(b*x + a)/(b^3*g^2))*c*d^2*i^3 + 1/2*(2*a^3/(b^5*g^2*x + a*b^4*g^2) + 6*a^2*log(b*x + a)/(b^4*g^2) + (b*x^2 - 4*a*x)/(b^3*g^2))*A*d^3*i^3 + 3*A*c^2*d*i^3*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - B*c^3*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*g^2*x + a*b*g^2) - A*c^3*i^3/(b^2*g^2*x + a*b*g^2) - 1/2*(5*b^3*c^3*d*i^3*n - 3*a*b^2*c^2*d^2*i^3*n - 2*a^2*b*c*d^3*i^3*n + 2*a^3*d^4*i^3*n)*B*log(d*x + c)/(b^5*c*g^2 - a*b^4*d*g^2) + 1/2*((b^4*c*d^3*i^3*log(e) - a*b^3*d^4*i^3*log(e))*B*x^3 - ((i^3*n - 6*i^3*log(e))*b^4*c^2*d^2 - (2*i^3*n - 9*i^3*log(e))*a*b^3*c*d^3 + (i^3*n - 3*i^3*log(e))*a^2*b^2*d^4)*B*x^2 - ((i^3*n - 6*i^3*log(e))*a*b^3*c^2*d^2 - 2*(i^3*n - 5*i^3*log(e))*a^2*b^2*c*d^3 + (i^3*n - 4*i^3*log(e))*a^3*b*d^4)*B*x - 3*((b^4*c^3*d*i^3*n - 3*a*b^3*c^2*d^2*i^3*n + 3*a^2*b^2*c*d^3*i^3*n - a^3*b*d^4*i^3*n)*B*x + (a*b^3*c^3*d*i^3*n - 3*a^2*b^2*c^2*d^2*i^3*n + 3*a^3*b*c*d^3*i^3*n - a^4*d^4*i^3*n)*B)*log(b*x + a)^2 + 2*(3*(i^3*n + i^3*log(e))*a*b^3*c^3*d - 6*(i^3*n + i^3*log(e))*a^2*b^2*c^2*d^2 + 4*(i^3*n + i^3*log(e))*a^3*b*c*d^3 - (i^3*n + i^3*log(e))*a^4*d^4)*B + ((6*b^4*c^3*d*i^3*log(e) + 6*(2*i^3*n - 3*i^3*log(e))*a*b^3*c^2*d^2 - (17*i^3*n - 18*i^3*log(e))*a^2*b^2*c*d^3 + (7*i^3*n - 6*i^3*log(e))*a^3*b*d^4)*B*x + (6*a*b^3*c^3*d*i^3*log(e) + 6*(2*i^3*n - 3*i^3*log(e))*a^2*b^2*c^2*d^2 - (17*i^3*n - 18*i^3*log(e))*a^3*b*c*d^3 + (7*i^3*n - 6*i^3*log(e))*a^4*d^4)*B)*log(b*x + a) + ((b^4*c*d^3*i^3 - a*b^3*d^4*i^3)*B*x^3 + 3*(2*b^4*c^2*d^2*i^3 - 3*a*b^3*c*d^3*i^3 + a^2*b^2*d^4*i^3)*B*x^2 + 2*(3*a*b^3*c^2*d^2*i^3 - 5*a^2*b^2*c*d^3*i^3 + 2*a^3*b*d^4*i^3)*B*x + 2*(3*a*b^3*c^3*d*i^3 - 6*a^2*b^2*c^2*d^2*i^3 + 4*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B + 6*((b^4*c^3*d*i^3 - 3*a*b^3*c^2*d^2*i^3 + 3*a^2*b^2*c*d^3*i^3 - a^3*b*d^4*i^3)*B*x + (a*b^3*c^3*d*i^3 - 3*a^2*b^2*c^2*d^2*i^3 + 3*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B)*log(b*x + a))*log((b*x + a)^n) - ((b^4*c*d^3*i^3 - a*b^3*d^4*i^3)*B*x^3 + 3*(2*b^4*c^2*d^2*i^3 - 3*a*b^3*c*d^3*i^3 + a^2*b^2*d^4*i^3)*B*x^2 + 2*(3*a*b^3*c^2*d^2*i^3 - 5*a^2*b^2*c*d^3*i^3 + 2*a^3*b*d^4*i^3)*B*x + 2*(3*a*b^3*c^3*d*i^3 - 6*a^2*b^2*c^2*d^2*i^3 + 4*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B + 6*((b^4*c^3*d*i^3 - 3*a*b^3*c^2*d^2*i^3 + 3*a^2*b^2*c*d^3*i^3 - a^3*b*d^4*i^3)*B*x + (a*b^3*c^3*d*i^3 - 3*a^2*b^2*c^2*d^2*i^3 + 3*a^3*b*c*d^3*i^3 - a^4*d^4*i^3)*B)*log(b*x + a))*log((d*x + c)^n))/(a*b^5*c*g^2 - a^2*b^4*d*g^2 + (b^6*c*g^2 - a*b^5*d*g^2)*x) + 3*(b^2*c^2*d*i^3*n - 2*a*b*c*d^2*i^3*n + a^2*d^3*i^3*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^4*g^2)","B",0
133,1,2746,0,5.097042," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{3}{4} \, B c^{2} d i^{3} n {\left(\frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{4} \, B c^{3} i^{3} n {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{1}{2} \, A d^{3} i^{3} {\left(\frac{6 \, a^{2} b x + 5 \, a^{3}}{b^{6} g^{3} x^{2} + 2 \, a b^{5} g^{3} x + a^{2} b^{4} g^{3}} - \frac{2 \, x}{b^{3} g^{3}} + \frac{6 \, a \log\left(b x + a\right)}{b^{4} g^{3}}\right)} + \frac{3}{2} \, A c d^{2} i^{3} {\left(\frac{4 \, a b x + 3 \, a^{2}}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + \frac{2 \, \log\left(b x + a\right)}{b^{3} g^{3}}\right)} - \frac{3 \, {\left(2 \, b x + a\right)} B c^{2} d i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{3 \, {\left(2 \, b x + a\right)} A c^{2} d i^{3}}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{B c^{3} i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{A c^{3} i^{3}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{{\left(2 \, b^{3} c^{3} d^{2} i^{3} n + 8 \, a b^{2} c^{2} d^{3} i^{3} n - 13 \, a^{2} b c d^{4} i^{3} n + 5 \, a^{3} d^{5} i^{3} n\right)} B \log\left(d x + c\right)}{2 \, {\left(b^{6} c^{2} g^{3} - 2 \, a b^{5} c d g^{3} + a^{2} b^{4} d^{2} g^{3}\right)}} + \frac{4 \, {\left(b^{5} c^{2} d^{3} i^{3} \log\left(e\right) - 2 \, a b^{4} c d^{4} i^{3} \log\left(e\right) + a^{2} b^{3} d^{5} i^{3} \log\left(e\right)\right)} B x^{3} + 8 \, {\left(a b^{4} c^{2} d^{3} i^{3} \log\left(e\right) - 2 \, a^{2} b^{3} c d^{4} i^{3} \log\left(e\right) + a^{3} b^{2} d^{5} i^{3} \log\left(e\right)\right)} B x^{2} + 2 \, {\left(12 \, {\left(i^{3} n + i^{3} \log\left(e\right)\right)} a b^{4} c^{3} d^{2} - {\left(27 \, i^{3} n + 28 \, i^{3} \log\left(e\right)\right)} a^{2} b^{3} c^{2} d^{3} + 20 \, {\left(i^{3} n + i^{3} \log\left(e\right)\right)} a^{3} b^{2} c d^{4} - {\left(5 \, i^{3} n + 4 \, i^{3} \log\left(e\right)\right)} a^{4} b d^{5}\right)} B x - 6 \, {\left({\left(b^{5} c^{3} d^{2} i^{3} n - 3 \, a b^{4} c^{2} d^{3} i^{3} n + 3 \, a^{2} b^{3} c d^{4} i^{3} n - a^{3} b^{2} d^{5} i^{3} n\right)} B x^{2} + 2 \, {\left(a b^{4} c^{3} d^{2} i^{3} n - 3 \, a^{2} b^{3} c^{2} d^{3} i^{3} n + 3 \, a^{3} b^{2} c d^{4} i^{3} n - a^{4} b d^{5} i^{3} n\right)} B x + {\left(a^{2} b^{3} c^{3} d^{2} i^{3} n - 3 \, a^{3} b^{2} c^{2} d^{3} i^{3} n + 3 \, a^{4} b c d^{4} i^{3} n - a^{5} d^{5} i^{3} n\right)} B\right)} \log\left(b x + a\right)^{2} + {\left(3 \, {\left(7 \, i^{3} n + 6 \, i^{3} \log\left(e\right)\right)} a^{2} b^{3} c^{3} d^{2} - {\left(47 \, i^{3} n + 46 \, i^{3} \log\left(e\right)\right)} a^{3} b^{2} c^{2} d^{3} + {\left(35 \, i^{3} n + 38 \, i^{3} \log\left(e\right)\right)} a^{4} b c d^{4} - {\left(9 \, i^{3} n + 10 \, i^{3} \log\left(e\right)\right)} a^{5} d^{5}\right)} B + 2 \, {\left({\left(6 \, b^{5} c^{3} d^{2} i^{3} \log\left(e\right) + 2 \, {\left(7 \, i^{3} n - 9 \, i^{3} \log\left(e\right)\right)} a b^{4} c^{2} d^{3} - {\left(19 \, i^{3} n - 18 \, i^{3} \log\left(e\right)\right)} a^{2} b^{3} c d^{4} + {\left(7 \, i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} a^{3} b^{2} d^{5}\right)} B x^{2} + 2 \, {\left(6 \, a b^{4} c^{3} d^{2} i^{3} \log\left(e\right) + 2 \, {\left(7 \, i^{3} n - 9 \, i^{3} \log\left(e\right)\right)} a^{2} b^{3} c^{2} d^{3} - {\left(19 \, i^{3} n - 18 \, i^{3} \log\left(e\right)\right)} a^{3} b^{2} c d^{4} + {\left(7 \, i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} a^{4} b d^{5}\right)} B x + {\left(6 \, a^{2} b^{3} c^{3} d^{2} i^{3} \log\left(e\right) + 2 \, {\left(7 \, i^{3} n - 9 \, i^{3} \log\left(e\right)\right)} a^{3} b^{2} c^{2} d^{3} - {\left(19 \, i^{3} n - 18 \, i^{3} \log\left(e\right)\right)} a^{4} b c d^{4} + {\left(7 \, i^{3} n - 6 \, i^{3} \log\left(e\right)\right)} a^{5} d^{5}\right)} B\right)} \log\left(b x + a\right) + 2 \, {\left(2 \, {\left(b^{5} c^{2} d^{3} i^{3} - 2 \, a b^{4} c d^{4} i^{3} + a^{2} b^{3} d^{5} i^{3}\right)} B x^{3} + 4 \, {\left(a b^{4} c^{2} d^{3} i^{3} - 2 \, a^{2} b^{3} c d^{4} i^{3} + a^{3} b^{2} d^{5} i^{3}\right)} B x^{2} + 4 \, {\left(3 \, a b^{4} c^{3} d^{2} i^{3} - 7 \, a^{2} b^{3} c^{2} d^{3} i^{3} + 5 \, a^{3} b^{2} c d^{4} i^{3} - a^{4} b d^{5} i^{3}\right)} B x + {\left(9 \, a^{2} b^{3} c^{3} d^{2} i^{3} - 23 \, a^{3} b^{2} c^{2} d^{3} i^{3} + 19 \, a^{4} b c d^{4} i^{3} - 5 \, a^{5} d^{5} i^{3}\right)} B + 6 \, {\left({\left(b^{5} c^{3} d^{2} i^{3} - 3 \, a b^{4} c^{2} d^{3} i^{3} + 3 \, a^{2} b^{3} c d^{4} i^{3} - a^{3} b^{2} d^{5} i^{3}\right)} B x^{2} + 2 \, {\left(a b^{4} c^{3} d^{2} i^{3} - 3 \, a^{2} b^{3} c^{2} d^{3} i^{3} + 3 \, a^{3} b^{2} c d^{4} i^{3} - a^{4} b d^{5} i^{3}\right)} B x + {\left(a^{2} b^{3} c^{3} d^{2} i^{3} - 3 \, a^{3} b^{2} c^{2} d^{3} i^{3} + 3 \, a^{4} b c d^{4} i^{3} - a^{5} d^{5} i^{3}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(2 \, {\left(b^{5} c^{2} d^{3} i^{3} - 2 \, a b^{4} c d^{4} i^{3} + a^{2} b^{3} d^{5} i^{3}\right)} B x^{3} + 4 \, {\left(a b^{4} c^{2} d^{3} i^{3} - 2 \, a^{2} b^{3} c d^{4} i^{3} + a^{3} b^{2} d^{5} i^{3}\right)} B x^{2} + 4 \, {\left(3 \, a b^{4} c^{3} d^{2} i^{3} - 7 \, a^{2} b^{3} c^{2} d^{3} i^{3} + 5 \, a^{3} b^{2} c d^{4} i^{3} - a^{4} b d^{5} i^{3}\right)} B x + {\left(9 \, a^{2} b^{3} c^{3} d^{2} i^{3} - 23 \, a^{3} b^{2} c^{2} d^{3} i^{3} + 19 \, a^{4} b c d^{4} i^{3} - 5 \, a^{5} d^{5} i^{3}\right)} B + 6 \, {\left({\left(b^{5} c^{3} d^{2} i^{3} - 3 \, a b^{4} c^{2} d^{3} i^{3} + 3 \, a^{2} b^{3} c d^{4} i^{3} - a^{3} b^{2} d^{5} i^{3}\right)} B x^{2} + 2 \, {\left(a b^{4} c^{3} d^{2} i^{3} - 3 \, a^{2} b^{3} c^{2} d^{3} i^{3} + 3 \, a^{3} b^{2} c d^{4} i^{3} - a^{4} b d^{5} i^{3}\right)} B x + {\left(a^{2} b^{3} c^{3} d^{2} i^{3} - 3 \, a^{3} b^{2} c^{2} d^{3} i^{3} + 3 \, a^{4} b c d^{4} i^{3} - a^{5} d^{5} i^{3}\right)} B\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{4 \, {\left(a^{2} b^{6} c^{2} g^{3} - 2 \, a^{3} b^{5} c d g^{3} + a^{4} b^{4} d^{2} g^{3} + {\left(b^{8} c^{2} g^{3} - 2 \, a b^{7} c d g^{3} + a^{2} b^{6} d^{2} g^{3}\right)} x^{2} + 2 \, {\left(a b^{7} c^{2} g^{3} - 2 \, a^{2} b^{6} c d g^{3} + a^{3} b^{5} d^{2} g^{3}\right)} x\right)}} + \frac{3 \, {\left(b c d^{2} i^{3} n - a d^{3} i^{3} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{b^{4} g^{3}}"," ",0,"-3/4*B*c^2*d*i^3*n*((3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/4*B*c^3*i^3*n*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - 1/2*A*d^3*i^3*((6*a^2*b*x + 5*a^3)/(b^6*g^3*x^2 + 2*a*b^5*g^3*x + a^2*b^4*g^3) - 2*x/(b^3*g^3) + 6*a*log(b*x + a)/(b^4*g^3)) + 3/2*A*c*d^2*i^3*((4*a*b*x + 3*a^2)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*log(b*x + a)/(b^3*g^3)) - 3/2*(2*b*x + a)*B*c^2*d*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 3/2*(2*b*x + a)*A*c^2*d*i^3/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*B*c^3*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A*c^3*i^3/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*(2*b^3*c^3*d^2*i^3*n + 8*a*b^2*c^2*d^3*i^3*n - 13*a^2*b*c*d^4*i^3*n + 5*a^3*d^5*i^3*n)*B*log(d*x + c)/(b^6*c^2*g^3 - 2*a*b^5*c*d*g^3 + a^2*b^4*d^2*g^3) + 1/4*(4*(b^5*c^2*d^3*i^3*log(e) - 2*a*b^4*c*d^4*i^3*log(e) + a^2*b^3*d^5*i^3*log(e))*B*x^3 + 8*(a*b^4*c^2*d^3*i^3*log(e) - 2*a^2*b^3*c*d^4*i^3*log(e) + a^3*b^2*d^5*i^3*log(e))*B*x^2 + 2*(12*(i^3*n + i^3*log(e))*a*b^4*c^3*d^2 - (27*i^3*n + 28*i^3*log(e))*a^2*b^3*c^2*d^3 + 20*(i^3*n + i^3*log(e))*a^3*b^2*c*d^4 - (5*i^3*n + 4*i^3*log(e))*a^4*b*d^5)*B*x - 6*((b^5*c^3*d^2*i^3*n - 3*a*b^4*c^2*d^3*i^3*n + 3*a^2*b^3*c*d^4*i^3*n - a^3*b^2*d^5*i^3*n)*B*x^2 + 2*(a*b^4*c^3*d^2*i^3*n - 3*a^2*b^3*c^2*d^3*i^3*n + 3*a^3*b^2*c*d^4*i^3*n - a^4*b*d^5*i^3*n)*B*x + (a^2*b^3*c^3*d^2*i^3*n - 3*a^3*b^2*c^2*d^3*i^3*n + 3*a^4*b*c*d^4*i^3*n - a^5*d^5*i^3*n)*B)*log(b*x + a)^2 + (3*(7*i^3*n + 6*i^3*log(e))*a^2*b^3*c^3*d^2 - (47*i^3*n + 46*i^3*log(e))*a^3*b^2*c^2*d^3 + (35*i^3*n + 38*i^3*log(e))*a^4*b*c*d^4 - (9*i^3*n + 10*i^3*log(e))*a^5*d^5)*B + 2*((6*b^5*c^3*d^2*i^3*log(e) + 2*(7*i^3*n - 9*i^3*log(e))*a*b^4*c^2*d^3 - (19*i^3*n - 18*i^3*log(e))*a^2*b^3*c*d^4 + (7*i^3*n - 6*i^3*log(e))*a^3*b^2*d^5)*B*x^2 + 2*(6*a*b^4*c^3*d^2*i^3*log(e) + 2*(7*i^3*n - 9*i^3*log(e))*a^2*b^3*c^2*d^3 - (19*i^3*n - 18*i^3*log(e))*a^3*b^2*c*d^4 + (7*i^3*n - 6*i^3*log(e))*a^4*b*d^5)*B*x + (6*a^2*b^3*c^3*d^2*i^3*log(e) + 2*(7*i^3*n - 9*i^3*log(e))*a^3*b^2*c^2*d^3 - (19*i^3*n - 18*i^3*log(e))*a^4*b*c*d^4 + (7*i^3*n - 6*i^3*log(e))*a^5*d^5)*B)*log(b*x + a) + 2*(2*(b^5*c^2*d^3*i^3 - 2*a*b^4*c*d^4*i^3 + a^2*b^3*d^5*i^3)*B*x^3 + 4*(a*b^4*c^2*d^3*i^3 - 2*a^2*b^3*c*d^4*i^3 + a^3*b^2*d^5*i^3)*B*x^2 + 4*(3*a*b^4*c^3*d^2*i^3 - 7*a^2*b^3*c^2*d^3*i^3 + 5*a^3*b^2*c*d^4*i^3 - a^4*b*d^5*i^3)*B*x + (9*a^2*b^3*c^3*d^2*i^3 - 23*a^3*b^2*c^2*d^3*i^3 + 19*a^4*b*c*d^4*i^3 - 5*a^5*d^5*i^3)*B + 6*((b^5*c^3*d^2*i^3 - 3*a*b^4*c^2*d^3*i^3 + 3*a^2*b^3*c*d^4*i^3 - a^3*b^2*d^5*i^3)*B*x^2 + 2*(a*b^4*c^3*d^2*i^3 - 3*a^2*b^3*c^2*d^3*i^3 + 3*a^3*b^2*c*d^4*i^3 - a^4*b*d^5*i^3)*B*x + (a^2*b^3*c^3*d^2*i^3 - 3*a^3*b^2*c^2*d^3*i^3 + 3*a^4*b*c*d^4*i^3 - a^5*d^5*i^3)*B)*log(b*x + a))*log((b*x + a)^n) - 2*(2*(b^5*c^2*d^3*i^3 - 2*a*b^4*c*d^4*i^3 + a^2*b^3*d^5*i^3)*B*x^3 + 4*(a*b^4*c^2*d^3*i^3 - 2*a^2*b^3*c*d^4*i^3 + a^3*b^2*d^5*i^3)*B*x^2 + 4*(3*a*b^4*c^3*d^2*i^3 - 7*a^2*b^3*c^2*d^3*i^3 + 5*a^3*b^2*c*d^4*i^3 - a^4*b*d^5*i^3)*B*x + (9*a^2*b^3*c^3*d^2*i^3 - 23*a^3*b^2*c^2*d^3*i^3 + 19*a^4*b*c*d^4*i^3 - 5*a^5*d^5*i^3)*B + 6*((b^5*c^3*d^2*i^3 - 3*a*b^4*c^2*d^3*i^3 + 3*a^2*b^3*c*d^4*i^3 - a^3*b^2*d^5*i^3)*B*x^2 + 2*(a*b^4*c^3*d^2*i^3 - 3*a^2*b^3*c^2*d^3*i^3 + 3*a^3*b^2*c*d^4*i^3 - a^4*b*d^5*i^3)*B*x + (a^2*b^3*c^3*d^2*i^3 - 3*a^3*b^2*c^2*d^3*i^3 + 3*a^4*b*c*d^4*i^3 - a^5*d^5*i^3)*B)*log(b*x + a))*log((d*x + c)^n))/(a^2*b^6*c^2*g^3 - 2*a^3*b^5*c*d*g^3 + a^4*b^4*d^2*g^3 + (b^8*c^2*g^3 - 2*a*b^7*c*d*g^3 + a^2*b^6*d^2*g^3)*x^2 + 2*(a*b^7*c^2*g^3 - 2*a^2*b^6*c*d*g^3 + a^3*b^5*d^2*g^3)*x) + 3*(b*c*d^2*i^3*n - a*d^3*i^3*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(b^4*g^3)","B",0
134,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{6} \, B c d^{2} i^{3} n {\left(\frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} - \frac{1}{18} \, B c^{3} i^{3} n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{1}{12} \, B c^{2} d i^{3} n {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} + \frac{1}{6} \, A d^{3} i^{3} {\left(\frac{18 \, a b^{2} x^{2} + 27 \, a^{2} b x + 11 \, a^{3}}{b^{7} g^{4} x^{3} + 3 \, a b^{6} g^{4} x^{2} + 3 \, a^{2} b^{5} g^{4} x + a^{3} b^{4} g^{4}} + \frac{6 \, \log\left(b x + a\right)}{b^{4} g^{4}}\right)} + \frac{1}{6} \, B d^{3} i^{3} {\left(\frac{{\left(18 \, a b^{2} x^{2} + 27 \, a^{2} b x + 11 \, a^{3} + 6 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(18 \, a b^{2} x^{2} + 27 \, a^{2} b x + 11 \, a^{3} + 6 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{7} g^{4} x^{3} + 3 \, a b^{6} g^{4} x^{2} + 3 \, a^{2} b^{5} g^{4} x + a^{3} b^{4} g^{4}} + 6 \, \int \frac{6 \, b^{4} d x^{4} \log\left(e\right) + 6 \, b^{4} c x^{3} \log\left(e\right) - 11 \, a^{3} b c n + 11 \, a^{4} d n - 18 \, {\left(a b^{3} c n - a^{2} b^{2} d n\right)} x^{2} - 27 \, {\left(a^{2} b^{2} c n - a^{3} b d n\right)} x - 6 \, {\left(a^{3} b c n - a^{4} d n + {\left(b^{4} c n - a b^{3} d n\right)} x^{3} + 3 \, {\left(a b^{3} c n - a^{2} b^{2} d n\right)} x^{2} + 3 \, {\left(a^{2} b^{2} c n - a^{3} b d n\right)} x\right)} \log\left(b x + a\right)}{6 \, {\left(b^{8} d g^{4} x^{5} + a^{4} b^{4} c g^{4} + {\left(b^{8} c g^{4} + 4 \, a b^{7} d g^{4}\right)} x^{4} + 2 \, {\left(2 \, a b^{7} c g^{4} + 3 \, a^{2} b^{6} d g^{4}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{6} c g^{4} + 2 \, a^{3} b^{5} d g^{4}\right)} x^{2} + {\left(4 \, a^{3} b^{5} c g^{4} + a^{4} b^{4} d g^{4}\right)} x\right)}}\,{d x}\right)} - \frac{{\left(3 \, b x + a\right)} B c^{2} d i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} B c d^{2} i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}} - \frac{{\left(3 \, b x + a\right)} A c^{2} d i^{3}}{2 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A c d^{2} i^{3}}{b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}} - \frac{B c^{3} i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{A c^{3} i^{3}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/6*B*c*d^2*i^3*n*((11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4)) - 1/18*B*c^3*i^3*n*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/12*B*c^2*d*i^3*n*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) + 1/6*A*d^3*i^3*((18*a*b^2*x^2 + 27*a^2*b*x + 11*a^3)/(b^7*g^4*x^3 + 3*a*b^6*g^4*x^2 + 3*a^2*b^5*g^4*x + a^3*b^4*g^4) + 6*log(b*x + a)/(b^4*g^4)) + 1/6*B*d^3*i^3*(((18*a*b^2*x^2 + 27*a^2*b*x + 11*a^3 + 6*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*log(b*x + a))*log((b*x + a)^n) - (18*a*b^2*x^2 + 27*a^2*b*x + 11*a^3 + 6*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*log(b*x + a))*log((d*x + c)^n))/(b^7*g^4*x^3 + 3*a*b^6*g^4*x^2 + 3*a^2*b^5*g^4*x + a^3*b^4*g^4) + 6*integrate(1/6*(6*b^4*d*x^4*log(e) + 6*b^4*c*x^3*log(e) - 11*a^3*b*c*n + 11*a^4*d*n - 18*(a*b^3*c*n - a^2*b^2*d*n)*x^2 - 27*(a^2*b^2*c*n - a^3*b*d*n)*x - 6*(a^3*b*c*n - a^4*d*n + (b^4*c*n - a*b^3*d*n)*x^3 + 3*(a*b^3*c*n - a^2*b^2*d*n)*x^2 + 3*(a^2*b^2*c*n - a^3*b*d*n)*x)*log(b*x + a))/(b^8*d*g^4*x^5 + a^4*b^4*c*g^4 + (b^8*c*g^4 + 4*a*b^7*d*g^4)*x^4 + 2*(2*a*b^7*c*g^4 + 3*a^2*b^6*d*g^4)*x^3 + 2*(3*a^2*b^6*c*g^4 + 2*a^3*b^5*d*g^4)*x^2 + (4*a^3*b^5*c*g^4 + a^4*b^4*d*g^4)*x), x)) - 1/2*(3*b*x + a)*B*c^2*d*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - (3*b^2*x^2 + 3*a*b*x + a^2)*B*c*d^2*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/2*(3*b*x + a)*A*c^2*d*i^3/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - (3*b^2*x^2 + 3*a*b*x + a^2)*A*c*d^2*i^3/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/3*B*c^3*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/3*A*c^3*i^3/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","F",0
135,1,1003,0,4.289842," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i),x, algorithm=""maxima"")","3 \, A a^{2} b g^{3} {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} - \frac{1}{6} \, A b^{3} g^{3} {\left(\frac{6 \, c^{3} \log\left(d x + c\right)}{d^{4} i} - \frac{2 \, d^{2} x^{3} - 3 \, c d x^{2} + 6 \, c^{2} x}{d^{3} i}\right)} + \frac{3}{2} \, A a b^{2} g^{3} {\left(\frac{2 \, c^{2} \log\left(d x + c\right)}{d^{3} i} + \frac{d x^{2} - 2 \, c x}{d^{2} i}\right)} + \frac{A a^{3} g^{3} \log\left(d i x + c i\right)}{d i} - \frac{{\left(b^{3} c^{3} g^{3} n - 3 \, a b^{2} c^{2} d g^{3} n + 3 \, a^{2} b c d^{2} g^{3} n - a^{3} d^{3} g^{3} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{4} i} + \frac{{\left(6 \, a^{3} d^{3} g^{3} \log\left(e\right) - {\left(11 \, g^{3} n + 6 \, g^{3} \log\left(e\right)\right)} b^{3} c^{3} + 9 \, {\left(3 \, g^{3} n + 2 \, g^{3} \log\left(e\right)\right)} a b^{2} c^{2} d - 18 \, {\left(g^{3} n + g^{3} \log\left(e\right)\right)} a^{2} b c d^{2}\right)} B \log\left(d x + c\right)}{6 \, d^{4} i} + \frac{2 \, B b^{3} d^{3} g^{3} x^{3} \log\left(e\right) - {\left({\left(g^{3} n + 3 \, g^{3} \log\left(e\right)\right)} b^{3} c d^{2} - {\left(g^{3} n + 9 \, g^{3} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B x^{2} + 6 \, {\left(b^{3} c^{3} g^{3} n - 3 \, a b^{2} c^{2} d g^{3} n + 3 \, a^{2} b c d^{2} g^{3} n - a^{3} d^{3} g^{3} n\right)} B \log\left(b x + a\right) \log\left(d x + c\right) - 3 \, {\left(b^{3} c^{3} g^{3} n - 3 \, a b^{2} c^{2} d g^{3} n + 3 \, a^{2} b c d^{2} g^{3} n - a^{3} d^{3} g^{3} n\right)} B \log\left(d x + c\right)^{2} + {\left({\left(5 \, g^{3} n + 6 \, g^{3} \log\left(e\right)\right)} b^{3} c^{2} d - 6 \, {\left(2 \, g^{3} n + 3 \, g^{3} \log\left(e\right)\right)} a b^{2} c d^{2} + {\left(7 \, g^{3} n + 18 \, g^{3} \log\left(e\right)\right)} a^{2} b d^{3}\right)} B x + {\left(6 \, a b^{2} c^{2} d g^{3} n - 15 \, a^{2} b c d^{2} g^{3} n + 11 \, a^{3} d^{3} g^{3} n\right)} B \log\left(b x + a\right) + {\left(2 \, B b^{3} d^{3} g^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} g^{3} - 3 \, a b^{2} d^{3} g^{3}\right)} B x^{2} + 6 \, {\left(b^{3} c^{2} d g^{3} - 3 \, a b^{2} c d^{2} g^{3} + 3 \, a^{2} b d^{3} g^{3}\right)} B x - 6 \, {\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - a^{3} d^{3} g^{3}\right)} B \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, B b^{3} d^{3} g^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} g^{3} - 3 \, a b^{2} d^{3} g^{3}\right)} B x^{2} + 6 \, {\left(b^{3} c^{2} d g^{3} - 3 \, a b^{2} c d^{2} g^{3} + 3 \, a^{2} b d^{3} g^{3}\right)} B x - 6 \, {\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - a^{3} d^{3} g^{3}\right)} B \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{6 \, d^{4} i}"," ",0,"3*A*a^2*b*g^3*(x/(d*i) - c*log(d*x + c)/(d^2*i)) - 1/6*A*b^3*g^3*(6*c^3*log(d*x + c)/(d^4*i) - (2*d^2*x^3 - 3*c*d*x^2 + 6*c^2*x)/(d^3*i)) + 3/2*A*a*b^2*g^3*(2*c^2*log(d*x + c)/(d^3*i) + (d*x^2 - 2*c*x)/(d^2*i)) + A*a^3*g^3*log(d*i*x + c*i)/(d*i) - (b^3*c^3*g^3*n - 3*a*b^2*c^2*d*g^3*n + 3*a^2*b*c*d^2*g^3*n - a^3*d^3*g^3*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^4*i) + 1/6*(6*a^3*d^3*g^3*log(e) - (11*g^3*n + 6*g^3*log(e))*b^3*c^3 + 9*(3*g^3*n + 2*g^3*log(e))*a*b^2*c^2*d - 18*(g^3*n + g^3*log(e))*a^2*b*c*d^2)*B*log(d*x + c)/(d^4*i) + 1/6*(2*B*b^3*d^3*g^3*x^3*log(e) - ((g^3*n + 3*g^3*log(e))*b^3*c*d^2 - (g^3*n + 9*g^3*log(e))*a*b^2*d^3)*B*x^2 + 6*(b^3*c^3*g^3*n - 3*a*b^2*c^2*d*g^3*n + 3*a^2*b*c*d^2*g^3*n - a^3*d^3*g^3*n)*B*log(b*x + a)*log(d*x + c) - 3*(b^3*c^3*g^3*n - 3*a*b^2*c^2*d*g^3*n + 3*a^2*b*c*d^2*g^3*n - a^3*d^3*g^3*n)*B*log(d*x + c)^2 + ((5*g^3*n + 6*g^3*log(e))*b^3*c^2*d - 6*(2*g^3*n + 3*g^3*log(e))*a*b^2*c*d^2 + (7*g^3*n + 18*g^3*log(e))*a^2*b*d^3)*B*x + (6*a*b^2*c^2*d*g^3*n - 15*a^2*b*c*d^2*g^3*n + 11*a^3*d^3*g^3*n)*B*log(b*x + a) + (2*B*b^3*d^3*g^3*x^3 - 3*(b^3*c*d^2*g^3 - 3*a*b^2*d^3*g^3)*B*x^2 + 6*(b^3*c^2*d*g^3 - 3*a*b^2*c*d^2*g^3 + 3*a^2*b*d^3*g^3)*B*x - 6*(b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - a^3*d^3*g^3)*B*log(d*x + c))*log((b*x + a)^n) - (2*B*b^3*d^3*g^3*x^3 - 3*(b^3*c*d^2*g^3 - 3*a*b^2*d^3*g^3)*B*x^2 + 6*(b^3*c^2*d*g^3 - 3*a*b^2*c*d^2*g^3 + 3*a^2*b*d^3*g^3)*B*x - 6*(b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - a^3*d^3*g^3)*B*log(d*x + c))*log((d*x + c)^n))/(d^4*i)","B",0
136,1,627,0,4.694291," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i),x, algorithm=""maxima"")","2 \, A a b g^{2} {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} + \frac{1}{2} \, A b^{2} g^{2} {\left(\frac{2 \, c^{2} \log\left(d x + c\right)}{d^{3} i} + \frac{d x^{2} - 2 \, c x}{d^{2} i}\right)} + \frac{A a^{2} g^{2} \log\left(d i x + c i\right)}{d i} + \frac{{\left(b^{2} c^{2} g^{2} n - 2 \, a b c d g^{2} n + a^{2} d^{2} g^{2} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{3} i} + \frac{{\left(2 \, a^{2} d^{2} g^{2} \log\left(e\right) + {\left(3 \, g^{2} n + 2 \, g^{2} \log\left(e\right)\right)} b^{2} c^{2} - 4 \, {\left(g^{2} n + g^{2} \log\left(e\right)\right)} a b c d\right)} B \log\left(d x + c\right)}{2 \, d^{3} i} + \frac{B b^{2} d^{2} g^{2} x^{2} \log\left(e\right) - 2 \, {\left(b^{2} c^{2} g^{2} n - 2 \, a b c d g^{2} n + a^{2} d^{2} g^{2} n\right)} B \log\left(b x + a\right) \log\left(d x + c\right) + {\left(b^{2} c^{2} g^{2} n - 2 \, a b c d g^{2} n + a^{2} d^{2} g^{2} n\right)} B \log\left(d x + c\right)^{2} - {\left({\left(g^{2} n + 2 \, g^{2} \log\left(e\right)\right)} b^{2} c d - {\left(g^{2} n + 4 \, g^{2} \log\left(e\right)\right)} a b d^{2}\right)} B x - {\left(2 \, a b c d g^{2} n - 3 \, a^{2} d^{2} g^{2} n\right)} B \log\left(b x + a\right) + {\left(B b^{2} d^{2} g^{2} x^{2} - 2 \, {\left(b^{2} c d g^{2} - 2 \, a b d^{2} g^{2}\right)} B x + 2 \, {\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + a^{2} d^{2} g^{2}\right)} B \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B b^{2} d^{2} g^{2} x^{2} - 2 \, {\left(b^{2} c d g^{2} - 2 \, a b d^{2} g^{2}\right)} B x + 2 \, {\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + a^{2} d^{2} g^{2}\right)} B \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, d^{3} i}"," ",0,"2*A*a*b*g^2*(x/(d*i) - c*log(d*x + c)/(d^2*i)) + 1/2*A*b^2*g^2*(2*c^2*log(d*x + c)/(d^3*i) + (d*x^2 - 2*c*x)/(d^2*i)) + A*a^2*g^2*log(d*i*x + c*i)/(d*i) + (b^2*c^2*g^2*n - 2*a*b*c*d*g^2*n + a^2*d^2*g^2*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^3*i) + 1/2*(2*a^2*d^2*g^2*log(e) + (3*g^2*n + 2*g^2*log(e))*b^2*c^2 - 4*(g^2*n + g^2*log(e))*a*b*c*d)*B*log(d*x + c)/(d^3*i) + 1/2*(B*b^2*d^2*g^2*x^2*log(e) - 2*(b^2*c^2*g^2*n - 2*a*b*c*d*g^2*n + a^2*d^2*g^2*n)*B*log(b*x + a)*log(d*x + c) + (b^2*c^2*g^2*n - 2*a*b*c*d*g^2*n + a^2*d^2*g^2*n)*B*log(d*x + c)^2 - ((g^2*n + 2*g^2*log(e))*b^2*c*d - (g^2*n + 4*g^2*log(e))*a*b*d^2)*B*x - (2*a*b*c*d*g^2*n - 3*a^2*d^2*g^2*n)*B*log(b*x + a) + (B*b^2*d^2*g^2*x^2 - 2*(b^2*c*d*g^2 - 2*a*b*d^2*g^2)*B*x + 2*(b^2*c^2*g^2 - 2*a*b*c*d*g^2 + a^2*d^2*g^2)*B*log(d*x + c))*log((b*x + a)^n) - (B*b^2*d^2*g^2*x^2 - 2*(b^2*c*d*g^2 - 2*a*b*d^2*g^2)*B*x + 2*(b^2*c^2*g^2 - 2*a*b*c*d*g^2 + a^2*d^2*g^2)*B*log(d*x + c))*log((d*x + c)^n))/(d^3*i)","B",0
137,1,306,0,4.051216," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i),x, algorithm=""maxima"")","A b g {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} + \frac{A a g \log\left(d i x + c i\right)}{d i} - \frac{{\left(b c g n - a d g n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{2} i} + \frac{{\left(a d g \log\left(e\right) - {\left(g n + g \log\left(e\right)\right)} b c\right)} B \log\left(d x + c\right)}{d^{2} i} + \frac{2 \, B a d g n \log\left(b x + a\right) + 2 \, B b d g x \log\left(e\right) + 2 \, {\left(b c g n - a d g n\right)} B \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b c g n - a d g n\right)} B \log\left(d x + c\right)^{2} + 2 \, {\left(B b d g x - {\left(b c g - a d g\right)} B \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B b d g x - {\left(b c g - a d g\right)} B \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, d^{2} i}"," ",0,"A*b*g*(x/(d*i) - c*log(d*x + c)/(d^2*i)) + A*a*g*log(d*i*x + c*i)/(d*i) - (b*c*g*n - a*d*g*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^2*i) + (a*d*g*log(e) - (g*n + g*log(e))*b*c)*B*log(d*x + c)/(d^2*i) + 1/2*(2*B*a*d*g*n*log(b*x + a) + 2*B*b*d*g*x*log(e) + 2*(b*c*g*n - a*d*g*n)*B*log(b*x + a)*log(d*x + c) - (b*c*g*n - a*d*g*n)*B*log(d*x + c)^2 + 2*(B*b*d*g*x - (b*c*g - a*d*g)*B*log(d*x + c))*log((b*x + a)^n) - 2*(B*b*d*g*x - (b*c*g - a*d*g)*B*log(d*x + c))*log((d*x + c)^n))/(d^2*i)","B",0
138,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i),x, algorithm=""maxima"")","-\frac{1}{2} \, B {\left(\frac{2 \, n \log\left(b x + a\right) \log\left(d x + c\right) - n \log\left(d x + c\right)^{2} - 2 \, \log\left(d x + c\right) \log\left({\left(b x + a\right)}^{n}\right) + 2 \, \log\left(d x + c\right) \log\left({\left(d x + c\right)}^{n}\right)}{d i} - 2 \, \int \frac{n \log\left(b x + a\right) + \log\left(e\right)}{d i x + c i}\,{d x}\right)} + \frac{A \log\left(d i x + c i\right)}{d i}"," ",0,"-1/2*B*((2*n*log(b*x + a)*log(d*x + c) - n*log(d*x + c)^2 - 2*log(d*x + c)*log((b*x + a)^n) + 2*log(d*x + c)*log((d*x + c)^n))/(d*i) - 2*integrate((n*log(b*x + a) + log(e))/(d*i*x + c*i), x)) + A*log(d*i*x + c*i)/(d*i)","F",0
139,1,175,0,1.217901," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)/(d*i*x+c*i),x, algorithm=""maxima"")","B {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right) + \log\left(d x + c\right)^{2}\right)} B n}{2 \, {\left(b c g i - a d g i\right)}} + A {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)}"," ",0,"B*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/2*(log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c) + log(d*x + c)^2)*B*n/(b*c*g*i - a*d*g*i) + A*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i))","B",0
140,1,427,0,1.292816," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2/(d*i*x+c*i),x, algorithm=""maxima"")","-B {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left({\left(b d x + a d\right)} \log\left(b x + a\right)^{2} + {\left(b d x + a d\right)} \log\left(d x + c\right)^{2} - 2 \, b c + 2 \, a d - 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right) + 2 \, {\left(b d x + a d - {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{2 \, {\left(a b^{2} c^{2} g^{2} i - 2 \, a^{2} b c d g^{2} i + a^{3} d^{2} g^{2} i + {\left(b^{3} c^{2} g^{2} i - 2 \, a b^{2} c d g^{2} i + a^{2} b d^{2} g^{2} i\right)} x\right)}} - A {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)}"," ",0,"-B*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*((b*d*x + a*d)*log(b*x + a)^2 + (b*d*x + a*d)*log(d*x + c)^2 - 2*b*c + 2*a*d - 2*(b*d*x + a*d)*log(b*x + a) + 2*(b*d*x + a*d - (b*d*x + a*d)*log(b*x + a))*log(d*x + c))*B*n/(a*b^2*c^2*g^2*i - 2*a^2*b*c*d*g^2*i + a^3*d^2*g^2*i + (b^3*c^2*g^2*i - 2*a*b^2*c*d*g^2*i + a^2*b*d^2*g^2*i)*x) - A*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i))","B",0
141,1,888,0,1.727126," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3/(d*i*x+c*i),x, algorithm=""maxima"")","\frac{1}{2} \, B {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(b^{2} c^{2} - 8 \, a b c d + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d - a b d^{2}\right)} x - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{4 \, {\left(a^{2} b^{3} c^{3} g^{3} i - 3 \, a^{3} b^{2} c^{2} d g^{3} i + 3 \, a^{4} b c d^{2} g^{3} i - a^{5} d^{3} g^{3} i + {\left(b^{5} c^{3} g^{3} i - 3 \, a b^{4} c^{2} d g^{3} i + 3 \, a^{2} b^{3} c d^{2} g^{3} i - a^{3} b^{2} d^{3} g^{3} i\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} g^{3} i - 3 \, a^{2} b^{3} c^{2} d g^{3} i + 3 \, a^{3} b^{2} c d^{2} g^{3} i - a^{4} b d^{3} g^{3} i\right)} x\right)}} + \frac{1}{2} \, A {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)}"," ",0,"1/2*B*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/4*(b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^2 - 6*(b^2*c*d - a*b*d^2)*x - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))*B*n/(a^2*b^3*c^3*g^3*i - 3*a^3*b^2*c^2*d*g^3*i + 3*a^4*b*c*d^2*g^3*i - a^5*d^3*g^3*i + (b^5*c^3*g^3*i - 3*a*b^4*c^2*d*g^3*i + 3*a^2*b^3*c*d^2*g^3*i - a^3*b^2*d^3*g^3*i)*x^2 + 2*(a*b^4*c^3*g^3*i - 3*a^2*b^3*c^2*d*g^3*i + 3*a^3*b^2*c*d^2*g^3*i - a^4*b*d^3*g^3*i)*x) + 1/2*A*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i))","B",0
142,1,1472,0,2.356891," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4/(d*i*x+c*i),x, algorithm=""maxima"")","-\frac{1}{6} \, B {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{36 \, {\left(a^{3} b^{4} c^{4} g^{4} i - 4 \, a^{4} b^{3} c^{3} d g^{4} i + 6 \, a^{5} b^{2} c^{2} d^{2} g^{4} i - 4 \, a^{6} b c d^{3} g^{4} i + a^{7} d^{4} g^{4} i + {\left(b^{7} c^{4} g^{4} i - 4 \, a b^{6} c^{3} d g^{4} i + 6 \, a^{2} b^{5} c^{2} d^{2} g^{4} i - 4 \, a^{3} b^{4} c d^{3} g^{4} i + a^{4} b^{3} d^{4} g^{4} i\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} g^{4} i - 4 \, a^{2} b^{5} c^{3} d g^{4} i + 6 \, a^{3} b^{4} c^{2} d^{2} g^{4} i - 4 \, a^{4} b^{3} c d^{3} g^{4} i + a^{5} b^{2} d^{4} g^{4} i\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} g^{4} i - 4 \, a^{3} b^{4} c^{3} d g^{4} i + 6 \, a^{4} b^{3} c^{2} d^{2} g^{4} i - 4 \, a^{5} b^{2} c d^{3} g^{4} i + a^{6} b d^{4} g^{4} i\right)} x\right)}} - \frac{1}{6} \, A {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)}"," ",0,"-1/6*B*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/36*(4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*B*n/(a^3*b^4*c^4*g^4*i - 4*a^4*b^3*c^3*d*g^4*i + 6*a^5*b^2*c^2*d^2*g^4*i - 4*a^6*b*c*d^3*g^4*i + a^7*d^4*g^4*i + (b^7*c^4*g^4*i - 4*a*b^6*c^3*d*g^4*i + 6*a^2*b^5*c^2*d^2*g^4*i - 4*a^3*b^4*c*d^3*g^4*i + a^4*b^3*d^4*g^4*i)*x^3 + 3*(a*b^6*c^4*g^4*i - 4*a^2*b^5*c^3*d*g^4*i + 6*a^3*b^4*c^2*d^2*g^4*i - 4*a^4*b^3*c*d^3*g^4*i + a^5*b^2*d^4*g^4*i)*x^2 + 3*(a^2*b^5*c^4*g^4*i - 4*a^3*b^4*c^3*d*g^4*i + 6*a^4*b^3*c^2*d^2*g^4*i - 4*a^5*b^2*c*d^3*g^4*i + a^6*b*d^4*g^4*i)*x) - 1/6*A*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i))","B",0
143,1,1892,0,4.404480," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^2,x, algorithm=""maxima"")","B a^{3} g^{3} n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} + \frac{1}{2} \, {\left(\frac{2 \, c^{3}}{d^{5} i^{2} x + c d^{4} i^{2}} + \frac{6 \, c^{2} \log\left(d x + c\right)}{d^{4} i^{2}} + \frac{d x^{2} - 4 \, c x}{d^{3} i^{2}}\right)} A b^{3} g^{3} - 3 \, A a b^{2} {\left(\frac{c^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \frac{x}{d^{2} i^{2}} + \frac{2 \, c \log\left(d x + c\right)}{d^{3} i^{2}}\right)} g^{3} + 3 \, A a^{2} b g^{3} {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - \frac{B a^{3} g^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{A a^{3} g^{3}}{d^{2} i^{2} x + c d i^{2}} - \frac{{\left(6 \, a^{3} b d^{3} g^{3} \log\left(e\right) - {\left(7 \, g^{3} n + 6 \, g^{3} \log\left(e\right)\right)} b^{4} c^{3} + {\left(17 \, g^{3} n + 18 \, g^{3} \log\left(e\right)\right)} a b^{3} c^{2} d - 6 \, {\left(2 \, g^{3} n + 3 \, g^{3} \log\left(e\right)\right)} a^{2} b^{2} c d^{2}\right)} B \log\left(d x + c\right)}{2 \, {\left(b c d^{4} i^{2} - a d^{5} i^{2}\right)}} + \frac{{\left(b^{4} c d^{3} g^{3} \log\left(e\right) - a b^{3} d^{4} g^{3} \log\left(e\right)\right)} B x^{3} - {\left({\left(g^{3} n + 3 \, g^{3} \log\left(e\right)\right)} b^{4} c^{2} d^{2} - {\left(2 \, g^{3} n + 9 \, g^{3} \log\left(e\right)\right)} a b^{3} c d^{3} + {\left(g^{3} n + 6 \, g^{3} \log\left(e\right)\right)} a^{2} b^{2} d^{4}\right)} B x^{2} - {\left({\left(g^{3} n + 4 \, g^{3} \log\left(e\right)\right)} b^{4} c^{3} d - 2 \, {\left(g^{3} n + 5 \, g^{3} \log\left(e\right)\right)} a b^{3} c^{2} d^{2} + {\left(g^{3} n + 6 \, g^{3} \log\left(e\right)\right)} a^{2} b^{2} c d^{3}\right)} B x - 6 \, {\left({\left(b^{4} c^{3} d g^{3} n - 3 \, a b^{3} c^{2} d^{2} g^{3} n + 3 \, a^{2} b^{2} c d^{3} g^{3} n - a^{3} b d^{4} g^{3} n\right)} B x + {\left(b^{4} c^{4} g^{3} n - 3 \, a b^{3} c^{3} d g^{3} n + 3 \, a^{2} b^{2} c^{2} d^{2} g^{3} n - a^{3} b c d^{3} g^{3} n\right)} B\right)} \log\left(b x + a\right) \log\left(d x + c\right) + 3 \, {\left({\left(b^{4} c^{3} d g^{3} n - 3 \, a b^{3} c^{2} d^{2} g^{3} n + 3 \, a^{2} b^{2} c d^{3} g^{3} n - a^{3} b d^{4} g^{3} n\right)} B x + {\left(b^{4} c^{4} g^{3} n - 3 \, a b^{3} c^{3} d g^{3} n + 3 \, a^{2} b^{2} c^{2} d^{2} g^{3} n - a^{3} b c d^{3} g^{3} n\right)} B\right)} \log\left(d x + c\right)^{2} - 2 \, {\left({\left(g^{3} n - g^{3} \log\left(e\right)\right)} b^{4} c^{4} - 4 \, {\left(g^{3} n - g^{3} \log\left(e\right)\right)} a b^{3} c^{3} d + 6 \, {\left(g^{3} n - g^{3} \log\left(e\right)\right)} a^{2} b^{2} c^{2} d^{2} - 3 \, {\left(g^{3} n - g^{3} \log\left(e\right)\right)} a^{3} b c d^{3}\right)} B - {\left({\left(2 \, b^{4} c^{3} d g^{3} n - 2 \, a b^{3} c^{2} d^{2} g^{3} n - 3 \, a^{2} b^{2} c d^{3} g^{3} n + 5 \, a^{3} b d^{4} g^{3} n\right)} B x + {\left(2 \, b^{4} c^{4} g^{3} n - 2 \, a b^{3} c^{3} d g^{3} n - 3 \, a^{2} b^{2} c^{2} d^{2} g^{3} n + 5 \, a^{3} b c d^{3} g^{3} n\right)} B\right)} \log\left(b x + a\right) + {\left({\left(b^{4} c d^{3} g^{3} - a b^{3} d^{4} g^{3}\right)} B x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 3 \, a b^{3} c d^{3} g^{3} + 2 \, a^{2} b^{2} d^{4} g^{3}\right)} B x^{2} - 2 \, {\left(2 \, b^{4} c^{3} d g^{3} - 5 \, a b^{3} c^{2} d^{2} g^{3} + 3 \, a^{2} b^{2} c d^{3} g^{3}\right)} B x + 2 \, {\left(b^{4} c^{4} g^{3} - 4 \, a b^{3} c^{3} d g^{3} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} - 3 \, a^{3} b c d^{3} g^{3}\right)} B + 6 \, {\left({\left(b^{4} c^{3} d g^{3} - 3 \, a b^{3} c^{2} d^{2} g^{3} + 3 \, a^{2} b^{2} c d^{3} g^{3} - a^{3} b d^{4} g^{3}\right)} B x + {\left(b^{4} c^{4} g^{3} - 3 \, a b^{3} c^{3} d g^{3} + 3 \, a^{2} b^{2} c^{2} d^{2} g^{3} - a^{3} b c d^{3} g^{3}\right)} B\right)} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b^{4} c d^{3} g^{3} - a b^{3} d^{4} g^{3}\right)} B x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 3 \, a b^{3} c d^{3} g^{3} + 2 \, a^{2} b^{2} d^{4} g^{3}\right)} B x^{2} - 2 \, {\left(2 \, b^{4} c^{3} d g^{3} - 5 \, a b^{3} c^{2} d^{2} g^{3} + 3 \, a^{2} b^{2} c d^{3} g^{3}\right)} B x + 2 \, {\left(b^{4} c^{4} g^{3} - 4 \, a b^{3} c^{3} d g^{3} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} - 3 \, a^{3} b c d^{3} g^{3}\right)} B + 6 \, {\left({\left(b^{4} c^{3} d g^{3} - 3 \, a b^{3} c^{2} d^{2} g^{3} + 3 \, a^{2} b^{2} c d^{3} g^{3} - a^{3} b d^{4} g^{3}\right)} B x + {\left(b^{4} c^{4} g^{3} - 3 \, a b^{3} c^{3} d g^{3} + 3 \, a^{2} b^{2} c^{2} d^{2} g^{3} - a^{3} b c d^{3} g^{3}\right)} B\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, {\left(b c^{2} d^{4} i^{2} - a c d^{5} i^{2} + {\left(b c d^{5} i^{2} - a d^{6} i^{2}\right)} x\right)}} + \frac{3 \, {\left(b^{3} c^{2} g^{3} n - 2 \, a b^{2} c d g^{3} n + a^{2} b d^{2} g^{3} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{4} i^{2}}"," ",0,"B*a^3*g^3*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) + 1/2*(2*c^3/(d^5*i^2*x + c*d^4*i^2) + 6*c^2*log(d*x + c)/(d^4*i^2) + (d*x^2 - 4*c*x)/(d^3*i^2))*A*b^3*g^3 - 3*A*a*b^2*(c^2/(d^4*i^2*x + c*d^3*i^2) - x/(d^2*i^2) + 2*c*log(d*x + c)/(d^3*i^2))*g^3 + 3*A*a^2*b*g^3*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - B*a^3*g^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*i^2*x + c*d*i^2) - A*a^3*g^3/(d^2*i^2*x + c*d*i^2) - 1/2*(6*a^3*b*d^3*g^3*log(e) - (7*g^3*n + 6*g^3*log(e))*b^4*c^3 + (17*g^3*n + 18*g^3*log(e))*a*b^3*c^2*d - 6*(2*g^3*n + 3*g^3*log(e))*a^2*b^2*c*d^2)*B*log(d*x + c)/(b*c*d^4*i^2 - a*d^5*i^2) + 1/2*((b^4*c*d^3*g^3*log(e) - a*b^3*d^4*g^3*log(e))*B*x^3 - ((g^3*n + 3*g^3*log(e))*b^4*c^2*d^2 - (2*g^3*n + 9*g^3*log(e))*a*b^3*c*d^3 + (g^3*n + 6*g^3*log(e))*a^2*b^2*d^4)*B*x^2 - ((g^3*n + 4*g^3*log(e))*b^4*c^3*d - 2*(g^3*n + 5*g^3*log(e))*a*b^3*c^2*d^2 + (g^3*n + 6*g^3*log(e))*a^2*b^2*c*d^3)*B*x - 6*((b^4*c^3*d*g^3*n - 3*a*b^3*c^2*d^2*g^3*n + 3*a^2*b^2*c*d^3*g^3*n - a^3*b*d^4*g^3*n)*B*x + (b^4*c^4*g^3*n - 3*a*b^3*c^3*d*g^3*n + 3*a^2*b^2*c^2*d^2*g^3*n - a^3*b*c*d^3*g^3*n)*B)*log(b*x + a)*log(d*x + c) + 3*((b^4*c^3*d*g^3*n - 3*a*b^3*c^2*d^2*g^3*n + 3*a^2*b^2*c*d^3*g^3*n - a^3*b*d^4*g^3*n)*B*x + (b^4*c^4*g^3*n - 3*a*b^3*c^3*d*g^3*n + 3*a^2*b^2*c^2*d^2*g^3*n - a^3*b*c*d^3*g^3*n)*B)*log(d*x + c)^2 - 2*((g^3*n - g^3*log(e))*b^4*c^4 - 4*(g^3*n - g^3*log(e))*a*b^3*c^3*d + 6*(g^3*n - g^3*log(e))*a^2*b^2*c^2*d^2 - 3*(g^3*n - g^3*log(e))*a^3*b*c*d^3)*B - ((2*b^4*c^3*d*g^3*n - 2*a*b^3*c^2*d^2*g^3*n - 3*a^2*b^2*c*d^3*g^3*n + 5*a^3*b*d^4*g^3*n)*B*x + (2*b^4*c^4*g^3*n - 2*a*b^3*c^3*d*g^3*n - 3*a^2*b^2*c^2*d^2*g^3*n + 5*a^3*b*c*d^3*g^3*n)*B)*log(b*x + a) + ((b^4*c*d^3*g^3 - a*b^3*d^4*g^3)*B*x^3 - 3*(b^4*c^2*d^2*g^3 - 3*a*b^3*c*d^3*g^3 + 2*a^2*b^2*d^4*g^3)*B*x^2 - 2*(2*b^4*c^3*d*g^3 - 5*a*b^3*c^2*d^2*g^3 + 3*a^2*b^2*c*d^3*g^3)*B*x + 2*(b^4*c^4*g^3 - 4*a*b^3*c^3*d*g^3 + 6*a^2*b^2*c^2*d^2*g^3 - 3*a^3*b*c*d^3*g^3)*B + 6*((b^4*c^3*d*g^3 - 3*a*b^3*c^2*d^2*g^3 + 3*a^2*b^2*c*d^3*g^3 - a^3*b*d^4*g^3)*B*x + (b^4*c^4*g^3 - 3*a*b^3*c^3*d*g^3 + 3*a^2*b^2*c^2*d^2*g^3 - a^3*b*c*d^3*g^3)*B)*log(d*x + c))*log((b*x + a)^n) - ((b^4*c*d^3*g^3 - a*b^3*d^4*g^3)*B*x^3 - 3*(b^4*c^2*d^2*g^3 - 3*a*b^3*c*d^3*g^3 + 2*a^2*b^2*d^4*g^3)*B*x^2 - 2*(2*b^4*c^3*d*g^3 - 5*a*b^3*c^2*d^2*g^3 + 3*a^2*b^2*c*d^3*g^3)*B*x + 2*(b^4*c^4*g^3 - 4*a*b^3*c^3*d*g^3 + 6*a^2*b^2*c^2*d^2*g^3 - 3*a^3*b*c*d^3*g^3)*B + 6*((b^4*c^3*d*g^3 - 3*a*b^3*c^2*d^2*g^3 + 3*a^2*b^2*c*d^3*g^3 - a^3*b*d^4*g^3)*B*x + (b^4*c^4*g^3 - 3*a*b^3*c^3*d*g^3 + 3*a^2*b^2*c^2*d^2*g^3 - a^3*b*c*d^3*g^3)*B)*log(d*x + c))*log((d*x + c)^n))/(b*c^2*d^4*i^2 - a*c*d^5*i^2 + (b*c*d^5*i^2 - a*d^6*i^2)*x) + 3*(b^3*c^2*g^3*n - 2*a*b^2*c*d*g^3*n + a^2*b*d^2*g^3*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^4*i^2)","B",0
144,1,1273,0,4.919619," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^2,x, algorithm=""maxima"")","B a^{2} g^{2} n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - A b^{2} {\left(\frac{c^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \frac{x}{d^{2} i^{2}} + \frac{2 \, c \log\left(d x + c\right)}{d^{3} i^{2}}\right)} g^{2} + 2 \, A a b g^{2} {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - \frac{B a^{2} g^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{A a^{2} g^{2}}{d^{2} i^{2} x + c d i^{2}} - \frac{{\left(2 \, a^{2} b d^{2} g^{2} \log\left(e\right) + 2 \, {\left(g^{2} n + g^{2} \log\left(e\right)\right)} b^{3} c^{2} - {\left(3 \, g^{2} n + 4 \, g^{2} \log\left(e\right)\right)} a b^{2} c d\right)} B \log\left(d x + c\right)}{b c d^{3} i^{2} - a d^{4} i^{2}} + \frac{{\left(b^{3} c d^{2} g^{2} \log\left(e\right) - a b^{2} d^{3} g^{2} \log\left(e\right)\right)} B x^{2} + {\left(b^{3} c^{2} d g^{2} \log\left(e\right) - a b^{2} c d^{2} g^{2} \log\left(e\right)\right)} B x + 2 \, {\left({\left(b^{3} c^{2} d g^{2} n - 2 \, a b^{2} c d^{2} g^{2} n + a^{2} b d^{3} g^{2} n\right)} B x + {\left(b^{3} c^{3} g^{2} n - 2 \, a b^{2} c^{2} d g^{2} n + a^{2} b c d^{2} g^{2} n\right)} B\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left({\left(b^{3} c^{2} d g^{2} n - 2 \, a b^{2} c d^{2} g^{2} n + a^{2} b d^{3} g^{2} n\right)} B x + {\left(b^{3} c^{3} g^{2} n - 2 \, a b^{2} c^{2} d g^{2} n + a^{2} b c d^{2} g^{2} n\right)} B\right)} \log\left(d x + c\right)^{2} + {\left({\left(g^{2} n - g^{2} \log\left(e\right)\right)} b^{3} c^{3} - 3 \, {\left(g^{2} n - g^{2} \log\left(e\right)\right)} a b^{2} c^{2} d + 2 \, {\left(g^{2} n - g^{2} \log\left(e\right)\right)} a^{2} b c d^{2}\right)} B + {\left({\left(b^{3} c^{2} d g^{2} n - a b^{2} c d^{2} g^{2} n - a^{2} b d^{3} g^{2} n\right)} B x + {\left(b^{3} c^{3} g^{2} n - a b^{2} c^{2} d g^{2} n - a^{2} b c d^{2} g^{2} n\right)} B\right)} \log\left(b x + a\right) + {\left({\left(b^{3} c d^{2} g^{2} - a b^{2} d^{3} g^{2}\right)} B x^{2} + {\left(b^{3} c^{2} d g^{2} - a b^{2} c d^{2} g^{2}\right)} B x - {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 2 \, a^{2} b c d^{2} g^{2}\right)} B - 2 \, {\left({\left(b^{3} c^{2} d g^{2} - 2 \, a b^{2} c d^{2} g^{2} + a^{2} b d^{3} g^{2}\right)} B x + {\left(b^{3} c^{3} g^{2} - 2 \, a b^{2} c^{2} d g^{2} + a^{2} b c d^{2} g^{2}\right)} B\right)} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b^{3} c d^{2} g^{2} - a b^{2} d^{3} g^{2}\right)} B x^{2} + {\left(b^{3} c^{2} d g^{2} - a b^{2} c d^{2} g^{2}\right)} B x - {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 2 \, a^{2} b c d^{2} g^{2}\right)} B - 2 \, {\left({\left(b^{3} c^{2} d g^{2} - 2 \, a b^{2} c d^{2} g^{2} + a^{2} b d^{3} g^{2}\right)} B x + {\left(b^{3} c^{3} g^{2} - 2 \, a b^{2} c^{2} d g^{2} + a^{2} b c d^{2} g^{2}\right)} B\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b c^{2} d^{3} i^{2} - a c d^{4} i^{2} + {\left(b c d^{4} i^{2} - a d^{5} i^{2}\right)} x} - \frac{2 \, {\left(b^{2} c g^{2} n - a b d g^{2} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{3} i^{2}}"," ",0,"B*a^2*g^2*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A*b^2*(c^2/(d^4*i^2*x + c*d^3*i^2) - x/(d^2*i^2) + 2*c*log(d*x + c)/(d^3*i^2))*g^2 + 2*A*a*b*g^2*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - B*a^2*g^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*i^2*x + c*d*i^2) - A*a^2*g^2/(d^2*i^2*x + c*d*i^2) - (2*a^2*b*d^2*g^2*log(e) + 2*(g^2*n + g^2*log(e))*b^3*c^2 - (3*g^2*n + 4*g^2*log(e))*a*b^2*c*d)*B*log(d*x + c)/(b*c*d^3*i^2 - a*d^4*i^2) + ((b^3*c*d^2*g^2*log(e) - a*b^2*d^3*g^2*log(e))*B*x^2 + (b^3*c^2*d*g^2*log(e) - a*b^2*c*d^2*g^2*log(e))*B*x + 2*((b^3*c^2*d*g^2*n - 2*a*b^2*c*d^2*g^2*n + a^2*b*d^3*g^2*n)*B*x + (b^3*c^3*g^2*n - 2*a*b^2*c^2*d*g^2*n + a^2*b*c*d^2*g^2*n)*B)*log(b*x + a)*log(d*x + c) - ((b^3*c^2*d*g^2*n - 2*a*b^2*c*d^2*g^2*n + a^2*b*d^3*g^2*n)*B*x + (b^3*c^3*g^2*n - 2*a*b^2*c^2*d*g^2*n + a^2*b*c*d^2*g^2*n)*B)*log(d*x + c)^2 + ((g^2*n - g^2*log(e))*b^3*c^3 - 3*(g^2*n - g^2*log(e))*a*b^2*c^2*d + 2*(g^2*n - g^2*log(e))*a^2*b*c*d^2)*B + ((b^3*c^2*d*g^2*n - a*b^2*c*d^2*g^2*n - a^2*b*d^3*g^2*n)*B*x + (b^3*c^3*g^2*n - a*b^2*c^2*d*g^2*n - a^2*b*c*d^2*g^2*n)*B)*log(b*x + a) + ((b^3*c*d^2*g^2 - a*b^2*d^3*g^2)*B*x^2 + (b^3*c^2*d*g^2 - a*b^2*c*d^2*g^2)*B*x - (b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 2*a^2*b*c*d^2*g^2)*B - 2*((b^3*c^2*d*g^2 - 2*a*b^2*c*d^2*g^2 + a^2*b*d^3*g^2)*B*x + (b^3*c^3*g^2 - 2*a*b^2*c^2*d*g^2 + a^2*b*c*d^2*g^2)*B)*log(d*x + c))*log((b*x + a)^n) - ((b^3*c*d^2*g^2 - a*b^2*d^3*g^2)*B*x^2 + (b^3*c^2*d*g^2 - a*b^2*c*d^2*g^2)*B*x - (b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 2*a^2*b*c*d^2*g^2)*B - 2*((b^3*c^2*d*g^2 - 2*a*b^2*c*d^2*g^2 + a^2*b*d^3*g^2)*B*x + (b^3*c^3*g^2 - 2*a*b^2*c^2*d*g^2 + a^2*b*c*d^2*g^2)*B)*log(d*x + c))*log((d*x + c)^n))/(b*c^2*d^3*i^2 - a*c*d^4*i^2 + (b*c*d^4*i^2 - a*d^5*i^2)*x) - 2*(b^2*c*g^2*n - a*b*d*g^2*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^3*i^2)","B",0
145,0,0,0,0.000000," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^2,x, algorithm=""maxima"")","B a g n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{1}{2} \, B b g {\left(\frac{2 \, {\left(d n x + c n\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(d n x + c n\right)} \log\left(d x + c\right)^{2} - 2 \, {\left({\left(d x + c\right)} \log\left(d x + c\right) + c\right)} \log\left({\left(b x + a\right)}^{n}\right) + 2 \, {\left({\left(d x + c\right)} \log\left(d x + c\right) + c\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{3} i^{2} x + c d^{2} i^{2}} - 2 \, \int \frac{b d^{2} x^{2} \log\left(e\right) + a d^{2} x \log\left(e\right) - b c^{2} n + a c d n + {\left(b d^{2} n x^{2} + a c d n + {\left(b c d n + a d^{2} n\right)} x\right)} \log\left(b x + a\right)}{b d^{4} i^{2} x^{3} + a c^{2} d^{2} i^{2} + {\left(2 \, b c d^{3} i^{2} + a d^{4} i^{2}\right)} x^{2} + {\left(b c^{2} d^{2} i^{2} + 2 \, a c d^{3} i^{2}\right)} x}\,{d x}\right)} + A b g {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - \frac{B a g \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{A a g}{d^{2} i^{2} x + c d i^{2}}"," ",0,"B*a*g*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - 1/2*B*b*g*((2*(d*n*x + c*n)*log(b*x + a)*log(d*x + c) - (d*n*x + c*n)*log(d*x + c)^2 - 2*((d*x + c)*log(d*x + c) + c)*log((b*x + a)^n) + 2*((d*x + c)*log(d*x + c) + c)*log((d*x + c)^n))/(d^3*i^2*x + c*d^2*i^2) - 2*integrate((b*d^2*x^2*log(e) + a*d^2*x*log(e) - b*c^2*n + a*c*d*n + (b*d^2*n*x^2 + a*c*d*n + (b*c*d*n + a*d^2*n)*x)*log(b*x + a))/(b*d^4*i^2*x^3 + a*c^2*d^2*i^2 + (2*b*c*d^3*i^2 + a*d^4*i^2)*x^2 + (b*c^2*d^2*i^2 + 2*a*c*d^3*i^2)*x), x)) + A*b*g*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - B*a*g*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*i^2*x + c*d*i^2) - A*a*g/(d^2*i^2*x + c*d*i^2)","F",0
146,1,136,0,1.303049," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^2,x, algorithm=""maxima"")","B n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{A}{d^{2} i^{2} x + c d i^{2}}"," ",0,"B*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*i^2*x + c*d*i^2) - A/(d^2*i^2*x + c*d*i^2)","A",0
147,1,424,0,1.425599," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)/(d*i*x+c*i)^2,x, algorithm=""maxima"")","B {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left({\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} + 2 \, b c - 2 \, a d + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 2 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{2 \, {\left(b^{2} c^{3} g i^{2} - 2 \, a b c^{2} d g i^{2} + a^{2} c d^{2} g i^{2} + {\left(b^{2} c^{2} d g i^{2} - 2 \, a b c d^{2} g i^{2} + a^{2} d^{3} g i^{2}\right)} x\right)}} + A {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)}"," ",0,"B*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/2*((b*d*x + b*c)*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 + 2*b*c - 2*a*d + 2*(b*d*x + b*c)*log(b*x + a) - 2*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c))*B*n/(b^2*c^3*g*i^2 - 2*a*b*c^2*d*g*i^2 + a^2*c*d^2*g*i^2 + (b^2*c^2*d*g*i^2 - 2*a*b*c*d^2*g*i^2 + a^2*d^3*g*i^2)*x) + A*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2))","B",0
148,1,862,0,1.475160," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-B {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)^{2}\right)} B n}{a b^{3} c^{4} g^{2} i^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} i^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} i^{2} - a^{4} c d^{3} g^{2} i^{2} + {\left(b^{4} c^{3} d g^{2} i^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} i^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} i^{2} - a^{3} b d^{4} g^{2} i^{2}\right)} x^{2} + {\left(b^{4} c^{4} g^{2} i^{2} - 2 \, a b^{3} c^{3} d g^{2} i^{2} + 2 \, a^{3} b c d^{3} g^{2} i^{2} - a^{4} d^{4} g^{2} i^{2}\right)} x} - A {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)}"," ",0,"-B*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)*log(d*x + c) - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c)^2)*B*n/(a*b^3*c^4*g^2*i^2 - 3*a^2*b^2*c^3*d*g^2*i^2 + 3*a^3*b*c^2*d^2*g^2*i^2 - a^4*c*d^3*g^2*i^2 + (b^4*c^3*d*g^2*i^2 - 3*a*b^3*c^2*d^2*g^2*i^2 + 3*a^2*b^2*c*d^3*g^2*i^2 - a^3*b*d^4*g^2*i^2)*x^2 + (b^4*c^4*g^2*i^2 - 2*a*b^3*c^3*d*g^2*i^2 + 2*a^3*b*c*d^3*g^2*i^2 - a^4*d^4*g^2*i^2)*x) - A*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2))","B",0
149,1,1724,0,2.403243," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3/(d*i*x+c*i)^2,x, algorithm=""maxima"")","\frac{1}{2} \, B {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(b^{3} c^{3} - 12 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{4 \, {\left(a^{2} b^{4} c^{5} g^{3} i^{2} - 4 \, a^{3} b^{3} c^{4} d g^{3} i^{2} + 6 \, a^{4} b^{2} c^{3} d^{2} g^{3} i^{2} - 4 \, a^{5} b c^{2} d^{3} g^{3} i^{2} + a^{6} c d^{4} g^{3} i^{2} + {\left(b^{6} c^{4} d g^{3} i^{2} - 4 \, a b^{5} c^{3} d^{2} g^{3} i^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} g^{3} i^{2} - 4 \, a^{3} b^{3} c d^{4} g^{3} i^{2} + a^{4} b^{2} d^{5} g^{3} i^{2}\right)} x^{3} + {\left(b^{6} c^{5} g^{3} i^{2} - 2 \, a b^{5} c^{4} d g^{3} i^{2} - 2 \, a^{2} b^{4} c^{3} d^{2} g^{3} i^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} g^{3} i^{2} - 7 \, a^{4} b^{2} c d^{4} g^{3} i^{2} + 2 \, a^{5} b d^{5} g^{3} i^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} g^{3} i^{2} - 7 \, a^{2} b^{4} c^{4} d g^{3} i^{2} + 8 \, a^{3} b^{3} c^{3} d^{2} g^{3} i^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} g^{3} i^{2} - 2 \, a^{5} b c d^{4} g^{3} i^{2} + a^{6} d^{5} g^{3} i^{2}\right)} x\right)}} + \frac{1}{2} \, A {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)}"," ",0,"1/2*B*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/4*(b^3*c^3 - 12*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c)^2 - 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c))*B*n/(a^2*b^4*c^5*g^3*i^2 - 4*a^3*b^3*c^4*d*g^3*i^2 + 6*a^4*b^2*c^3*d^2*g^3*i^2 - 4*a^5*b*c^2*d^3*g^3*i^2 + a^6*c*d^4*g^3*i^2 + (b^6*c^4*d*g^3*i^2 - 4*a*b^5*c^3*d^2*g^3*i^2 + 6*a^2*b^4*c^2*d^3*g^3*i^2 - 4*a^3*b^3*c*d^4*g^3*i^2 + a^4*b^2*d^5*g^3*i^2)*x^3 + (b^6*c^5*g^3*i^2 - 2*a*b^5*c^4*d*g^3*i^2 - 2*a^2*b^4*c^3*d^2*g^3*i^2 + 8*a^3*b^3*c^2*d^3*g^3*i^2 - 7*a^4*b^2*c*d^4*g^3*i^2 + 2*a^5*b*d^5*g^3*i^2)*x^2 + (2*a*b^5*c^5*g^3*i^2 - 7*a^2*b^4*c^4*d*g^3*i^2 + 8*a^3*b^3*c^3*d^2*g^3*i^2 - 2*a^4*b^2*c^2*d^3*g^3*i^2 - 2*a^5*b*c*d^4*g^3*i^2 + a^6*d^5*g^3*i^2)*x) + 1/2*A*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2))","B",0
150,1,2563,0,3.460964," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, B {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(b^{4} c^{4} - 9 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} - 55 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4} + 30 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(11 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} - 19 \, a^{2} b^{2} d^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - {\left(5 \, b^{4} c^{3} d - 81 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} + 19 \, a^{3} b d^{4}\right)} x + 30 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{3} b c d^{3} + 5 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 15 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 6 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{9 \, {\left(a^{3} b^{5} c^{6} g^{4} i^{2} - 5 \, a^{4} b^{4} c^{5} d g^{4} i^{2} + 10 \, a^{5} b^{3} c^{4} d^{2} g^{4} i^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{7} b c^{2} d^{4} g^{4} i^{2} - a^{8} c d^{5} g^{4} i^{2} + {\left(b^{8} c^{5} d g^{4} i^{2} - 5 \, a b^{7} c^{4} d^{2} g^{4} i^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} g^{4} i^{2} - 10 \, a^{3} b^{5} c^{2} d^{4} g^{4} i^{2} + 5 \, a^{4} b^{4} c d^{5} g^{4} i^{2} - a^{5} b^{3} d^{6} g^{4} i^{2}\right)} x^{4} + {\left(b^{8} c^{6} g^{4} i^{2} - 2 \, a b^{7} c^{5} d g^{4} i^{2} - 5 \, a^{2} b^{6} c^{4} d^{2} g^{4} i^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} g^{4} i^{2} - 25 \, a^{4} b^{4} c^{2} d^{4} g^{4} i^{2} + 14 \, a^{5} b^{3} c d^{5} g^{4} i^{2} - 3 \, a^{6} b^{2} d^{6} g^{4} i^{2}\right)} x^{3} + 3 \, {\left(a b^{7} c^{6} g^{4} i^{2} - 4 \, a^{2} b^{6} c^{5} d g^{4} i^{2} + 5 \, a^{3} b^{5} c^{4} d^{2} g^{4} i^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} g^{4} i^{2} + 4 \, a^{6} b^{2} c d^{5} g^{4} i^{2} - a^{7} b d^{6} g^{4} i^{2}\right)} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} g^{4} i^{2} - 14 \, a^{3} b^{5} c^{5} d g^{4} i^{2} + 25 \, a^{4} b^{4} c^{4} d^{2} g^{4} i^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{6} b^{2} c^{2} d^{4} g^{4} i^{2} + 2 \, a^{7} b c d^{5} g^{4} i^{2} - a^{8} d^{6} g^{4} i^{2}\right)} x\right)}} - \frac{1}{3} \, A {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)}"," ",0,"-1/3*B*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/9*(b^4*c^4 - 9*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 - 55*a^3*b*c*d^3 + 9*a^4*d^4 + 30*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 3*(11*b^4*c^2*d^2 + 8*a*b^3*c*d^3 - 19*a^2*b^2*d^4)*x^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(d*x + c)^2 - (5*b^4*c^3*d - 81*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 + 19*a^3*b*d^4)*x + 30*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a) - 6*(5*b^4*d^4*x^4 + 5*a^3*b*c*d^3 + 5*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 15*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 5*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 6*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c))*B*n/(a^3*b^5*c^6*g^4*i^2 - 5*a^4*b^4*c^5*d*g^4*i^2 + 10*a^5*b^3*c^4*d^2*g^4*i^2 - 10*a^6*b^2*c^3*d^3*g^4*i^2 + 5*a^7*b*c^2*d^4*g^4*i^2 - a^8*c*d^5*g^4*i^2 + (b^8*c^5*d*g^4*i^2 - 5*a*b^7*c^4*d^2*g^4*i^2 + 10*a^2*b^6*c^3*d^3*g^4*i^2 - 10*a^3*b^5*c^2*d^4*g^4*i^2 + 5*a^4*b^4*c*d^5*g^4*i^2 - a^5*b^3*d^6*g^4*i^2)*x^4 + (b^8*c^6*g^4*i^2 - 2*a*b^7*c^5*d*g^4*i^2 - 5*a^2*b^6*c^4*d^2*g^4*i^2 + 20*a^3*b^5*c^3*d^3*g^4*i^2 - 25*a^4*b^4*c^2*d^4*g^4*i^2 + 14*a^5*b^3*c*d^5*g^4*i^2 - 3*a^6*b^2*d^6*g^4*i^2)*x^3 + 3*(a*b^7*c^6*g^4*i^2 - 4*a^2*b^6*c^5*d*g^4*i^2 + 5*a^3*b^5*c^4*d^2*g^4*i^2 - 5*a^5*b^3*c^2*d^4*g^4*i^2 + 4*a^6*b^2*c*d^5*g^4*i^2 - a^7*b*d^6*g^4*i^2)*x^2 + (3*a^2*b^6*c^6*g^4*i^2 - 14*a^3*b^5*c^5*d*g^4*i^2 + 25*a^4*b^4*c^4*d^2*g^4*i^2 - 20*a^5*b^3*c^3*d^3*g^4*i^2 + 5*a^6*b^2*c^2*d^4*g^4*i^2 + 2*a^7*b*c*d^5*g^4*i^2 - a^8*d^6*g^4*i^2)*x) - 1/3*A*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2))","B",0
151,1,2894,0,5.518036," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{3}{4} \, B a^{2} b g^{3} n {\left(\frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{4} \, B a^{3} g^{3} n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{1}{2} \, A b^{3} g^{3} {\left(\frac{6 \, c^{2} d x + 5 \, c^{3}}{d^{6} i^{3} x^{2} + 2 \, c d^{5} i^{3} x + c^{2} d^{4} i^{3}} - \frac{2 \, x}{d^{3} i^{3}} + \frac{6 \, c \log\left(d x + c\right)}{d^{4} i^{3}}\right)} + \frac{3}{2} \, A a b^{2} g^{3} {\left(\frac{4 \, c d x + 3 \, c^{2}}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} + \frac{2 \, \log\left(d x + c\right)}{d^{3} i^{3}}\right)} - \frac{3 \, {\left(2 \, d x + c\right)} B a^{2} b g^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{3 \, {\left(2 \, d x + c\right)} A a^{2} b g^{3}}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{B a^{3} g^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{A a^{3} g^{3}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} + \frac{{\left(6 \, a^{3} b^{2} d^{3} g^{3} \log\left(e\right) - {\left(7 \, g^{3} n + 6 \, g^{3} \log\left(e\right)\right)} b^{5} c^{3} + {\left(19 \, g^{3} n + 18 \, g^{3} \log\left(e\right)\right)} a b^{4} c^{2} d - 2 \, {\left(7 \, g^{3} n + 9 \, g^{3} \log\left(e\right)\right)} a^{2} b^{3} c d^{2}\right)} B \log\left(d x + c\right)}{2 \, {\left(b^{2} c^{2} d^{4} i^{3} - 2 \, a b c d^{5} i^{3} + a^{2} d^{6} i^{3}\right)}} + \frac{4 \, {\left(b^{5} c^{2} d^{3} g^{3} \log\left(e\right) - 2 \, a b^{4} c d^{4} g^{3} \log\left(e\right) + a^{2} b^{3} d^{5} g^{3} \log\left(e\right)\right)} B x^{3} + 8 \, {\left(b^{5} c^{3} d^{2} g^{3} \log\left(e\right) - 2 \, a b^{4} c^{2} d^{3} g^{3} \log\left(e\right) + a^{2} b^{3} c d^{4} g^{3} \log\left(e\right)\right)} B x^{2} + 2 \, {\left({\left(5 \, g^{3} n - 4 \, g^{3} \log\left(e\right)\right)} b^{5} c^{4} d - 20 \, {\left(g^{3} n - g^{3} \log\left(e\right)\right)} a b^{4} c^{3} d^{2} + {\left(27 \, g^{3} n - 28 \, g^{3} \log\left(e\right)\right)} a^{2} b^{3} c^{2} d^{3} - 12 \, {\left(g^{3} n - g^{3} \log\left(e\right)\right)} a^{3} b^{2} c d^{4}\right)} B x + 12 \, {\left({\left(b^{5} c^{3} d^{2} g^{3} n - 3 \, a b^{4} c^{2} d^{3} g^{3} n + 3 \, a^{2} b^{3} c d^{4} g^{3} n - a^{3} b^{2} d^{5} g^{3} n\right)} B x^{2} + 2 \, {\left(b^{5} c^{4} d g^{3} n - 3 \, a b^{4} c^{3} d^{2} g^{3} n + 3 \, a^{2} b^{3} c^{2} d^{3} g^{3} n - a^{3} b^{2} c d^{4} g^{3} n\right)} B x + {\left(b^{5} c^{5} g^{3} n - 3 \, a b^{4} c^{4} d g^{3} n + 3 \, a^{2} b^{3} c^{3} d^{2} g^{3} n - a^{3} b^{2} c^{2} d^{3} g^{3} n\right)} B\right)} \log\left(b x + a\right) \log\left(d x + c\right) - 6 \, {\left({\left(b^{5} c^{3} d^{2} g^{3} n - 3 \, a b^{4} c^{2} d^{3} g^{3} n + 3 \, a^{2} b^{3} c d^{4} g^{3} n - a^{3} b^{2} d^{5} g^{3} n\right)} B x^{2} + 2 \, {\left(b^{5} c^{4} d g^{3} n - 3 \, a b^{4} c^{3} d^{2} g^{3} n + 3 \, a^{2} b^{3} c^{2} d^{3} g^{3} n - a^{3} b^{2} c d^{4} g^{3} n\right)} B x + {\left(b^{5} c^{5} g^{3} n - 3 \, a b^{4} c^{4} d g^{3} n + 3 \, a^{2} b^{3} c^{3} d^{2} g^{3} n - a^{3} b^{2} c^{2} d^{3} g^{3} n\right)} B\right)} \log\left(d x + c\right)^{2} + {\left({\left(9 \, g^{3} n - 10 \, g^{3} \log\left(e\right)\right)} b^{5} c^{5} - {\left(35 \, g^{3} n - 38 \, g^{3} \log\left(e\right)\right)} a b^{4} c^{4} d + {\left(47 \, g^{3} n - 46 \, g^{3} \log\left(e\right)\right)} a^{2} b^{3} c^{3} d^{2} - 3 \, {\left(7 \, g^{3} n - 6 \, g^{3} \log\left(e\right)\right)} a^{3} b^{2} c^{2} d^{3}\right)} B + 2 \, {\left({\left(5 \, b^{5} c^{3} d^{2} g^{3} n - 13 \, a b^{4} c^{2} d^{3} g^{3} n + 8 \, a^{2} b^{3} c d^{4} g^{3} n + 2 \, a^{3} b^{2} d^{5} g^{3} n\right)} B x^{2} + 2 \, {\left(5 \, b^{5} c^{4} d g^{3} n - 13 \, a b^{4} c^{3} d^{2} g^{3} n + 8 \, a^{2} b^{3} c^{2} d^{3} g^{3} n + 2 \, a^{3} b^{2} c d^{4} g^{3} n\right)} B x + {\left(5 \, b^{5} c^{5} g^{3} n - 13 \, a b^{4} c^{4} d g^{3} n + 8 \, a^{2} b^{3} c^{3} d^{2} g^{3} n + 2 \, a^{3} b^{2} c^{2} d^{3} g^{3} n\right)} B\right)} \log\left(b x + a\right) + 2 \, {\left(2 \, {\left(b^{5} c^{2} d^{3} g^{3} - 2 \, a b^{4} c d^{4} g^{3} + a^{2} b^{3} d^{5} g^{3}\right)} B x^{3} + 4 \, {\left(b^{5} c^{3} d^{2} g^{3} - 2 \, a b^{4} c^{2} d^{3} g^{3} + a^{2} b^{3} c d^{4} g^{3}\right)} B x^{2} - 4 \, {\left(b^{5} c^{4} d g^{3} - 5 \, a b^{4} c^{3} d^{2} g^{3} + 7 \, a^{2} b^{3} c^{2} d^{3} g^{3} - 3 \, a^{3} b^{2} c d^{4} g^{3}\right)} B x - {\left(5 \, b^{5} c^{5} g^{3} - 19 \, a b^{4} c^{4} d g^{3} + 23 \, a^{2} b^{3} c^{3} d^{2} g^{3} - 9 \, a^{3} b^{2} c^{2} d^{3} g^{3}\right)} B - 6 \, {\left({\left(b^{5} c^{3} d^{2} g^{3} - 3 \, a b^{4} c^{2} d^{3} g^{3} + 3 \, a^{2} b^{3} c d^{4} g^{3} - a^{3} b^{2} d^{5} g^{3}\right)} B x^{2} + 2 \, {\left(b^{5} c^{4} d g^{3} - 3 \, a b^{4} c^{3} d^{2} g^{3} + 3 \, a^{2} b^{3} c^{2} d^{3} g^{3} - a^{3} b^{2} c d^{4} g^{3}\right)} B x + {\left(b^{5} c^{5} g^{3} - 3 \, a b^{4} c^{4} d g^{3} + 3 \, a^{2} b^{3} c^{3} d^{2} g^{3} - a^{3} b^{2} c^{2} d^{3} g^{3}\right)} B\right)} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(2 \, {\left(b^{5} c^{2} d^{3} g^{3} - 2 \, a b^{4} c d^{4} g^{3} + a^{2} b^{3} d^{5} g^{3}\right)} B x^{3} + 4 \, {\left(b^{5} c^{3} d^{2} g^{3} - 2 \, a b^{4} c^{2} d^{3} g^{3} + a^{2} b^{3} c d^{4} g^{3}\right)} B x^{2} - 4 \, {\left(b^{5} c^{4} d g^{3} - 5 \, a b^{4} c^{3} d^{2} g^{3} + 7 \, a^{2} b^{3} c^{2} d^{3} g^{3} - 3 \, a^{3} b^{2} c d^{4} g^{3}\right)} B x - {\left(5 \, b^{5} c^{5} g^{3} - 19 \, a b^{4} c^{4} d g^{3} + 23 \, a^{2} b^{3} c^{3} d^{2} g^{3} - 9 \, a^{3} b^{2} c^{2} d^{3} g^{3}\right)} B - 6 \, {\left({\left(b^{5} c^{3} d^{2} g^{3} - 3 \, a b^{4} c^{2} d^{3} g^{3} + 3 \, a^{2} b^{3} c d^{4} g^{3} - a^{3} b^{2} d^{5} g^{3}\right)} B x^{2} + 2 \, {\left(b^{5} c^{4} d g^{3} - 3 \, a b^{4} c^{3} d^{2} g^{3} + 3 \, a^{2} b^{3} c^{2} d^{3} g^{3} - a^{3} b^{2} c d^{4} g^{3}\right)} B x + {\left(b^{5} c^{5} g^{3} - 3 \, a b^{4} c^{4} d g^{3} + 3 \, a^{2} b^{3} c^{3} d^{2} g^{3} - a^{3} b^{2} c^{2} d^{3} g^{3}\right)} B\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{4 \, {\left(b^{2} c^{4} d^{4} i^{3} - 2 \, a b c^{3} d^{5} i^{3} + a^{2} c^{2} d^{6} i^{3} + {\left(b^{2} c^{2} d^{6} i^{3} - 2 \, a b c d^{7} i^{3} + a^{2} d^{8} i^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{5} i^{3} - 2 \, a b c^{2} d^{6} i^{3} + a^{2} c d^{7} i^{3}\right)} x\right)}} - \frac{3 \, {\left(b^{3} c g^{3} n - a b^{2} d g^{3} n\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B}{d^{4} i^{3}}"," ",0,"3/4*B*a^2*b*g^3*n*((b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) + 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) - 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/4*B*a^3*g^3*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*A*b^3*g^3*((6*c^2*d*x + 5*c^3)/(d^6*i^3*x^2 + 2*c*d^5*i^3*x + c^2*d^4*i^3) - 2*x/(d^3*i^3) + 6*c*log(d*x + c)/(d^4*i^3)) + 3/2*A*a*b^2*g^3*((4*c*d*x + 3*c^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) + 2*log(d*x + c)/(d^3*i^3)) - 3/2*(2*d*x + c)*B*a^2*b*g^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 3/2*(2*d*x + c)*A*a^2*b*g^3/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*B*a^3*g^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A*a^3*g^3/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 1/2*(6*a^3*b^2*d^3*g^3*log(e) - (7*g^3*n + 6*g^3*log(e))*b^5*c^3 + (19*g^3*n + 18*g^3*log(e))*a*b^4*c^2*d - 2*(7*g^3*n + 9*g^3*log(e))*a^2*b^3*c*d^2)*B*log(d*x + c)/(b^2*c^2*d^4*i^3 - 2*a*b*c*d^5*i^3 + a^2*d^6*i^3) + 1/4*(4*(b^5*c^2*d^3*g^3*log(e) - 2*a*b^4*c*d^4*g^3*log(e) + a^2*b^3*d^5*g^3*log(e))*B*x^3 + 8*(b^5*c^3*d^2*g^3*log(e) - 2*a*b^4*c^2*d^3*g^3*log(e) + a^2*b^3*c*d^4*g^3*log(e))*B*x^2 + 2*((5*g^3*n - 4*g^3*log(e))*b^5*c^4*d - 20*(g^3*n - g^3*log(e))*a*b^4*c^3*d^2 + (27*g^3*n - 28*g^3*log(e))*a^2*b^3*c^2*d^3 - 12*(g^3*n - g^3*log(e))*a^3*b^2*c*d^4)*B*x + 12*((b^5*c^3*d^2*g^3*n - 3*a*b^4*c^2*d^3*g^3*n + 3*a^2*b^3*c*d^4*g^3*n - a^3*b^2*d^5*g^3*n)*B*x^2 + 2*(b^5*c^4*d*g^3*n - 3*a*b^4*c^3*d^2*g^3*n + 3*a^2*b^3*c^2*d^3*g^3*n - a^3*b^2*c*d^4*g^3*n)*B*x + (b^5*c^5*g^3*n - 3*a*b^4*c^4*d*g^3*n + 3*a^2*b^3*c^3*d^2*g^3*n - a^3*b^2*c^2*d^3*g^3*n)*B)*log(b*x + a)*log(d*x + c) - 6*((b^5*c^3*d^2*g^3*n - 3*a*b^4*c^2*d^3*g^3*n + 3*a^2*b^3*c*d^4*g^3*n - a^3*b^2*d^5*g^3*n)*B*x^2 + 2*(b^5*c^4*d*g^3*n - 3*a*b^4*c^3*d^2*g^3*n + 3*a^2*b^3*c^2*d^3*g^3*n - a^3*b^2*c*d^4*g^3*n)*B*x + (b^5*c^5*g^3*n - 3*a*b^4*c^4*d*g^3*n + 3*a^2*b^3*c^3*d^2*g^3*n - a^3*b^2*c^2*d^3*g^3*n)*B)*log(d*x + c)^2 + ((9*g^3*n - 10*g^3*log(e))*b^5*c^5 - (35*g^3*n - 38*g^3*log(e))*a*b^4*c^4*d + (47*g^3*n - 46*g^3*log(e))*a^2*b^3*c^3*d^2 - 3*(7*g^3*n - 6*g^3*log(e))*a^3*b^2*c^2*d^3)*B + 2*((5*b^5*c^3*d^2*g^3*n - 13*a*b^4*c^2*d^3*g^3*n + 8*a^2*b^3*c*d^4*g^3*n + 2*a^3*b^2*d^5*g^3*n)*B*x^2 + 2*(5*b^5*c^4*d*g^3*n - 13*a*b^4*c^3*d^2*g^3*n + 8*a^2*b^3*c^2*d^3*g^3*n + 2*a^3*b^2*c*d^4*g^3*n)*B*x + (5*b^5*c^5*g^3*n - 13*a*b^4*c^4*d*g^3*n + 8*a^2*b^3*c^3*d^2*g^3*n + 2*a^3*b^2*c^2*d^3*g^3*n)*B)*log(b*x + a) + 2*(2*(b^5*c^2*d^3*g^3 - 2*a*b^4*c*d^4*g^3 + a^2*b^3*d^5*g^3)*B*x^3 + 4*(b^5*c^3*d^2*g^3 - 2*a*b^4*c^2*d^3*g^3 + a^2*b^3*c*d^4*g^3)*B*x^2 - 4*(b^5*c^4*d*g^3 - 5*a*b^4*c^3*d^2*g^3 + 7*a^2*b^3*c^2*d^3*g^3 - 3*a^3*b^2*c*d^4*g^3)*B*x - (5*b^5*c^5*g^3 - 19*a*b^4*c^4*d*g^3 + 23*a^2*b^3*c^3*d^2*g^3 - 9*a^3*b^2*c^2*d^3*g^3)*B - 6*((b^5*c^3*d^2*g^3 - 3*a*b^4*c^2*d^3*g^3 + 3*a^2*b^3*c*d^4*g^3 - a^3*b^2*d^5*g^3)*B*x^2 + 2*(b^5*c^4*d*g^3 - 3*a*b^4*c^3*d^2*g^3 + 3*a^2*b^3*c^2*d^3*g^3 - a^3*b^2*c*d^4*g^3)*B*x + (b^5*c^5*g^3 - 3*a*b^4*c^4*d*g^3 + 3*a^2*b^3*c^3*d^2*g^3 - a^3*b^2*c^2*d^3*g^3)*B)*log(d*x + c))*log((b*x + a)^n) - 2*(2*(b^5*c^2*d^3*g^3 - 2*a*b^4*c*d^4*g^3 + a^2*b^3*d^5*g^3)*B*x^3 + 4*(b^5*c^3*d^2*g^3 - 2*a*b^4*c^2*d^3*g^3 + a^2*b^3*c*d^4*g^3)*B*x^2 - 4*(b^5*c^4*d*g^3 - 5*a*b^4*c^3*d^2*g^3 + 7*a^2*b^3*c^2*d^3*g^3 - 3*a^3*b^2*c*d^4*g^3)*B*x - (5*b^5*c^5*g^3 - 19*a*b^4*c^4*d*g^3 + 23*a^2*b^3*c^3*d^2*g^3 - 9*a^3*b^2*c^2*d^3*g^3)*B - 6*((b^5*c^3*d^2*g^3 - 3*a*b^4*c^2*d^3*g^3 + 3*a^2*b^3*c*d^4*g^3 - a^3*b^2*d^5*g^3)*B*x^2 + 2*(b^5*c^4*d*g^3 - 3*a*b^4*c^3*d^2*g^3 + 3*a^2*b^3*c^2*d^3*g^3 - a^3*b^2*c*d^4*g^3)*B*x + (b^5*c^5*g^3 - 3*a*b^4*c^4*d*g^3 + 3*a^2*b^3*c^3*d^2*g^3 - a^3*b^2*c^2*d^3*g^3)*B)*log(d*x + c))*log((d*x + c)^n))/(b^2*c^4*d^4*i^3 - 2*a*b*c^3*d^5*i^3 + a^2*c^2*d^6*i^3 + (b^2*c^2*d^6*i^3 - 2*a*b*c*d^7*i^3 + a^2*d^8*i^3)*x^2 + 2*(b^2*c^3*d^5*i^3 - 2*a*b*c^2*d^6*i^3 + a^2*c*d^7*i^3)*x) - 3*(b^3*c*g^3*n - a*b^2*d*g^3*n)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B/(d^4*i^3)","B",0
152,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B a b g^{2} n {\left(\frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{4} \, B a^{2} g^{2} n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} + \frac{1}{2} \, A b^{2} g^{2} {\left(\frac{4 \, c d x + 3 \, c^{2}}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} + \frac{2 \, \log\left(d x + c\right)}{d^{3} i^{3}}\right)} - \frac{1}{2} \, B b^{2} g^{2} {\left(\frac{2 \, {\left(d^{2} n x^{2} + 2 \, c d n x + c^{2} n\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(d^{2} n x^{2} + 2 \, c d n x + c^{2} n\right)} \log\left(d x + c\right)^{2} - {\left(4 \, c d x + 3 \, c^{2} + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + {\left(4 \, c d x + 3 \, c^{2} + 2 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} - 2 \, \int \frac{2 \, b d^{3} x^{3} \log\left(e\right) + 2 \, a d^{3} x^{2} \log\left(e\right) - 3 \, b c^{3} n + 3 \, a c^{2} d n - 4 \, {\left(b c^{2} d n - a c d^{2} n\right)} x + 2 \, {\left(b d^{3} n x^{3} + a c^{2} d n + {\left(2 \, b c d^{2} n + a d^{3} n\right)} x^{2} + {\left(b c^{2} d n + 2 \, a c d^{2} n\right)} x\right)} \log\left(b x + a\right)}{2 \, {\left(b d^{6} i^{3} x^{4} + a c^{3} d^{3} i^{3} + {\left(3 \, b c d^{5} i^{3} + a d^{6} i^{3}\right)} x^{3} + 3 \, {\left(b c^{2} d^{4} i^{3} + a c d^{5} i^{3}\right)} x^{2} + {\left(b c^{3} d^{3} i^{3} + 3 \, a c^{2} d^{4} i^{3}\right)} x\right)}}\,{d x}\right)} - \frac{{\left(2 \, d x + c\right)} B a b g^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{{\left(2 \, d x + c\right)} A a b g^{2}}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{B a^{2} g^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{A a^{2} g^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"1/2*B*a*b*g^2*n*((b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) + 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) - 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/4*B*a^2*g^2*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) + 1/2*A*b^2*g^2*((4*c*d*x + 3*c^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) + 2*log(d*x + c)/(d^3*i^3)) - 1/2*B*b^2*g^2*((2*(d^2*n*x^2 + 2*c*d*n*x + c^2*n)*log(b*x + a)*log(d*x + c) - (d^2*n*x^2 + 2*c*d*n*x + c^2*n)*log(d*x + c)^2 - (4*c*d*x + 3*c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*log(d*x + c))*log((b*x + a)^n) + (4*c*d*x + 3*c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*log(d*x + c))*log((d*x + c)^n))/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) - 2*integrate(1/2*(2*b*d^3*x^3*log(e) + 2*a*d^3*x^2*log(e) - 3*b*c^3*n + 3*a*c^2*d*n - 4*(b*c^2*d*n - a*c*d^2*n)*x + 2*(b*d^3*n*x^3 + a*c^2*d*n + (2*b*c*d^2*n + a*d^3*n)*x^2 + (b*c^2*d*n + 2*a*c*d^2*n)*x)*log(b*x + a))/(b*d^6*i^3*x^4 + a*c^3*d^3*i^3 + (3*b*c*d^5*i^3 + a*d^6*i^3)*x^3 + 3*(b*c^2*d^4*i^3 + a*c*d^5*i^3)*x^2 + (b*c^3*d^3*i^3 + 3*a*c^2*d^4*i^3)*x), x)) - (2*d*x + c)*B*a*b*g^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - (2*d*x + c)*A*a*b*g^2/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*B*a^2*g^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A*a^2*g^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","F",0
153,1,578,0,1.530027," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{4} \, B b g n {\left(\frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{4} \, B a g n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{{\left(2 \, d x + c\right)} B b g \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{{\left(2 \, d x + c\right)} A b g}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{B a g \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{A a g}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"1/4*B*b*g*n*((b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) + 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) - 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/4*B*a*g*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*(2*d*x + c)*B*b*g*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*(2*d*x + c)*A*b*g/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*B*a*g*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A*a*g/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","B",0
154,1,259,0,1.457302," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{4} \, B n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{A}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"1/4*B*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","A",0
155,1,888,0,1.981343," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{4 \, {\left(b^{3} c^{5} g i^{3} - 3 \, a b^{2} c^{4} d g i^{3} + 3 \, a^{2} b c^{3} d^{2} g i^{3} - a^{3} c^{2} d^{3} g i^{3} + {\left(b^{3} c^{3} d^{2} g i^{3} - 3 \, a b^{2} c^{2} d^{3} g i^{3} + 3 \, a^{2} b c d^{4} g i^{3} - a^{3} d^{5} g i^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d g i^{3} - 3 \, a b^{2} c^{3} d^{2} g i^{3} + 3 \, a^{2} b c^{2} d^{3} g i^{3} - a^{3} c d^{4} g i^{3}\right)} x\right)}} + \frac{1}{2} \, A {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)}"," ",0,"1/2*B*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/4*(7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*B*n/(b^3*c^5*g*i^3 - 3*a*b^2*c^4*d*g*i^3 + 3*a^2*b*c^3*d^2*g*i^3 - a^3*c^2*d^3*g*i^3 + (b^3*c^3*d^2*g*i^3 - 3*a*b^2*c^2*d^3*g*i^3 + 3*a^2*b*c*d^4*g*i^3 - a^3*d^5*g*i^3)*x^2 + 2*(b^3*c^4*d*g*i^3 - 3*a*b^2*c^3*d^2*g*i^3 + 3*a^2*b*c^2*d^3*g*i^3 - a^3*c*d^4*g*i^3)*x) + 1/2*A*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3))","B",0
156,1,1724,0,2.764054," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(4 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} - a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{4 \, {\left(a b^{4} c^{6} g^{2} i^{3} - 4 \, a^{2} b^{3} c^{5} d g^{2} i^{3} + 6 \, a^{3} b^{2} c^{4} d^{2} g^{2} i^{3} - 4 \, a^{4} b c^{3} d^{3} g^{2} i^{3} + a^{5} c^{2} d^{4} g^{2} i^{3} + {\left(b^{5} c^{4} d^{2} g^{2} i^{3} - 4 \, a b^{4} c^{3} d^{3} g^{2} i^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} g^{2} i^{3} - 4 \, a^{3} b^{2} c d^{5} g^{2} i^{3} + a^{4} b d^{6} g^{2} i^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d g^{2} i^{3} - 7 \, a b^{4} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{2} b^{3} c^{3} d^{3} g^{2} i^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} g^{2} i^{3} - 2 \, a^{4} b c d^{5} g^{2} i^{3} + a^{5} d^{6} g^{2} i^{3}\right)} x^{2} + {\left(b^{5} c^{6} g^{2} i^{3} - 2 \, a b^{4} c^{5} d g^{2} i^{3} - 2 \, a^{2} b^{3} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 7 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 2 \, a^{5} c d^{5} g^{2} i^{3}\right)} x\right)}} - \frac{1}{2} \, A {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)}"," ",0,"-1/2*B*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/4*(4*b^3*c^3 - 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 - a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c)^2 - 3*(b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c))*B*n/(a*b^4*c^6*g^2*i^3 - 4*a^2*b^3*c^5*d*g^2*i^3 + 6*a^3*b^2*c^4*d^2*g^2*i^3 - 4*a^4*b*c^3*d^3*g^2*i^3 + a^5*c^2*d^4*g^2*i^3 + (b^5*c^4*d^2*g^2*i^3 - 4*a*b^4*c^3*d^3*g^2*i^3 + 6*a^2*b^3*c^2*d^4*g^2*i^3 - 4*a^3*b^2*c*d^5*g^2*i^3 + a^4*b*d^6*g^2*i^3)*x^3 + (2*b^5*c^5*d*g^2*i^3 - 7*a*b^4*c^4*d^2*g^2*i^3 + 8*a^2*b^3*c^3*d^3*g^2*i^3 - 2*a^3*b^2*c^2*d^4*g^2*i^3 - 2*a^4*b*c*d^5*g^2*i^3 + a^5*d^6*g^2*i^3)*x^2 + (b^5*c^6*g^2*i^3 - 2*a*b^4*c^5*d*g^2*i^3 - 2*a^2*b^3*c^4*d^2*g^2*i^3 + 8*a^3*b^2*c^3*d^3*g^2*i^3 - 7*a^4*b*c^2*d^4*g^2*i^3 + 2*a^5*c*d^5*g^2*i^3)*x) - 1/2*A*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3))","B",0
157,1,2383,0,2.516487," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} - 16 \, a^{3} b c d^{3} + a^{4} d^{4} - 12 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} - 24 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 12 \, {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} B n}{4 \, {\left(a^{2} b^{5} c^{7} g^{3} i^{3} - 5 \, a^{3} b^{4} c^{6} d g^{3} i^{3} + 10 \, a^{4} b^{3} c^{5} d^{2} g^{3} i^{3} - 10 \, a^{5} b^{2} c^{4} d^{3} g^{3} i^{3} + 5 \, a^{6} b c^{3} d^{4} g^{3} i^{3} - a^{7} c^{2} d^{5} g^{3} i^{3} + {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 5 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} - 10 \, a^{3} b^{4} c^{2} d^{5} g^{3} i^{3} + 5 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d g^{3} i^{3} - 4 \, a b^{6} c^{5} d^{2} g^{3} i^{3} + 5 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} + 4 \, a^{5} b^{2} c d^{6} g^{3} i^{3} - a^{6} b d^{7} g^{3} i^{3}\right)} x^{3} + {\left(b^{7} c^{7} g^{3} i^{3} - a b^{6} c^{6} d g^{3} i^{3} - 9 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 25 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} + 9 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} g^{3} i^{3} - 4 \, a^{2} b^{5} c^{6} d g^{3} i^{3} + 5 \, a^{3} b^{4} c^{5} d^{2} g^{3} i^{3} - 5 \, a^{5} b^{2} c^{3} d^{4} g^{3} i^{3} + 4 \, a^{6} b c^{2} d^{5} g^{3} i^{3} - a^{7} c d^{6} g^{3} i^{3}\right)} x\right)}} + \frac{1}{2} \, A {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)}"," ",0,"1/2*B*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/4*(b^4*c^4 - 16*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 - 16*a^3*b*c*d^3 + a^4*d^4 - 12*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^2 - 24*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)*log(d*x + c) + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c)^2 - 12*(b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x)*B*n/(a^2*b^5*c^7*g^3*i^3 - 5*a^3*b^4*c^6*d*g^3*i^3 + 10*a^4*b^3*c^5*d^2*g^3*i^3 - 10*a^5*b^2*c^4*d^3*g^3*i^3 + 5*a^6*b*c^3*d^4*g^3*i^3 - a^7*c^2*d^5*g^3*i^3 + (b^7*c^5*d^2*g^3*i^3 - 5*a*b^6*c^4*d^3*g^3*i^3 + 10*a^2*b^5*c^3*d^4*g^3*i^3 - 10*a^3*b^4*c^2*d^5*g^3*i^3 + 5*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3)*x^4 + 2*(b^7*c^6*d*g^3*i^3 - 4*a*b^6*c^5*d^2*g^3*i^3 + 5*a^2*b^5*c^4*d^3*g^3*i^3 - 5*a^4*b^3*c^2*d^5*g^3*i^3 + 4*a^5*b^2*c*d^6*g^3*i^3 - a^6*b*d^7*g^3*i^3)*x^3 + (b^7*c^7*g^3*i^3 - a*b^6*c^6*d*g^3*i^3 - 9*a^2*b^5*c^5*d^2*g^3*i^3 + 25*a^3*b^4*c^4*d^3*g^3*i^3 - 25*a^4*b^3*c^3*d^4*g^3*i^3 + 9*a^5*b^2*c^2*d^5*g^3*i^3 + a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*x^2 + 2*(a*b^6*c^7*g^3*i^3 - 4*a^2*b^5*c^6*d*g^3*i^3 + 5*a^3*b^4*c^5*d^2*g^3*i^3 - 5*a^5*b^2*c^3*d^4*g^3*i^3 + 4*a^6*b*c^2*d^5*g^3*i^3 - a^7*c*d^6*g^3*i^3)*x) + 1/2*A*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3))","B",0
158,1,3819,0,4.954335," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{6} \, B {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(4 \, b^{5} c^{5} - 45 \, a b^{4} c^{4} d + 360 \, a^{2} b^{3} c^{3} d^{2} - 490 \, a^{3} b^{2} c^{2} d^{3} + 180 \, a^{4} b c d^{4} - 9 \, a^{5} d^{5} + 120 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 120 \, {\left(3 \, b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} - a^{2} b^{3} d^{5}\right)} x^{3} + 20 \, {\left(11 \, b^{5} c^{3} d^{2} + 21 \, a b^{4} c^{2} d^{3} - 39 \, a^{2} b^{3} c d^{4} + 7 \, a^{3} b^{2} d^{5}\right)} x^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(5 \, b^{5} c^{4} d - 108 \, a b^{4} c^{3} d^{2} + 78 \, a^{2} b^{3} c^{2} d^{3} + 52 \, a^{3} b^{2} c d^{4} - 27 \, a^{4} b d^{5}\right)} x + 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 3 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} B n}{36 \, {\left(a^{3} b^{6} c^{8} g^{4} i^{3} - 6 \, a^{4} b^{5} c^{7} d g^{4} i^{3} + 15 \, a^{5} b^{4} c^{6} d^{2} g^{4} i^{3} - 20 \, a^{6} b^{3} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} g^{4} i^{3} - 6 \, a^{8} b c^{3} d^{5} g^{4} i^{3} + a^{9} c^{2} d^{6} g^{4} i^{3} + {\left(b^{9} c^{6} d^{2} g^{4} i^{3} - 6 \, a b^{8} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} g^{4} i^{3} - 20 \, a^{3} b^{6} c^{3} d^{5} g^{4} i^{3} + 15 \, a^{4} b^{5} c^{2} d^{6} g^{4} i^{3} - 6 \, a^{5} b^{4} c d^{7} g^{4} i^{3} + a^{6} b^{3} d^{8} g^{4} i^{3}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d g^{4} i^{3} - 9 \, a b^{8} c^{6} d^{2} g^{4} i^{3} + 12 \, a^{2} b^{7} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} g^{4} i^{3} - 30 \, a^{4} b^{5} c^{3} d^{5} g^{4} i^{3} + 33 \, a^{5} b^{4} c^{2} d^{6} g^{4} i^{3} - 16 \, a^{6} b^{3} c d^{7} g^{4} i^{3} + 3 \, a^{7} b^{2} d^{8} g^{4} i^{3}\right)} x^{4} + {\left(b^{9} c^{8} g^{4} i^{3} - 18 \, a^{2} b^{7} c^{6} d^{2} g^{4} i^{3} + 52 \, a^{3} b^{6} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} g^{4} i^{3} + 24 \, a^{5} b^{4} c^{3} d^{5} g^{4} i^{3} + 10 \, a^{6} b^{3} c^{2} d^{6} g^{4} i^{3} - 12 \, a^{7} b^{2} c d^{7} g^{4} i^{3} + 3 \, a^{8} b d^{8} g^{4} i^{3}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} g^{4} i^{3} - 12 \, a^{2} b^{7} c^{7} d g^{4} i^{3} + 10 \, a^{3} b^{6} c^{6} d^{2} g^{4} i^{3} + 24 \, a^{4} b^{5} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} g^{4} i^{3} + 52 \, a^{6} b^{3} c^{3} d^{5} g^{4} i^{3} - 18 \, a^{7} b^{2} c^{2} d^{6} g^{4} i^{3} + a^{9} d^{8} g^{4} i^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} g^{4} i^{3} - 16 \, a^{3} b^{6} c^{7} d g^{4} i^{3} + 33 \, a^{4} b^{5} c^{6} d^{2} g^{4} i^{3} - 30 \, a^{5} b^{4} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} g^{4} i^{3} + 12 \, a^{7} b^{2} c^{3} d^{5} g^{4} i^{3} - 9 \, a^{8} b c^{2} d^{6} g^{4} i^{3} + 2 \, a^{9} c d^{7} g^{4} i^{3}\right)} x\right)}} - \frac{1}{6} \, A {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)}"," ",0,"-1/6*B*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/36*(4*b^5*c^5 - 45*a*b^4*c^4*d + 360*a^2*b^3*c^3*d^2 - 490*a^3*b^2*c^2*d^3 + 180*a^4*b*c*d^4 - 9*a^5*d^5 + 120*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 120*(3*b^5*c^2*d^3 - 2*a*b^4*c*d^4 - a^2*b^3*d^5)*x^3 + 20*(11*b^5*c^3*d^2 + 21*a*b^4*c^2*d^3 - 39*a^2*b^3*c*d^4 + 7*a^3*b^2*d^5)*x^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c)^2 - 5*(5*b^5*c^4*d - 108*a*b^4*c^3*d^2 + 78*a^2*b^3*c^2*d^3 + 52*a^3*b^2*c*d^4 - 27*a^4*b*d^5)*x + 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 3*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c))*B*n/(a^3*b^6*c^8*g^4*i^3 - 6*a^4*b^5*c^7*d*g^4*i^3 + 15*a^5*b^4*c^6*d^2*g^4*i^3 - 20*a^6*b^3*c^5*d^3*g^4*i^3 + 15*a^7*b^2*c^4*d^4*g^4*i^3 - 6*a^8*b*c^3*d^5*g^4*i^3 + a^9*c^2*d^6*g^4*i^3 + (b^9*c^6*d^2*g^4*i^3 - 6*a*b^8*c^5*d^3*g^4*i^3 + 15*a^2*b^7*c^4*d^4*g^4*i^3 - 20*a^3*b^6*c^3*d^5*g^4*i^3 + 15*a^4*b^5*c^2*d^6*g^4*i^3 - 6*a^5*b^4*c*d^7*g^4*i^3 + a^6*b^3*d^8*g^4*i^3)*x^5 + (2*b^9*c^7*d*g^4*i^3 - 9*a*b^8*c^6*d^2*g^4*i^3 + 12*a^2*b^7*c^5*d^3*g^4*i^3 + 5*a^3*b^6*c^4*d^4*g^4*i^3 - 30*a^4*b^5*c^3*d^5*g^4*i^3 + 33*a^5*b^4*c^2*d^6*g^4*i^3 - 16*a^6*b^3*c*d^7*g^4*i^3 + 3*a^7*b^2*d^8*g^4*i^3)*x^4 + (b^9*c^8*g^4*i^3 - 18*a^2*b^7*c^6*d^2*g^4*i^3 + 52*a^3*b^6*c^5*d^3*g^4*i^3 - 60*a^4*b^5*c^4*d^4*g^4*i^3 + 24*a^5*b^4*c^3*d^5*g^4*i^3 + 10*a^6*b^3*c^2*d^6*g^4*i^3 - 12*a^7*b^2*c*d^7*g^4*i^3 + 3*a^8*b*d^8*g^4*i^3)*x^3 + (3*a*b^8*c^8*g^4*i^3 - 12*a^2*b^7*c^7*d*g^4*i^3 + 10*a^3*b^6*c^6*d^2*g^4*i^3 + 24*a^4*b^5*c^5*d^3*g^4*i^3 - 60*a^5*b^4*c^4*d^4*g^4*i^3 + 52*a^6*b^3*c^3*d^5*g^4*i^3 - 18*a^7*b^2*c^2*d^6*g^4*i^3 + a^9*d^8*g^4*i^3)*x^2 + (3*a^2*b^7*c^8*g^4*i^3 - 16*a^3*b^6*c^7*d*g^4*i^3 + 33*a^4*b^5*c^6*d^2*g^4*i^3 - 30*a^5*b^4*c^5*d^3*g^4*i^3 + 5*a^6*b^3*c^4*d^4*g^4*i^3 + 12*a^7*b^2*c^3*d^5*g^4*i^3 - 9*a^8*b*c^2*d^6*g^4*i^3 + 2*a^9*c*d^7*g^4*i^3)*x) - 1/6*A*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3))","B",0
159,1,3764,0,7.666901," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{5} \, A B b^{3} d g^{3} i x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{5} \, A^{2} b^{3} d g^{3} i x^{5} + \frac{1}{2} \, A B b^{3} c g^{3} i x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A B a b^{2} d g^{3} i x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A^{2} b^{3} c g^{3} i x^{4} + \frac{3}{4} \, A^{2} a b^{2} d g^{3} i x^{4} + 2 \, A B a b^{2} c g^{3} i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A B a^{2} b d g^{3} i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a b^{2} c g^{3} i x^{3} + A^{2} a^{2} b d g^{3} i x^{3} + 3 \, A B a^{2} b c g^{3} i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A B a^{3} d g^{3} i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A^{2} a^{2} b c g^{3} i x^{2} + \frac{1}{2} \, A^{2} a^{3} d g^{3} i x^{2} + \frac{1}{30} \, A B b^{3} d g^{3} i n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{12} \, A B b^{3} c g^{3} i n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{4} \, A B a b^{2} d g^{3} i n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + A B a b^{2} c g^{3} i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + A B a^{2} b d g^{3} i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - 3 \, A B a^{2} b c g^{3} i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - A B a^{3} d g^{3} i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a^{3} c g^{3} i n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a^{3} c g^{3} i x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{3} c g^{3} i x - \frac{{\left(6 \, a^{4} c d^{4} g^{3} i n^{2} - {\left(5 \, g^{3} i n^{2} + 6 \, g^{3} i n \log\left(e\right)\right)} b^{4} c^{5} + {\left(19 \, g^{3} i n^{2} + 30 \, g^{3} i n \log\left(e\right)\right)} a b^{3} c^{4} d - {\left(23 \, g^{3} i n^{2} + 60 \, g^{3} i n \log\left(e\right)\right)} a^{2} b^{2} c^{3} d^{2} + 3 \, {\left(g^{3} i n^{2} + 20 \, g^{3} i n \log\left(e\right)\right)} a^{3} b c^{2} d^{3}\right)} B^{2} \log\left(d x + c\right)}{60 \, b d^{4}} + \frac{{\left(b^{5} c^{5} g^{3} i n^{2} - 5 \, a b^{4} c^{4} d g^{3} i n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{3} i n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{3} i n^{2} + 5 \, a^{4} b c d^{4} g^{3} i n^{2} - a^{5} d^{5} g^{3} i n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{10 \, b^{2} d^{4}} + \frac{12 \, B^{2} b^{5} d^{5} g^{3} i x^{5} \log\left(e\right)^{2} - 3 \, {\left({\left(2 \, g^{3} i n \log\left(e\right) - 5 \, g^{3} i \log\left(e\right)^{2}\right)} b^{5} c d^{4} - {\left(2 \, g^{3} i n \log\left(e\right) + 15 \, g^{3} i \log\left(e\right)^{2}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left({\left(g^{3} i n^{2} - g^{3} i n \log\left(e\right)\right)} b^{5} c^{2} d^{3} - 2 \, {\left(g^{3} i n^{2} + 5 \, g^{3} i n \log\left(e\right) - 15 \, g^{3} i \log\left(e\right)^{2}\right)} a b^{4} c d^{4} + {\left(g^{3} i n^{2} + 11 \, g^{3} i n \log\left(e\right) + 30 \, g^{3} i \log\left(e\right)^{2}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left({\left(2 \, g^{3} i n^{2} - 3 \, g^{3} i n \log\left(e\right)\right)} b^{5} c^{3} d^{2} - 3 \, {\left(4 \, g^{3} i n^{2} - 5 \, g^{3} i n \log\left(e\right)\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(6 \, g^{3} i n^{2} + 5 \, g^{3} i n \log\left(e\right) - 30 \, g^{3} i \log\left(e\right)^{2}\right)} a^{2} b^{3} c d^{4} - {\left(8 \, g^{3} i n^{2} + 27 \, g^{3} i n \log\left(e\right) + 30 \, g^{3} i \log\left(e\right)^{2}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 3 \, {\left(5 \, a^{4} b c d^{4} g^{3} i n^{2} - a^{5} d^{5} g^{3} i n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{5} c^{5} g^{3} i n^{2} - 5 \, a b^{4} c^{4} d g^{3} i n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{3} i n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{3} i n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) + 3 \, {\left(b^{5} c^{5} g^{3} i n^{2} - 5 \, a b^{4} c^{4} d g^{3} i n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{3} i n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{3} i n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + {\left({\left(g^{3} i n^{2} - 6 \, g^{3} i n \log\left(e\right)\right)} b^{5} c^{4} d - 2 \, {\left(4 \, g^{3} i n^{2} - 15 \, g^{3} i n \log\left(e\right)\right)} a b^{4} c^{3} d^{2} + 12 \, {\left(2 \, g^{3} i n^{2} - 5 \, g^{3} i n \log\left(e\right)\right)} a^{2} b^{3} c^{2} d^{3} - 2 \, {\left(14 \, g^{3} i n^{2} - 15 \, g^{3} i n \log\left(e\right) - 30 \, g^{3} i \log\left(e\right)^{2}\right)} a^{3} b^{2} c d^{4} + {\left(11 \, g^{3} i n^{2} + 6 \, g^{3} i n \log\left(e\right)\right)} a^{4} b d^{5}\right)} B^{2} x - {\left(6 \, a b^{4} c^{4} d g^{3} i n^{2} - 27 \, a^{2} b^{3} c^{3} d^{2} g^{3} i n^{2} + 47 \, a^{3} b^{2} c^{2} d^{3} g^{3} i n^{2} - {\left(31 \, g^{3} i n^{2} + 30 \, g^{3} i n \log\left(e\right)\right)} a^{4} b c d^{4} + {\left(5 \, g^{3} i n^{2} + 6 \, g^{3} i n \log\left(e\right)\right)} a^{5} d^{5}\right)} B^{2} \log\left(b x + a\right) + 3 \, {\left(4 \, B^{2} b^{5} d^{5} g^{3} i x^{5} + 20 \, B^{2} a^{3} b^{2} c d^{4} g^{3} i x + 5 \, {\left(b^{5} c d^{4} g^{3} i + 3 \, a b^{4} d^{5} g^{3} i\right)} B^{2} x^{4} + 20 \, {\left(a b^{4} c d^{4} g^{3} i + a^{2} b^{3} d^{5} g^{3} i\right)} B^{2} x^{3} + 10 \, {\left(3 \, a^{2} b^{3} c d^{4} g^{3} i + a^{3} b^{2} d^{5} g^{3} i\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(4 \, B^{2} b^{5} d^{5} g^{3} i x^{5} + 20 \, B^{2} a^{3} b^{2} c d^{4} g^{3} i x + 5 \, {\left(b^{5} c d^{4} g^{3} i + 3 \, a b^{4} d^{5} g^{3} i\right)} B^{2} x^{4} + 20 \, {\left(a b^{4} c d^{4} g^{3} i + a^{2} b^{3} d^{5} g^{3} i\right)} B^{2} x^{3} + 10 \, {\left(3 \, a^{2} b^{3} c d^{4} g^{3} i + a^{3} b^{2} d^{5} g^{3} i\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(24 \, B^{2} b^{5} d^{5} g^{3} i x^{5} \log\left(e\right) - 6 \, {\left({\left(g^{3} i n - 5 \, g^{3} i \log\left(e\right)\right)} b^{5} c d^{4} - {\left(g^{3} i n + 15 \, g^{3} i \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 2 \, {\left(b^{5} c^{2} d^{3} g^{3} i n + 10 \, {\left(g^{3} i n - 6 \, g^{3} i \log\left(e\right)\right)} a b^{4} c d^{4} - {\left(11 \, g^{3} i n + 60 \, g^{3} i \log\left(e\right)\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + 3 \, {\left(b^{5} c^{3} d^{2} g^{3} i n - 5 \, a b^{4} c^{2} d^{3} g^{3} i n - 5 \, {\left(g^{3} i n - 12 \, g^{3} i \log\left(e\right)\right)} a^{2} b^{3} c d^{4} + {\left(9 \, g^{3} i n + 20 \, g^{3} i \log\left(e\right)\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{5} c^{4} d g^{3} i n - 5 \, a b^{4} c^{3} d^{2} g^{3} i n + 10 \, a^{2} b^{3} c^{2} d^{3} g^{3} i n - a^{4} b d^{5} g^{3} i n - 5 \, {\left(g^{3} i n + 4 \, g^{3} i \log\left(e\right)\right)} a^{3} b^{2} c d^{4}\right)} B^{2} x + 6 \, {\left(5 \, a^{4} b c d^{4} g^{3} i n - a^{5} d^{5} g^{3} i n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(b^{5} c^{5} g^{3} i n - 5 \, a b^{4} c^{4} d g^{3} i n + 10 \, a^{2} b^{3} c^{3} d^{2} g^{3} i n - 10 \, a^{3} b^{2} c^{2} d^{3} g^{3} i n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(24 \, B^{2} b^{5} d^{5} g^{3} i x^{5} \log\left(e\right) - 6 \, {\left({\left(g^{3} i n - 5 \, g^{3} i \log\left(e\right)\right)} b^{5} c d^{4} - {\left(g^{3} i n + 15 \, g^{3} i \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 2 \, {\left(b^{5} c^{2} d^{3} g^{3} i n + 10 \, {\left(g^{3} i n - 6 \, g^{3} i \log\left(e\right)\right)} a b^{4} c d^{4} - {\left(11 \, g^{3} i n + 60 \, g^{3} i \log\left(e\right)\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + 3 \, {\left(b^{5} c^{3} d^{2} g^{3} i n - 5 \, a b^{4} c^{2} d^{3} g^{3} i n - 5 \, {\left(g^{3} i n - 12 \, g^{3} i \log\left(e\right)\right)} a^{2} b^{3} c d^{4} + {\left(9 \, g^{3} i n + 20 \, g^{3} i \log\left(e\right)\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{5} c^{4} d g^{3} i n - 5 \, a b^{4} c^{3} d^{2} g^{3} i n + 10 \, a^{2} b^{3} c^{2} d^{3} g^{3} i n - a^{4} b d^{5} g^{3} i n - 5 \, {\left(g^{3} i n + 4 \, g^{3} i \log\left(e\right)\right)} a^{3} b^{2} c d^{4}\right)} B^{2} x + 6 \, {\left(5 \, a^{4} b c d^{4} g^{3} i n - a^{5} d^{5} g^{3} i n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(b^{5} c^{5} g^{3} i n - 5 \, a b^{4} c^{4} d g^{3} i n + 10 \, a^{2} b^{3} c^{3} d^{2} g^{3} i n - 10 \, a^{3} b^{2} c^{2} d^{3} g^{3} i n\right)} B^{2} \log\left(d x + c\right) + 6 \, {\left(4 \, B^{2} b^{5} d^{5} g^{3} i x^{5} + 20 \, B^{2} a^{3} b^{2} c d^{4} g^{3} i x + 5 \, {\left(b^{5} c d^{4} g^{3} i + 3 \, a b^{4} d^{5} g^{3} i\right)} B^{2} x^{4} + 20 \, {\left(a b^{4} c d^{4} g^{3} i + a^{2} b^{3} d^{5} g^{3} i\right)} B^{2} x^{3} + 10 \, {\left(3 \, a^{2} b^{3} c d^{4} g^{3} i + a^{3} b^{2} d^{5} g^{3} i\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{60 \, b^{2} d^{4}}"," ",0,"2/5*A*B*b^3*d*g^3*i*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A^2*b^3*d*g^3*i*x^5 + 1/2*A*B*b^3*c*g^3*i*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*B*a*b^2*d*g^3*i*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*b^3*c*g^3*i*x^4 + 3/4*A^2*a*b^2*d*g^3*i*x^4 + 2*A*B*a*b^2*c*g^3*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*B*a^2*b*d*g^3*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b^2*c*g^3*i*x^3 + A^2*a^2*b*d*g^3*i*x^3 + 3*A*B*a^2*b*c*g^3*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*B*a^3*d*g^3*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A^2*a^2*b*c*g^3*i*x^2 + 1/2*A^2*a^3*d*g^3*i*x^2 + 1/30*A*B*b^3*d*g^3*i*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/12*A*B*b^3*c*g^3*i*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/4*A*B*a*b^2*d*g^3*i*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + A*B*a*b^2*c*g^3*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + A*B*a^2*b*d*g^3*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 3*A*B*a^2*b*c*g^3*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - A*B*a^3*d*g^3*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a^3*c*g^3*i*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^3*c*g^3*i*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^3*c*g^3*i*x - 1/60*(6*a^4*c*d^4*g^3*i*n^2 - (5*g^3*i*n^2 + 6*g^3*i*n*log(e))*b^4*c^5 + (19*g^3*i*n^2 + 30*g^3*i*n*log(e))*a*b^3*c^4*d - (23*g^3*i*n^2 + 60*g^3*i*n*log(e))*a^2*b^2*c^3*d^2 + 3*(g^3*i*n^2 + 20*g^3*i*n*log(e))*a^3*b*c^2*d^3)*B^2*log(d*x + c)/(b*d^4) + 1/10*(b^5*c^5*g^3*i*n^2 - 5*a*b^4*c^4*d*g^3*i*n^2 + 10*a^2*b^3*c^3*d^2*g^3*i*n^2 - 10*a^3*b^2*c^2*d^3*g^3*i*n^2 + 5*a^4*b*c*d^4*g^3*i*n^2 - a^5*d^5*g^3*i*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^2*d^4) + 1/60*(12*B^2*b^5*d^5*g^3*i*x^5*log(e)^2 - 3*((2*g^3*i*n*log(e) - 5*g^3*i*log(e)^2)*b^5*c*d^4 - (2*g^3*i*n*log(e) + 15*g^3*i*log(e)^2)*a*b^4*d^5)*B^2*x^4 + 2*((g^3*i*n^2 - g^3*i*n*log(e))*b^5*c^2*d^3 - 2*(g^3*i*n^2 + 5*g^3*i*n*log(e) - 15*g^3*i*log(e)^2)*a*b^4*c*d^4 + (g^3*i*n^2 + 11*g^3*i*n*log(e) + 30*g^3*i*log(e)^2)*a^2*b^3*d^5)*B^2*x^3 - ((2*g^3*i*n^2 - 3*g^3*i*n*log(e))*b^5*c^3*d^2 - 3*(4*g^3*i*n^2 - 5*g^3*i*n*log(e))*a*b^4*c^2*d^3 + 3*(6*g^3*i*n^2 + 5*g^3*i*n*log(e) - 30*g^3*i*log(e)^2)*a^2*b^3*c*d^4 - (8*g^3*i*n^2 + 27*g^3*i*n*log(e) + 30*g^3*i*log(e)^2)*a^3*b^2*d^5)*B^2*x^2 - 3*(5*a^4*b*c*d^4*g^3*i*n^2 - a^5*d^5*g^3*i*n^2)*B^2*log(b*x + a)^2 - 6*(b^5*c^5*g^3*i*n^2 - 5*a*b^4*c^4*d*g^3*i*n^2 + 10*a^2*b^3*c^3*d^2*g^3*i*n^2 - 10*a^3*b^2*c^2*d^3*g^3*i*n^2)*B^2*log(b*x + a)*log(d*x + c) + 3*(b^5*c^5*g^3*i*n^2 - 5*a*b^4*c^4*d*g^3*i*n^2 + 10*a^2*b^3*c^3*d^2*g^3*i*n^2 - 10*a^3*b^2*c^2*d^3*g^3*i*n^2)*B^2*log(d*x + c)^2 + ((g^3*i*n^2 - 6*g^3*i*n*log(e))*b^5*c^4*d - 2*(4*g^3*i*n^2 - 15*g^3*i*n*log(e))*a*b^4*c^3*d^2 + 12*(2*g^3*i*n^2 - 5*g^3*i*n*log(e))*a^2*b^3*c^2*d^3 - 2*(14*g^3*i*n^2 - 15*g^3*i*n*log(e) - 30*g^3*i*log(e)^2)*a^3*b^2*c*d^4 + (11*g^3*i*n^2 + 6*g^3*i*n*log(e))*a^4*b*d^5)*B^2*x - (6*a*b^4*c^4*d*g^3*i*n^2 - 27*a^2*b^3*c^3*d^2*g^3*i*n^2 + 47*a^3*b^2*c^2*d^3*g^3*i*n^2 - (31*g^3*i*n^2 + 30*g^3*i*n*log(e))*a^4*b*c*d^4 + (5*g^3*i*n^2 + 6*g^3*i*n*log(e))*a^5*d^5)*B^2*log(b*x + a) + 3*(4*B^2*b^5*d^5*g^3*i*x^5 + 20*B^2*a^3*b^2*c*d^4*g^3*i*x + 5*(b^5*c*d^4*g^3*i + 3*a*b^4*d^5*g^3*i)*B^2*x^4 + 20*(a*b^4*c*d^4*g^3*i + a^2*b^3*d^5*g^3*i)*B^2*x^3 + 10*(3*a^2*b^3*c*d^4*g^3*i + a^3*b^2*d^5*g^3*i)*B^2*x^2)*log((b*x + a)^n)^2 + 3*(4*B^2*b^5*d^5*g^3*i*x^5 + 20*B^2*a^3*b^2*c*d^4*g^3*i*x + 5*(b^5*c*d^4*g^3*i + 3*a*b^4*d^5*g^3*i)*B^2*x^4 + 20*(a*b^4*c*d^4*g^3*i + a^2*b^3*d^5*g^3*i)*B^2*x^3 + 10*(3*a^2*b^3*c*d^4*g^3*i + a^3*b^2*d^5*g^3*i)*B^2*x^2)*log((d*x + c)^n)^2 + (24*B^2*b^5*d^5*g^3*i*x^5*log(e) - 6*((g^3*i*n - 5*g^3*i*log(e))*b^5*c*d^4 - (g^3*i*n + 15*g^3*i*log(e))*a*b^4*d^5)*B^2*x^4 - 2*(b^5*c^2*d^3*g^3*i*n + 10*(g^3*i*n - 6*g^3*i*log(e))*a*b^4*c*d^4 - (11*g^3*i*n + 60*g^3*i*log(e))*a^2*b^3*d^5)*B^2*x^3 + 3*(b^5*c^3*d^2*g^3*i*n - 5*a*b^4*c^2*d^3*g^3*i*n - 5*(g^3*i*n - 12*g^3*i*log(e))*a^2*b^3*c*d^4 + (9*g^3*i*n + 20*g^3*i*log(e))*a^3*b^2*d^5)*B^2*x^2 - 6*(b^5*c^4*d*g^3*i*n - 5*a*b^4*c^3*d^2*g^3*i*n + 10*a^2*b^3*c^2*d^3*g^3*i*n - a^4*b*d^5*g^3*i*n - 5*(g^3*i*n + 4*g^3*i*log(e))*a^3*b^2*c*d^4)*B^2*x + 6*(5*a^4*b*c*d^4*g^3*i*n - a^5*d^5*g^3*i*n)*B^2*log(b*x + a) + 6*(b^5*c^5*g^3*i*n - 5*a*b^4*c^4*d*g^3*i*n + 10*a^2*b^3*c^3*d^2*g^3*i*n - 10*a^3*b^2*c^2*d^3*g^3*i*n)*B^2*log(d*x + c))*log((b*x + a)^n) - (24*B^2*b^5*d^5*g^3*i*x^5*log(e) - 6*((g^3*i*n - 5*g^3*i*log(e))*b^5*c*d^4 - (g^3*i*n + 15*g^3*i*log(e))*a*b^4*d^5)*B^2*x^4 - 2*(b^5*c^2*d^3*g^3*i*n + 10*(g^3*i*n - 6*g^3*i*log(e))*a*b^4*c*d^4 - (11*g^3*i*n + 60*g^3*i*log(e))*a^2*b^3*d^5)*B^2*x^3 + 3*(b^5*c^3*d^2*g^3*i*n - 5*a*b^4*c^2*d^3*g^3*i*n - 5*(g^3*i*n - 12*g^3*i*log(e))*a^2*b^3*c*d^4 + (9*g^3*i*n + 20*g^3*i*log(e))*a^3*b^2*d^5)*B^2*x^2 - 6*(b^5*c^4*d*g^3*i*n - 5*a*b^4*c^3*d^2*g^3*i*n + 10*a^2*b^3*c^2*d^3*g^3*i*n - a^4*b*d^5*g^3*i*n - 5*(g^3*i*n + 4*g^3*i*log(e))*a^3*b^2*c*d^4)*B^2*x + 6*(5*a^4*b*c*d^4*g^3*i*n - a^5*d^5*g^3*i*n)*B^2*log(b*x + a) + 6*(b^5*c^5*g^3*i*n - 5*a*b^4*c^4*d*g^3*i*n + 10*a^2*b^3*c^3*d^2*g^3*i*n - 10*a^3*b^2*c^2*d^3*g^3*i*n)*B^2*log(d*x + c) + 6*(4*B^2*b^5*d^5*g^3*i*x^5 + 20*B^2*a^3*b^2*c*d^4*g^3*i*x + 5*(b^5*c*d^4*g^3*i + 3*a*b^4*d^5*g^3*i)*B^2*x^4 + 20*(a*b^4*c*d^4*g^3*i + a^2*b^3*d^5*g^3*i)*B^2*x^3 + 10*(3*a^2*b^3*c*d^4*g^3*i + a^3*b^2*d^5*g^3*i)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d^4)","B",0
160,1,2691,0,6.916083," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A B b^{2} d g^{2} i x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A^{2} b^{2} d g^{2} i x^{4} + \frac{2}{3} \, A B b^{2} c g^{2} i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{4}{3} \, A B a b d g^{2} i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A^{2} b^{2} c g^{2} i x^{3} + \frac{2}{3} \, A^{2} a b d g^{2} i x^{3} + 2 \, A B a b c g^{2} i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A B a^{2} d g^{2} i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a b c g^{2} i x^{2} + \frac{1}{2} \, A^{2} a^{2} d g^{2} i x^{2} - \frac{1}{12} \, A B b^{2} d g^{2} i n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{3} \, A B b^{2} c g^{2} i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{2}{3} \, A B a b d g^{2} i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - 2 \, A B a b c g^{2} i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - A B a^{2} d g^{2} i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a^{2} c g^{2} i n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a^{2} c g^{2} i x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{2} c g^{2} i x - \frac{{\left(2 \, a^{3} c d^{3} g^{2} i n^{2} + {\left(g^{2} i n^{2} + 2 \, g^{2} i n \log\left(e\right)\right)} b^{3} c^{4} - 2 \, {\left(g^{2} i n^{2} + 4 \, g^{2} i n \log\left(e\right)\right)} a b^{2} c^{3} d - {\left(g^{2} i n^{2} - 12 \, g^{2} i n \log\left(e\right)\right)} a^{2} b c^{2} d^{2}\right)} B^{2} \log\left(d x + c\right)}{12 \, b d^{3}} - \frac{{\left(b^{4} c^{4} g^{2} i n^{2} - 4 \, a b^{3} c^{3} d g^{2} i n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{2} i n^{2} - 4 \, a^{3} b c d^{3} g^{2} i n^{2} + a^{4} d^{4} g^{2} i n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{6 \, b^{2} d^{3}} + \frac{3 \, B^{2} b^{4} d^{4} g^{2} i x^{4} \log\left(e\right)^{2} - 2 \, {\left({\left(g^{2} i n \log\left(e\right) - 2 \, g^{2} i \log\left(e\right)^{2}\right)} b^{4} c d^{3} - {\left(g^{2} i n \log\left(e\right) + 4 \, g^{2} i \log\left(e\right)^{2}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left({\left(g^{2} i n^{2} - g^{2} i n \log\left(e\right)\right)} b^{4} c^{2} d^{2} - 2 \, {\left(g^{2} i n^{2} + 2 \, g^{2} i n \log\left(e\right) - 6 \, g^{2} i \log\left(e\right)^{2}\right)} a b^{3} c d^{3} + {\left(g^{2} i n^{2} + 5 \, g^{2} i n \log\left(e\right) + 6 \, g^{2} i \log\left(e\right)^{2}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - {\left(4 \, a^{3} b c d^{3} g^{2} i n^{2} - a^{4} d^{4} g^{2} i n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{4} c^{4} g^{2} i n^{2} - 4 \, a b^{3} c^{3} d g^{2} i n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{2} i n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{4} c^{4} g^{2} i n^{2} - 4 \, a b^{3} c^{3} d g^{2} i n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{2} i n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} - {\left({\left(g^{2} i n^{2} - 2 \, g^{2} i n \log\left(e\right)\right)} b^{4} c^{3} d - {\left(5 \, g^{2} i n^{2} - 8 \, g^{2} i n \log\left(e\right)\right)} a b^{3} c^{2} d^{2} + {\left(7 \, g^{2} i n^{2} - 4 \, g^{2} i n \log\left(e\right) - 12 \, g^{2} i \log\left(e\right)^{2}\right)} a^{2} b^{2} c d^{3} - {\left(3 \, g^{2} i n^{2} + 2 \, g^{2} i n \log\left(e\right)\right)} a^{3} b d^{4}\right)} B^{2} x + {\left(2 \, a b^{3} c^{3} d g^{2} i n^{2} - 7 \, a^{2} b^{2} c^{2} d^{2} g^{2} i n^{2} + 2 \, {\left(3 \, g^{2} i n^{2} + 4 \, g^{2} i n \log\left(e\right)\right)} a^{3} b c d^{3} - {\left(g^{2} i n^{2} + 2 \, g^{2} i n \log\left(e\right)\right)} a^{4} d^{4}\right)} B^{2} \log\left(b x + a\right) + {\left(3 \, B^{2} b^{4} d^{4} g^{2} i x^{4} + 12 \, B^{2} a^{2} b^{2} c d^{3} g^{2} i x + 4 \, {\left(b^{4} c d^{3} g^{2} i + 2 \, a b^{3} d^{4} g^{2} i\right)} B^{2} x^{3} + 6 \, {\left(2 \, a b^{3} c d^{3} g^{2} i + a^{2} b^{2} d^{4} g^{2} i\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(3 \, B^{2} b^{4} d^{4} g^{2} i x^{4} + 12 \, B^{2} a^{2} b^{2} c d^{3} g^{2} i x + 4 \, {\left(b^{4} c d^{3} g^{2} i + 2 \, a b^{3} d^{4} g^{2} i\right)} B^{2} x^{3} + 6 \, {\left(2 \, a b^{3} c d^{3} g^{2} i + a^{2} b^{2} d^{4} g^{2} i\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g^{2} i x^{4} \log\left(e\right) - 2 \, {\left({\left(g^{2} i n - 4 \, g^{2} i \log\left(e\right)\right)} b^{4} c d^{3} - {\left(g^{2} i n + 8 \, g^{2} i \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - {\left(b^{4} c^{2} d^{2} g^{2} i n + 4 \, {\left(g^{2} i n - 6 \, g^{2} i \log\left(e\right)\right)} a b^{3} c d^{3} - {\left(5 \, g^{2} i n + 12 \, g^{2} i \log\left(e\right)\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 2 \, {\left(b^{4} c^{3} d g^{2} i n - 4 \, a b^{3} c^{2} d^{2} g^{2} i n + a^{3} b d^{4} g^{2} i n + 2 \, {\left(g^{2} i n + 6 \, g^{2} i \log\left(e\right)\right)} a^{2} b^{2} c d^{3}\right)} B^{2} x + 2 \, {\left(4 \, a^{3} b c d^{3} g^{2} i n - a^{4} d^{4} g^{2} i n\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b^{4} c^{4} g^{2} i n - 4 \, a b^{3} c^{3} d g^{2} i n + 6 \, a^{2} b^{2} c^{2} d^{2} g^{2} i n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(6 \, B^{2} b^{4} d^{4} g^{2} i x^{4} \log\left(e\right) - 2 \, {\left({\left(g^{2} i n - 4 \, g^{2} i \log\left(e\right)\right)} b^{4} c d^{3} - {\left(g^{2} i n + 8 \, g^{2} i \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - {\left(b^{4} c^{2} d^{2} g^{2} i n + 4 \, {\left(g^{2} i n - 6 \, g^{2} i \log\left(e\right)\right)} a b^{3} c d^{3} - {\left(5 \, g^{2} i n + 12 \, g^{2} i \log\left(e\right)\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 2 \, {\left(b^{4} c^{3} d g^{2} i n - 4 \, a b^{3} c^{2} d^{2} g^{2} i n + a^{3} b d^{4} g^{2} i n + 2 \, {\left(g^{2} i n + 6 \, g^{2} i \log\left(e\right)\right)} a^{2} b^{2} c d^{3}\right)} B^{2} x + 2 \, {\left(4 \, a^{3} b c d^{3} g^{2} i n - a^{4} d^{4} g^{2} i n\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b^{4} c^{4} g^{2} i n - 4 \, a b^{3} c^{3} d g^{2} i n + 6 \, a^{2} b^{2} c^{2} d^{2} g^{2} i n\right)} B^{2} \log\left(d x + c\right) + 2 \, {\left(3 \, B^{2} b^{4} d^{4} g^{2} i x^{4} + 12 \, B^{2} a^{2} b^{2} c d^{3} g^{2} i x + 4 \, {\left(b^{4} c d^{3} g^{2} i + 2 \, a b^{3} d^{4} g^{2} i\right)} B^{2} x^{3} + 6 \, {\left(2 \, a b^{3} c d^{3} g^{2} i + a^{2} b^{2} d^{4} g^{2} i\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{12 \, b^{2} d^{3}}"," ",0,"1/2*A*B*b^2*d*g^2*i*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*b^2*d*g^2*i*x^4 + 2/3*A*B*b^2*c*g^2*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 4/3*A*B*a*b*d*g^2*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A^2*b^2*c*g^2*i*x^3 + 2/3*A^2*a*b*d*g^2*i*x^3 + 2*A*B*a*b*c*g^2*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*B*a^2*d*g^2*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b*c*g^2*i*x^2 + 1/2*A^2*a^2*d*g^2*i*x^2 - 1/12*A*B*b^2*d*g^2*i*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/3*A*B*b^2*c*g^2*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 2/3*A*B*a*b*d*g^2*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 2*A*B*a*b*c*g^2*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - A*B*a^2*d*g^2*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a^2*c*g^2*i*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^2*c*g^2*i*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^2*c*g^2*i*x - 1/12*(2*a^3*c*d^3*g^2*i*n^2 + (g^2*i*n^2 + 2*g^2*i*n*log(e))*b^3*c^4 - 2*(g^2*i*n^2 + 4*g^2*i*n*log(e))*a*b^2*c^3*d - (g^2*i*n^2 - 12*g^2*i*n*log(e))*a^2*b*c^2*d^2)*B^2*log(d*x + c)/(b*d^3) - 1/6*(b^4*c^4*g^2*i*n^2 - 4*a*b^3*c^3*d*g^2*i*n^2 + 6*a^2*b^2*c^2*d^2*g^2*i*n^2 - 4*a^3*b*c*d^3*g^2*i*n^2 + a^4*d^4*g^2*i*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^2*d^3) + 1/12*(3*B^2*b^4*d^4*g^2*i*x^4*log(e)^2 - 2*((g^2*i*n*log(e) - 2*g^2*i*log(e)^2)*b^4*c*d^3 - (g^2*i*n*log(e) + 4*g^2*i*log(e)^2)*a*b^3*d^4)*B^2*x^3 + ((g^2*i*n^2 - g^2*i*n*log(e))*b^4*c^2*d^2 - 2*(g^2*i*n^2 + 2*g^2*i*n*log(e) - 6*g^2*i*log(e)^2)*a*b^3*c*d^3 + (g^2*i*n^2 + 5*g^2*i*n*log(e) + 6*g^2*i*log(e)^2)*a^2*b^2*d^4)*B^2*x^2 - (4*a^3*b*c*d^3*g^2*i*n^2 - a^4*d^4*g^2*i*n^2)*B^2*log(b*x + a)^2 + 2*(b^4*c^4*g^2*i*n^2 - 4*a*b^3*c^3*d*g^2*i*n^2 + 6*a^2*b^2*c^2*d^2*g^2*i*n^2)*B^2*log(b*x + a)*log(d*x + c) - (b^4*c^4*g^2*i*n^2 - 4*a*b^3*c^3*d*g^2*i*n^2 + 6*a^2*b^2*c^2*d^2*g^2*i*n^2)*B^2*log(d*x + c)^2 - ((g^2*i*n^2 - 2*g^2*i*n*log(e))*b^4*c^3*d - (5*g^2*i*n^2 - 8*g^2*i*n*log(e))*a*b^3*c^2*d^2 + (7*g^2*i*n^2 - 4*g^2*i*n*log(e) - 12*g^2*i*log(e)^2)*a^2*b^2*c*d^3 - (3*g^2*i*n^2 + 2*g^2*i*n*log(e))*a^3*b*d^4)*B^2*x + (2*a*b^3*c^3*d*g^2*i*n^2 - 7*a^2*b^2*c^2*d^2*g^2*i*n^2 + 2*(3*g^2*i*n^2 + 4*g^2*i*n*log(e))*a^3*b*c*d^3 - (g^2*i*n^2 + 2*g^2*i*n*log(e))*a^4*d^4)*B^2*log(b*x + a) + (3*B^2*b^4*d^4*g^2*i*x^4 + 12*B^2*a^2*b^2*c*d^3*g^2*i*x + 4*(b^4*c*d^3*g^2*i + 2*a*b^3*d^4*g^2*i)*B^2*x^3 + 6*(2*a*b^3*c*d^3*g^2*i + a^2*b^2*d^4*g^2*i)*B^2*x^2)*log((b*x + a)^n)^2 + (3*B^2*b^4*d^4*g^2*i*x^4 + 12*B^2*a^2*b^2*c*d^3*g^2*i*x + 4*(b^4*c*d^3*g^2*i + 2*a*b^3*d^4*g^2*i)*B^2*x^3 + 6*(2*a*b^3*c*d^3*g^2*i + a^2*b^2*d^4*g^2*i)*B^2*x^2)*log((d*x + c)^n)^2 + (6*B^2*b^4*d^4*g^2*i*x^4*log(e) - 2*((g^2*i*n - 4*g^2*i*log(e))*b^4*c*d^3 - (g^2*i*n + 8*g^2*i*log(e))*a*b^3*d^4)*B^2*x^3 - (b^4*c^2*d^2*g^2*i*n + 4*(g^2*i*n - 6*g^2*i*log(e))*a*b^3*c*d^3 - (5*g^2*i*n + 12*g^2*i*log(e))*a^2*b^2*d^4)*B^2*x^2 + 2*(b^4*c^3*d*g^2*i*n - 4*a*b^3*c^2*d^2*g^2*i*n + a^3*b*d^4*g^2*i*n + 2*(g^2*i*n + 6*g^2*i*log(e))*a^2*b^2*c*d^3)*B^2*x + 2*(4*a^3*b*c*d^3*g^2*i*n - a^4*d^4*g^2*i*n)*B^2*log(b*x + a) - 2*(b^4*c^4*g^2*i*n - 4*a*b^3*c^3*d*g^2*i*n + 6*a^2*b^2*c^2*d^2*g^2*i*n)*B^2*log(d*x + c))*log((b*x + a)^n) - (6*B^2*b^4*d^4*g^2*i*x^4*log(e) - 2*((g^2*i*n - 4*g^2*i*log(e))*b^4*c*d^3 - (g^2*i*n + 8*g^2*i*log(e))*a*b^3*d^4)*B^2*x^3 - (b^4*c^2*d^2*g^2*i*n + 4*(g^2*i*n - 6*g^2*i*log(e))*a*b^3*c*d^3 - (5*g^2*i*n + 12*g^2*i*log(e))*a^2*b^2*d^4)*B^2*x^2 + 2*(b^4*c^3*d*g^2*i*n - 4*a*b^3*c^2*d^2*g^2*i*n + a^3*b*d^4*g^2*i*n + 2*(g^2*i*n + 6*g^2*i*log(e))*a^2*b^2*c*d^3)*B^2*x + 2*(4*a^3*b*c*d^3*g^2*i*n - a^4*d^4*g^2*i*n)*B^2*log(b*x + a) - 2*(b^4*c^4*g^2*i*n - 4*a*b^3*c^3*d*g^2*i*n + 6*a^2*b^2*c^2*d^2*g^2*i*n)*B^2*log(d*x + c) + 2*(3*B^2*b^4*d^4*g^2*i*x^4 + 12*B^2*a^2*b^2*c*d^3*g^2*i*x + 4*(b^4*c*d^3*g^2*i + 2*a*b^3*d^4*g^2*i)*B^2*x^3 + 6*(2*a*b^3*c*d^3*g^2*i + a^2*b^2*d^4*g^2*i)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d^3)","B",0
161,1,1542,0,6.924427," ","integrate((b*g*x+a*g)*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{3} \, A B b d g i x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A^{2} b d g i x^{3} + A B b c g i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A B a d g i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A^{2} b c g i x^{2} + \frac{1}{2} \, A^{2} a d g i x^{2} + \frac{1}{3} \, A B b d g i n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - A B b c g i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - A B a d g i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a c g i n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a c g i x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a c g i x - \frac{{\left(a^{2} c d^{2} g i n^{2} - b^{2} c^{3} g i n \log\left(e\right) - {\left(g i n^{2} - 3 \, g i n \log\left(e\right)\right)} a b c^{2} d\right)} B^{2} \log\left(d x + c\right)}{3 \, b d^{2}} + \frac{{\left(b^{3} c^{3} g i n^{2} - 3 \, a b^{2} c^{2} d g i n^{2} + 3 \, a^{2} b c d^{2} g i n^{2} - a^{3} d^{3} g i n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{3 \, b^{2} d^{2}} + \frac{2 \, B^{2} b^{3} d^{3} g i x^{3} \log\left(e\right)^{2} - {\left({\left(2 \, g i n \log\left(e\right) - 3 \, g i \log\left(e\right)^{2}\right)} b^{3} c d^{2} - {\left(2 \, g i n \log\left(e\right) + 3 \, g i \log\left(e\right)^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - {\left(3 \, a^{2} b c d^{2} g i n^{2} - a^{3} d^{3} g i n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} - 2 \, {\left(b^{3} c^{3} g i n^{2} - 3 \, a b^{2} c^{2} d g i n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) + {\left(b^{3} c^{3} g i n^{2} - 3 \, a b^{2} c^{2} d g i n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + 2 \, {\left({\left(g i n^{2} - g i n \log\left(e\right)\right)} b^{3} c^{2} d - {\left(2 \, g i n^{2} - 3 \, g i \log\left(e\right)^{2}\right)} a b^{2} c d^{2} + {\left(g i n^{2} + g i n \log\left(e\right)\right)} a^{2} b d^{3}\right)} B^{2} x - 2 \, {\left(a b^{2} c^{2} d g i n^{2} + a^{3} d^{3} g i n \log\left(e\right) - {\left(g i n^{2} + 3 \, g i n \log\left(e\right)\right)} a^{2} b c d^{2}\right)} B^{2} \log\left(b x + a\right) + {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} + 6 \, B^{2} a b^{2} c d^{2} g i x + 3 \, {\left(b^{3} c d^{2} g i + a b^{2} d^{3} g i\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} + 6 \, B^{2} a b^{2} c d^{2} g i x + 3 \, {\left(b^{3} c d^{2} g i + a b^{2} d^{3} g i\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} \log\left(e\right) - {\left({\left(g i n - 3 \, g i \log\left(e\right)\right)} b^{3} c d^{2} - {\left(g i n + 3 \, g i \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - {\left(b^{3} c^{2} d g i n - a^{2} b d^{3} g i n - 6 \, a b^{2} c d^{2} g i \log\left(e\right)\right)} B^{2} x + {\left(3 \, a^{2} b c d^{2} g i n - a^{3} d^{3} g i n\right)} B^{2} \log\left(b x + a\right) + {\left(b^{3} c^{3} g i n - 3 \, a b^{2} c^{2} d g i n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} \log\left(e\right) - {\left({\left(g i n - 3 \, g i \log\left(e\right)\right)} b^{3} c d^{2} - {\left(g i n + 3 \, g i \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - {\left(b^{3} c^{2} d g i n - a^{2} b d^{3} g i n - 6 \, a b^{2} c d^{2} g i \log\left(e\right)\right)} B^{2} x + {\left(3 \, a^{2} b c d^{2} g i n - a^{3} d^{3} g i n\right)} B^{2} \log\left(b x + a\right) + {\left(b^{3} c^{3} g i n - 3 \, a b^{2} c^{2} d g i n\right)} B^{2} \log\left(d x + c\right) + {\left(2 \, B^{2} b^{3} d^{3} g i x^{3} + 6 \, B^{2} a b^{2} c d^{2} g i x + 3 \, {\left(b^{3} c d^{2} g i + a b^{2} d^{3} g i\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{6 \, b^{2} d^{2}}"," ",0,"2/3*A*B*b*d*g*i*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A^2*b*d*g*i*x^3 + A*B*b*c*g*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*B*a*d*g*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*b*c*g*i*x^2 + 1/2*A^2*a*d*g*i*x^2 + 1/3*A*B*b*d*g*i*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - A*B*b*c*g*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - A*B*a*d*g*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a*c*g*i*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a*c*g*i*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*c*g*i*x - 1/3*(a^2*c*d^2*g*i*n^2 - b^2*c^3*g*i*n*log(e) - (g*i*n^2 - 3*g*i*n*log(e))*a*b*c^2*d)*B^2*log(d*x + c)/(b*d^2) + 1/3*(b^3*c^3*g*i*n^2 - 3*a*b^2*c^2*d*g*i*n^2 + 3*a^2*b*c*d^2*g*i*n^2 - a^3*d^3*g*i*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^2*d^2) + 1/6*(2*B^2*b^3*d^3*g*i*x^3*log(e)^2 - ((2*g*i*n*log(e) - 3*g*i*log(e)^2)*b^3*c*d^2 - (2*g*i*n*log(e) + 3*g*i*log(e)^2)*a*b^2*d^3)*B^2*x^2 - (3*a^2*b*c*d^2*g*i*n^2 - a^3*d^3*g*i*n^2)*B^2*log(b*x + a)^2 - 2*(b^3*c^3*g*i*n^2 - 3*a*b^2*c^2*d*g*i*n^2)*B^2*log(b*x + a)*log(d*x + c) + (b^3*c^3*g*i*n^2 - 3*a*b^2*c^2*d*g*i*n^2)*B^2*log(d*x + c)^2 + 2*((g*i*n^2 - g*i*n*log(e))*b^3*c^2*d - (2*g*i*n^2 - 3*g*i*log(e)^2)*a*b^2*c*d^2 + (g*i*n^2 + g*i*n*log(e))*a^2*b*d^3)*B^2*x - 2*(a*b^2*c^2*d*g*i*n^2 + a^3*d^3*g*i*n*log(e) - (g*i*n^2 + 3*g*i*n*log(e))*a^2*b*c*d^2)*B^2*log(b*x + a) + (2*B^2*b^3*d^3*g*i*x^3 + 6*B^2*a*b^2*c*d^2*g*i*x + 3*(b^3*c*d^2*g*i + a*b^2*d^3*g*i)*B^2*x^2)*log((b*x + a)^n)^2 + (2*B^2*b^3*d^3*g*i*x^3 + 6*B^2*a*b^2*c*d^2*g*i*x + 3*(b^3*c*d^2*g*i + a*b^2*d^3*g*i)*B^2*x^2)*log((d*x + c)^n)^2 + 2*(2*B^2*b^3*d^3*g*i*x^3*log(e) - ((g*i*n - 3*g*i*log(e))*b^3*c*d^2 - (g*i*n + 3*g*i*log(e))*a*b^2*d^3)*B^2*x^2 - (b^3*c^2*d*g*i*n - a^2*b*d^3*g*i*n - 6*a*b^2*c*d^2*g*i*log(e))*B^2*x + (3*a^2*b*c*d^2*g*i*n - a^3*d^3*g*i*n)*B^2*log(b*x + a) + (b^3*c^3*g*i*n - 3*a*b^2*c^2*d*g*i*n)*B^2*log(d*x + c))*log((b*x + a)^n) - 2*(2*B^2*b^3*d^3*g*i*x^3*log(e) - ((g*i*n - 3*g*i*log(e))*b^3*c*d^2 - (g*i*n + 3*g*i*log(e))*a*b^2*d^3)*B^2*x^2 - (b^3*c^2*d*g*i*n - a^2*b*d^3*g*i*n - 6*a*b^2*c*d^2*g*i*log(e))*B^2*x + (3*a^2*b*c*d^2*g*i*n - a^3*d^3*g*i*n)*B^2*log(b*x + a) + (b^3*c^3*g*i*n - 3*a*b^2*c^2*d*g*i*n)*B^2*log(d*x + c) + (2*B^2*b^3*d^3*g*i*x^3 + 6*B^2*a*b^2*c*d^2*g*i*x + 3*(b^3*c*d^2*g*i + a*b^2*d^3*g*i)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d^2)","B",0
162,1,825,0,6.645336," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","A B d i x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A^{2} d i x^{2} - A B d i n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B c i n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B c i x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c i x - \frac{{\left(a c d i n^{2} - {\left(i n^{2} - i n \log\left(e\right)\right)} b c^{2}\right)} B^{2} \log\left(d x + c\right)}{b d} - \frac{{\left(b^{2} c^{2} i n^{2} - 2 \, a b c d i n^{2} + a^{2} d^{2} i n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{b^{2} d} + \frac{2 \, B^{2} b^{2} c^{2} i n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - B^{2} b^{2} c^{2} i n^{2} \log\left(d x + c\right)^{2} + B^{2} b^{2} d^{2} i x^{2} \log\left(e\right)^{2} - {\left(2 \, a b c d i n^{2} - a^{2} d^{2} i n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + 2 \, {\left(a b d^{2} i n \log\left(e\right) - {\left(i n \log\left(e\right) - i \log\left(e\right)^{2}\right)} b^{2} c d\right)} B^{2} x - 2 \, {\left({\left(i n^{2} - 2 \, i n \log\left(e\right)\right)} a b c d - {\left(i n^{2} - i n \log\left(e\right)\right)} a^{2} d^{2}\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(B^{2} b^{2} d^{2} i x^{2} \log\left(e\right) - B^{2} b^{2} c^{2} i n \log\left(d x + c\right) + {\left(a b d^{2} i n - {\left(i n - 2 \, i \log\left(e\right)\right)} b^{2} c d\right)} B^{2} x + {\left(2 \, a b c d i n - a^{2} d^{2} i n\right)} B^{2} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B^{2} b^{2} d^{2} i x^{2} \log\left(e\right) - B^{2} b^{2} c^{2} i n \log\left(d x + c\right) + {\left(a b d^{2} i n - {\left(i n - 2 \, i \log\left(e\right)\right)} b^{2} c d\right)} B^{2} x + {\left(2 \, a b c d i n - a^{2} d^{2} i n\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, b^{2} d}"," ",0,"A*B*d*i*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*d*i*x^2 - A*B*d*i*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*c*i*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*c*i*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c*i*x - (a*c*d*i*n^2 - (i*n^2 - i*n*log(e))*b*c^2)*B^2*log(d*x + c)/(b*d) - (b^2*c^2*i*n^2 - 2*a*b*c*d*i*n^2 + a^2*d^2*i*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^2*d) + 1/2*(2*B^2*b^2*c^2*i*n^2*log(b*x + a)*log(d*x + c) - B^2*b^2*c^2*i*n^2*log(d*x + c)^2 + B^2*b^2*d^2*i*x^2*log(e)^2 - (2*a*b*c*d*i*n^2 - a^2*d^2*i*n^2)*B^2*log(b*x + a)^2 + 2*(a*b*d^2*i*n*log(e) - (i*n*log(e) - i*log(e)^2)*b^2*c*d)*B^2*x - 2*((i*n^2 - 2*i*n*log(e))*a*b*c*d - (i*n^2 - i*n*log(e))*a^2*d^2)*B^2*log(b*x + a) + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x)*log((b*x + a)^n)^2 + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x)*log((d*x + c)^n)^2 + 2*(B^2*b^2*d^2*i*x^2*log(e) - B^2*b^2*c^2*i*n*log(d*x + c) + (a*b*d^2*i*n - (i*n - 2*i*log(e))*b^2*c*d)*B^2*x + (2*a*b*c*d*i*n - a^2*d^2*i*n)*B^2*log(b*x + a))*log((b*x + a)^n) - 2*(B^2*b^2*d^2*i*x^2*log(e) - B^2*b^2*c^2*i*n*log(d*x + c) + (a*b*d^2*i*n - (i*n - 2*i*log(e))*b^2*c*d)*B^2*x + (2*a*b*c*d*i*n - a^2*d^2*i*n)*B^2*log(b*x + a) + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d)","B",0
163,0,0,0,0.000000," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g),x, algorithm=""maxima"")","A^{2} d i {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} + \frac{A^{2} c i \log\left(b g x + a g\right)}{b g} + \frac{{\left(B^{2} b d i x + {\left(b c i - a d i\right)} B^{2} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{b^{2} g} - \int -\frac{B^{2} b^{2} c^{2} i \log\left(e\right)^{2} + 2 \, A B b^{2} c^{2} i \log\left(e\right) + {\left(B^{2} b^{2} d^{2} i \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} i \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + B^{2} b^{2} c^{2} i\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(B^{2} b^{2} c d i \log\left(e\right)^{2} + 2 \, A B b^{2} c d i \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{2} c^{2} i \log\left(e\right) + A B b^{2} c^{2} i + {\left(B^{2} b^{2} d^{2} i \log\left(e\right) + A B b^{2} d^{2} i\right)} x^{2} + 2 \, {\left(B^{2} b^{2} c d i \log\left(e\right) + A B b^{2} c d i\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B^{2} b^{2} c^{2} i \log\left(e\right) + A B b^{2} c^{2} i + {\left({\left(i n + i \log\left(e\right)\right)} B^{2} b^{2} d^{2} + A B b^{2} d^{2} i\right)} x^{2} + {\left(2 \, A B b^{2} c d i + {\left(a b d^{2} i n + 2 \, b^{2} c d i \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b^{2} c d i n - a b d^{2} i n\right)} B^{2} x + {\left(a b c d i n - a^{2} d^{2} i n\right)} B^{2}\right)} \log\left(b x + a\right) + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + B^{2} b^{2} c^{2} i\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{3} d g x^{2} + a b^{2} c g + {\left(b^{3} c g + a b^{2} d g\right)} x}\,{d x}"," ",0,"A^2*d*i*(x/(b*g) - a*log(b*x + a)/(b^2*g)) + A^2*c*i*log(b*g*x + a*g)/(b*g) + (B^2*b*d*i*x + (b*c*i - a*d*i)*B^2*log(b*x + a))*log((d*x + c)^n)^2/(b^2*g) - integrate(-(B^2*b^2*c^2*i*log(e)^2 + 2*A*B*b^2*c^2*i*log(e) + (B^2*b^2*d^2*i*log(e)^2 + 2*A*B*b^2*d^2*i*log(e))*x^2 + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + B^2*b^2*c^2*i)*log((b*x + a)^n)^2 + 2*(B^2*b^2*c*d*i*log(e)^2 + 2*A*B*b^2*c*d*i*log(e))*x + 2*(B^2*b^2*c^2*i*log(e) + A*B*b^2*c^2*i + (B^2*b^2*d^2*i*log(e) + A*B*b^2*d^2*i)*x^2 + 2*(B^2*b^2*c*d*i*log(e) + A*B*b^2*c*d*i)*x)*log((b*x + a)^n) - 2*(B^2*b^2*c^2*i*log(e) + A*B*b^2*c^2*i + ((i*n + i*log(e))*B^2*b^2*d^2 + A*B*b^2*d^2*i)*x^2 + (2*A*B*b^2*c*d*i + (a*b*d^2*i*n + 2*b^2*c*d*i*log(e))*B^2)*x + ((b^2*c*d*i*n - a*b*d^2*i*n)*B^2*x + (a*b*c*d*i*n - a^2*d^2*i*n)*B^2)*log(b*x + a) + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + B^2*b^2*c^2*i)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d*g*x^2 + a*b^2*c*g + (b^3*c*g + a*b^2*d*g)*x), x)","F",0
164,0,0,0,0.000000," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-2 \, A B c i n {\left(\frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} + A^{2} d i {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - \frac{2 \, A B c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{2} g^{2} x + a b g^{2}} - \frac{A^{2} c i}{b^{2} g^{2} x + a b g^{2}} - \frac{{\left({\left(b c i - a d i\right)} B^{2} - {\left(B^{2} b d i x + B^{2} a d i\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{b^{3} g^{2} x + a b^{2} g^{2}} - \int -\frac{B^{2} b^{2} c^{2} i \log\left(e\right)^{2} + {\left(B^{2} b^{2} d^{2} i \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} i \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + B^{2} b^{2} c^{2} i\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(B^{2} b^{2} c d i \log\left(e\right)^{2} + A B b^{2} c d i \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{2} c^{2} i \log\left(e\right) + {\left(B^{2} b^{2} d^{2} i \log\left(e\right) + A B b^{2} d^{2} i\right)} x^{2} + {\left(2 \, B^{2} b^{2} c d i \log\left(e\right) + A B b^{2} c d i\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) + 2 \, {\left({\left(a b c d i n - a^{2} d^{2} i n - b^{2} c^{2} i \log\left(e\right)\right)} B^{2} - {\left(B^{2} b^{2} d^{2} i \log\left(e\right) + A B b^{2} d^{2} i\right)} x^{2} - {\left(A B b^{2} c d i + {\left(a b d^{2} i n - {\left(i n - 2 \, i \log\left(e\right)\right)} b^{2} c d\right)} B^{2}\right)} x - {\left(B^{2} b^{2} d^{2} i n x^{2} + 2 \, B^{2} a b d^{2} i n x + B^{2} a^{2} d^{2} i n\right)} \log\left(b x + a\right) - {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + B^{2} b^{2} c^{2} i\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{4} d g^{2} x^{3} + a^{2} b^{2} c g^{2} + {\left(b^{4} c g^{2} + 2 \, a b^{3} d g^{2}\right)} x^{2} + {\left(2 \, a b^{3} c g^{2} + a^{2} b^{2} d g^{2}\right)} x}\,{d x}"," ",0,"-2*A*B*c*i*n*(1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) + A^2*d*i*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - 2*A*B*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*g^2*x + a*b*g^2) - A^2*c*i/(b^2*g^2*x + a*b*g^2) - ((b*c*i - a*d*i)*B^2 - (B^2*b*d*i*x + B^2*a*d*i)*log(b*x + a))*log((d*x + c)^n)^2/(b^3*g^2*x + a*b^2*g^2) - integrate(-(B^2*b^2*c^2*i*log(e)^2 + (B^2*b^2*d^2*i*log(e)^2 + 2*A*B*b^2*d^2*i*log(e))*x^2 + (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + B^2*b^2*c^2*i)*log((b*x + a)^n)^2 + 2*(B^2*b^2*c*d*i*log(e)^2 + A*B*b^2*c*d*i*log(e))*x + 2*(B^2*b^2*c^2*i*log(e) + (B^2*b^2*d^2*i*log(e) + A*B*b^2*d^2*i)*x^2 + (2*B^2*b^2*c*d*i*log(e) + A*B*b^2*c*d*i)*x)*log((b*x + a)^n) + 2*((a*b*c*d*i*n - a^2*d^2*i*n - b^2*c^2*i*log(e))*B^2 - (B^2*b^2*d^2*i*log(e) + A*B*b^2*d^2*i)*x^2 - (A*B*b^2*c*d*i + (a*b*d^2*i*n - (i*n - 2*i*log(e))*b^2*c*d)*B^2)*x - (B^2*b^2*d^2*i*n*x^2 + 2*B^2*a*b*d^2*i*n*x + B^2*a^2*d^2*i*n)*log(b*x + a) - (B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + B^2*b^2*c^2*i)*log((b*x + a)^n))*log((d*x + c)^n))/(b^4*d*g^2*x^3 + a^2*b^2*c*g^2 + (b^4*c*g^2 + 2*a*b^3*d*g^2)*x^2 + (2*a*b^3*c*g^2 + a^2*b^2*d*g^2)*x), x)","F",0
165,1,2017,0,2.243574," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, A B d i n {\left(\frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{2} \, A B c i n {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{{\left(2 \, b x + a\right)} B^{2} d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} + \frac{1}{4} \, {\left(2 \, n {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(b^{2} c^{2} - 8 \, a b c d + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d - a b d^{2}\right)} x - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{2} b^{3} c^{2} g^{3} - 2 \, a^{3} b^{2} c d g^{3} + a^{4} b d^{2} g^{3} + {\left(b^{5} c^{2} g^{3} - 2 \, a b^{4} c d g^{3} + a^{2} b^{3} d^{2} g^{3}\right)} x^{2} + 2 \, {\left(a b^{4} c^{2} g^{3} - 2 \, a^{2} b^{3} c d g^{3} + a^{3} b^{2} d^{2} g^{3}\right)} x}\right)} B^{2} c i - \frac{1}{4} \, {\left(2 \, n {\left(\frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(7 \, a b^{2} c^{2} - 8 \, a^{2} b c d + a^{3} d^{2} - 2 \, {\left(2 \, a^{2} b c d - a^{3} d^{2} + {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} - 2 \, {\left(2 \, a^{2} b c d - a^{3} d^{2} + {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(4 \, b^{3} c^{2} - 5 \, a b^{2} c d + a^{2} b d^{2}\right)} x + 2 \, {\left(4 \, a^{2} b c d - a^{3} d^{2} + {\left(4 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(4 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(4 \, a^{2} b c d - a^{3} d^{2} + {\left(4 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(4 \, a b^{2} c d - a^{2} b d^{2}\right)} x - 2 \, {\left(2 \, a^{2} b c d - a^{3} d^{2} + {\left(2 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 2 \, {\left(2 \, a b^{2} c d - a^{2} b d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{2} b^{4} c^{2} g^{3} - 2 \, a^{3} b^{3} c d g^{3} + a^{4} b^{2} d^{2} g^{3} + {\left(b^{6} c^{2} g^{3} - 2 \, a b^{5} c d g^{3} + a^{2} b^{4} d^{2} g^{3}\right)} x^{2} + 2 \, {\left(a b^{5} c^{2} g^{3} - 2 \, a^{2} b^{4} c d g^{3} + a^{3} b^{3} d^{2} g^{3}\right)} x}\right)} B^{2} d i - \frac{{\left(2 \, b x + a\right)} A B d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} - \frac{B^{2} c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{{\left(2 \, b x + a\right)} A^{2} d i}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{A B c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} - \frac{A^{2} c i}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"-1/2*A*B*d*i*n*((3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/2*A*B*c*i*n*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - 1/2*(2*b*x + a)*B^2*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) + 1/4*(2*n*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^2 - 6*(b^2*c*d - a*b*d^2)*x - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))*n^2/(a^2*b^3*c^2*g^3 - 2*a^3*b^2*c*d*g^3 + a^4*b*d^2*g^3 + (b^5*c^2*g^3 - 2*a*b^4*c*d*g^3 + a^2*b^3*d^2*g^3)*x^2 + 2*(a*b^4*c^2*g^3 - 2*a^2*b^3*c*d*g^3 + a^3*b^2*d^2*g^3)*x))*B^2*c*i - 1/4*(2*n*((3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (7*a*b^2*c^2 - 8*a^2*b*c*d + a^3*d^2 - 2*(2*a^2*b*c*d - a^3*d^2 + (2*b^3*c*d - a*b^2*d^2)*x^2 + 2*(2*a*b^2*c*d - a^2*b*d^2)*x)*log(b*x + a)^2 - 2*(2*a^2*b*c*d - a^3*d^2 + (2*b^3*c*d - a*b^2*d^2)*x^2 + 2*(2*a*b^2*c*d - a^2*b*d^2)*x)*log(d*x + c)^2 + 2*(4*b^3*c^2 - 5*a*b^2*c*d + a^2*b*d^2)*x + 2*(4*a^2*b*c*d - a^3*d^2 + (4*b^3*c*d - a*b^2*d^2)*x^2 + 2*(4*a*b^2*c*d - a^2*b*d^2)*x)*log(b*x + a) - 2*(4*a^2*b*c*d - a^3*d^2 + (4*b^3*c*d - a*b^2*d^2)*x^2 + 2*(4*a*b^2*c*d - a^2*b*d^2)*x - 2*(2*a^2*b*c*d - a^3*d^2 + (2*b^3*c*d - a*b^2*d^2)*x^2 + 2*(2*a*b^2*c*d - a^2*b*d^2)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^2*b^4*c^2*g^3 - 2*a^3*b^3*c*d*g^3 + a^4*b^2*d^2*g^3 + (b^6*c^2*g^3 - 2*a*b^5*c*d*g^3 + a^2*b^4*d^2*g^3)*x^2 + 2*(a*b^5*c^2*g^3 - 2*a^2*b^4*c*d*g^3 + a^3*b^3*d^2*g^3)*x))*B^2*d*i - (2*b*x + a)*A*B*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 1/2*B^2*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*(2*b*x + a)*A^2*d*i/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - A*B*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A^2*c*i/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
166,1,3312,0,3.500357," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{9} \, A B c i n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{1}{18} \, A B d i n {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{{\left(3 \, b x + a\right)} B^{2} d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{6 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{1}{54} \, {\left(6 \, n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{3} b^{4} c^{3} g^{4} - 3 \, a^{4} b^{3} c^{2} d g^{4} + 3 \, a^{5} b^{2} c d^{2} g^{4} - a^{6} b d^{3} g^{4} + {\left(b^{7} c^{3} g^{4} - 3 \, a b^{6} c^{2} d g^{4} + 3 \, a^{2} b^{5} c d^{2} g^{4} - a^{3} b^{4} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{6} c^{3} g^{4} - 3 \, a^{2} b^{5} c^{2} d g^{4} + 3 \, a^{3} b^{4} c d^{2} g^{4} - a^{4} b^{3} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{3} g^{4} - 3 \, a^{3} b^{4} c^{2} d g^{4} + 3 \, a^{4} b^{3} c d^{2} g^{4} - a^{5} b^{2} d^{3} g^{4}\right)} x}\right)} B^{2} c i - \frac{1}{108} \, {\left(6 \, n {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(19 \, a b^{3} c^{3} - 189 \, a^{2} b^{2} c^{2} d + 189 \, a^{3} b c d^{2} - 19 \, a^{4} d^{3} - 6 \, {\left(27 \, b^{4} c^{2} d - 32 \, a b^{3} c d^{2} + 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 18 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 18 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(9 \, b^{4} c^{3} - 125 \, a b^{3} c^{2} d + 135 \, a^{2} b^{2} c d^{2} - 19 \, a^{3} b d^{3}\right)} x - 6 \, {\left(27 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(27 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(27 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(27 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(27 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(27 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(27 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(27 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x - 6 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{3} b^{5} c^{3} g^{4} - 3 \, a^{4} b^{4} c^{2} d g^{4} + 3 \, a^{5} b^{3} c d^{2} g^{4} - a^{6} b^{2} d^{3} g^{4} + {\left(b^{8} c^{3} g^{4} - 3 \, a b^{7} c^{2} d g^{4} + 3 \, a^{2} b^{6} c d^{2} g^{4} - a^{3} b^{5} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{7} c^{3} g^{4} - 3 \, a^{2} b^{6} c^{2} d g^{4} + 3 \, a^{3} b^{5} c d^{2} g^{4} - a^{4} b^{4} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} c^{3} g^{4} - 3 \, a^{3} b^{5} c^{2} d g^{4} + 3 \, a^{4} b^{4} c d^{2} g^{4} - a^{5} b^{3} d^{3} g^{4}\right)} x}\right)} B^{2} d i - \frac{{\left(3 \, b x + a\right)} A B d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{B^{2} c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{{\left(3 \, b x + a\right)} A^{2} d i}{6 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{2 \, A B c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{A^{2} c i}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/9*A*B*c*i*n*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/18*A*B*d*i*n*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/6*(3*b*x + a)*B^2*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/54*(6*n*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*n^2/(a^3*b^4*c^3*g^4 - 3*a^4*b^3*c^2*d*g^4 + 3*a^5*b^2*c*d^2*g^4 - a^6*b*d^3*g^4 + (b^7*c^3*g^4 - 3*a*b^6*c^2*d*g^4 + 3*a^2*b^5*c*d^2*g^4 - a^3*b^4*d^3*g^4)*x^3 + 3*(a*b^6*c^3*g^4 - 3*a^2*b^5*c^2*d*g^4 + 3*a^3*b^4*c*d^2*g^4 - a^4*b^3*d^3*g^4)*x^2 + 3*(a^2*b^5*c^3*g^4 - 3*a^3*b^4*c^2*d*g^4 + 3*a^4*b^3*c*d^2*g^4 - a^5*b^2*d^3*g^4)*x))*B^2*c*i - 1/108*(6*n*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (19*a*b^3*c^3 - 189*a^2*b^2*c^2*d + 189*a^3*b*c*d^2 - 19*a^4*d^3 - 6*(27*b^4*c^2*d - 32*a*b^3*c*d^2 + 5*a^2*b^2*d^3)*x^2 + 18*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(b*x + a)^2 + 18*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(d*x + c)^2 + 3*(9*b^4*c^3 - 125*a*b^3*c^2*d + 135*a^2*b^2*c*d^2 - 19*a^3*b*d^3)*x - 6*(27*a^3*b*c*d^2 - 5*a^4*d^3 + (27*b^4*c*d^2 - 5*a*b^3*d^3)*x^3 + 3*(27*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^2 + 3*(27*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x)*log(b*x + a) + 6*(27*a^3*b*c*d^2 - 5*a^4*d^3 + (27*b^4*c*d^2 - 5*a*b^3*d^3)*x^3 + 3*(27*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^2 + 3*(27*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x - 6*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^3*b^5*c^3*g^4 - 3*a^4*b^4*c^2*d*g^4 + 3*a^5*b^3*c*d^2*g^4 - a^6*b^2*d^3*g^4 + (b^8*c^3*g^4 - 3*a*b^7*c^2*d*g^4 + 3*a^2*b^6*c*d^2*g^4 - a^3*b^5*d^3*g^4)*x^3 + 3*(a*b^7*c^3*g^4 - 3*a^2*b^6*c^2*d*g^4 + 3*a^3*b^5*c*d^2*g^4 - a^4*b^4*d^3*g^4)*x^2 + 3*(a^2*b^6*c^3*g^4 - 3*a^3*b^5*c^2*d*g^4 + 3*a^4*b^4*c*d^2*g^4 - a^5*b^3*d^3*g^4)*x))*B^2*d*i - 1/3*(3*b*x + a)*A*B*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*B^2*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/6*(3*b*x + a)*A^2*d*i/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 2/3*A*B*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/3*A^2*c*i/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","B",0
167,1,4838,0,4.867279," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\frac{1}{24} \, A B c i n {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{1}{72} \, A B d i n {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} - \frac{{\left(4 \, b x + a\right)} B^{2} d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{12 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} + \frac{1}{288} \, {\left(12 \, n {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(9 \, b^{4} c^{4} - 64 \, a b^{3} c^{3} d + 216 \, a^{2} b^{2} c^{2} d^{2} - 576 \, a^{3} b c d^{3} + 415 \, a^{4} d^{4} - 300 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(13 \, b^{4} c^{2} d^{2} - 176 \, a b^{3} c d^{3} + 163 \, a^{2} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(7 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 324 \, a^{2} b^{2} c d^{3} - 271 \, a^{3} b d^{4}\right)} x - 300 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(25 \, b^{4} d^{4} x^{4} + 100 \, a b^{3} d^{4} x^{3} + 150 \, a^{2} b^{2} d^{4} x^{2} + 100 \, a^{3} b d^{4} x + 25 \, a^{4} d^{4} - 12 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{4} b^{5} c^{4} g^{5} - 4 \, a^{5} b^{4} c^{3} d g^{5} + 6 \, a^{6} b^{3} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{2} c d^{3} g^{5} + a^{8} b d^{4} g^{5} + {\left(b^{9} c^{4} g^{5} - 4 \, a b^{8} c^{3} d g^{5} + 6 \, a^{2} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{6} c d^{3} g^{5} + a^{4} b^{5} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} g^{5} - 4 \, a^{2} b^{7} c^{3} d g^{5} + 6 \, a^{3} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{5} c d^{3} g^{5} + a^{5} b^{4} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} g^{5} - 4 \, a^{3} b^{6} c^{3} d g^{5} + 6 \, a^{4} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{4} c d^{3} g^{5} + a^{6} b^{3} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} g^{5} - 4 \, a^{4} b^{5} c^{3} d g^{5} + 6 \, a^{5} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{3} c d^{3} g^{5} + a^{7} b^{2} d^{4} g^{5}\right)} x}\right)} B^{2} c i - \frac{1}{864} \, {\left(12 \, n {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(37 \, a b^{4} c^{4} - 304 \, a^{2} b^{3} c^{3} d + 1512 \, a^{3} b^{2} c^{2} d^{2} - 1360 \, a^{4} b c d^{3} + 115 \, a^{5} d^{4} + 12 \, {\left(88 \, b^{5} c^{2} d^{2} - 101 \, a b^{4} c d^{3} + 13 \, a^{2} b^{3} d^{4}\right)} x^{3} - 6 \, {\left(40 \, b^{5} c^{3} d - 609 \, a b^{4} c^{2} d^{2} + 648 \, a^{2} b^{3} c d^{3} - 79 \, a^{3} b^{2} d^{4}\right)} x^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(16 \, b^{5} c^{4} - 163 \, a b^{4} c^{3} d + 1068 \, a^{2} b^{3} c^{2} d^{2} - 1036 \, a^{3} b^{2} c d^{3} + 115 \, a^{4} b d^{4}\right)} x + 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x - 12 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{4} b^{6} c^{4} g^{5} - 4 \, a^{5} b^{5} c^{3} d g^{5} + 6 \, a^{6} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{3} c d^{3} g^{5} + a^{8} b^{2} d^{4} g^{5} + {\left(b^{10} c^{4} g^{5} - 4 \, a b^{9} c^{3} d g^{5} + 6 \, a^{2} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{7} c d^{3} g^{5} + a^{4} b^{6} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{9} c^{4} g^{5} - 4 \, a^{2} b^{8} c^{3} d g^{5} + 6 \, a^{3} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{6} c d^{3} g^{5} + a^{5} b^{5} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} c^{4} g^{5} - 4 \, a^{3} b^{7} c^{3} d g^{5} + 6 \, a^{4} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{5} c d^{3} g^{5} + a^{6} b^{4} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} c^{4} g^{5} - 4 \, a^{4} b^{6} c^{3} d g^{5} + 6 \, a^{5} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{4} c d^{3} g^{5} + a^{7} b^{3} d^{4} g^{5}\right)} x}\right)} B^{2} d i - \frac{{\left(4 \, b x + a\right)} A B d i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{6 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{B^{2} c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{{\left(4 \, b x + a\right)} A^{2} d i}{12 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{A B c i \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{A^{2} c i}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"1/24*A*B*c*i*n*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/72*A*B*d*i*n*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) - 1/12*(4*b*x + a)*B^2*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) + 1/288*(12*n*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (9*b^4*c^4 - 64*a*b^3*c^3*d + 216*a^2*b^2*c^2*d^2 - 576*a^3*b*c*d^3 + 415*a^4*d^4 - 300*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 6*(13*b^4*c^2*d^2 - 176*a*b^3*c*d^3 + 163*a^2*b^2*d^4)*x^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a)^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(d*x + c)^2 - 4*(7*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 324*a^2*b^2*c*d^3 - 271*a^3*b*d^4)*x - 300*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a) + 12*(25*b^4*d^4*x^4 + 100*a*b^3*d^4*x^3 + 150*a^2*b^2*d^4*x^2 + 100*a^3*b*d^4*x + 25*a^4*d^4 - 12*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a))*log(d*x + c))*n^2/(a^4*b^5*c^4*g^5 - 4*a^5*b^4*c^3*d*g^5 + 6*a^6*b^3*c^2*d^2*g^5 - 4*a^7*b^2*c*d^3*g^5 + a^8*b*d^4*g^5 + (b^9*c^4*g^5 - 4*a*b^8*c^3*d*g^5 + 6*a^2*b^7*c^2*d^2*g^5 - 4*a^3*b^6*c*d^3*g^5 + a^4*b^5*d^4*g^5)*x^4 + 4*(a*b^8*c^4*g^5 - 4*a^2*b^7*c^3*d*g^5 + 6*a^3*b^6*c^2*d^2*g^5 - 4*a^4*b^5*c*d^3*g^5 + a^5*b^4*d^4*g^5)*x^3 + 6*(a^2*b^7*c^4*g^5 - 4*a^3*b^6*c^3*d*g^5 + 6*a^4*b^5*c^2*d^2*g^5 - 4*a^5*b^4*c*d^3*g^5 + a^6*b^3*d^4*g^5)*x^2 + 4*(a^3*b^6*c^4*g^5 - 4*a^4*b^5*c^3*d*g^5 + 6*a^5*b^4*c^2*d^2*g^5 - 4*a^6*b^3*c*d^3*g^5 + a^7*b^2*d^4*g^5)*x))*B^2*c*i - 1/864*(12*n*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (37*a*b^4*c^4 - 304*a^2*b^3*c^3*d + 1512*a^3*b^2*c^2*d^2 - 1360*a^4*b*c*d^3 + 115*a^5*d^4 + 12*(88*b^5*c^2*d^2 - 101*a*b^4*c*d^3 + 13*a^2*b^3*d^4)*x^3 - 6*(40*b^5*c^3*d - 609*a*b^4*c^2*d^2 + 648*a^2*b^3*c*d^3 - 79*a^3*b^2*d^4)*x^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a)^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(d*x + c)^2 + 4*(16*b^5*c^4 - 163*a*b^4*c^3*d + 1068*a^2*b^3*c^2*d^2 - 1036*a^3*b^2*c*d^3 + 115*a^4*b*d^4)*x + 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x)*log(b*x + a) - 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x - 12*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^4*b^6*c^4*g^5 - 4*a^5*b^5*c^3*d*g^5 + 6*a^6*b^4*c^2*d^2*g^5 - 4*a^7*b^3*c*d^3*g^5 + a^8*b^2*d^4*g^5 + (b^10*c^4*g^5 - 4*a*b^9*c^3*d*g^5 + 6*a^2*b^8*c^2*d^2*g^5 - 4*a^3*b^7*c*d^3*g^5 + a^4*b^6*d^4*g^5)*x^4 + 4*(a*b^9*c^4*g^5 - 4*a^2*b^8*c^3*d*g^5 + 6*a^3*b^7*c^2*d^2*g^5 - 4*a^4*b^6*c*d^3*g^5 + a^5*b^5*d^4*g^5)*x^3 + 6*(a^2*b^8*c^4*g^5 - 4*a^3*b^7*c^3*d*g^5 + 6*a^4*b^6*c^2*d^2*g^5 - 4*a^5*b^5*c*d^3*g^5 + a^6*b^4*d^4*g^5)*x^2 + 4*(a^3*b^7*c^4*g^5 - 4*a^4*b^6*c^3*d*g^5 + 6*a^5*b^5*c^2*d^2*g^5 - 4*a^6*b^4*c*d^3*g^5 + a^7*b^3*d^4*g^5)*x))*B^2*d*i - 1/6*(4*b*x + a)*A*B*d*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/4*B^2*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/12*(4*b*x + a)*A^2*d*i/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/2*A*B*c*i*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/4*A^2*c*i/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
168,1,5952,0,8.098171," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A B b^{3} d^{2} g^{3} i^{2} x^{6} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{6} \, A^{2} b^{3} d^{2} g^{3} i^{2} x^{6} + \frac{4}{5} \, A B b^{3} c d g^{3} i^{2} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{6}{5} \, A B a b^{2} d^{2} g^{3} i^{2} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{5} \, A^{2} b^{3} c d g^{3} i^{2} x^{5} + \frac{3}{5} \, A^{2} a b^{2} d^{2} g^{3} i^{2} x^{5} + \frac{1}{2} \, A B b^{3} c^{2} g^{3} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 3 \, A B a b^{2} c d g^{3} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A B a^{2} b d^{2} g^{3} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A^{2} b^{3} c^{2} g^{3} i^{2} x^{4} + \frac{3}{2} \, A^{2} a b^{2} c d g^{3} i^{2} x^{4} + \frac{3}{4} \, A^{2} a^{2} b d^{2} g^{3} i^{2} x^{4} + 2 \, A B a b^{2} c^{2} g^{3} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 4 \, A B a^{2} b c d g^{3} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{3} \, A B a^{3} d^{2} g^{3} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a b^{2} c^{2} g^{3} i^{2} x^{3} + 2 \, A^{2} a^{2} b c d g^{3} i^{2} x^{3} + \frac{1}{3} \, A^{2} a^{3} d^{2} g^{3} i^{2} x^{3} + 3 \, A B a^{2} b c^{2} g^{3} i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A B a^{3} c d g^{3} i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A^{2} a^{2} b c^{2} g^{3} i^{2} x^{2} + A^{2} a^{3} c d g^{3} i^{2} x^{2} - \frac{1}{180} \, A B b^{3} d^{2} g^{3} i^{2} n {\left(\frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} - \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} + \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} + \frac{1}{15} \, A B b^{3} c d g^{3} i^{2} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} + \frac{1}{10} \, A B a b^{2} d^{2} g^{3} i^{2} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{12} \, A B b^{3} c^{2} g^{3} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{2} \, A B a b^{2} c d g^{3} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{4} \, A B a^{2} b d^{2} g^{3} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + A B a b^{2} c^{2} g^{3} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + 2 \, A B a^{2} b c d g^{3} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{3} \, A B a^{3} d^{2} g^{3} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - 3 \, A B a^{2} b c^{2} g^{3} i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - 2 \, A B a^{3} c d g^{3} i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a^{3} c^{2} g^{3} i^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a^{3} c^{2} g^{3} i^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{3} c^{2} g^{3} i^{2} x - \frac{{\left(33 \, a^{4} b c^{2} d^{4} g^{3} i^{2} n^{2} - 6 \, a^{5} c d^{5} g^{3} i^{2} n^{2} - 2 \, {\left(g^{3} i^{2} n^{2} + 3 \, g^{3} i^{2} n \log\left(e\right)\right)} b^{5} c^{6} + 6 \, {\left(g^{3} i^{2} n^{2} + 6 \, g^{3} i^{2} n \log\left(e\right)\right)} a b^{4} c^{5} d + 3 \, {\left(g^{3} i^{2} n^{2} - 30 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{2} b^{3} c^{4} d^{2} - 2 \, {\left(17 \, g^{3} i^{2} n^{2} - 60 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{3} b^{2} c^{3} d^{3}\right)} B^{2} \log\left(d x + c\right)}{180 \, b^{2} d^{4}} + \frac{{\left(b^{6} c^{6} g^{3} i^{2} n^{2} - 6 \, a b^{5} c^{5} d g^{3} i^{2} n^{2} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} n^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2} n^{2} + 15 \, a^{4} b^{2} c^{2} d^{4} g^{3} i^{2} n^{2} - 6 \, a^{5} b c d^{5} g^{3} i^{2} n^{2} + a^{6} d^{6} g^{3} i^{2} n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{30 \, b^{3} d^{4}} + \frac{60 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} \log\left(e\right)^{2} - 24 \, {\left({\left(g^{3} i^{2} n \log\left(e\right) - 6 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} b^{6} c d^{5} - {\left(g^{3} i^{2} n \log\left(e\right) + 9 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a b^{5} d^{6}\right)} B^{2} x^{5} + 6 \, {\left({\left(g^{3} i^{2} n^{2} - 7 \, g^{3} i^{2} n \log\left(e\right) + 15 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} b^{6} c^{2} d^{4} - 2 \, {\left(g^{3} i^{2} n^{2} + 3 \, g^{3} i^{2} n \log\left(e\right) - 45 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a b^{5} c d^{5} + {\left(g^{3} i^{2} n^{2} + 13 \, g^{3} i^{2} n \log\left(e\right) + 45 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} + 2 \, {\left({\left(3 \, g^{3} i^{2} n^{2} - 2 \, g^{3} i^{2} n \log\left(e\right)\right)} b^{6} c^{3} d^{3} + 3 \, {\left(g^{3} i^{2} n^{2} - 26 \, g^{3} i^{2} n \log\left(e\right) + 60 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a b^{5} c^{2} d^{4} - 3 \, {\left(5 \, g^{3} i^{2} n^{2} - 14 \, g^{3} i^{2} n \log\left(e\right) - 120 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a^{2} b^{4} c d^{5} + {\left(9 \, g^{3} i^{2} n^{2} + 38 \, g^{3} i^{2} n \log\left(e\right) + 60 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a^{3} b^{3} d^{6}\right)} B^{2} x^{3} - {\left({\left(7 \, g^{3} i^{2} n^{2} - 6 \, g^{3} i^{2} n \log\left(e\right)\right)} b^{6} c^{4} d^{2} - 2 \, {\left(23 \, g^{3} i^{2} n^{2} - 18 \, g^{3} i^{2} n \log\left(e\right)\right)} a b^{5} c^{3} d^{3} + 60 \, {\left(g^{3} i^{2} n^{2} + 3 \, g^{3} i^{2} n \log\left(e\right) - 9 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a^{2} b^{4} c^{2} d^{4} - 2 \, {\left(5 \, g^{3} i^{2} n^{2} + 102 \, g^{3} i^{2} n \log\left(e\right) + 180 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a^{3} b^{3} c d^{5} - {\left(11 \, g^{3} i^{2} n^{2} + 6 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{4} b^{2} d^{6}\right)} B^{2} x^{2} - 6 \, {\left(15 \, a^{4} b^{2} c^{2} d^{4} g^{3} i^{2} n^{2} - 6 \, a^{5} b c d^{5} g^{3} i^{2} n^{2} + a^{6} d^{6} g^{3} i^{2} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} - 12 \, {\left(b^{6} c^{6} g^{3} i^{2} n^{2} - 6 \, a b^{5} c^{5} d g^{3} i^{2} n^{2} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} n^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) + 6 \, {\left(b^{6} c^{6} g^{3} i^{2} n^{2} - 6 \, a b^{5} c^{5} d g^{3} i^{2} n^{2} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} n^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(2 \, g^{3} i^{2} n^{2} - 3 \, g^{3} i^{2} n \log\left(e\right)\right)} b^{6} c^{5} d - 9 \, {\left(3 \, g^{3} i^{2} n^{2} - 4 \, g^{3} i^{2} n \log\left(e\right)\right)} a b^{5} c^{4} d^{2} + {\left(77 \, g^{3} i^{2} n^{2} - 90 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{2} b^{4} c^{3} d^{3} - {\left(97 \, g^{3} i^{2} n^{2} - 30 \, g^{3} i^{2} n \log\left(e\right) - 180 \, g^{3} i^{2} \log\left(e\right)^{2}\right)} a^{3} b^{3} c^{2} d^{4} + 3 \, {\left(17 \, g^{3} i^{2} n^{2} + 12 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{4} b^{2} c d^{5} - 2 \, {\left(4 \, g^{3} i^{2} n^{2} + 3 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{5} b d^{6}\right)} B^{2} x - 2 \, {\left(6 \, a b^{5} c^{5} d g^{3} i^{2} n^{2} - 33 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} n^{2} + 74 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2} n^{2} - 9 \, {\left(7 \, g^{3} i^{2} n^{2} + 10 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{4} b^{2} c^{2} d^{4} + 18 \, {\left(g^{3} i^{2} n^{2} + 2 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{5} b c d^{5} - 2 \, {\left(g^{3} i^{2} n^{2} + 3 \, g^{3} i^{2} n \log\left(e\right)\right)} a^{6} d^{6}\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} + 60 \, B^{2} a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} x + 12 \, {\left(2 \, b^{6} c d^{5} g^{3} i^{2} + 3 \, a b^{5} d^{6} g^{3} i^{2}\right)} B^{2} x^{5} + 15 \, {\left(b^{6} c^{2} d^{4} g^{3} i^{2} + 6 \, a b^{5} c d^{5} g^{3} i^{2} + 3 \, a^{2} b^{4} d^{6} g^{3} i^{2}\right)} B^{2} x^{4} + 20 \, {\left(3 \, a b^{5} c^{2} d^{4} g^{3} i^{2} + 6 \, a^{2} b^{4} c d^{5} g^{3} i^{2} + a^{3} b^{3} d^{6} g^{3} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(3 \, a^{2} b^{4} c^{2} d^{4} g^{3} i^{2} + 2 \, a^{3} b^{3} c d^{5} g^{3} i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} + 60 \, B^{2} a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} x + 12 \, {\left(2 \, b^{6} c d^{5} g^{3} i^{2} + 3 \, a b^{5} d^{6} g^{3} i^{2}\right)} B^{2} x^{5} + 15 \, {\left(b^{6} c^{2} d^{4} g^{3} i^{2} + 6 \, a b^{5} c d^{5} g^{3} i^{2} + 3 \, a^{2} b^{4} d^{6} g^{3} i^{2}\right)} B^{2} x^{4} + 20 \, {\left(3 \, a b^{5} c^{2} d^{4} g^{3} i^{2} + 6 \, a^{2} b^{4} c d^{5} g^{3} i^{2} + a^{3} b^{3} d^{6} g^{3} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(3 \, a^{2} b^{4} c^{2} d^{4} g^{3} i^{2} + 2 \, a^{3} b^{3} c d^{5} g^{3} i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(60 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} \log\left(e\right) - 12 \, {\left({\left(g^{3} i^{2} n - 12 \, g^{3} i^{2} \log\left(e\right)\right)} b^{6} c d^{5} - {\left(g^{3} i^{2} n + 18 \, g^{3} i^{2} \log\left(e\right)\right)} a b^{5} d^{6}\right)} B^{2} x^{5} - 3 \, {\left({\left(7 \, g^{3} i^{2} n - 30 \, g^{3} i^{2} \log\left(e\right)\right)} b^{6} c^{2} d^{4} + 6 \, {\left(g^{3} i^{2} n - 30 \, g^{3} i^{2} \log\left(e\right)\right)} a b^{5} c d^{5} - {\left(13 \, g^{3} i^{2} n + 90 \, g^{3} i^{2} \log\left(e\right)\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} - 2 \, {\left(b^{6} c^{3} d^{3} g^{3} i^{2} n + 3 \, {\left(13 \, g^{3} i^{2} n - 60 \, g^{3} i^{2} \log\left(e\right)\right)} a b^{5} c^{2} d^{4} - 3 \, {\left(7 \, g^{3} i^{2} n + 120 \, g^{3} i^{2} \log\left(e\right)\right)} a^{2} b^{4} c d^{5} - {\left(19 \, g^{3} i^{2} n + 60 \, g^{3} i^{2} \log\left(e\right)\right)} a^{3} b^{3} d^{6}\right)} B^{2} x^{3} + 3 \, {\left(b^{6} c^{4} d^{2} g^{3} i^{2} n - 6 \, a b^{5} c^{3} d^{3} g^{3} i^{2} n + a^{4} b^{2} d^{6} g^{3} i^{2} n - 30 \, {\left(g^{3} i^{2} n - 6 \, g^{3} i^{2} \log\left(e\right)\right)} a^{2} b^{4} c^{2} d^{4} + 2 \, {\left(17 \, g^{3} i^{2} n + 60 \, g^{3} i^{2} \log\left(e\right)\right)} a^{3} b^{3} c d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{6} c^{5} d g^{3} i^{2} n - 6 \, a b^{5} c^{4} d^{2} g^{3} i^{2} n + 15 \, a^{2} b^{4} c^{3} d^{3} g^{3} i^{2} n - 6 \, a^{4} b^{2} c d^{5} g^{3} i^{2} n + a^{5} b d^{6} g^{3} i^{2} n - 5 \, {\left(g^{3} i^{2} n + 12 \, g^{3} i^{2} \log\left(e\right)\right)} a^{3} b^{3} c^{2} d^{4}\right)} B^{2} x + 6 \, {\left(15 \, a^{4} b^{2} c^{2} d^{4} g^{3} i^{2} n - 6 \, a^{5} b c d^{5} g^{3} i^{2} n + a^{6} d^{6} g^{3} i^{2} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(b^{6} c^{6} g^{3} i^{2} n - 6 \, a b^{5} c^{5} d g^{3} i^{2} n + 15 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} n - 20 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2} n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(60 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} \log\left(e\right) - 12 \, {\left({\left(g^{3} i^{2} n - 12 \, g^{3} i^{2} \log\left(e\right)\right)} b^{6} c d^{5} - {\left(g^{3} i^{2} n + 18 \, g^{3} i^{2} \log\left(e\right)\right)} a b^{5} d^{6}\right)} B^{2} x^{5} - 3 \, {\left({\left(7 \, g^{3} i^{2} n - 30 \, g^{3} i^{2} \log\left(e\right)\right)} b^{6} c^{2} d^{4} + 6 \, {\left(g^{3} i^{2} n - 30 \, g^{3} i^{2} \log\left(e\right)\right)} a b^{5} c d^{5} - {\left(13 \, g^{3} i^{2} n + 90 \, g^{3} i^{2} \log\left(e\right)\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} - 2 \, {\left(b^{6} c^{3} d^{3} g^{3} i^{2} n + 3 \, {\left(13 \, g^{3} i^{2} n - 60 \, g^{3} i^{2} \log\left(e\right)\right)} a b^{5} c^{2} d^{4} - 3 \, {\left(7 \, g^{3} i^{2} n + 120 \, g^{3} i^{2} \log\left(e\right)\right)} a^{2} b^{4} c d^{5} - {\left(19 \, g^{3} i^{2} n + 60 \, g^{3} i^{2} \log\left(e\right)\right)} a^{3} b^{3} d^{6}\right)} B^{2} x^{3} + 3 \, {\left(b^{6} c^{4} d^{2} g^{3} i^{2} n - 6 \, a b^{5} c^{3} d^{3} g^{3} i^{2} n + a^{4} b^{2} d^{6} g^{3} i^{2} n - 30 \, {\left(g^{3} i^{2} n - 6 \, g^{3} i^{2} \log\left(e\right)\right)} a^{2} b^{4} c^{2} d^{4} + 2 \, {\left(17 \, g^{3} i^{2} n + 60 \, g^{3} i^{2} \log\left(e\right)\right)} a^{3} b^{3} c d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{6} c^{5} d g^{3} i^{2} n - 6 \, a b^{5} c^{4} d^{2} g^{3} i^{2} n + 15 \, a^{2} b^{4} c^{3} d^{3} g^{3} i^{2} n - 6 \, a^{4} b^{2} c d^{5} g^{3} i^{2} n + a^{5} b d^{6} g^{3} i^{2} n - 5 \, {\left(g^{3} i^{2} n + 12 \, g^{3} i^{2} \log\left(e\right)\right)} a^{3} b^{3} c^{2} d^{4}\right)} B^{2} x + 6 \, {\left(15 \, a^{4} b^{2} c^{2} d^{4} g^{3} i^{2} n - 6 \, a^{5} b c d^{5} g^{3} i^{2} n + a^{6} d^{6} g^{3} i^{2} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(b^{6} c^{6} g^{3} i^{2} n - 6 \, a b^{5} c^{5} d g^{3} i^{2} n + 15 \, a^{2} b^{4} c^{4} d^{2} g^{3} i^{2} n - 20 \, a^{3} b^{3} c^{3} d^{3} g^{3} i^{2} n\right)} B^{2} \log\left(d x + c\right) + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{3} i^{2} x^{6} + 60 \, B^{2} a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} x + 12 \, {\left(2 \, b^{6} c d^{5} g^{3} i^{2} + 3 \, a b^{5} d^{6} g^{3} i^{2}\right)} B^{2} x^{5} + 15 \, {\left(b^{6} c^{2} d^{4} g^{3} i^{2} + 6 \, a b^{5} c d^{5} g^{3} i^{2} + 3 \, a^{2} b^{4} d^{6} g^{3} i^{2}\right)} B^{2} x^{4} + 20 \, {\left(3 \, a b^{5} c^{2} d^{4} g^{3} i^{2} + 6 \, a^{2} b^{4} c d^{5} g^{3} i^{2} + a^{3} b^{3} d^{6} g^{3} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(3 \, a^{2} b^{4} c^{2} d^{4} g^{3} i^{2} + 2 \, a^{3} b^{3} c d^{5} g^{3} i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{360 \, b^{3} d^{4}}"," ",0,"1/3*A*B*b^3*d^2*g^3*i^2*x^6*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/6*A^2*b^3*d^2*g^3*i^2*x^6 + 4/5*A*B*b^3*c*d*g^3*i^2*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 6/5*A*B*a*b^2*d^2*g^3*i^2*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/5*A^2*b^3*c*d*g^3*i^2*x^5 + 3/5*A^2*a*b^2*d^2*g^3*i^2*x^5 + 1/2*A*B*b^3*c^2*g^3*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3*A*B*a*b^2*c*d*g^3*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*B*a^2*b*d^2*g^3*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*b^3*c^2*g^3*i^2*x^4 + 3/2*A^2*a*b^2*c*d*g^3*i^2*x^4 + 3/4*A^2*a^2*b*d^2*g^3*i^2*x^4 + 2*A*B*a*b^2*c^2*g^3*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 4*A*B*a^2*b*c*d*g^3*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/3*A*B*a^3*d^2*g^3*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b^2*c^2*g^3*i^2*x^3 + 2*A^2*a^2*b*c*d*g^3*i^2*x^3 + 1/3*A^2*a^3*d^2*g^3*i^2*x^3 + 3*A*B*a^2*b*c^2*g^3*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*B*a^3*c*d*g^3*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A^2*a^2*b*c^2*g^3*i^2*x^2 + A^2*a^3*c*d*g^3*i^2*x^2 - 1/180*A*B*b^3*d^2*g^3*i^2*n*(60*a^6*log(b*x + a)/b^6 - 60*c^6*log(d*x + c)/d^6 + (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5)) + 1/15*A*B*b^3*c*d*g^3*i^2*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) + 1/10*A*B*a*b^2*d^2*g^3*i^2*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/12*A*B*b^3*c^2*g^3*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/2*A*B*a*b^2*c*d*g^3*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/4*A*B*a^2*b*d^2*g^3*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + A*B*a*b^2*c^2*g^3*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 2*A*B*a^2*b*c*d*g^3*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/3*A*B*a^3*d^2*g^3*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 3*A*B*a^2*b*c^2*g^3*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 2*A*B*a^3*c*d*g^3*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a^3*c^2*g^3*i^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^3*c^2*g^3*i^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^3*c^2*g^3*i^2*x - 1/180*(33*a^4*b*c^2*d^4*g^3*i^2*n^2 - 6*a^5*c*d^5*g^3*i^2*n^2 - 2*(g^3*i^2*n^2 + 3*g^3*i^2*n*log(e))*b^5*c^6 + 6*(g^3*i^2*n^2 + 6*g^3*i^2*n*log(e))*a*b^4*c^5*d + 3*(g^3*i^2*n^2 - 30*g^3*i^2*n*log(e))*a^2*b^3*c^4*d^2 - 2*(17*g^3*i^2*n^2 - 60*g^3*i^2*n*log(e))*a^3*b^2*c^3*d^3)*B^2*log(d*x + c)/(b^2*d^4) + 1/30*(b^6*c^6*g^3*i^2*n^2 - 6*a*b^5*c^5*d*g^3*i^2*n^2 + 15*a^2*b^4*c^4*d^2*g^3*i^2*n^2 - 20*a^3*b^3*c^3*d^3*g^3*i^2*n^2 + 15*a^4*b^2*c^2*d^4*g^3*i^2*n^2 - 6*a^5*b*c*d^5*g^3*i^2*n^2 + a^6*d^6*g^3*i^2*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^3*d^4) + 1/360*(60*B^2*b^6*d^6*g^3*i^2*x^6*log(e)^2 - 24*((g^3*i^2*n*log(e) - 6*g^3*i^2*log(e)^2)*b^6*c*d^5 - (g^3*i^2*n*log(e) + 9*g^3*i^2*log(e)^2)*a*b^5*d^6)*B^2*x^5 + 6*((g^3*i^2*n^2 - 7*g^3*i^2*n*log(e) + 15*g^3*i^2*log(e)^2)*b^6*c^2*d^4 - 2*(g^3*i^2*n^2 + 3*g^3*i^2*n*log(e) - 45*g^3*i^2*log(e)^2)*a*b^5*c*d^5 + (g^3*i^2*n^2 + 13*g^3*i^2*n*log(e) + 45*g^3*i^2*log(e)^2)*a^2*b^4*d^6)*B^2*x^4 + 2*((3*g^3*i^2*n^2 - 2*g^3*i^2*n*log(e))*b^6*c^3*d^3 + 3*(g^3*i^2*n^2 - 26*g^3*i^2*n*log(e) + 60*g^3*i^2*log(e)^2)*a*b^5*c^2*d^4 - 3*(5*g^3*i^2*n^2 - 14*g^3*i^2*n*log(e) - 120*g^3*i^2*log(e)^2)*a^2*b^4*c*d^5 + (9*g^3*i^2*n^2 + 38*g^3*i^2*n*log(e) + 60*g^3*i^2*log(e)^2)*a^3*b^3*d^6)*B^2*x^3 - ((7*g^3*i^2*n^2 - 6*g^3*i^2*n*log(e))*b^6*c^4*d^2 - 2*(23*g^3*i^2*n^2 - 18*g^3*i^2*n*log(e))*a*b^5*c^3*d^3 + 60*(g^3*i^2*n^2 + 3*g^3*i^2*n*log(e) - 9*g^3*i^2*log(e)^2)*a^2*b^4*c^2*d^4 - 2*(5*g^3*i^2*n^2 + 102*g^3*i^2*n*log(e) + 180*g^3*i^2*log(e)^2)*a^3*b^3*c*d^5 - (11*g^3*i^2*n^2 + 6*g^3*i^2*n*log(e))*a^4*b^2*d^6)*B^2*x^2 - 6*(15*a^4*b^2*c^2*d^4*g^3*i^2*n^2 - 6*a^5*b*c*d^5*g^3*i^2*n^2 + a^6*d^6*g^3*i^2*n^2)*B^2*log(b*x + a)^2 - 12*(b^6*c^6*g^3*i^2*n^2 - 6*a*b^5*c^5*d*g^3*i^2*n^2 + 15*a^2*b^4*c^4*d^2*g^3*i^2*n^2 - 20*a^3*b^3*c^3*d^3*g^3*i^2*n^2)*B^2*log(b*x + a)*log(d*x + c) + 6*(b^6*c^6*g^3*i^2*n^2 - 6*a*b^5*c^5*d*g^3*i^2*n^2 + 15*a^2*b^4*c^4*d^2*g^3*i^2*n^2 - 20*a^3*b^3*c^3*d^3*g^3*i^2*n^2)*B^2*log(d*x + c)^2 + 2*(2*(2*g^3*i^2*n^2 - 3*g^3*i^2*n*log(e))*b^6*c^5*d - 9*(3*g^3*i^2*n^2 - 4*g^3*i^2*n*log(e))*a*b^5*c^4*d^2 + (77*g^3*i^2*n^2 - 90*g^3*i^2*n*log(e))*a^2*b^4*c^3*d^3 - (97*g^3*i^2*n^2 - 30*g^3*i^2*n*log(e) - 180*g^3*i^2*log(e)^2)*a^3*b^3*c^2*d^4 + 3*(17*g^3*i^2*n^2 + 12*g^3*i^2*n*log(e))*a^4*b^2*c*d^5 - 2*(4*g^3*i^2*n^2 + 3*g^3*i^2*n*log(e))*a^5*b*d^6)*B^2*x - 2*(6*a*b^5*c^5*d*g^3*i^2*n^2 - 33*a^2*b^4*c^4*d^2*g^3*i^2*n^2 + 74*a^3*b^3*c^3*d^3*g^3*i^2*n^2 - 9*(7*g^3*i^2*n^2 + 10*g^3*i^2*n*log(e))*a^4*b^2*c^2*d^4 + 18*(g^3*i^2*n^2 + 2*g^3*i^2*n*log(e))*a^5*b*c*d^5 - 2*(g^3*i^2*n^2 + 3*g^3*i^2*n*log(e))*a^6*d^6)*B^2*log(b*x + a) + 6*(10*B^2*b^6*d^6*g^3*i^2*x^6 + 60*B^2*a^3*b^3*c^2*d^4*g^3*i^2*x + 12*(2*b^6*c*d^5*g^3*i^2 + 3*a*b^5*d^6*g^3*i^2)*B^2*x^5 + 15*(b^6*c^2*d^4*g^3*i^2 + 6*a*b^5*c*d^5*g^3*i^2 + 3*a^2*b^4*d^6*g^3*i^2)*B^2*x^4 + 20*(3*a*b^5*c^2*d^4*g^3*i^2 + 6*a^2*b^4*c*d^5*g^3*i^2 + a^3*b^3*d^6*g^3*i^2)*B^2*x^3 + 30*(3*a^2*b^4*c^2*d^4*g^3*i^2 + 2*a^3*b^3*c*d^5*g^3*i^2)*B^2*x^2)*log((b*x + a)^n)^2 + 6*(10*B^2*b^6*d^6*g^3*i^2*x^6 + 60*B^2*a^3*b^3*c^2*d^4*g^3*i^2*x + 12*(2*b^6*c*d^5*g^3*i^2 + 3*a*b^5*d^6*g^3*i^2)*B^2*x^5 + 15*(b^6*c^2*d^4*g^3*i^2 + 6*a*b^5*c*d^5*g^3*i^2 + 3*a^2*b^4*d^6*g^3*i^2)*B^2*x^4 + 20*(3*a*b^5*c^2*d^4*g^3*i^2 + 6*a^2*b^4*c*d^5*g^3*i^2 + a^3*b^3*d^6*g^3*i^2)*B^2*x^3 + 30*(3*a^2*b^4*c^2*d^4*g^3*i^2 + 2*a^3*b^3*c*d^5*g^3*i^2)*B^2*x^2)*log((d*x + c)^n)^2 + 2*(60*B^2*b^6*d^6*g^3*i^2*x^6*log(e) - 12*((g^3*i^2*n - 12*g^3*i^2*log(e))*b^6*c*d^5 - (g^3*i^2*n + 18*g^3*i^2*log(e))*a*b^5*d^6)*B^2*x^5 - 3*((7*g^3*i^2*n - 30*g^3*i^2*log(e))*b^6*c^2*d^4 + 6*(g^3*i^2*n - 30*g^3*i^2*log(e))*a*b^5*c*d^5 - (13*g^3*i^2*n + 90*g^3*i^2*log(e))*a^2*b^4*d^6)*B^2*x^4 - 2*(b^6*c^3*d^3*g^3*i^2*n + 3*(13*g^3*i^2*n - 60*g^3*i^2*log(e))*a*b^5*c^2*d^4 - 3*(7*g^3*i^2*n + 120*g^3*i^2*log(e))*a^2*b^4*c*d^5 - (19*g^3*i^2*n + 60*g^3*i^2*log(e))*a^3*b^3*d^6)*B^2*x^3 + 3*(b^6*c^4*d^2*g^3*i^2*n - 6*a*b^5*c^3*d^3*g^3*i^2*n + a^4*b^2*d^6*g^3*i^2*n - 30*(g^3*i^2*n - 6*g^3*i^2*log(e))*a^2*b^4*c^2*d^4 + 2*(17*g^3*i^2*n + 60*g^3*i^2*log(e))*a^3*b^3*c*d^5)*B^2*x^2 - 6*(b^6*c^5*d*g^3*i^2*n - 6*a*b^5*c^4*d^2*g^3*i^2*n + 15*a^2*b^4*c^3*d^3*g^3*i^2*n - 6*a^4*b^2*c*d^5*g^3*i^2*n + a^5*b*d^6*g^3*i^2*n - 5*(g^3*i^2*n + 12*g^3*i^2*log(e))*a^3*b^3*c^2*d^4)*B^2*x + 6*(15*a^4*b^2*c^2*d^4*g^3*i^2*n - 6*a^5*b*c*d^5*g^3*i^2*n + a^6*d^6*g^3*i^2*n)*B^2*log(b*x + a) + 6*(b^6*c^6*g^3*i^2*n - 6*a*b^5*c^5*d*g^3*i^2*n + 15*a^2*b^4*c^4*d^2*g^3*i^2*n - 20*a^3*b^3*c^3*d^3*g^3*i^2*n)*B^2*log(d*x + c))*log((b*x + a)^n) - 2*(60*B^2*b^6*d^6*g^3*i^2*x^6*log(e) - 12*((g^3*i^2*n - 12*g^3*i^2*log(e))*b^6*c*d^5 - (g^3*i^2*n + 18*g^3*i^2*log(e))*a*b^5*d^6)*B^2*x^5 - 3*((7*g^3*i^2*n - 30*g^3*i^2*log(e))*b^6*c^2*d^4 + 6*(g^3*i^2*n - 30*g^3*i^2*log(e))*a*b^5*c*d^5 - (13*g^3*i^2*n + 90*g^3*i^2*log(e))*a^2*b^4*d^6)*B^2*x^4 - 2*(b^6*c^3*d^3*g^3*i^2*n + 3*(13*g^3*i^2*n - 60*g^3*i^2*log(e))*a*b^5*c^2*d^4 - 3*(7*g^3*i^2*n + 120*g^3*i^2*log(e))*a^2*b^4*c*d^5 - (19*g^3*i^2*n + 60*g^3*i^2*log(e))*a^3*b^3*d^6)*B^2*x^3 + 3*(b^6*c^4*d^2*g^3*i^2*n - 6*a*b^5*c^3*d^3*g^3*i^2*n + a^4*b^2*d^6*g^3*i^2*n - 30*(g^3*i^2*n - 6*g^3*i^2*log(e))*a^2*b^4*c^2*d^4 + 2*(17*g^3*i^2*n + 60*g^3*i^2*log(e))*a^3*b^3*c*d^5)*B^2*x^2 - 6*(b^6*c^5*d*g^3*i^2*n - 6*a*b^5*c^4*d^2*g^3*i^2*n + 15*a^2*b^4*c^3*d^3*g^3*i^2*n - 6*a^4*b^2*c*d^5*g^3*i^2*n + a^5*b*d^6*g^3*i^2*n - 5*(g^3*i^2*n + 12*g^3*i^2*log(e))*a^3*b^3*c^2*d^4)*B^2*x + 6*(15*a^4*b^2*c^2*d^4*g^3*i^2*n - 6*a^5*b*c*d^5*g^3*i^2*n + a^6*d^6*g^3*i^2*n)*B^2*log(b*x + a) + 6*(b^6*c^6*g^3*i^2*n - 6*a*b^5*c^5*d*g^3*i^2*n + 15*a^2*b^4*c^4*d^2*g^3*i^2*n - 20*a^3*b^3*c^3*d^3*g^3*i^2*n)*B^2*log(d*x + c) + 6*(10*B^2*b^6*d^6*g^3*i^2*x^6 + 60*B^2*a^3*b^3*c^2*d^4*g^3*i^2*x + 12*(2*b^6*c*d^5*g^3*i^2 + 3*a*b^5*d^6*g^3*i^2)*B^2*x^5 + 15*(b^6*c^2*d^4*g^3*i^2 + 6*a*b^5*c*d^5*g^3*i^2 + 3*a^2*b^4*d^6*g^3*i^2)*B^2*x^4 + 20*(3*a*b^5*c^2*d^4*g^3*i^2 + 6*a^2*b^4*c*d^5*g^3*i^2 + a^3*b^3*d^6*g^3*i^2)*B^2*x^3 + 30*(3*a^2*b^4*c^2*d^4*g^3*i^2 + 2*a^3*b^3*c*d^5*g^3*i^2)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d^4)","B",0
169,1,4247,0,7.580430," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{5} \, A B b^{2} d^{2} g^{2} i^{2} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{5} \, A^{2} b^{2} d^{2} g^{2} i^{2} x^{5} + A B b^{2} c d g^{2} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A B a b d^{2} g^{2} i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A^{2} b^{2} c d g^{2} i^{2} x^{4} + \frac{1}{2} \, A^{2} a b d^{2} g^{2} i^{2} x^{4} + \frac{2}{3} \, A B b^{2} c^{2} g^{2} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{8}{3} \, A B a b c d g^{2} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{3} \, A B a^{2} d^{2} g^{2} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A^{2} b^{2} c^{2} g^{2} i^{2} x^{3} + \frac{4}{3} \, A^{2} a b c d g^{2} i^{2} x^{3} + \frac{1}{3} \, A^{2} a^{2} d^{2} g^{2} i^{2} x^{3} + 2 \, A B a b c^{2} g^{2} i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A B a^{2} c d g^{2} i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a b c^{2} g^{2} i^{2} x^{2} + A^{2} a^{2} c d g^{2} i^{2} x^{2} + \frac{1}{30} \, A B b^{2} d^{2} g^{2} i^{2} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{6} \, A B b^{2} c d g^{2} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{6} \, A B a b d^{2} g^{2} i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{3} \, A B b^{2} c^{2} g^{2} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{4}{3} \, A B a b c d g^{2} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{3} \, A B a^{2} d^{2} g^{2} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - 2 \, A B a b c^{2} g^{2} i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - 2 \, A B a^{2} c d g^{2} i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a^{2} c^{2} g^{2} i^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a^{2} c^{2} g^{2} i^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{2} c^{2} g^{2} i^{2} x - \frac{{\left(9 \, a^{3} b c^{2} d^{3} g^{2} i^{2} n^{2} - 2 \, a^{4} c d^{4} g^{2} i^{2} n^{2} + 2 \, b^{4} c^{5} g^{2} i^{2} n \log\left(e\right) + 2 \, {\left(g^{2} i^{2} n^{2} - 5 \, g^{2} i^{2} n \log\left(e\right)\right)} a b^{3} c^{4} d - {\left(9 \, g^{2} i^{2} n^{2} - 20 \, g^{2} i^{2} n \log\left(e\right)\right)} a^{2} b^{2} c^{3} d^{2}\right)} B^{2} \log\left(d x + c\right)}{30 \, b^{2} d^{3}} - \frac{{\left(b^{5} c^{5} g^{2} i^{2} n^{2} - 5 \, a b^{4} c^{4} d g^{2} i^{2} n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2} n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{2} i^{2} n^{2} + 5 \, a^{4} b c d^{4} g^{2} i^{2} n^{2} - a^{5} d^{5} g^{2} i^{2} n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{15 \, b^{3} d^{3}} + \frac{12 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} \log\left(e\right)^{2} - 6 \, {\left({\left(g^{2} i^{2} n \log\left(e\right) - 5 \, g^{2} i^{2} \log\left(e\right)^{2}\right)} b^{5} c d^{4} - {\left(g^{2} i^{2} n \log\left(e\right) + 5 \, g^{2} i^{2} \log\left(e\right)^{2}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left({\left(g^{2} i^{2} n^{2} - 6 \, g^{2} i^{2} n \log\left(e\right) + 10 \, g^{2} i^{2} \log\left(e\right)^{2}\right)} b^{5} c^{2} d^{3} - 2 \, {\left(g^{2} i^{2} n^{2} - 20 \, g^{2} i^{2} \log\left(e\right)^{2}\right)} a b^{4} c d^{4} + {\left(g^{2} i^{2} n^{2} + 6 \, g^{2} i^{2} n \log\left(e\right) + 10 \, g^{2} i^{2} \log\left(e\right)^{2}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + {\left({\left(3 \, g^{2} i^{2} n^{2} - 2 \, g^{2} i^{2} n \log\left(e\right)\right)} b^{5} c^{3} d^{2} - 3 \, {\left(g^{2} i^{2} n^{2} + 10 \, g^{2} i^{2} n \log\left(e\right) - 20 \, g^{2} i^{2} \log\left(e\right)^{2}\right)} a b^{4} c^{2} d^{3} - 3 \, {\left(g^{2} i^{2} n^{2} - 10 \, g^{2} i^{2} n \log\left(e\right) - 20 \, g^{2} i^{2} \log\left(e\right)^{2}\right)} a^{2} b^{3} c d^{4} + {\left(3 \, g^{2} i^{2} n^{2} + 2 \, g^{2} i^{2} n \log\left(e\right)\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 2 \, {\left(10 \, a^{3} b^{2} c^{2} d^{3} g^{2} i^{2} n^{2} - 5 \, a^{4} b c d^{4} g^{2} i^{2} n^{2} + a^{5} d^{5} g^{2} i^{2} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + 4 \, {\left(b^{5} c^{5} g^{2} i^{2} n^{2} - 5 \, a b^{4} c^{4} d g^{2} i^{2} n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) - 2 \, {\left(b^{5} c^{5} g^{2} i^{2} n^{2} - 5 \, a b^{4} c^{4} d g^{2} i^{2} n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(g^{2} i^{2} n^{2} - g^{2} i^{2} n \log\left(e\right)\right)} b^{5} c^{4} d - {\left(11 \, g^{2} i^{2} n^{2} - 10 \, g^{2} i^{2} n \log\left(e\right)\right)} a b^{4} c^{3} d^{2} + 6 \, {\left(3 \, g^{2} i^{2} n^{2} - 5 \, g^{2} i^{2} \log\left(e\right)^{2}\right)} a^{2} b^{3} c^{2} d^{3} - {\left(11 \, g^{2} i^{2} n^{2} + 10 \, g^{2} i^{2} n \log\left(e\right)\right)} a^{3} b^{2} c d^{4} + 2 \, {\left(g^{2} i^{2} n^{2} + g^{2} i^{2} n \log\left(e\right)\right)} a^{4} b d^{5}\right)} B^{2} x + 2 \, {\left(2 \, a b^{4} c^{4} d g^{2} i^{2} n^{2} - 9 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2} n^{2} + 2 \, a^{5} d^{5} g^{2} i^{2} n \log\left(e\right) + {\left(9 \, g^{2} i^{2} n^{2} + 20 \, g^{2} i^{2} n \log\left(e\right)\right)} a^{3} b^{2} c^{2} d^{3} - 2 \, {\left(g^{2} i^{2} n^{2} + 5 \, g^{2} i^{2} n \log\left(e\right)\right)} a^{4} b c d^{4}\right)} B^{2} \log\left(b x + a\right) + 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} + 30 \, B^{2} a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} x + 15 \, {\left(b^{5} c d^{4} g^{2} i^{2} + a b^{4} d^{5} g^{2} i^{2}\right)} B^{2} x^{4} + 10 \, {\left(b^{5} c^{2} d^{3} g^{2} i^{2} + 4 \, a b^{4} c d^{4} g^{2} i^{2} + a^{2} b^{3} d^{5} g^{2} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(a b^{4} c^{2} d^{3} g^{2} i^{2} + a^{2} b^{3} c d^{4} g^{2} i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} + 30 \, B^{2} a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} x + 15 \, {\left(b^{5} c d^{4} g^{2} i^{2} + a b^{4} d^{5} g^{2} i^{2}\right)} B^{2} x^{4} + 10 \, {\left(b^{5} c^{2} d^{3} g^{2} i^{2} + 4 \, a b^{4} c d^{4} g^{2} i^{2} + a^{2} b^{3} d^{5} g^{2} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(a b^{4} c^{2} d^{3} g^{2} i^{2} + a^{2} b^{3} c d^{4} g^{2} i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} \log\left(e\right) - 3 \, {\left({\left(g^{2} i^{2} n - 10 \, g^{2} i^{2} \log\left(e\right)\right)} b^{5} c d^{4} - {\left(g^{2} i^{2} n + 10 \, g^{2} i^{2} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left(40 \, a b^{4} c d^{4} g^{2} i^{2} \log\left(e\right) - {\left(3 \, g^{2} i^{2} n - 10 \, g^{2} i^{2} \log\left(e\right)\right)} b^{5} c^{2} d^{3} + {\left(3 \, g^{2} i^{2} n + 10 \, g^{2} i^{2} \log\left(e\right)\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left(b^{5} c^{3} d^{2} g^{2} i^{2} n - a^{3} b^{2} d^{5} g^{2} i^{2} n + 15 \, {\left(g^{2} i^{2} n - 4 \, g^{2} i^{2} \log\left(e\right)\right)} a b^{4} c^{2} d^{3} - 15 \, {\left(g^{2} i^{2} n + 4 \, g^{2} i^{2} \log\left(e\right)\right)} a^{2} b^{3} c d^{4}\right)} B^{2} x^{2} + 2 \, {\left(b^{5} c^{4} d g^{2} i^{2} n - 5 \, a b^{4} c^{3} d^{2} g^{2} i^{2} n + 5 \, a^{3} b^{2} c d^{4} g^{2} i^{2} n - a^{4} b d^{5} g^{2} i^{2} n + 30 \, a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} \log\left(e\right)\right)} B^{2} x + 2 \, {\left(10 \, a^{3} b^{2} c^{2} d^{3} g^{2} i^{2} n - 5 \, a^{4} b c d^{4} g^{2} i^{2} n + a^{5} d^{5} g^{2} i^{2} n\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b^{5} c^{5} g^{2} i^{2} n - 5 \, a b^{4} c^{4} d g^{2} i^{2} n + 10 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2} n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} \log\left(e\right) - 3 \, {\left({\left(g^{2} i^{2} n - 10 \, g^{2} i^{2} \log\left(e\right)\right)} b^{5} c d^{4} - {\left(g^{2} i^{2} n + 10 \, g^{2} i^{2} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left(40 \, a b^{4} c d^{4} g^{2} i^{2} \log\left(e\right) - {\left(3 \, g^{2} i^{2} n - 10 \, g^{2} i^{2} \log\left(e\right)\right)} b^{5} c^{2} d^{3} + {\left(3 \, g^{2} i^{2} n + 10 \, g^{2} i^{2} \log\left(e\right)\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left(b^{5} c^{3} d^{2} g^{2} i^{2} n - a^{3} b^{2} d^{5} g^{2} i^{2} n + 15 \, {\left(g^{2} i^{2} n - 4 \, g^{2} i^{2} \log\left(e\right)\right)} a b^{4} c^{2} d^{3} - 15 \, {\left(g^{2} i^{2} n + 4 \, g^{2} i^{2} \log\left(e\right)\right)} a^{2} b^{3} c d^{4}\right)} B^{2} x^{2} + 2 \, {\left(b^{5} c^{4} d g^{2} i^{2} n - 5 \, a b^{4} c^{3} d^{2} g^{2} i^{2} n + 5 \, a^{3} b^{2} c d^{4} g^{2} i^{2} n - a^{4} b d^{5} g^{2} i^{2} n + 30 \, a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} \log\left(e\right)\right)} B^{2} x + 2 \, {\left(10 \, a^{3} b^{2} c^{2} d^{3} g^{2} i^{2} n - 5 \, a^{4} b c d^{4} g^{2} i^{2} n + a^{5} d^{5} g^{2} i^{2} n\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b^{5} c^{5} g^{2} i^{2} n - 5 \, a b^{4} c^{4} d g^{2} i^{2} n + 10 \, a^{2} b^{3} c^{3} d^{2} g^{2} i^{2} n\right)} B^{2} \log\left(d x + c\right) + 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{2} i^{2} x^{5} + 30 \, B^{2} a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} x + 15 \, {\left(b^{5} c d^{4} g^{2} i^{2} + a b^{4} d^{5} g^{2} i^{2}\right)} B^{2} x^{4} + 10 \, {\left(b^{5} c^{2} d^{3} g^{2} i^{2} + 4 \, a b^{4} c d^{4} g^{2} i^{2} + a^{2} b^{3} d^{5} g^{2} i^{2}\right)} B^{2} x^{3} + 30 \, {\left(a b^{4} c^{2} d^{3} g^{2} i^{2} + a^{2} b^{3} c d^{4} g^{2} i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{60 \, b^{3} d^{3}}"," ",0,"2/5*A*B*b^2*d^2*g^2*i^2*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A^2*b^2*d^2*g^2*i^2*x^5 + A*B*b^2*c*d*g^2*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*B*a*b*d^2*g^2*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*b^2*c*d*g^2*i^2*x^4 + 1/2*A^2*a*b*d^2*g^2*i^2*x^4 + 2/3*A*B*b^2*c^2*g^2*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 8/3*A*B*a*b*c*d*g^2*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/3*A*B*a^2*d^2*g^2*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A^2*b^2*c^2*g^2*i^2*x^3 + 4/3*A^2*a*b*c*d*g^2*i^2*x^3 + 1/3*A^2*a^2*d^2*g^2*i^2*x^3 + 2*A*B*a*b*c^2*g^2*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*B*a^2*c*d*g^2*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b*c^2*g^2*i^2*x^2 + A^2*a^2*c*d*g^2*i^2*x^2 + 1/30*A*B*b^2*d^2*g^2*i^2*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/6*A*B*b^2*c*d*g^2*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/6*A*B*a*b*d^2*g^2*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/3*A*B*b^2*c^2*g^2*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 4/3*A*B*a*b*c*d*g^2*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/3*A*B*a^2*d^2*g^2*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 2*A*B*a*b*c^2*g^2*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 2*A*B*a^2*c*d*g^2*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a^2*c^2*g^2*i^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^2*c^2*g^2*i^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^2*c^2*g^2*i^2*x - 1/30*(9*a^3*b*c^2*d^3*g^2*i^2*n^2 - 2*a^4*c*d^4*g^2*i^2*n^2 + 2*b^4*c^5*g^2*i^2*n*log(e) + 2*(g^2*i^2*n^2 - 5*g^2*i^2*n*log(e))*a*b^3*c^4*d - (9*g^2*i^2*n^2 - 20*g^2*i^2*n*log(e))*a^2*b^2*c^3*d^2)*B^2*log(d*x + c)/(b^2*d^3) - 1/15*(b^5*c^5*g^2*i^2*n^2 - 5*a*b^4*c^4*d*g^2*i^2*n^2 + 10*a^2*b^3*c^3*d^2*g^2*i^2*n^2 - 10*a^3*b^2*c^2*d^3*g^2*i^2*n^2 + 5*a^4*b*c*d^4*g^2*i^2*n^2 - a^5*d^5*g^2*i^2*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^3*d^3) + 1/60*(12*B^2*b^5*d^5*g^2*i^2*x^5*log(e)^2 - 6*((g^2*i^2*n*log(e) - 5*g^2*i^2*log(e)^2)*b^5*c*d^4 - (g^2*i^2*n*log(e) + 5*g^2*i^2*log(e)^2)*a*b^4*d^5)*B^2*x^4 + 2*((g^2*i^2*n^2 - 6*g^2*i^2*n*log(e) + 10*g^2*i^2*log(e)^2)*b^5*c^2*d^3 - 2*(g^2*i^2*n^2 - 20*g^2*i^2*log(e)^2)*a*b^4*c*d^4 + (g^2*i^2*n^2 + 6*g^2*i^2*n*log(e) + 10*g^2*i^2*log(e)^2)*a^2*b^3*d^5)*B^2*x^3 + ((3*g^2*i^2*n^2 - 2*g^2*i^2*n*log(e))*b^5*c^3*d^2 - 3*(g^2*i^2*n^2 + 10*g^2*i^2*n*log(e) - 20*g^2*i^2*log(e)^2)*a*b^4*c^2*d^3 - 3*(g^2*i^2*n^2 - 10*g^2*i^2*n*log(e) - 20*g^2*i^2*log(e)^2)*a^2*b^3*c*d^4 + (3*g^2*i^2*n^2 + 2*g^2*i^2*n*log(e))*a^3*b^2*d^5)*B^2*x^2 - 2*(10*a^3*b^2*c^2*d^3*g^2*i^2*n^2 - 5*a^4*b*c*d^4*g^2*i^2*n^2 + a^5*d^5*g^2*i^2*n^2)*B^2*log(b*x + a)^2 + 4*(b^5*c^5*g^2*i^2*n^2 - 5*a*b^4*c^4*d*g^2*i^2*n^2 + 10*a^2*b^3*c^3*d^2*g^2*i^2*n^2)*B^2*log(b*x + a)*log(d*x + c) - 2*(b^5*c^5*g^2*i^2*n^2 - 5*a*b^4*c^4*d*g^2*i^2*n^2 + 10*a^2*b^3*c^3*d^2*g^2*i^2*n^2)*B^2*log(d*x + c)^2 - 2*(2*(g^2*i^2*n^2 - g^2*i^2*n*log(e))*b^5*c^4*d - (11*g^2*i^2*n^2 - 10*g^2*i^2*n*log(e))*a*b^4*c^3*d^2 + 6*(3*g^2*i^2*n^2 - 5*g^2*i^2*log(e)^2)*a^2*b^3*c^2*d^3 - (11*g^2*i^2*n^2 + 10*g^2*i^2*n*log(e))*a^3*b^2*c*d^4 + 2*(g^2*i^2*n^2 + g^2*i^2*n*log(e))*a^4*b*d^5)*B^2*x + 2*(2*a*b^4*c^4*d*g^2*i^2*n^2 - 9*a^2*b^3*c^3*d^2*g^2*i^2*n^2 + 2*a^5*d^5*g^2*i^2*n*log(e) + (9*g^2*i^2*n^2 + 20*g^2*i^2*n*log(e))*a^3*b^2*c^2*d^3 - 2*(g^2*i^2*n^2 + 5*g^2*i^2*n*log(e))*a^4*b*c*d^4)*B^2*log(b*x + a) + 2*(6*B^2*b^5*d^5*g^2*i^2*x^5 + 30*B^2*a^2*b^3*c^2*d^3*g^2*i^2*x + 15*(b^5*c*d^4*g^2*i^2 + a*b^4*d^5*g^2*i^2)*B^2*x^4 + 10*(b^5*c^2*d^3*g^2*i^2 + 4*a*b^4*c*d^4*g^2*i^2 + a^2*b^3*d^5*g^2*i^2)*B^2*x^3 + 30*(a*b^4*c^2*d^3*g^2*i^2 + a^2*b^3*c*d^4*g^2*i^2)*B^2*x^2)*log((b*x + a)^n)^2 + 2*(6*B^2*b^5*d^5*g^2*i^2*x^5 + 30*B^2*a^2*b^3*c^2*d^3*g^2*i^2*x + 15*(b^5*c*d^4*g^2*i^2 + a*b^4*d^5*g^2*i^2)*B^2*x^4 + 10*(b^5*c^2*d^3*g^2*i^2 + 4*a*b^4*c*d^4*g^2*i^2 + a^2*b^3*d^5*g^2*i^2)*B^2*x^3 + 30*(a*b^4*c^2*d^3*g^2*i^2 + a^2*b^3*c*d^4*g^2*i^2)*B^2*x^2)*log((d*x + c)^n)^2 + 2*(12*B^2*b^5*d^5*g^2*i^2*x^5*log(e) - 3*((g^2*i^2*n - 10*g^2*i^2*log(e))*b^5*c*d^4 - (g^2*i^2*n + 10*g^2*i^2*log(e))*a*b^4*d^5)*B^2*x^4 + 2*(40*a*b^4*c*d^4*g^2*i^2*log(e) - (3*g^2*i^2*n - 10*g^2*i^2*log(e))*b^5*c^2*d^3 + (3*g^2*i^2*n + 10*g^2*i^2*log(e))*a^2*b^3*d^5)*B^2*x^3 - (b^5*c^3*d^2*g^2*i^2*n - a^3*b^2*d^5*g^2*i^2*n + 15*(g^2*i^2*n - 4*g^2*i^2*log(e))*a*b^4*c^2*d^3 - 15*(g^2*i^2*n + 4*g^2*i^2*log(e))*a^2*b^3*c*d^4)*B^2*x^2 + 2*(b^5*c^4*d*g^2*i^2*n - 5*a*b^4*c^3*d^2*g^2*i^2*n + 5*a^3*b^2*c*d^4*g^2*i^2*n - a^4*b*d^5*g^2*i^2*n + 30*a^2*b^3*c^2*d^3*g^2*i^2*log(e))*B^2*x + 2*(10*a^3*b^2*c^2*d^3*g^2*i^2*n - 5*a^4*b*c*d^4*g^2*i^2*n + a^5*d^5*g^2*i^2*n)*B^2*log(b*x + a) - 2*(b^5*c^5*g^2*i^2*n - 5*a*b^4*c^4*d*g^2*i^2*n + 10*a^2*b^3*c^3*d^2*g^2*i^2*n)*B^2*log(d*x + c))*log((b*x + a)^n) - 2*(12*B^2*b^5*d^5*g^2*i^2*x^5*log(e) - 3*((g^2*i^2*n - 10*g^2*i^2*log(e))*b^5*c*d^4 - (g^2*i^2*n + 10*g^2*i^2*log(e))*a*b^4*d^5)*B^2*x^4 + 2*(40*a*b^4*c*d^4*g^2*i^2*log(e) - (3*g^2*i^2*n - 10*g^2*i^2*log(e))*b^5*c^2*d^3 + (3*g^2*i^2*n + 10*g^2*i^2*log(e))*a^2*b^3*d^5)*B^2*x^3 - (b^5*c^3*d^2*g^2*i^2*n - a^3*b^2*d^5*g^2*i^2*n + 15*(g^2*i^2*n - 4*g^2*i^2*log(e))*a*b^4*c^2*d^3 - 15*(g^2*i^2*n + 4*g^2*i^2*log(e))*a^2*b^3*c*d^4)*B^2*x^2 + 2*(b^5*c^4*d*g^2*i^2*n - 5*a*b^4*c^3*d^2*g^2*i^2*n + 5*a^3*b^2*c*d^4*g^2*i^2*n - a^4*b*d^5*g^2*i^2*n + 30*a^2*b^3*c^2*d^3*g^2*i^2*log(e))*B^2*x + 2*(10*a^3*b^2*c^2*d^3*g^2*i^2*n - 5*a^4*b*c*d^4*g^2*i^2*n + a^5*d^5*g^2*i^2*n)*B^2*log(b*x + a) - 2*(b^5*c^5*g^2*i^2*n - 5*a*b^4*c^4*d*g^2*i^2*n + 10*a^2*b^3*c^3*d^2*g^2*i^2*n)*B^2*log(d*x + c) + 2*(6*B^2*b^5*d^5*g^2*i^2*x^5 + 30*B^2*a^2*b^3*c^2*d^3*g^2*i^2*x + 15*(b^5*c*d^4*g^2*i^2 + a*b^4*d^5*g^2*i^2)*B^2*x^4 + 10*(b^5*c^2*d^3*g^2*i^2 + 4*a*b^4*c*d^4*g^2*i^2 + a^2*b^3*d^5*g^2*i^2)*B^2*x^3 + 30*(a*b^4*c^2*d^3*g^2*i^2 + a^2*b^3*c*d^4*g^2*i^2)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d^3)","B",0
170,1,2662,0,7.606908," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A B b d^{2} g i^{2} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A^{2} b d^{2} g i^{2} x^{4} + \frac{4}{3} \, A B b c d g i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{3} \, A B a d^{2} g i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{2}{3} \, A^{2} b c d g i^{2} x^{3} + \frac{1}{3} \, A^{2} a d^{2} g i^{2} x^{3} + A B b c^{2} g i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A B a c d g i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A^{2} b c^{2} g i^{2} x^{2} + A^{2} a c d g i^{2} x^{2} - \frac{1}{12} \, A B b d^{2} g i^{2} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{2}{3} \, A B b c d g i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + \frac{1}{3} \, A B a d^{2} g i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - A B b c^{2} g i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - 2 \, A B a c d g i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a c^{2} g i^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a c^{2} g i^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a c^{2} g i^{2} x - \frac{{\left(7 \, a^{2} b c^{2} d^{2} g i^{2} n^{2} - 2 \, a^{3} c d^{3} g i^{2} n^{2} + {\left(g i^{2} n^{2} - 2 \, g i^{2} n \log\left(e\right)\right)} b^{3} c^{4} - 2 \, {\left(3 \, g i^{2} n^{2} - 4 \, g i^{2} n \log\left(e\right)\right)} a b^{2} c^{3} d\right)} B^{2} \log\left(d x + c\right)}{12 \, b^{2} d^{2}} + \frac{{\left(b^{4} c^{4} g i^{2} n^{2} - 4 \, a b^{3} c^{3} d g i^{2} n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g i^{2} n^{2} - 4 \, a^{3} b c d^{3} g i^{2} n^{2} + a^{4} d^{4} g i^{2} n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{6 \, b^{3} d^{2}} + \frac{3 \, B^{2} b^{4} d^{4} g i^{2} x^{4} \log\left(e\right)^{2} - 2 \, {\left({\left(g i^{2} n \log\left(e\right) - 4 \, g i^{2} \log\left(e\right)^{2}\right)} b^{4} c d^{3} - {\left(g i^{2} n \log\left(e\right) + 2 \, g i^{2} \log\left(e\right)^{2}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left({\left(g i^{2} n^{2} - 5 \, g i^{2} n \log\left(e\right) + 6 \, g i^{2} \log\left(e\right)^{2}\right)} b^{4} c^{2} d^{2} - 2 \, {\left(g i^{2} n^{2} - 2 \, g i^{2} n \log\left(e\right) - 6 \, g i^{2} \log\left(e\right)^{2}\right)} a b^{3} c d^{3} + {\left(g i^{2} n^{2} + g i^{2} n \log\left(e\right)\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - {\left(6 \, a^{2} b^{2} c^{2} d^{2} g i^{2} n^{2} - 4 \, a^{3} b c d^{3} g i^{2} n^{2} + a^{4} d^{4} g i^{2} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} - 2 \, {\left(b^{4} c^{4} g i^{2} n^{2} - 4 \, a b^{3} c^{3} d g i^{2} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) + {\left(b^{4} c^{4} g i^{2} n^{2} - 4 \, a b^{3} c^{3} d g i^{2} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + {\left({\left(3 \, g i^{2} n^{2} - 2 \, g i^{2} n \log\left(e\right)\right)} b^{4} c^{3} d - {\left(7 \, g i^{2} n^{2} + 4 \, g i^{2} n \log\left(e\right) - 12 \, g i^{2} \log\left(e\right)^{2}\right)} a b^{3} c^{2} d^{2} + {\left(5 \, g i^{2} n^{2} + 8 \, g i^{2} n \log\left(e\right)\right)} a^{2} b^{2} c d^{3} - {\left(g i^{2} n^{2} + 2 \, g i^{2} n \log\left(e\right)\right)} a^{3} b d^{4}\right)} B^{2} x - {\left(2 \, a b^{3} c^{3} d g i^{2} n^{2} - {\left(g i^{2} n^{2} + 12 \, g i^{2} n \log\left(e\right)\right)} a^{2} b^{2} c^{2} d^{2} - 2 \, {\left(g i^{2} n^{2} - 4 \, g i^{2} n \log\left(e\right)\right)} a^{3} b c d^{3} + {\left(g i^{2} n^{2} - 2 \, g i^{2} n \log\left(e\right)\right)} a^{4} d^{4}\right)} B^{2} \log\left(b x + a\right) + {\left(3 \, B^{2} b^{4} d^{4} g i^{2} x^{4} + 12 \, B^{2} a b^{3} c^{2} d^{2} g i^{2} x + 4 \, {\left(2 \, b^{4} c d^{3} g i^{2} + a b^{3} d^{4} g i^{2}\right)} B^{2} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} g i^{2} + 2 \, a b^{3} c d^{3} g i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(3 \, B^{2} b^{4} d^{4} g i^{2} x^{4} + 12 \, B^{2} a b^{3} c^{2} d^{2} g i^{2} x + 4 \, {\left(2 \, b^{4} c d^{3} g i^{2} + a b^{3} d^{4} g i^{2}\right)} B^{2} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} g i^{2} + 2 \, a b^{3} c d^{3} g i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g i^{2} x^{4} \log\left(e\right) - 2 \, {\left({\left(g i^{2} n - 8 \, g i^{2} \log\left(e\right)\right)} b^{4} c d^{3} - {\left(g i^{2} n + 4 \, g i^{2} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left(a^{2} b^{2} d^{4} g i^{2} n - {\left(5 \, g i^{2} n - 12 \, g i^{2} \log\left(e\right)\right)} b^{4} c^{2} d^{2} + 4 \, {\left(g i^{2} n + 6 \, g i^{2} \log\left(e\right)\right)} a b^{3} c d^{3}\right)} B^{2} x^{2} - 2 \, {\left(b^{4} c^{3} d g i^{2} n - 4 \, a^{2} b^{2} c d^{3} g i^{2} n + a^{3} b d^{4} g i^{2} n + 2 \, {\left(g i^{2} n - 6 \, g i^{2} \log\left(e\right)\right)} a b^{3} c^{2} d^{2}\right)} B^{2} x + 2 \, {\left(6 \, a^{2} b^{2} c^{2} d^{2} g i^{2} n - 4 \, a^{3} b c d^{3} g i^{2} n + a^{4} d^{4} g i^{2} n\right)} B^{2} \log\left(b x + a\right) + 2 \, {\left(b^{4} c^{4} g i^{2} n - 4 \, a b^{3} c^{3} d g i^{2} n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(6 \, B^{2} b^{4} d^{4} g i^{2} x^{4} \log\left(e\right) - 2 \, {\left({\left(g i^{2} n - 8 \, g i^{2} \log\left(e\right)\right)} b^{4} c d^{3} - {\left(g i^{2} n + 4 \, g i^{2} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left(a^{2} b^{2} d^{4} g i^{2} n - {\left(5 \, g i^{2} n - 12 \, g i^{2} \log\left(e\right)\right)} b^{4} c^{2} d^{2} + 4 \, {\left(g i^{2} n + 6 \, g i^{2} \log\left(e\right)\right)} a b^{3} c d^{3}\right)} B^{2} x^{2} - 2 \, {\left(b^{4} c^{3} d g i^{2} n - 4 \, a^{2} b^{2} c d^{3} g i^{2} n + a^{3} b d^{4} g i^{2} n + 2 \, {\left(g i^{2} n - 6 \, g i^{2} \log\left(e\right)\right)} a b^{3} c^{2} d^{2}\right)} B^{2} x + 2 \, {\left(6 \, a^{2} b^{2} c^{2} d^{2} g i^{2} n - 4 \, a^{3} b c d^{3} g i^{2} n + a^{4} d^{4} g i^{2} n\right)} B^{2} \log\left(b x + a\right) + 2 \, {\left(b^{4} c^{4} g i^{2} n - 4 \, a b^{3} c^{3} d g i^{2} n\right)} B^{2} \log\left(d x + c\right) + 2 \, {\left(3 \, B^{2} b^{4} d^{4} g i^{2} x^{4} + 12 \, B^{2} a b^{3} c^{2} d^{2} g i^{2} x + 4 \, {\left(2 \, b^{4} c d^{3} g i^{2} + a b^{3} d^{4} g i^{2}\right)} B^{2} x^{3} + 6 \, {\left(b^{4} c^{2} d^{2} g i^{2} + 2 \, a b^{3} c d^{3} g i^{2}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{12 \, b^{3} d^{2}}"," ",0,"1/2*A*B*b*d^2*g*i^2*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*b*d^2*g*i^2*x^4 + 4/3*A*B*b*c*d*g*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/3*A*B*a*d^2*g*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2/3*A^2*b*c*d*g*i^2*x^3 + 1/3*A^2*a*d^2*g*i^2*x^3 + A*B*b*c^2*g*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*B*a*c*d*g*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*b*c^2*g*i^2*x^2 + A^2*a*c*d*g*i^2*x^2 - 1/12*A*B*b*d^2*g*i^2*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 2/3*A*B*b*c*d*g*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 1/3*A*B*a*d^2*g*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - A*B*b*c^2*g*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 2*A*B*a*c*d*g*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a*c^2*g*i^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a*c^2*g*i^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*c^2*g*i^2*x - 1/12*(7*a^2*b*c^2*d^2*g*i^2*n^2 - 2*a^3*c*d^3*g*i^2*n^2 + (g*i^2*n^2 - 2*g*i^2*n*log(e))*b^3*c^4 - 2*(3*g*i^2*n^2 - 4*g*i^2*n*log(e))*a*b^2*c^3*d)*B^2*log(d*x + c)/(b^2*d^2) + 1/6*(b^4*c^4*g*i^2*n^2 - 4*a*b^3*c^3*d*g*i^2*n^2 + 6*a^2*b^2*c^2*d^2*g*i^2*n^2 - 4*a^3*b*c*d^3*g*i^2*n^2 + a^4*d^4*g*i^2*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^3*d^2) + 1/12*(3*B^2*b^4*d^4*g*i^2*x^4*log(e)^2 - 2*((g*i^2*n*log(e) - 4*g*i^2*log(e)^2)*b^4*c*d^3 - (g*i^2*n*log(e) + 2*g*i^2*log(e)^2)*a*b^3*d^4)*B^2*x^3 + ((g*i^2*n^2 - 5*g*i^2*n*log(e) + 6*g*i^2*log(e)^2)*b^4*c^2*d^2 - 2*(g*i^2*n^2 - 2*g*i^2*n*log(e) - 6*g*i^2*log(e)^2)*a*b^3*c*d^3 + (g*i^2*n^2 + g*i^2*n*log(e))*a^2*b^2*d^4)*B^2*x^2 - (6*a^2*b^2*c^2*d^2*g*i^2*n^2 - 4*a^3*b*c*d^3*g*i^2*n^2 + a^4*d^4*g*i^2*n^2)*B^2*log(b*x + a)^2 - 2*(b^4*c^4*g*i^2*n^2 - 4*a*b^3*c^3*d*g*i^2*n^2)*B^2*log(b*x + a)*log(d*x + c) + (b^4*c^4*g*i^2*n^2 - 4*a*b^3*c^3*d*g*i^2*n^2)*B^2*log(d*x + c)^2 + ((3*g*i^2*n^2 - 2*g*i^2*n*log(e))*b^4*c^3*d - (7*g*i^2*n^2 + 4*g*i^2*n*log(e) - 12*g*i^2*log(e)^2)*a*b^3*c^2*d^2 + (5*g*i^2*n^2 + 8*g*i^2*n*log(e))*a^2*b^2*c*d^3 - (g*i^2*n^2 + 2*g*i^2*n*log(e))*a^3*b*d^4)*B^2*x - (2*a*b^3*c^3*d*g*i^2*n^2 - (g*i^2*n^2 + 12*g*i^2*n*log(e))*a^2*b^2*c^2*d^2 - 2*(g*i^2*n^2 - 4*g*i^2*n*log(e))*a^3*b*c*d^3 + (g*i^2*n^2 - 2*g*i^2*n*log(e))*a^4*d^4)*B^2*log(b*x + a) + (3*B^2*b^4*d^4*g*i^2*x^4 + 12*B^2*a*b^3*c^2*d^2*g*i^2*x + 4*(2*b^4*c*d^3*g*i^2 + a*b^3*d^4*g*i^2)*B^2*x^3 + 6*(b^4*c^2*d^2*g*i^2 + 2*a*b^3*c*d^3*g*i^2)*B^2*x^2)*log((b*x + a)^n)^2 + (3*B^2*b^4*d^4*g*i^2*x^4 + 12*B^2*a*b^3*c^2*d^2*g*i^2*x + 4*(2*b^4*c*d^3*g*i^2 + a*b^3*d^4*g*i^2)*B^2*x^3 + 6*(b^4*c^2*d^2*g*i^2 + 2*a*b^3*c*d^3*g*i^2)*B^2*x^2)*log((d*x + c)^n)^2 + (6*B^2*b^4*d^4*g*i^2*x^4*log(e) - 2*((g*i^2*n - 8*g*i^2*log(e))*b^4*c*d^3 - (g*i^2*n + 4*g*i^2*log(e))*a*b^3*d^4)*B^2*x^3 + (a^2*b^2*d^4*g*i^2*n - (5*g*i^2*n - 12*g*i^2*log(e))*b^4*c^2*d^2 + 4*(g*i^2*n + 6*g*i^2*log(e))*a*b^3*c*d^3)*B^2*x^2 - 2*(b^4*c^3*d*g*i^2*n - 4*a^2*b^2*c*d^3*g*i^2*n + a^3*b*d^4*g*i^2*n + 2*(g*i^2*n - 6*g*i^2*log(e))*a*b^3*c^2*d^2)*B^2*x + 2*(6*a^2*b^2*c^2*d^2*g*i^2*n - 4*a^3*b*c*d^3*g*i^2*n + a^4*d^4*g*i^2*n)*B^2*log(b*x + a) + 2*(b^4*c^4*g*i^2*n - 4*a*b^3*c^3*d*g*i^2*n)*B^2*log(d*x + c))*log((b*x + a)^n) - (6*B^2*b^4*d^4*g*i^2*x^4*log(e) - 2*((g*i^2*n - 8*g*i^2*log(e))*b^4*c*d^3 - (g*i^2*n + 4*g*i^2*log(e))*a*b^3*d^4)*B^2*x^3 + (a^2*b^2*d^4*g*i^2*n - (5*g*i^2*n - 12*g*i^2*log(e))*b^4*c^2*d^2 + 4*(g*i^2*n + 6*g*i^2*log(e))*a*b^3*c*d^3)*B^2*x^2 - 2*(b^4*c^3*d*g*i^2*n - 4*a^2*b^2*c*d^3*g*i^2*n + a^3*b*d^4*g*i^2*n + 2*(g*i^2*n - 6*g*i^2*log(e))*a*b^3*c^2*d^2)*B^2*x + 2*(6*a^2*b^2*c^2*d^2*g*i^2*n - 4*a^3*b*c*d^3*g*i^2*n + a^4*d^4*g*i^2*n)*B^2*log(b*x + a) + 2*(b^4*c^4*g*i^2*n - 4*a*b^3*c^3*d*g*i^2*n)*B^2*log(d*x + c) + 2*(3*B^2*b^4*d^4*g*i^2*x^4 + 12*B^2*a*b^3*c^2*d^2*g*i^2*x + 4*(2*b^4*c*d^3*g*i^2 + a*b^3*d^4*g*i^2)*B^2*x^3 + 6*(b^4*c^2*d^2*g*i^2 + 2*a*b^3*c*d^3*g*i^2)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d^2)","B",0
171,1,1473,0,6.457050," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{3} \, A B d^{2} i^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A^{2} d^{2} i^{2} x^{3} + 2 \, A B c d i^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c d i^{2} x^{2} + \frac{1}{3} \, A B d^{2} i^{2} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - 2 \, A B c d i^{2} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B c^{2} i^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B c^{2} i^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c^{2} i^{2} x - \frac{{\left(5 \, a b c^{2} d i^{2} n^{2} - 2 \, a^{2} c d^{2} i^{2} n^{2} - {\left(3 \, i^{2} n^{2} - 2 \, i^{2} n \log\left(e\right)\right)} b^{2} c^{3}\right)} B^{2} \log\left(d x + c\right)}{3 \, b^{2} d} - \frac{2 \, {\left(b^{3} c^{3} i^{2} n^{2} - 3 \, a b^{2} c^{2} d i^{2} n^{2} + 3 \, a^{2} b c d^{2} i^{2} n^{2} - a^{3} d^{3} i^{2} n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{3 \, b^{3} d} + \frac{B^{2} b^{3} d^{3} i^{2} x^{3} \log\left(e\right)^{2} + 2 \, B^{2} b^{3} c^{3} i^{2} n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - B^{2} b^{3} c^{3} i^{2} n^{2} \log\left(d x + c\right)^{2} + {\left(a b^{2} d^{3} i^{2} n \log\left(e\right) - {\left(i^{2} n \log\left(e\right) - 3 \, i^{2} \log\left(e\right)^{2}\right)} b^{3} c d^{2}\right)} B^{2} x^{2} - {\left(3 \, a b^{2} c^{2} d i^{2} n^{2} - 3 \, a^{2} b c d^{2} i^{2} n^{2} + a^{3} d^{3} i^{2} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + {\left({\left(i^{2} n^{2} - 4 \, i^{2} n \log\left(e\right) + 3 \, i^{2} \log\left(e\right)^{2}\right)} b^{3} c^{2} d - 2 \, {\left(i^{2} n^{2} - 3 \, i^{2} n \log\left(e\right)\right)} a b^{2} c d^{2} + {\left(i^{2} n^{2} - 2 \, i^{2} n \log\left(e\right)\right)} a^{2} b d^{3}\right)} B^{2} x - {\left(2 \, {\left(2 \, i^{2} n^{2} - 3 \, i^{2} n \log\left(e\right)\right)} a b^{2} c^{2} d - {\left(7 \, i^{2} n^{2} - 6 \, i^{2} n \log\left(e\right)\right)} a^{2} b c d^{2} + {\left(3 \, i^{2} n^{2} - 2 \, i^{2} n \log\left(e\right)\right)} a^{3} d^{3}\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} i^{2} x^{3} \log\left(e\right) - 2 \, B^{2} b^{3} c^{3} i^{2} n \log\left(d x + c\right) + {\left(a b^{2} d^{3} i^{2} n - {\left(i^{2} n - 6 \, i^{2} \log\left(e\right)\right)} b^{3} c d^{2}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} c d^{2} i^{2} n - a^{2} b d^{3} i^{2} n - {\left(2 \, i^{2} n - 3 \, i^{2} \log\left(e\right)\right)} b^{3} c^{2} d\right)} B^{2} x + 2 \, {\left(3 \, a b^{2} c^{2} d i^{2} n - 3 \, a^{2} b c d^{2} i^{2} n + a^{3} d^{3} i^{2} n\right)} B^{2} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, B^{2} b^{3} d^{3} i^{2} x^{3} \log\left(e\right) - 2 \, B^{2} b^{3} c^{3} i^{2} n \log\left(d x + c\right) + {\left(a b^{2} d^{3} i^{2} n - {\left(i^{2} n - 6 \, i^{2} \log\left(e\right)\right)} b^{3} c d^{2}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} c d^{2} i^{2} n - a^{2} b d^{3} i^{2} n - {\left(2 \, i^{2} n - 3 \, i^{2} \log\left(e\right)\right)} b^{3} c^{2} d\right)} B^{2} x + 2 \, {\left(3 \, a b^{2} c^{2} d i^{2} n - 3 \, a^{2} b c d^{2} i^{2} n + a^{3} d^{3} i^{2} n\right)} B^{2} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{3 \, b^{3} d}"," ",0,"2/3*A*B*d^2*i^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A^2*d^2*i^2*x^3 + 2*A*B*c*d*i^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c*d*i^2*x^2 + 1/3*A*B*d^2*i^2*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 2*A*B*c*d*i^2*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*c^2*i^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*c^2*i^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c^2*i^2*x - 1/3*(5*a*b*c^2*d*i^2*n^2 - 2*a^2*c*d^2*i^2*n^2 - (3*i^2*n^2 - 2*i^2*n*log(e))*b^2*c^3)*B^2*log(d*x + c)/(b^2*d) - 2/3*(b^3*c^3*i^2*n^2 - 3*a*b^2*c^2*d*i^2*n^2 + 3*a^2*b*c*d^2*i^2*n^2 - a^3*d^3*i^2*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^3*d) + 1/3*(B^2*b^3*d^3*i^2*x^3*log(e)^2 + 2*B^2*b^3*c^3*i^2*n^2*log(b*x + a)*log(d*x + c) - B^2*b^3*c^3*i^2*n^2*log(d*x + c)^2 + (a*b^2*d^3*i^2*n*log(e) - (i^2*n*log(e) - 3*i^2*log(e)^2)*b^3*c*d^2)*B^2*x^2 - (3*a*b^2*c^2*d*i^2*n^2 - 3*a^2*b*c*d^2*i^2*n^2 + a^3*d^3*i^2*n^2)*B^2*log(b*x + a)^2 + ((i^2*n^2 - 4*i^2*n*log(e) + 3*i^2*log(e)^2)*b^3*c^2*d - 2*(i^2*n^2 - 3*i^2*n*log(e))*a*b^2*c*d^2 + (i^2*n^2 - 2*i^2*n*log(e))*a^2*b*d^3)*B^2*x - (2*(2*i^2*n^2 - 3*i^2*n*log(e))*a*b^2*c^2*d - (7*i^2*n^2 - 6*i^2*n*log(e))*a^2*b*c*d^2 + (3*i^2*n^2 - 2*i^2*n*log(e))*a^3*d^3)*B^2*log(b*x + a) + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x)*log((b*x + a)^n)^2 + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x)*log((d*x + c)^n)^2 + (2*B^2*b^3*d^3*i^2*x^3*log(e) - 2*B^2*b^3*c^3*i^2*n*log(d*x + c) + (a*b^2*d^3*i^2*n - (i^2*n - 6*i^2*log(e))*b^3*c*d^2)*B^2*x^2 + 2*(3*a*b^2*c*d^2*i^2*n - a^2*b*d^3*i^2*n - (2*i^2*n - 3*i^2*log(e))*b^3*c^2*d)*B^2*x + 2*(3*a*b^2*c^2*d*i^2*n - 3*a^2*b*c*d^2*i^2*n + a^3*d^3*i^2*n)*B^2*log(b*x + a))*log((b*x + a)^n) - (2*B^2*b^3*d^3*i^2*x^3*log(e) - 2*B^2*b^3*c^3*i^2*n*log(d*x + c) + (a*b^2*d^3*i^2*n - (i^2*n - 6*i^2*log(e))*b^3*c*d^2)*B^2*x^2 + 2*(3*a*b^2*c*d^2*i^2*n - a^2*b*d^3*i^2*n - (2*i^2*n - 3*i^2*log(e))*b^3*c^2*d)*B^2*x + 2*(3*a*b^2*c^2*d*i^2*n - 3*a^2*b*c*d^2*i^2*n + a^3*d^3*i^2*n)*B^2*log(b*x + a) + 2*(B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d)","B",0
172,0,0,0,0.000000," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g),x, algorithm=""maxima"")","2 \, A^{2} c d i^{2} {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} + \frac{1}{2} \, A^{2} d^{2} i^{2} {\left(\frac{2 \, a^{2} \log\left(b x + a\right)}{b^{3} g} + \frac{b x^{2} - 2 \, a x}{b^{2} g}\right)} + \frac{A^{2} c^{2} i^{2} \log\left(b g x + a g\right)}{b g} + \frac{{\left(B^{2} b^{2} d^{2} i^{2} x^{2} + 2 \, {\left(2 \, b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B^{2} x + 2 \, {\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} B^{2} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, b^{3} g} - \int -\frac{B^{2} b^{3} c^{3} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c^{3} i^{2} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} i^{2} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c d^{2} i^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{2} b^{3} c^{2} d i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c^{2} d i^{2} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{3} c^{3} i^{2} \log\left(e\right) + A B b^{3} c^{3} i^{2} + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right) + A B b^{3} d^{3} i^{2}\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} \log\left(e\right) + A B b^{3} c d^{2} i^{2}\right)} x^{2} + 3 \, {\left(B^{2} b^{3} c^{2} d i^{2} \log\left(e\right) + A B b^{3} c^{2} d i^{2}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, B^{2} b^{3} c^{3} i^{2} \log\left(e\right) + 2 \, A B b^{3} c^{3} i^{2} + {\left(2 \, A B b^{3} d^{3} i^{2} + {\left(i^{2} n + 2 \, i^{2} \log\left(e\right)\right)} B^{2} b^{3} d^{3}\right)} x^{3} + {\left(6 \, A B b^{3} c d^{2} i^{2} - {\left(a b^{2} d^{3} i^{2} n - 2 \, {\left(2 \, i^{2} n + 3 \, i^{2} \log\left(e\right)\right)} b^{3} c d^{2}\right)} B^{2}\right)} x^{2} + 2 \, {\left(3 \, A B b^{3} c^{2} d i^{2} + {\left(2 \, a b^{2} c d^{2} i^{2} n - a^{2} b d^{3} i^{2} n + 3 \, b^{3} c^{2} d i^{2} \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b^{3} c^{2} d i^{2} n - 2 \, a b^{2} c d^{2} i^{2} n + a^{2} b d^{3} i^{2} n\right)} B^{2} x + {\left(a b^{2} c^{2} d i^{2} n - 2 \, a^{2} b c d^{2} i^{2} n + a^{3} d^{3} i^{2} n\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{4} d g x^{2} + a b^{3} c g + {\left(b^{4} c g + a b^{3} d g\right)} x}\,{d x}"," ",0,"2*A^2*c*d*i^2*(x/(b*g) - a*log(b*x + a)/(b^2*g)) + 1/2*A^2*d^2*i^2*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2*g)) + A^2*c^2*i^2*log(b*g*x + a*g)/(b*g) + 1/2*(B^2*b^2*d^2*i^2*x^2 + 2*(2*b^2*c*d*i^2 - a*b*d^2*i^2)*B^2*x + 2*(b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*B^2*log(b*x + a))*log((d*x + c)^n)^2/(b^3*g) - integrate(-(B^2*b^3*c^3*i^2*log(e)^2 + 2*A*B*b^3*c^3*i^2*log(e) + (B^2*b^3*d^3*i^2*log(e)^2 + 2*A*B*b^3*d^3*i^2*log(e))*x^3 + 3*(B^2*b^3*c*d^2*i^2*log(e)^2 + 2*A*B*b^3*c*d^2*i^2*log(e))*x^2 + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log((b*x + a)^n)^2 + 3*(B^2*b^3*c^2*d*i^2*log(e)^2 + 2*A*B*b^3*c^2*d*i^2*log(e))*x + 2*(B^2*b^3*c^3*i^2*log(e) + A*B*b^3*c^3*i^2 + (B^2*b^3*d^3*i^2*log(e) + A*B*b^3*d^3*i^2)*x^3 + 3*(B^2*b^3*c*d^2*i^2*log(e) + A*B*b^3*c*d^2*i^2)*x^2 + 3*(B^2*b^3*c^2*d*i^2*log(e) + A*B*b^3*c^2*d*i^2)*x)*log((b*x + a)^n) - (2*B^2*b^3*c^3*i^2*log(e) + 2*A*B*b^3*c^3*i^2 + (2*A*B*b^3*d^3*i^2 + (i^2*n + 2*i^2*log(e))*B^2*b^3*d^3)*x^3 + (6*A*B*b^3*c*d^2*i^2 - (a*b^2*d^3*i^2*n - 2*(2*i^2*n + 3*i^2*log(e))*b^3*c*d^2)*B^2)*x^2 + 2*(3*A*B*b^3*c^2*d*i^2 + (2*a*b^2*c*d^2*i^2*n - a^2*b*d^3*i^2*n + 3*b^3*c^2*d*i^2*log(e))*B^2)*x + 2*((b^3*c^2*d*i^2*n - 2*a*b^2*c*d^2*i^2*n + a^2*b*d^3*i^2*n)*B^2*x + (a*b^2*c^2*d*i^2*n - 2*a^2*b*c*d^2*i^2*n + a^3*d^3*i^2*n)*B^2)*log(b*x + a) + 2*(B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^4*d*g*x^2 + a*b^3*c*g + (b^4*c*g + a*b^3*d*g)*x), x)","F",0
173,0,0,0,0.000000," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-2 \, A B c^{2} i^{2} n {\left(\frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - A^{2} {\left(\frac{a^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \frac{x}{b^{2} g^{2}} + \frac{2 \, a \log\left(b x + a\right)}{b^{3} g^{2}}\right)} d^{2} i^{2} + 2 \, A^{2} c d i^{2} {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - \frac{2 \, A B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{2} g^{2} x + a b g^{2}} - \frac{A^{2} c^{2} i^{2}}{b^{2} g^{2} x + a b g^{2}} + \frac{{\left(B^{2} b^{2} d^{2} i^{2} x^{2} + B^{2} a b d^{2} i^{2} x - {\left(b^{2} c^{2} i^{2} - 2 \, a b c d i^{2} + a^{2} d^{2} i^{2}\right)} B^{2} + 2 \, {\left({\left(b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B^{2} x + {\left(a b c d i^{2} - a^{2} d^{2} i^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \int -\frac{B^{2} b^{3} c^{3} i^{2} \log\left(e\right)^{2} + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} i^{2} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c d^{2} i^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(3 \, B^{2} b^{3} c^{2} d i^{2} \log\left(e\right)^{2} + 4 \, A B b^{3} c^{2} d i^{2} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{3} c^{3} i^{2} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right) + A B b^{3} d^{3} i^{2}\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} \log\left(e\right) + A B b^{3} c d^{2} i^{2}\right)} x^{2} + {\left(3 \, B^{2} b^{3} c^{2} d i^{2} \log\left(e\right) + 2 \, A B b^{3} c^{2} d i^{2}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left({\left(A B b^{3} d^{3} i^{2} + {\left(i^{2} n + i^{2} \log\left(e\right)\right)} B^{2} b^{3} d^{3}\right)} x^{3} - {\left(a b^{2} c^{2} d i^{2} n - 2 \, a^{2} b c d^{2} i^{2} n + a^{3} d^{3} i^{2} n - b^{3} c^{3} i^{2} \log\left(e\right)\right)} B^{2} + {\left(3 \, A B b^{3} c d^{2} i^{2} + {\left(2 \, a b^{2} d^{3} i^{2} n + 3 \, b^{3} c d^{2} i^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + {\left(2 \, A B b^{3} c^{2} d i^{2} + {\left(2 \, a b^{2} c d^{2} i^{2} n - {\left(i^{2} n - 3 \, i^{2} \log\left(e\right)\right)} b^{3} c^{2} d\right)} B^{2}\right)} x + 2 \, {\left({\left(b^{3} c d^{2} i^{2} n - a b^{2} d^{3} i^{2} n\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c d^{2} i^{2} n - a^{2} b d^{3} i^{2} n\right)} B^{2} x + {\left(a^{2} b c d^{2} i^{2} n - a^{3} d^{3} i^{2} n\right)} B^{2}\right)} \log\left(b x + a\right) + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{5} d g^{2} x^{3} + a^{2} b^{3} c g^{2} + {\left(b^{5} c g^{2} + 2 \, a b^{4} d g^{2}\right)} x^{2} + {\left(2 \, a b^{4} c g^{2} + a^{2} b^{3} d g^{2}\right)} x}\,{d x}"," ",0,"-2*A*B*c^2*i^2*n*(1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A^2*(a^2/(b^4*g^2*x + a*b^3*g^2) - x/(b^2*g^2) + 2*a*log(b*x + a)/(b^3*g^2))*d^2*i^2 + 2*A^2*c*d*i^2*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - 2*A*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*g^2*x + a*b*g^2) - A^2*c^2*i^2/(b^2*g^2*x + a*b*g^2) + (B^2*b^2*d^2*i^2*x^2 + B^2*a*b*d^2*i^2*x - (b^2*c^2*i^2 - 2*a*b*c*d*i^2 + a^2*d^2*i^2)*B^2 + 2*((b^2*c*d*i^2 - a*b*d^2*i^2)*B^2*x + (a*b*c*d*i^2 - a^2*d^2*i^2)*B^2)*log(b*x + a))*log((d*x + c)^n)^2/(b^4*g^2*x + a*b^3*g^2) - integrate(-(B^2*b^3*c^3*i^2*log(e)^2 + (B^2*b^3*d^3*i^2*log(e)^2 + 2*A*B*b^3*d^3*i^2*log(e))*x^3 + 3*(B^2*b^3*c*d^2*i^2*log(e)^2 + 2*A*B*b^3*c*d^2*i^2*log(e))*x^2 + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log((b*x + a)^n)^2 + (3*B^2*b^3*c^2*d*i^2*log(e)^2 + 4*A*B*b^3*c^2*d*i^2*log(e))*x + 2*(B^2*b^3*c^3*i^2*log(e) + (B^2*b^3*d^3*i^2*log(e) + A*B*b^3*d^3*i^2)*x^3 + 3*(B^2*b^3*c*d^2*i^2*log(e) + A*B*b^3*c*d^2*i^2)*x^2 + (3*B^2*b^3*c^2*d*i^2*log(e) + 2*A*B*b^3*c^2*d*i^2)*x)*log((b*x + a)^n) - 2*((A*B*b^3*d^3*i^2 + (i^2*n + i^2*log(e))*B^2*b^3*d^3)*x^3 - (a*b^2*c^2*d*i^2*n - 2*a^2*b*c*d^2*i^2*n + a^3*d^3*i^2*n - b^3*c^3*i^2*log(e))*B^2 + (3*A*B*b^3*c*d^2*i^2 + (2*a*b^2*d^3*i^2*n + 3*b^3*c*d^2*i^2*log(e))*B^2)*x^2 + (2*A*B*b^3*c^2*d*i^2 + (2*a*b^2*c*d^2*i^2*n - (i^2*n - 3*i^2*log(e))*b^3*c^2*d)*B^2)*x + 2*((b^3*c*d^2*i^2*n - a*b^2*d^3*i^2*n)*B^2*x^2 + 2*(a*b^2*c*d^2*i^2*n - a^2*b*d^3*i^2*n)*B^2*x + (a^2*b*c*d^2*i^2*n - a^3*d^3*i^2*n)*B^2)*log(b*x + a) + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^5*d*g^2*x^3 + a^2*b^3*c*g^2 + (b^5*c*g^2 + 2*a*b^4*d*g^2)*x^2 + (2*a*b^4*c*g^2 + a^2*b^3*d*g^2)*x), x)","F",0
174,0,0,0,0.000000," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-A B c d i^{2} n {\left(\frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{2} \, A B c^{2} i^{2} n {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} + \frac{1}{2} \, A^{2} d^{2} i^{2} {\left(\frac{4 \, a b x + 3 \, a^{2}}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + \frac{2 \, \log\left(b x + a\right)}{b^{3} g^{3}}\right)} - \frac{2 \, {\left(2 \, b x + a\right)} A B c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} - \frac{{\left(2 \, b x + a\right)} A^{2} c d i^{2}}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} - \frac{A B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} - \frac{A^{2} c^{2} i^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{{\left(4 \, {\left(b^{2} c d i^{2} - a b d^{2} i^{2}\right)} B^{2} x + {\left(b^{2} c^{2} i^{2} + 2 \, a b c d i^{2} - 3 \, a^{2} d^{2} i^{2}\right)} B^{2} - 2 \, {\left(B^{2} b^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} a b d^{2} i^{2} x + B^{2} a^{2} d^{2} i^{2}\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, {\left(b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}\right)}} - \int -\frac{3 \, B^{2} b^{3} c^{2} d i^{2} x \log\left(e\right)^{2} + B^{2} b^{3} c^{3} i^{2} \log\left(e\right)^{2} + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} i^{2} \log\left(e\right)\right)} x^{3} + {\left(3 \, B^{2} b^{3} c d^{2} i^{2} \log\left(e\right)^{2} + 2 \, A B b^{3} c d^{2} i^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(3 \, B^{2} b^{3} c^{2} d i^{2} x \log\left(e\right) + B^{2} b^{3} c^{3} i^{2} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right) + A B b^{3} d^{3} i^{2}\right)} x^{3} + {\left(3 \, B^{2} b^{3} c d^{2} i^{2} \log\left(e\right) + A B b^{3} c d^{2} i^{2}\right)} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) + {\left({\left(6 \, a b^{2} c d^{2} i^{2} n - 7 \, a^{2} b d^{3} i^{2} n + {\left(i^{2} n - 6 \, i^{2} \log\left(e\right)\right)} b^{3} c^{2} d\right)} B^{2} x - 2 \, {\left(B^{2} b^{3} d^{3} i^{2} \log\left(e\right) + A B b^{3} d^{3} i^{2}\right)} x^{3} + {\left(a b^{2} c^{2} d i^{2} n + 2 \, a^{2} b c d^{2} i^{2} n - 3 \, a^{3} d^{3} i^{2} n - 2 \, b^{3} c^{3} i^{2} \log\left(e\right)\right)} B^{2} - 2 \, {\left(A B b^{3} c d^{2} i^{2} + {\left(2 \, a b^{2} d^{3} i^{2} n - {\left(2 \, i^{2} n - 3 \, i^{2} \log\left(e\right)\right)} b^{3} c d^{2}\right)} B^{2}\right)} x^{2} - 2 \, {\left(B^{2} b^{3} d^{3} i^{2} n x^{3} + 3 \, B^{2} a b^{2} d^{3} i^{2} n x^{2} + 3 \, B^{2} a^{2} b d^{3} i^{2} n x + B^{2} a^{3} d^{3} i^{2} n\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{6} d g^{3} x^{4} + a^{3} b^{3} c g^{3} + {\left(b^{6} c g^{3} + 3 \, a b^{5} d g^{3}\right)} x^{3} + 3 \, {\left(a b^{5} c g^{3} + a^{2} b^{4} d g^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{4} c g^{3} + a^{3} b^{3} d g^{3}\right)} x}\,{d x}"," ",0,"-A*B*c*d*i^2*n*((3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/2*A*B*c^2*i^2*n*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) + 1/2*A^2*d^2*i^2*((4*a*b*x + 3*a^2)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*log(b*x + a)/(b^3*g^3)) - 2*(2*b*x + a)*A*B*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - (2*b*x + a)*A^2*c*d*i^2/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - A*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A^2*c^2*i^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*(4*(b^2*c*d*i^2 - a*b*d^2*i^2)*B^2*x + (b^2*c^2*i^2 + 2*a*b*c*d*i^2 - 3*a^2*d^2*i^2)*B^2 - 2*(B^2*b^2*d^2*i^2*x^2 + 2*B^2*a*b*d^2*i^2*x + B^2*a^2*d^2*i^2)*log(b*x + a))*log((d*x + c)^n)^2/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) - integrate(-(3*B^2*b^3*c^2*d*i^2*x*log(e)^2 + B^2*b^3*c^3*i^2*log(e)^2 + (B^2*b^3*d^3*i^2*log(e)^2 + 2*A*B*b^3*d^3*i^2*log(e))*x^3 + (3*B^2*b^3*c*d^2*i^2*log(e)^2 + 2*A*B*b^3*c*d^2*i^2*log(e))*x^2 + (B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log((b*x + a)^n)^2 + 2*(3*B^2*b^3*c^2*d*i^2*x*log(e) + B^2*b^3*c^3*i^2*log(e) + (B^2*b^3*d^3*i^2*log(e) + A*B*b^3*d^3*i^2)*x^3 + (3*B^2*b^3*c*d^2*i^2*log(e) + A*B*b^3*c*d^2*i^2)*x^2)*log((b*x + a)^n) + ((6*a*b^2*c*d^2*i^2*n - 7*a^2*b*d^3*i^2*n + (i^2*n - 6*i^2*log(e))*b^3*c^2*d)*B^2*x - 2*(B^2*b^3*d^3*i^2*log(e) + A*B*b^3*d^3*i^2)*x^3 + (a*b^2*c^2*d*i^2*n + 2*a^2*b*c*d^2*i^2*n - 3*a^3*d^3*i^2*n - 2*b^3*c^3*i^2*log(e))*B^2 - 2*(A*B*b^3*c*d^2*i^2 + (2*a*b^2*d^3*i^2*n - (2*i^2*n - 3*i^2*log(e))*b^3*c*d^2)*B^2)*x^2 - 2*(B^2*b^3*d^3*i^2*n*x^3 + 3*B^2*a*b^2*d^3*i^2*n*x^2 + 3*B^2*a^2*b*d^3*i^2*n*x + B^2*a^3*d^3*i^2*n)*log(b*x + a) - 2*(B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^6*d*g^3*x^4 + a^3*b^3*c*g^3 + (b^6*c*g^3 + 3*a*b^5*d*g^3)*x^3 + 3*(a*b^5*c*g^3 + a^2*b^4*d*g^3)*x^2 + (3*a^2*b^4*c*g^3 + a^3*b^3*d*g^3)*x), x)","F",0
175,1,5588,0,4.966978," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{9} \, A B d^{2} i^{2} n {\left(\frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} - \frac{1}{9} \, A B c^{2} i^{2} n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{1}{9} \, A B c d i^{2} n {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} - \frac{{\left(3 \, b x + a\right)} B^{2} c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} B^{2} d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{3 \, {\left(b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}\right)}} - \frac{1}{54} \, {\left(6 \, n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{3} b^{4} c^{3} g^{4} - 3 \, a^{4} b^{3} c^{2} d g^{4} + 3 \, a^{5} b^{2} c d^{2} g^{4} - a^{6} b d^{3} g^{4} + {\left(b^{7} c^{3} g^{4} - 3 \, a b^{6} c^{2} d g^{4} + 3 \, a^{2} b^{5} c d^{2} g^{4} - a^{3} b^{4} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{6} c^{3} g^{4} - 3 \, a^{2} b^{5} c^{2} d g^{4} + 3 \, a^{3} b^{4} c d^{2} g^{4} - a^{4} b^{3} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{3} g^{4} - 3 \, a^{3} b^{4} c^{2} d g^{4} + 3 \, a^{4} b^{3} c d^{2} g^{4} - a^{5} b^{2} d^{3} g^{4}\right)} x}\right)} B^{2} c^{2} i^{2} - \frac{1}{54} \, {\left(6 \, n {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(19 \, a b^{3} c^{3} - 189 \, a^{2} b^{2} c^{2} d + 189 \, a^{3} b c d^{2} - 19 \, a^{4} d^{3} - 6 \, {\left(27 \, b^{4} c^{2} d - 32 \, a b^{3} c d^{2} + 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 18 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 18 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(9 \, b^{4} c^{3} - 125 \, a b^{3} c^{2} d + 135 \, a^{2} b^{2} c d^{2} - 19 \, a^{3} b d^{3}\right)} x - 6 \, {\left(27 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(27 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(27 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(27 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(27 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3} + {\left(27 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(27 \, a b^{3} c d^{2} - 5 \, a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(27 \, a^{2} b^{2} c d^{2} - 5 \, a^{3} b d^{3}\right)} x - 6 \, {\left(3 \, a^{3} b c d^{2} - a^{4} d^{3} + {\left(3 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{3} c d^{2} - a^{2} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{3} b^{5} c^{3} g^{4} - 3 \, a^{4} b^{4} c^{2} d g^{4} + 3 \, a^{5} b^{3} c d^{2} g^{4} - a^{6} b^{2} d^{3} g^{4} + {\left(b^{8} c^{3} g^{4} - 3 \, a b^{7} c^{2} d g^{4} + 3 \, a^{2} b^{6} c d^{2} g^{4} - a^{3} b^{5} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{7} c^{3} g^{4} - 3 \, a^{2} b^{6} c^{2} d g^{4} + 3 \, a^{3} b^{5} c d^{2} g^{4} - a^{4} b^{4} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{6} c^{3} g^{4} - 3 \, a^{3} b^{5} c^{2} d g^{4} + 3 \, a^{4} b^{4} c d^{2} g^{4} - a^{5} b^{3} d^{3} g^{4}\right)} x}\right)} B^{2} c d i^{2} - \frac{1}{54} \, {\left(6 \, n {\left(\frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(85 \, a^{2} b^{3} c^{3} - 108 \, a^{3} b^{2} c^{2} d + 27 \, a^{4} b c d^{2} - 4 \, a^{5} d^{3} + 6 \, {\left(18 \, b^{5} c^{3} - 27 \, a b^{4} c^{2} d + 11 \, a^{2} b^{3} c d^{2} - 2 \, a^{3} b^{2} d^{3}\right)} x^{2} - 18 \, {\left(3 \, a^{3} b^{2} c^{2} d - 3 \, a^{4} b c d^{2} + a^{5} d^{3} + {\left(3 \, b^{5} c^{2} d - 3 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{4} c^{2} d - 3 \, a^{2} b^{3} c d^{2} + a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{3} c^{2} d - 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(3 \, a^{3} b^{2} c^{2} d - 3 \, a^{4} b c d^{2} + a^{5} d^{3} + {\left(3 \, b^{5} c^{2} d - 3 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{4} c^{2} d - 3 \, a^{2} b^{3} c d^{2} + a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{3} c^{2} d - 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(63 \, a b^{4} c^{3} - 86 \, a^{2} b^{3} c^{2} d + 27 \, a^{3} b^{2} c d^{2} - 4 \, a^{4} b d^{3}\right)} x + 6 \, {\left(18 \, a^{3} b^{2} c^{2} d - 9 \, a^{4} b c d^{2} + 2 \, a^{5} d^{3} + {\left(18 \, b^{5} c^{2} d - 9 \, a b^{4} c d^{2} + 2 \, a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(18 \, a b^{4} c^{2} d - 9 \, a^{2} b^{3} c d^{2} + 2 \, a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(18 \, a^{2} b^{3} c^{2} d - 9 \, a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(18 \, a^{3} b^{2} c^{2} d - 9 \, a^{4} b c d^{2} + 2 \, a^{5} d^{3} + {\left(18 \, b^{5} c^{2} d - 9 \, a b^{4} c d^{2} + 2 \, a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(18 \, a b^{4} c^{2} d - 9 \, a^{2} b^{3} c d^{2} + 2 \, a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(18 \, a^{2} b^{3} c^{2} d - 9 \, a^{3} b^{2} c d^{2} + 2 \, a^{4} b d^{3}\right)} x - 6 \, {\left(3 \, a^{3} b^{2} c^{2} d - 3 \, a^{4} b c d^{2} + a^{5} d^{3} + {\left(3 \, b^{5} c^{2} d - 3 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, a b^{4} c^{2} d - 3 \, a^{2} b^{3} c d^{2} + a^{3} b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, a^{2} b^{3} c^{2} d - 3 \, a^{3} b^{2} c d^{2} + a^{4} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{3} b^{6} c^{3} g^{4} - 3 \, a^{4} b^{5} c^{2} d g^{4} + 3 \, a^{5} b^{4} c d^{2} g^{4} - a^{6} b^{3} d^{3} g^{4} + {\left(b^{9} c^{3} g^{4} - 3 \, a b^{8} c^{2} d g^{4} + 3 \, a^{2} b^{7} c d^{2} g^{4} - a^{3} b^{6} d^{3} g^{4}\right)} x^{3} + 3 \, {\left(a b^{8} c^{3} g^{4} - 3 \, a^{2} b^{7} c^{2} d g^{4} + 3 \, a^{3} b^{6} c d^{2} g^{4} - a^{4} b^{5} d^{3} g^{4}\right)} x^{2} + 3 \, {\left(a^{2} b^{7} c^{3} g^{4} - 3 \, a^{3} b^{6} c^{2} d g^{4} + 3 \, a^{4} b^{5} c d^{2} g^{4} - a^{5} b^{4} d^{3} g^{4}\right)} x}\right)} B^{2} d^{2} i^{2} - \frac{2 \, {\left(3 \, b x + a\right)} A B c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{2 \, {\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A B d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}\right)}} - \frac{B^{2} c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{{\left(3 \, b x + a\right)} A^{2} c d i^{2}}{3 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A^{2} d^{2} i^{2}}{3 \, {\left(b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}\right)}} - \frac{2 \, A B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{A^{2} c^{2} i^{2}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}}"," ",0,"-1/9*A*B*d^2*i^2*n*((11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4)) - 1/9*A*B*c^2*i^2*n*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/9*A*B*c*d*i^2*n*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) - 1/3*(3*b*x + a)*B^2*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*(3*b^2*x^2 + 3*a*b*x + a^2)*B^2*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/54*(6*n*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*n^2/(a^3*b^4*c^3*g^4 - 3*a^4*b^3*c^2*d*g^4 + 3*a^5*b^2*c*d^2*g^4 - a^6*b*d^3*g^4 + (b^7*c^3*g^4 - 3*a*b^6*c^2*d*g^4 + 3*a^2*b^5*c*d^2*g^4 - a^3*b^4*d^3*g^4)*x^3 + 3*(a*b^6*c^3*g^4 - 3*a^2*b^5*c^2*d*g^4 + 3*a^3*b^4*c*d^2*g^4 - a^4*b^3*d^3*g^4)*x^2 + 3*(a^2*b^5*c^3*g^4 - 3*a^3*b^4*c^2*d*g^4 + 3*a^4*b^3*c*d^2*g^4 - a^5*b^2*d^3*g^4)*x))*B^2*c^2*i^2 - 1/54*(6*n*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (19*a*b^3*c^3 - 189*a^2*b^2*c^2*d + 189*a^3*b*c*d^2 - 19*a^4*d^3 - 6*(27*b^4*c^2*d - 32*a*b^3*c*d^2 + 5*a^2*b^2*d^3)*x^2 + 18*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(b*x + a)^2 + 18*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(d*x + c)^2 + 3*(9*b^4*c^3 - 125*a*b^3*c^2*d + 135*a^2*b^2*c*d^2 - 19*a^3*b*d^3)*x - 6*(27*a^3*b*c*d^2 - 5*a^4*d^3 + (27*b^4*c*d^2 - 5*a*b^3*d^3)*x^3 + 3*(27*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^2 + 3*(27*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x)*log(b*x + a) + 6*(27*a^3*b*c*d^2 - 5*a^4*d^3 + (27*b^4*c*d^2 - 5*a*b^3*d^3)*x^3 + 3*(27*a*b^3*c*d^2 - 5*a^2*b^2*d^3)*x^2 + 3*(27*a^2*b^2*c*d^2 - 5*a^3*b*d^3)*x - 6*(3*a^3*b*c*d^2 - a^4*d^3 + (3*b^4*c*d^2 - a*b^3*d^3)*x^3 + 3*(3*a*b^3*c*d^2 - a^2*b^2*d^3)*x^2 + 3*(3*a^2*b^2*c*d^2 - a^3*b*d^3)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^3*b^5*c^3*g^4 - 3*a^4*b^4*c^2*d*g^4 + 3*a^5*b^3*c*d^2*g^4 - a^6*b^2*d^3*g^4 + (b^8*c^3*g^4 - 3*a*b^7*c^2*d*g^4 + 3*a^2*b^6*c*d^2*g^4 - a^3*b^5*d^3*g^4)*x^3 + 3*(a*b^7*c^3*g^4 - 3*a^2*b^6*c^2*d*g^4 + 3*a^3*b^5*c*d^2*g^4 - a^4*b^4*d^3*g^4)*x^2 + 3*(a^2*b^6*c^3*g^4 - 3*a^3*b^5*c^2*d*g^4 + 3*a^4*b^4*c*d^2*g^4 - a^5*b^3*d^3*g^4)*x))*B^2*c*d*i^2 - 1/54*(6*n*((11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (85*a^2*b^3*c^3 - 108*a^3*b^2*c^2*d + 27*a^4*b*c*d^2 - 4*a^5*d^3 + 6*(18*b^5*c^3 - 27*a*b^4*c^2*d + 11*a^2*b^3*c*d^2 - 2*a^3*b^2*d^3)*x^2 - 18*(3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2 + a^5*d^3 + (3*b^5*c^2*d - 3*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 3*(3*a*b^4*c^2*d - 3*a^2*b^3*c*d^2 + a^3*b^2*d^3)*x^2 + 3*(3*a^2*b^3*c^2*d - 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x)*log(b*x + a)^2 - 18*(3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2 + a^5*d^3 + (3*b^5*c^2*d - 3*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 3*(3*a*b^4*c^2*d - 3*a^2*b^3*c*d^2 + a^3*b^2*d^3)*x^2 + 3*(3*a^2*b^3*c^2*d - 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x)*log(d*x + c)^2 + 3*(63*a*b^4*c^3 - 86*a^2*b^3*c^2*d + 27*a^3*b^2*c*d^2 - 4*a^4*b*d^3)*x + 6*(18*a^3*b^2*c^2*d - 9*a^4*b*c*d^2 + 2*a^5*d^3 + (18*b^5*c^2*d - 9*a*b^4*c*d^2 + 2*a^2*b^3*d^3)*x^3 + 3*(18*a*b^4*c^2*d - 9*a^2*b^3*c*d^2 + 2*a^3*b^2*d^3)*x^2 + 3*(18*a^2*b^3*c^2*d - 9*a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x)*log(b*x + a) - 6*(18*a^3*b^2*c^2*d - 9*a^4*b*c*d^2 + 2*a^5*d^3 + (18*b^5*c^2*d - 9*a*b^4*c*d^2 + 2*a^2*b^3*d^3)*x^3 + 3*(18*a*b^4*c^2*d - 9*a^2*b^3*c*d^2 + 2*a^3*b^2*d^3)*x^2 + 3*(18*a^2*b^3*c^2*d - 9*a^3*b^2*c*d^2 + 2*a^4*b*d^3)*x - 6*(3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2 + a^5*d^3 + (3*b^5*c^2*d - 3*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 3*(3*a*b^4*c^2*d - 3*a^2*b^3*c*d^2 + a^3*b^2*d^3)*x^2 + 3*(3*a^2*b^3*c^2*d - 3*a^3*b^2*c*d^2 + a^4*b*d^3)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^3*b^6*c^3*g^4 - 3*a^4*b^5*c^2*d*g^4 + 3*a^5*b^4*c*d^2*g^4 - a^6*b^3*d^3*g^4 + (b^9*c^3*g^4 - 3*a*b^8*c^2*d*g^4 + 3*a^2*b^7*c*d^2*g^4 - a^3*b^6*d^3*g^4)*x^3 + 3*(a*b^8*c^3*g^4 - 3*a^2*b^7*c^2*d*g^4 + 3*a^3*b^6*c*d^2*g^4 - a^4*b^5*d^3*g^4)*x^2 + 3*(a^2*b^7*c^3*g^4 - 3*a^3*b^6*c^2*d*g^4 + 3*a^4*b^5*c*d^2*g^4 - a^5*b^4*d^3*g^4)*x))*B^2*d^2*i^2 - 2/3*(3*b*x + a)*A*B*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 2/3*(3*b^2*x^2 + 3*a*b*x + a^2)*A*B*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/3*B^2*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/3*(3*b*x + a)*A^2*c*d*i^2/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 1/3*(3*b^2*x^2 + 3*a*b*x + a^2)*A^2*d^2*i^2/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 2/3*A*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/3*A^2*c^2*i^2/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4)","B",0
176,1,8087,0,7.605375," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\frac{1}{24} \, A B c^{2} i^{2} n {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} - \frac{1}{72} \, A B d^{2} i^{2} n {\left(\frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} - \frac{1}{36} \, A B c d i^{2} n {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} - \frac{{\left(4 \, b x + a\right)} B^{2} c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{6 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} B^{2} d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{12 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} + \frac{1}{288} \, {\left(12 \, n {\left(\frac{12 \, b^{3} d^{3} x^{3} - 3 \, b^{3} c^{3} + 13 \, a b^{2} c^{2} d - 23 \, a^{2} b c d^{2} + 25 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - 7 \, a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + 13 \, a^{2} b d^{3}\right)} x}{{\left(b^{8} c^{3} - 3 \, a b^{7} c^{2} d + 3 \, a^{2} b^{6} c d^{2} - a^{3} b^{5} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{7} c^{3} - 3 \, a^{2} b^{6} c^{2} d + 3 \, a^{3} b^{5} c d^{2} - a^{4} b^{4} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{6} c^{3} - 3 \, a^{3} b^{5} c^{2} d + 3 \, a^{4} b^{4} c d^{2} - a^{5} b^{3} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{5} c^{3} - 3 \, a^{4} b^{4} c^{2} d + 3 \, a^{5} b^{3} c d^{2} - a^{6} b^{2} d^{3}\right)} g^{5} x + {\left(a^{4} b^{4} c^{3} - 3 \, a^{5} b^{3} c^{2} d + 3 \, a^{6} b^{2} c d^{2} - a^{7} b d^{3}\right)} g^{5}} + \frac{12 \, d^{4} \log\left(b x + a\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}} - \frac{12 \, d^{4} \log\left(d x + c\right)}{{\left(b^{5} c^{4} - 4 \, a b^{4} c^{3} d + 6 \, a^{2} b^{3} c^{2} d^{2} - 4 \, a^{3} b^{2} c d^{3} + a^{4} b d^{4}\right)} g^{5}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(9 \, b^{4} c^{4} - 64 \, a b^{3} c^{3} d + 216 \, a^{2} b^{2} c^{2} d^{2} - 576 \, a^{3} b c d^{3} + 415 \, a^{4} d^{4} - 300 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(13 \, b^{4} c^{2} d^{2} - 176 \, a b^{3} c d^{3} + 163 \, a^{2} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(7 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 324 \, a^{2} b^{2} c d^{3} - 271 \, a^{3} b d^{4}\right)} x - 300 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right) + 12 \, {\left(25 \, b^{4} d^{4} x^{4} + 100 \, a b^{3} d^{4} x^{3} + 150 \, a^{2} b^{2} d^{4} x^{2} + 100 \, a^{3} b d^{4} x + 25 \, a^{4} d^{4} - 12 \, {\left(b^{4} d^{4} x^{4} + 4 \, a b^{3} d^{4} x^{3} + 6 \, a^{2} b^{2} d^{4} x^{2} + 4 \, a^{3} b d^{4} x + a^{4} d^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{4} b^{5} c^{4} g^{5} - 4 \, a^{5} b^{4} c^{3} d g^{5} + 6 \, a^{6} b^{3} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{2} c d^{3} g^{5} + a^{8} b d^{4} g^{5} + {\left(b^{9} c^{4} g^{5} - 4 \, a b^{8} c^{3} d g^{5} + 6 \, a^{2} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{6} c d^{3} g^{5} + a^{4} b^{5} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} g^{5} - 4 \, a^{2} b^{7} c^{3} d g^{5} + 6 \, a^{3} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{5} c d^{3} g^{5} + a^{5} b^{4} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} g^{5} - 4 \, a^{3} b^{6} c^{3} d g^{5} + 6 \, a^{4} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{4} c d^{3} g^{5} + a^{6} b^{3} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} g^{5} - 4 \, a^{4} b^{5} c^{3} d g^{5} + 6 \, a^{5} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{3} c d^{3} g^{5} + a^{7} b^{2} d^{4} g^{5}\right)} x}\right)} B^{2} c^{2} i^{2} - \frac{1}{432} \, {\left(12 \, n {\left(\frac{7 \, a b^{3} c^{3} - 33 \, a^{2} b^{2} c^{2} d + 75 \, a^{3} b c d^{2} - 13 \, a^{4} d^{3} + 12 \, {\left(4 \, b^{4} c d^{2} - a b^{3} d^{3}\right)} x^{3} - 6 \, {\left(4 \, b^{4} c^{2} d - 29 \, a b^{3} c d^{2} + 7 \, a^{2} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(4 \, b^{4} c^{3} - 21 \, a b^{3} c^{2} d + 57 \, a^{2} b^{2} c d^{2} - 13 \, a^{3} b d^{3}\right)} x}{{\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}} + \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}} - \frac{12 \, {\left(4 \, b c d^{3} - a d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{4} - 4 \, a b^{5} c^{3} d + 6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} g^{5}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(37 \, a b^{4} c^{4} - 304 \, a^{2} b^{3} c^{3} d + 1512 \, a^{3} b^{2} c^{2} d^{2} - 1360 \, a^{4} b c d^{3} + 115 \, a^{5} d^{4} + 12 \, {\left(88 \, b^{5} c^{2} d^{2} - 101 \, a b^{4} c d^{3} + 13 \, a^{2} b^{3} d^{4}\right)} x^{3} - 6 \, {\left(40 \, b^{5} c^{3} d - 609 \, a b^{4} c^{2} d^{2} + 648 \, a^{2} b^{3} c d^{3} - 79 \, a^{3} b^{2} d^{4}\right)} x^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 72 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(16 \, b^{5} c^{4} - 163 \, a b^{4} c^{3} d + 1068 \, a^{2} b^{3} c^{2} d^{2} - 1036 \, a^{3} b^{2} c d^{3} + 115 \, a^{4} b d^{4}\right)} x + 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 12 \, {\left(88 \, a^{4} b c d^{3} - 13 \, a^{5} d^{4} + {\left(88 \, b^{5} c d^{3} - 13 \, a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(88 \, a b^{4} c d^{3} - 13 \, a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(88 \, a^{2} b^{3} c d^{3} - 13 \, a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(88 \, a^{3} b^{2} c d^{3} - 13 \, a^{4} b d^{4}\right)} x - 12 \, {\left(4 \, a^{4} b c d^{3} - a^{5} d^{4} + {\left(4 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 4 \, {\left(4 \, a b^{4} c d^{3} - a^{2} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(4 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(4 \, a^{3} b^{2} c d^{3} - a^{4} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{4} b^{6} c^{4} g^{5} - 4 \, a^{5} b^{5} c^{3} d g^{5} + 6 \, a^{6} b^{4} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{3} c d^{3} g^{5} + a^{8} b^{2} d^{4} g^{5} + {\left(b^{10} c^{4} g^{5} - 4 \, a b^{9} c^{3} d g^{5} + 6 \, a^{2} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{7} c d^{3} g^{5} + a^{4} b^{6} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{9} c^{4} g^{5} - 4 \, a^{2} b^{8} c^{3} d g^{5} + 6 \, a^{3} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{6} c d^{3} g^{5} + a^{5} b^{5} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{8} c^{4} g^{5} - 4 \, a^{3} b^{7} c^{3} d g^{5} + 6 \, a^{4} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{5} c d^{3} g^{5} + a^{6} b^{4} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{7} c^{4} g^{5} - 4 \, a^{4} b^{6} c^{3} d g^{5} + 6 \, a^{5} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{4} c d^{3} g^{5} + a^{7} b^{3} d^{4} g^{5}\right)} x}\right)} B^{2} c d i^{2} - \frac{1}{864} \, {\left(12 \, n {\left(\frac{13 \, a^{2} b^{3} c^{3} - 75 \, a^{3} b^{2} c^{2} d + 33 \, a^{4} b c d^{2} - 7 \, a^{5} d^{3} - 12 \, {\left(6 \, b^{5} c^{2} d - 4 \, a b^{4} c d^{2} + a^{2} b^{3} d^{3}\right)} x^{3} + 6 \, {\left(6 \, b^{5} c^{3} - 46 \, a b^{4} c^{2} d + 29 \, a^{2} b^{3} c d^{2} - 7 \, a^{3} b^{2} d^{3}\right)} x^{2} + 4 \, {\left(10 \, a b^{4} c^{3} - 63 \, a^{2} b^{3} c^{2} d + 33 \, a^{3} b^{2} c d^{2} - 7 \, a^{4} b d^{3}\right)} x}{{\left(b^{10} c^{3} - 3 \, a b^{9} c^{2} d + 3 \, a^{2} b^{8} c d^{2} - a^{3} b^{7} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{9} c^{3} - 3 \, a^{2} b^{8} c^{2} d + 3 \, a^{3} b^{7} c d^{2} - a^{4} b^{6} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{8} c^{3} - 3 \, a^{3} b^{7} c^{2} d + 3 \, a^{4} b^{6} c d^{2} - a^{5} b^{5} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{7} c^{3} - 3 \, a^{4} b^{6} c^{2} d + 3 \, a^{5} b^{5} c d^{2} - a^{6} b^{4} d^{3}\right)} g^{5} x + {\left(a^{4} b^{6} c^{3} - 3 \, a^{5} b^{5} c^{2} d + 3 \, a^{6} b^{4} c d^{2} - a^{7} b^{3} d^{3}\right)} g^{5}} - \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}} + \frac{12 \, {\left(6 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + a^{2} d^{4}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{5}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(115 \, a^{2} b^{4} c^{4} - 1360 \, a^{3} b^{3} c^{3} d + 1512 \, a^{4} b^{2} c^{2} d^{2} - 304 \, a^{5} b c d^{3} + 37 \, a^{6} d^{4} - 12 \, {\left(108 \, b^{6} c^{3} d - 148 \, a b^{5} c^{2} d^{2} + 47 \, a^{2} b^{4} c d^{3} - 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(36 \, b^{6} c^{4} - 712 \, a b^{5} c^{3} d + 903 \, a^{2} b^{4} c^{2} d^{2} - 264 \, a^{3} b^{3} c d^{3} + 37 \, a^{4} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(76 \, a b^{5} c^{4} - 1057 \, a^{2} b^{4} c^{3} d + 1248 \, a^{3} b^{3} c^{2} d^{2} - 304 \, a^{4} b^{2} c d^{3} + 37 \, a^{5} b d^{4}\right)} x - 12 \, {\left(108 \, a^{4} b^{2} c^{2} d^{2} - 40 \, a^{5} b c d^{3} + 7 \, a^{6} d^{4} + {\left(108 \, b^{6} c^{2} d^{2} - 40 \, a b^{5} c d^{3} + 7 \, a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(108 \, a b^{5} c^{2} d^{2} - 40 \, a^{2} b^{4} c d^{3} + 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(108 \, a^{2} b^{4} c^{2} d^{2} - 40 \, a^{3} b^{3} c d^{3} + 7 \, a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(108 \, a^{3} b^{3} c^{2} d^{2} - 40 \, a^{4} b^{2} c d^{3} + 7 \, a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(108 \, a^{4} b^{2} c^{2} d^{2} - 40 \, a^{5} b c d^{3} + 7 \, a^{6} d^{4} + {\left(108 \, b^{6} c^{2} d^{2} - 40 \, a b^{5} c d^{3} + 7 \, a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(108 \, a b^{5} c^{2} d^{2} - 40 \, a^{2} b^{4} c d^{3} + 7 \, a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(108 \, a^{2} b^{4} c^{2} d^{2} - 40 \, a^{3} b^{3} c d^{3} + 7 \, a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(108 \, a^{3} b^{3} c^{2} d^{2} - 40 \, a^{4} b^{2} c d^{3} + 7 \, a^{5} b d^{4}\right)} x - 12 \, {\left(6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4} + {\left(6 \, b^{6} c^{2} d^{2} - 4 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left(6 \, a b^{5} c^{2} d^{2} - 4 \, a^{2} b^{4} c d^{3} + a^{3} b^{3} d^{4}\right)} x^{3} + 6 \, {\left(6 \, a^{2} b^{4} c^{2} d^{2} - 4 \, a^{3} b^{3} c d^{3} + a^{4} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(6 \, a^{3} b^{3} c^{2} d^{2} - 4 \, a^{4} b^{2} c d^{3} + a^{5} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{4} b^{7} c^{4} g^{5} - 4 \, a^{5} b^{6} c^{3} d g^{5} + 6 \, a^{6} b^{5} c^{2} d^{2} g^{5} - 4 \, a^{7} b^{4} c d^{3} g^{5} + a^{8} b^{3} d^{4} g^{5} + {\left(b^{11} c^{4} g^{5} - 4 \, a b^{10} c^{3} d g^{5} + 6 \, a^{2} b^{9} c^{2} d^{2} g^{5} - 4 \, a^{3} b^{8} c d^{3} g^{5} + a^{4} b^{7} d^{4} g^{5}\right)} x^{4} + 4 \, {\left(a b^{10} c^{4} g^{5} - 4 \, a^{2} b^{9} c^{3} d g^{5} + 6 \, a^{3} b^{8} c^{2} d^{2} g^{5} - 4 \, a^{4} b^{7} c d^{3} g^{5} + a^{5} b^{6} d^{4} g^{5}\right)} x^{3} + 6 \, {\left(a^{2} b^{9} c^{4} g^{5} - 4 \, a^{3} b^{8} c^{3} d g^{5} + 6 \, a^{4} b^{7} c^{2} d^{2} g^{5} - 4 \, a^{5} b^{6} c d^{3} g^{5} + a^{6} b^{5} d^{4} g^{5}\right)} x^{2} + 4 \, {\left(a^{3} b^{8} c^{4} g^{5} - 4 \, a^{4} b^{7} c^{3} d g^{5} + 6 \, a^{5} b^{6} c^{2} d^{2} g^{5} - 4 \, a^{6} b^{5} c d^{3} g^{5} + a^{7} b^{4} d^{4} g^{5}\right)} x}\right)} B^{2} d^{2} i^{2} - \frac{{\left(4 \, b x + a\right)} A B c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} A B d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{6 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{B^{2} c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{{\left(4 \, b x + a\right)} A^{2} c d i^{2}}{6 \, {\left(b^{6} g^{5} x^{4} + 4 \, a b^{5} g^{5} x^{3} + 6 \, a^{2} b^{4} g^{5} x^{2} + 4 \, a^{3} b^{3} g^{5} x + a^{4} b^{2} g^{5}\right)}} - \frac{{\left(6 \, b^{2} x^{2} + 4 \, a b x + a^{2}\right)} A^{2} d^{2} i^{2}}{12 \, {\left(b^{7} g^{5} x^{4} + 4 \, a b^{6} g^{5} x^{3} + 6 \, a^{2} b^{5} g^{5} x^{2} + 4 \, a^{3} b^{4} g^{5} x + a^{4} b^{3} g^{5}\right)}} - \frac{A B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}} - \frac{A^{2} c^{2} i^{2}}{4 \, {\left(b^{5} g^{5} x^{4} + 4 \, a b^{4} g^{5} x^{3} + 6 \, a^{2} b^{3} g^{5} x^{2} + 4 \, a^{3} b^{2} g^{5} x + a^{4} b g^{5}\right)}}"," ",0,"1/24*A*B*c^2*i^2*n*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5)) - 1/72*A*B*d^2*i^2*n*((13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5)) - 1/36*A*B*c*d*i^2*n*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5)) - 1/6*(4*b*x + a)*B^2*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/12*(6*b^2*x^2 + 4*a*b*x + a^2)*B^2*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) + 1/288*(12*n*((12*b^3*d^3*x^3 - 3*b^3*c^3 + 13*a*b^2*c^2*d - 23*a^2*b*c*d^2 + 25*a^3*d^3 - 6*(b^3*c*d^2 - 7*a*b^2*d^3)*x^2 + 4*(b^3*c^2*d - 5*a*b^2*c*d^2 + 13*a^2*b*d^3)*x)/((b^8*c^3 - 3*a*b^7*c^2*d + 3*a^2*b^6*c*d^2 - a^3*b^5*d^3)*g^5*x^4 + 4*(a*b^7*c^3 - 3*a^2*b^6*c^2*d + 3*a^3*b^5*c*d^2 - a^4*b^4*d^3)*g^5*x^3 + 6*(a^2*b^6*c^3 - 3*a^3*b^5*c^2*d + 3*a^4*b^4*c*d^2 - a^5*b^3*d^3)*g^5*x^2 + 4*(a^3*b^5*c^3 - 3*a^4*b^4*c^2*d + 3*a^5*b^3*c*d^2 - a^6*b^2*d^3)*g^5*x + (a^4*b^4*c^3 - 3*a^5*b^3*c^2*d + 3*a^6*b^2*c*d^2 - a^7*b*d^3)*g^5) + 12*d^4*log(b*x + a)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5) - 12*d^4*log(d*x + c)/((b^5*c^4 - 4*a*b^4*c^3*d + 6*a^2*b^3*c^2*d^2 - 4*a^3*b^2*c*d^3 + a^4*b*d^4)*g^5))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (9*b^4*c^4 - 64*a*b^3*c^3*d + 216*a^2*b^2*c^2*d^2 - 576*a^3*b*c*d^3 + 415*a^4*d^4 - 300*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 6*(13*b^4*c^2*d^2 - 176*a*b^3*c*d^3 + 163*a^2*b^2*d^4)*x^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a)^2 + 72*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(d*x + c)^2 - 4*(7*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 324*a^2*b^2*c*d^3 - 271*a^3*b*d^4)*x - 300*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a) + 12*(25*b^4*d^4*x^4 + 100*a*b^3*d^4*x^3 + 150*a^2*b^2*d^4*x^2 + 100*a^3*b*d^4*x + 25*a^4*d^4 - 12*(b^4*d^4*x^4 + 4*a*b^3*d^4*x^3 + 6*a^2*b^2*d^4*x^2 + 4*a^3*b*d^4*x + a^4*d^4)*log(b*x + a))*log(d*x + c))*n^2/(a^4*b^5*c^4*g^5 - 4*a^5*b^4*c^3*d*g^5 + 6*a^6*b^3*c^2*d^2*g^5 - 4*a^7*b^2*c*d^3*g^5 + a^8*b*d^4*g^5 + (b^9*c^4*g^5 - 4*a*b^8*c^3*d*g^5 + 6*a^2*b^7*c^2*d^2*g^5 - 4*a^3*b^6*c*d^3*g^5 + a^4*b^5*d^4*g^5)*x^4 + 4*(a*b^8*c^4*g^5 - 4*a^2*b^7*c^3*d*g^5 + 6*a^3*b^6*c^2*d^2*g^5 - 4*a^4*b^5*c*d^3*g^5 + a^5*b^4*d^4*g^5)*x^3 + 6*(a^2*b^7*c^4*g^5 - 4*a^3*b^6*c^3*d*g^5 + 6*a^4*b^5*c^2*d^2*g^5 - 4*a^5*b^4*c*d^3*g^5 + a^6*b^3*d^4*g^5)*x^2 + 4*(a^3*b^6*c^4*g^5 - 4*a^4*b^5*c^3*d*g^5 + 6*a^5*b^4*c^2*d^2*g^5 - 4*a^6*b^3*c*d^3*g^5 + a^7*b^2*d^4*g^5)*x))*B^2*c^2*i^2 - 1/432*(12*n*((7*a*b^3*c^3 - 33*a^2*b^2*c^2*d + 75*a^3*b*c*d^2 - 13*a^4*d^3 + 12*(4*b^4*c*d^2 - a*b^3*d^3)*x^3 - 6*(4*b^4*c^2*d - 29*a*b^3*c*d^2 + 7*a^2*b^2*d^3)*x^2 + 4*(4*b^4*c^3 - 21*a*b^3*c^2*d + 57*a^2*b^2*c*d^2 - 13*a^3*b*d^3)*x)/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5) + 12*(4*b*c*d^3 - a*d^4)*log(b*x + a)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5) - 12*(4*b*c*d^3 - a*d^4)*log(d*x + c)/((b^6*c^4 - 4*a*b^5*c^3*d + 6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*g^5))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (37*a*b^4*c^4 - 304*a^2*b^3*c^3*d + 1512*a^3*b^2*c^2*d^2 - 1360*a^4*b*c*d^3 + 115*a^5*d^4 + 12*(88*b^5*c^2*d^2 - 101*a*b^4*c*d^3 + 13*a^2*b^3*d^4)*x^3 - 6*(40*b^5*c^3*d - 609*a*b^4*c^2*d^2 + 648*a^2*b^3*c*d^3 - 79*a^3*b^2*d^4)*x^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a)^2 - 72*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(d*x + c)^2 + 4*(16*b^5*c^4 - 163*a*b^4*c^3*d + 1068*a^2*b^3*c^2*d^2 - 1036*a^3*b^2*c*d^3 + 115*a^4*b*d^4)*x + 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x)*log(b*x + a) - 12*(88*a^4*b*c*d^3 - 13*a^5*d^4 + (88*b^5*c*d^3 - 13*a*b^4*d^4)*x^4 + 4*(88*a*b^4*c*d^3 - 13*a^2*b^3*d^4)*x^3 + 6*(88*a^2*b^3*c*d^3 - 13*a^3*b^2*d^4)*x^2 + 4*(88*a^3*b^2*c*d^3 - 13*a^4*b*d^4)*x - 12*(4*a^4*b*c*d^3 - a^5*d^4 + (4*b^5*c*d^3 - a*b^4*d^4)*x^4 + 4*(4*a*b^4*c*d^3 - a^2*b^3*d^4)*x^3 + 6*(4*a^2*b^3*c*d^3 - a^3*b^2*d^4)*x^2 + 4*(4*a^3*b^2*c*d^3 - a^4*b*d^4)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^4*b^6*c^4*g^5 - 4*a^5*b^5*c^3*d*g^5 + 6*a^6*b^4*c^2*d^2*g^5 - 4*a^7*b^3*c*d^3*g^5 + a^8*b^2*d^4*g^5 + (b^10*c^4*g^5 - 4*a*b^9*c^3*d*g^5 + 6*a^2*b^8*c^2*d^2*g^5 - 4*a^3*b^7*c*d^3*g^5 + a^4*b^6*d^4*g^5)*x^4 + 4*(a*b^9*c^4*g^5 - 4*a^2*b^8*c^3*d*g^5 + 6*a^3*b^7*c^2*d^2*g^5 - 4*a^4*b^6*c*d^3*g^5 + a^5*b^5*d^4*g^5)*x^3 + 6*(a^2*b^8*c^4*g^5 - 4*a^3*b^7*c^3*d*g^5 + 6*a^4*b^6*c^2*d^2*g^5 - 4*a^5*b^5*c*d^3*g^5 + a^6*b^4*d^4*g^5)*x^2 + 4*(a^3*b^7*c^4*g^5 - 4*a^4*b^6*c^3*d*g^5 + 6*a^5*b^5*c^2*d^2*g^5 - 4*a^6*b^4*c*d^3*g^5 + a^7*b^3*d^4*g^5)*x))*B^2*c*d*i^2 - 1/864*(12*n*((13*a^2*b^3*c^3 - 75*a^3*b^2*c^2*d + 33*a^4*b*c*d^2 - 7*a^5*d^3 - 12*(6*b^5*c^2*d - 4*a*b^4*c*d^2 + a^2*b^3*d^3)*x^3 + 6*(6*b^5*c^3 - 46*a*b^4*c^2*d + 29*a^2*b^3*c*d^2 - 7*a^3*b^2*d^3)*x^2 + 4*(10*a*b^4*c^3 - 63*a^2*b^3*c^2*d + 33*a^3*b^2*c*d^2 - 7*a^4*b*d^3)*x)/((b^10*c^3 - 3*a*b^9*c^2*d + 3*a^2*b^8*c*d^2 - a^3*b^7*d^3)*g^5*x^4 + 4*(a*b^9*c^3 - 3*a^2*b^8*c^2*d + 3*a^3*b^7*c*d^2 - a^4*b^6*d^3)*g^5*x^3 + 6*(a^2*b^8*c^3 - 3*a^3*b^7*c^2*d + 3*a^4*b^6*c*d^2 - a^5*b^5*d^3)*g^5*x^2 + 4*(a^3*b^7*c^3 - 3*a^4*b^6*c^2*d + 3*a^5*b^5*c*d^2 - a^6*b^4*d^3)*g^5*x + (a^4*b^6*c^3 - 3*a^5*b^5*c^2*d + 3*a^6*b^4*c*d^2 - a^7*b^3*d^3)*g^5) - 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(b*x + a)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5) + 12*(6*b^2*c^2*d^2 - 4*a*b*c*d^3 + a^2*d^4)*log(d*x + c)/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^5))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (115*a^2*b^4*c^4 - 1360*a^3*b^3*c^3*d + 1512*a^4*b^2*c^2*d^2 - 304*a^5*b*c*d^3 + 37*a^6*d^4 - 12*(108*b^6*c^3*d - 148*a*b^5*c^2*d^2 + 47*a^2*b^4*c*d^3 - 7*a^3*b^3*d^4)*x^3 + 6*(36*b^6*c^4 - 712*a*b^5*c^3*d + 903*a^2*b^4*c^2*d^2 - 264*a^3*b^3*c*d^3 + 37*a^4*b^2*d^4)*x^2 + 72*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(b*x + a)^2 + 72*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(d*x + c)^2 + 4*(76*a*b^5*c^4 - 1057*a^2*b^4*c^3*d + 1248*a^3*b^3*c^2*d^2 - 304*a^4*b^2*c*d^3 + 37*a^5*b*d^4)*x - 12*(108*a^4*b^2*c^2*d^2 - 40*a^5*b*c*d^3 + 7*a^6*d^4 + (108*b^6*c^2*d^2 - 40*a*b^5*c*d^3 + 7*a^2*b^4*d^4)*x^4 + 4*(108*a*b^5*c^2*d^2 - 40*a^2*b^4*c*d^3 + 7*a^3*b^3*d^4)*x^3 + 6*(108*a^2*b^4*c^2*d^2 - 40*a^3*b^3*c*d^3 + 7*a^4*b^2*d^4)*x^2 + 4*(108*a^3*b^3*c^2*d^2 - 40*a^4*b^2*c*d^3 + 7*a^5*b*d^4)*x)*log(b*x + a) + 12*(108*a^4*b^2*c^2*d^2 - 40*a^5*b*c*d^3 + 7*a^6*d^4 + (108*b^6*c^2*d^2 - 40*a*b^5*c*d^3 + 7*a^2*b^4*d^4)*x^4 + 4*(108*a*b^5*c^2*d^2 - 40*a^2*b^4*c*d^3 + 7*a^3*b^3*d^4)*x^3 + 6*(108*a^2*b^4*c^2*d^2 - 40*a^3*b^3*c*d^3 + 7*a^4*b^2*d^4)*x^2 + 4*(108*a^3*b^3*c^2*d^2 - 40*a^4*b^2*c*d^3 + 7*a^5*b*d^4)*x - 12*(6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4 + (6*b^6*c^2*d^2 - 4*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 + 4*(6*a*b^5*c^2*d^2 - 4*a^2*b^4*c*d^3 + a^3*b^3*d^4)*x^3 + 6*(6*a^2*b^4*c^2*d^2 - 4*a^3*b^3*c*d^3 + a^4*b^2*d^4)*x^2 + 4*(6*a^3*b^3*c^2*d^2 - 4*a^4*b^2*c*d^3 + a^5*b*d^4)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^4*b^7*c^4*g^5 - 4*a^5*b^6*c^3*d*g^5 + 6*a^6*b^5*c^2*d^2*g^5 - 4*a^7*b^4*c*d^3*g^5 + a^8*b^3*d^4*g^5 + (b^11*c^4*g^5 - 4*a*b^10*c^3*d*g^5 + 6*a^2*b^9*c^2*d^2*g^5 - 4*a^3*b^8*c*d^3*g^5 + a^4*b^7*d^4*g^5)*x^4 + 4*(a*b^10*c^4*g^5 - 4*a^2*b^9*c^3*d*g^5 + 6*a^3*b^8*c^2*d^2*g^5 - 4*a^4*b^7*c*d^3*g^5 + a^5*b^6*d^4*g^5)*x^3 + 6*(a^2*b^9*c^4*g^5 - 4*a^3*b^8*c^3*d*g^5 + 6*a^4*b^7*c^2*d^2*g^5 - 4*a^5*b^6*c*d^3*g^5 + a^6*b^5*d^4*g^5)*x^2 + 4*(a^3*b^8*c^4*g^5 - 4*a^4*b^7*c^3*d*g^5 + 6*a^5*b^6*c^2*d^2*g^5 - 4*a^6*b^5*c*d^3*g^5 + a^7*b^4*d^4*g^5)*x))*B^2*d^2*i^2 - 1/3*(4*b*x + a)*A*B*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/6*(6*b^2*x^2 + 4*a*b*x + a^2)*A*B*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/4*B^2*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/6*(4*b*x + a)*A^2*c*d*i^2/(b^6*g^5*x^4 + 4*a*b^5*g^5*x^3 + 6*a^2*b^4*g^5*x^2 + 4*a^3*b^3*g^5*x + a^4*b^2*g^5) - 1/12*(6*b^2*x^2 + 4*a*b*x + a^2)*A^2*d^2*i^2/(b^7*g^5*x^4 + 4*a*b^6*g^5*x^3 + 6*a^2*b^5*g^5*x^2 + 4*a^3*b^4*g^5*x + a^4*b^3*g^5) - 1/2*A*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5) - 1/4*A^2*c^2*i^2/(b^5*g^5*x^4 + 4*a*b^4*g^5*x^3 + 6*a^2*b^3*g^5*x^2 + 4*a^3*b^2*g^5*x + a^4*b*g^5)","B",0
177,1,10936,0,11.751144," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^6,x, algorithm=""maxima"")","-\frac{1}{150} \, A B c^{2} i^{2} n {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} - \frac{1}{900} \, A B d^{2} i^{2} n {\left(\frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} - \frac{1}{300} \, A B c d i^{2} n {\left(\frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} - \frac{{\left(5 \, b x + a\right)} B^{2} c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{10 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} B^{2} d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{30 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{1}{9000} \, {\left(60 \, n {\left(\frac{60 \, b^{4} d^{4} x^{4} + 12 \, b^{4} c^{4} - 63 \, a b^{3} c^{3} d + 137 \, a^{2} b^{2} c^{2} d^{2} - 163 \, a^{3} b c d^{3} + 137 \, a^{4} d^{4} - 30 \, {\left(b^{4} c d^{3} - 9 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} - 13 \, a b^{3} c d^{3} + 47 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(3 \, b^{4} c^{3} d - 17 \, a b^{3} c^{2} d^{2} + 43 \, a^{2} b^{2} c d^{3} - 77 \, a^{3} b d^{4}\right)} x}{{\left(b^{10} c^{4} - 4 \, a b^{9} c^{3} d + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{3} b^{7} c d^{3} + a^{4} b^{6} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{9} c^{4} - 4 \, a^{2} b^{8} c^{3} d + 6 \, a^{3} b^{7} c^{2} d^{2} - 4 \, a^{4} b^{6} c d^{3} + a^{5} b^{5} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{8} c^{4} - 4 \, a^{3} b^{7} c^{3} d + 6 \, a^{4} b^{6} c^{2} d^{2} - 4 \, a^{5} b^{5} c d^{3} + a^{6} b^{4} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{7} c^{4} - 4 \, a^{4} b^{6} c^{3} d + 6 \, a^{5} b^{5} c^{2} d^{2} - 4 \, a^{6} b^{4} c d^{3} + a^{7} b^{3} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{6} c^{4} - 4 \, a^{5} b^{5} c^{3} d + 6 \, a^{6} b^{4} c^{2} d^{2} - 4 \, a^{7} b^{3} c d^{3} + a^{8} b^{2} d^{4}\right)} g^{6} x + {\left(a^{5} b^{5} c^{4} - 4 \, a^{6} b^{4} c^{3} d + 6 \, a^{7} b^{3} c^{2} d^{2} - 4 \, a^{8} b^{2} c d^{3} + a^{9} b d^{4}\right)} g^{6}} + \frac{60 \, d^{5} \log\left(b x + a\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}} - \frac{60 \, d^{5} \log\left(d x + c\right)}{{\left(b^{6} c^{5} - 5 \, a b^{5} c^{4} d + 10 \, a^{2} b^{4} c^{3} d^{2} - 10 \, a^{3} b^{3} c^{2} d^{3} + 5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} g^{6}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(144 \, b^{5} c^{5} - 1125 \, a b^{4} c^{4} d + 4000 \, a^{2} b^{3} c^{3} d^{2} - 9000 \, a^{3} b^{2} c^{2} d^{3} + 18000 \, a^{4} b c d^{4} - 12019 \, a^{5} d^{5} + 8220 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} - 30 \, {\left(77 \, b^{5} c^{2} d^{3} - 1250 \, a b^{4} c d^{4} + 1173 \, a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(94 \, b^{5} c^{3} d^{2} - 975 \, a b^{4} c^{2} d^{3} + 6600 \, a^{2} b^{3} c d^{4} - 5719 \, a^{3} b^{2} d^{5}\right)} x^{2} - 1800 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right)^{2} - 1800 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(81 \, b^{5} c^{4} d - 700 \, a b^{4} c^{3} d^{2} + 3000 \, a^{2} b^{3} c^{2} d^{3} - 10800 \, a^{3} b^{2} c d^{4} + 8419 \, a^{4} b d^{5}\right)} x + 8220 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right) - 60 \, {\left(137 \, b^{5} d^{5} x^{5} + 685 \, a b^{4} d^{5} x^{4} + 1370 \, a^{2} b^{3} d^{5} x^{3} + 1370 \, a^{3} b^{2} d^{5} x^{2} + 685 \, a^{4} b d^{5} x + 137 \, a^{5} d^{5} - 60 \, {\left(b^{5} d^{5} x^{5} + 5 \, a b^{4} d^{5} x^{4} + 10 \, a^{2} b^{3} d^{5} x^{3} + 10 \, a^{3} b^{2} d^{5} x^{2} + 5 \, a^{4} b d^{5} x + a^{5} d^{5}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{5} b^{6} c^{5} g^{6} - 5 \, a^{6} b^{5} c^{4} d g^{6} + 10 \, a^{7} b^{4} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{3} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{2} c d^{4} g^{6} - a^{10} b d^{5} g^{6} + {\left(b^{11} c^{5} g^{6} - 5 \, a b^{10} c^{4} d g^{6} + 10 \, a^{2} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{7} c d^{4} g^{6} - a^{5} b^{6} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{10} c^{5} g^{6} - 5 \, a^{2} b^{9} c^{4} d g^{6} + 10 \, a^{3} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{6} c d^{4} g^{6} - a^{6} b^{5} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{9} c^{5} g^{6} - 5 \, a^{3} b^{8} c^{4} d g^{6} + 10 \, a^{4} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{5} c d^{4} g^{6} - a^{7} b^{4} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{8} c^{5} g^{6} - 5 \, a^{4} b^{7} c^{4} d g^{6} + 10 \, a^{5} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{4} c d^{4} g^{6} - a^{8} b^{3} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{7} c^{5} g^{6} - 5 \, a^{5} b^{6} c^{4} d g^{6} + 10 \, a^{6} b^{5} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{4} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{3} c d^{4} g^{6} - a^{9} b^{2} d^{5} g^{6}\right)} x}\right)} B^{2} c^{2} i^{2} - \frac{1}{18000} \, {\left(60 \, n {\left(\frac{27 \, a b^{4} c^{4} - 148 \, a^{2} b^{3} c^{3} d + 352 \, a^{3} b^{2} c^{2} d^{2} - 548 \, a^{4} b c d^{3} + 77 \, a^{5} d^{4} - 60 \, {\left(5 \, b^{5} c d^{3} - a b^{4} d^{4}\right)} x^{4} + 30 \, {\left(5 \, b^{5} c^{2} d^{2} - 46 \, a b^{4} c d^{3} + 9 \, a^{2} b^{3} d^{4}\right)} x^{3} - 10 \, {\left(10 \, b^{5} c^{3} d - 67 \, a b^{4} c^{2} d^{2} + 248 \, a^{2} b^{3} c d^{3} - 47 \, a^{3} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(15 \, b^{5} c^{4} - 88 \, a b^{4} c^{3} d + 232 \, a^{2} b^{3} c^{2} d^{2} - 428 \, a^{3} b^{2} c d^{3} + 77 \, a^{4} b d^{4}\right)} x}{{\left(b^{11} c^{4} - 4 \, a b^{10} c^{3} d + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{3} b^{8} c d^{3} + a^{4} b^{7} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{4} - 4 \, a^{2} b^{9} c^{3} d + 6 \, a^{3} b^{8} c^{2} d^{2} - 4 \, a^{4} b^{7} c d^{3} + a^{5} b^{6} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{4} - 4 \, a^{3} b^{8} c^{3} d + 6 \, a^{4} b^{7} c^{2} d^{2} - 4 \, a^{5} b^{6} c d^{3} + a^{6} b^{5} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{4} - 4 \, a^{4} b^{7} c^{3} d + 6 \, a^{5} b^{6} c^{2} d^{2} - 4 \, a^{6} b^{5} c d^{3} + a^{7} b^{4} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{4} - 4 \, a^{5} b^{6} c^{3} d + 6 \, a^{6} b^{5} c^{2} d^{2} - 4 \, a^{7} b^{4} c d^{3} + a^{8} b^{3} d^{4}\right)} g^{6} x + {\left(a^{5} b^{6} c^{4} - 4 \, a^{6} b^{5} c^{3} d + 6 \, a^{7} b^{4} c^{2} d^{2} - 4 \, a^{8} b^{3} c d^{3} + a^{9} b^{2} d^{4}\right)} g^{6}} - \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}} + \frac{60 \, {\left(5 \, b c d^{4} - a d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{7} c^{5} - 5 \, a b^{6} c^{4} d + 10 \, a^{2} b^{5} c^{3} d^{2} - 10 \, a^{3} b^{4} c^{2} d^{3} + 5 \, a^{4} b^{3} c d^{4} - a^{5} b^{2} d^{5}\right)} g^{6}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(549 \, a b^{5} c^{5} - 4625 \, a^{2} b^{4} c^{4} d + 19000 \, a^{3} b^{3} c^{3} d^{2} - 63000 \, a^{4} b^{2} c^{2} d^{3} + 51875 \, a^{5} b c d^{4} - 3799 \, a^{6} d^{5} - 60 \, {\left(625 \, b^{6} c^{2} d^{3} - 702 \, a b^{5} c d^{4} + 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 30 \, {\left(325 \, b^{6} c^{3} d^{2} - 5667 \, a b^{5} c^{2} d^{3} + 5975 \, a^{2} b^{4} c d^{4} - 633 \, a^{3} b^{3} d^{5}\right)} x^{3} - 10 \, {\left(350 \, b^{6} c^{4} d - 3949 \, a b^{5} c^{3} d^{2} + 29475 \, a^{2} b^{4} c^{2} d^{3} - 28775 \, a^{3} b^{3} c d^{4} + 2899 \, a^{4} b^{2} d^{5}\right)} x^{2} + 1800 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right)^{2} + 1800 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(d x + c\right)^{2} + 5 \, {\left(225 \, b^{6} c^{5} - 2201 \, a b^{5} c^{4} d + 10900 \, a^{2} b^{4} c^{3} d^{2} - 46200 \, a^{3} b^{3} c^{2} d^{3} + 41075 \, a^{4} b^{2} c d^{4} - 3799 \, a^{5} b d^{5}\right)} x - 60 \, {\left(625 \, a^{5} b c d^{4} - 77 \, a^{6} d^{5} + {\left(625 \, b^{6} c d^{4} - 77 \, a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(625 \, a b^{5} c d^{4} - 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(625 \, a^{2} b^{4} c d^{4} - 77 \, a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(625 \, a^{3} b^{3} c d^{4} - 77 \, a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(625 \, a^{4} b^{2} c d^{4} - 77 \, a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right) + 60 \, {\left(625 \, a^{5} b c d^{4} - 77 \, a^{6} d^{5} + {\left(625 \, b^{6} c d^{4} - 77 \, a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(625 \, a b^{5} c d^{4} - 77 \, a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(625 \, a^{2} b^{4} c d^{4} - 77 \, a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(625 \, a^{3} b^{3} c d^{4} - 77 \, a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(625 \, a^{4} b^{2} c d^{4} - 77 \, a^{5} b d^{5}\right)} x - 60 \, {\left(5 \, a^{5} b c d^{4} - a^{6} d^{5} + {\left(5 \, b^{6} c d^{4} - a b^{5} d^{5}\right)} x^{5} + 5 \, {\left(5 \, a b^{5} c d^{4} - a^{2} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(5 \, a^{2} b^{4} c d^{4} - a^{3} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(5 \, a^{3} b^{3} c d^{4} - a^{4} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(5 \, a^{4} b^{2} c d^{4} - a^{5} b d^{5}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{5} b^{7} c^{5} g^{6} - 5 \, a^{6} b^{6} c^{4} d g^{6} + 10 \, a^{7} b^{5} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{4} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{3} c d^{4} g^{6} - a^{10} b^{2} d^{5} g^{6} + {\left(b^{12} c^{5} g^{6} - 5 \, a b^{11} c^{4} d g^{6} + 10 \, a^{2} b^{10} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{9} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{8} c d^{4} g^{6} - a^{5} b^{7} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{11} c^{5} g^{6} - 5 \, a^{2} b^{10} c^{4} d g^{6} + 10 \, a^{3} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{7} c d^{4} g^{6} - a^{6} b^{6} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{10} c^{5} g^{6} - 5 \, a^{3} b^{9} c^{4} d g^{6} + 10 \, a^{4} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{6} c d^{4} g^{6} - a^{7} b^{5} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{9} c^{5} g^{6} - 5 \, a^{4} b^{8} c^{4} d g^{6} + 10 \, a^{5} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{5} c d^{4} g^{6} - a^{8} b^{4} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{8} c^{5} g^{6} - 5 \, a^{5} b^{7} c^{4} d g^{6} + 10 \, a^{6} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{4} c d^{4} g^{6} - a^{9} b^{3} d^{5} g^{6}\right)} x}\right)} B^{2} c d i^{2} - \frac{1}{54000} \, {\left(60 \, n {\left(\frac{47 \, a^{2} b^{4} c^{4} - 278 \, a^{3} b^{3} c^{3} d + 822 \, a^{4} b^{2} c^{2} d^{2} - 278 \, a^{5} b c d^{3} + 47 \, a^{6} d^{4} + 60 \, {\left(10 \, b^{6} c^{2} d^{2} - 5 \, a b^{5} c d^{3} + a^{2} b^{4} d^{4}\right)} x^{4} - 30 \, {\left(10 \, b^{6} c^{3} d - 95 \, a b^{5} c^{2} d^{2} + 46 \, a^{2} b^{4} c d^{3} - 9 \, a^{3} b^{3} d^{4}\right)} x^{3} + 10 \, {\left(20 \, b^{6} c^{4} - 140 \, a b^{5} c^{3} d + 537 \, a^{2} b^{4} c^{2} d^{2} - 248 \, a^{3} b^{3} c d^{3} + 47 \, a^{4} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(35 \, a b^{5} c^{4} - 218 \, a^{2} b^{4} c^{3} d + 702 \, a^{3} b^{3} c^{2} d^{2} - 278 \, a^{4} b^{2} c d^{3} + 47 \, a^{5} b d^{4}\right)} x}{{\left(b^{12} c^{4} - 4 \, a b^{11} c^{3} d + 6 \, a^{2} b^{10} c^{2} d^{2} - 4 \, a^{3} b^{9} c d^{3} + a^{4} b^{8} d^{4}\right)} g^{6} x^{5} + 5 \, {\left(a b^{11} c^{4} - 4 \, a^{2} b^{10} c^{3} d + 6 \, a^{3} b^{9} c^{2} d^{2} - 4 \, a^{4} b^{8} c d^{3} + a^{5} b^{7} d^{4}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{10} c^{4} - 4 \, a^{3} b^{9} c^{3} d + 6 \, a^{4} b^{8} c^{2} d^{2} - 4 \, a^{5} b^{7} c d^{3} + a^{6} b^{6} d^{4}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{9} c^{4} - 4 \, a^{4} b^{8} c^{3} d + 6 \, a^{5} b^{7} c^{2} d^{2} - 4 \, a^{6} b^{6} c d^{3} + a^{7} b^{5} d^{4}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{8} c^{4} - 4 \, a^{5} b^{7} c^{3} d + 6 \, a^{6} b^{6} c^{2} d^{2} - 4 \, a^{7} b^{5} c d^{3} + a^{8} b^{4} d^{4}\right)} g^{6} x + {\left(a^{5} b^{7} c^{4} - 4 \, a^{6} b^{6} c^{3} d + 6 \, a^{7} b^{5} c^{2} d^{2} - 4 \, a^{8} b^{4} c d^{3} + a^{9} b^{3} d^{4}\right)} g^{6}} + \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(b x + a\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}} - \frac{60 \, {\left(10 \, b^{2} c^{2} d^{3} - 5 \, a b c d^{4} + a^{2} d^{5}\right)} \log\left(d x + c\right)}{{\left(b^{8} c^{5} - 5 \, a b^{7} c^{4} d + 10 \, a^{2} b^{6} c^{3} d^{2} - 10 \, a^{3} b^{5} c^{2} d^{3} + 5 \, a^{4} b^{4} c d^{4} - a^{5} b^{3} d^{5}\right)} g^{6}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{{\left(1489 \, a^{2} b^{5} c^{5} - 14375 \, a^{3} b^{4} c^{4} d + 85000 \, a^{4} b^{3} c^{3} d^{2} - 85000 \, a^{5} b^{2} c^{2} d^{3} + 14375 \, a^{6} b c d^{4} - 1489 \, a^{7} d^{5} + 60 \, {\left(1100 \, b^{7} c^{3} d^{2} - 1425 \, a b^{6} c^{2} d^{3} + 372 \, a^{2} b^{5} c d^{4} - 47 \, a^{3} b^{4} d^{5}\right)} x^{4} - 30 \, {\left(500 \, b^{7} c^{4} d - 9825 \, a b^{6} c^{3} d^{2} + 11937 \, a^{2} b^{5} c^{2} d^{3} - 2975 \, a^{3} b^{4} c d^{4} + 363 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(400 \, b^{7} c^{5} - 5450 \, a b^{6} c^{4} d + 49189 \, a^{2} b^{5} c^{3} d^{2} - 55525 \, a^{3} b^{4} c^{2} d^{3} + 12875 \, a^{4} b^{3} c d^{4} - 1489 \, a^{5} b^{2} d^{5}\right)} x^{2} - 1800 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right)^{2} - 1800 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(d x + c\right)^{2} + 5 \, {\left(925 \, a b^{6} c^{5} - 9911 \, a^{2} b^{5} c^{4} d + 67900 \, a^{3} b^{4} c^{3} d^{2} - 71800 \, a^{4} b^{3} c^{2} d^{3} + 14375 \, a^{5} b^{2} c d^{4} - 1489 \, a^{6} b d^{5}\right)} x + 60 \, {\left(1100 \, a^{5} b^{2} c^{2} d^{3} - 325 \, a^{6} b c d^{4} + 47 \, a^{7} d^{5} + {\left(1100 \, b^{7} c^{2} d^{3} - 325 \, a b^{6} c d^{4} + 47 \, a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(1100 \, a b^{6} c^{2} d^{3} - 325 \, a^{2} b^{5} c d^{4} + 47 \, a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(1100 \, a^{2} b^{5} c^{2} d^{3} - 325 \, a^{3} b^{4} c d^{4} + 47 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(1100 \, a^{3} b^{4} c^{2} d^{3} - 325 \, a^{4} b^{3} c d^{4} + 47 \, a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(1100 \, a^{4} b^{3} c^{2} d^{3} - 325 \, a^{5} b^{2} c d^{4} + 47 \, a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(1100 \, a^{5} b^{2} c^{2} d^{3} - 325 \, a^{6} b c d^{4} + 47 \, a^{7} d^{5} + {\left(1100 \, b^{7} c^{2} d^{3} - 325 \, a b^{6} c d^{4} + 47 \, a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(1100 \, a b^{6} c^{2} d^{3} - 325 \, a^{2} b^{5} c d^{4} + 47 \, a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(1100 \, a^{2} b^{5} c^{2} d^{3} - 325 \, a^{3} b^{4} c d^{4} + 47 \, a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(1100 \, a^{3} b^{4} c^{2} d^{3} - 325 \, a^{4} b^{3} c d^{4} + 47 \, a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(1100 \, a^{4} b^{3} c^{2} d^{3} - 325 \, a^{5} b^{2} c d^{4} + 47 \, a^{6} b d^{5}\right)} x - 60 \, {\left(10 \, a^{5} b^{2} c^{2} d^{3} - 5 \, a^{6} b c d^{4} + a^{7} d^{5} + {\left(10 \, b^{7} c^{2} d^{3} - 5 \, a b^{6} c d^{4} + a^{2} b^{5} d^{5}\right)} x^{5} + 5 \, {\left(10 \, a b^{6} c^{2} d^{3} - 5 \, a^{2} b^{5} c d^{4} + a^{3} b^{4} d^{5}\right)} x^{4} + 10 \, {\left(10 \, a^{2} b^{5} c^{2} d^{3} - 5 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(10 \, a^{3} b^{4} c^{2} d^{3} - 5 \, a^{4} b^{3} c d^{4} + a^{5} b^{2} d^{5}\right)} x^{2} + 5 \, {\left(10 \, a^{4} b^{3} c^{2} d^{3} - 5 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{5} b^{8} c^{5} g^{6} - 5 \, a^{6} b^{7} c^{4} d g^{6} + 10 \, a^{7} b^{6} c^{3} d^{2} g^{6} - 10 \, a^{8} b^{5} c^{2} d^{3} g^{6} + 5 \, a^{9} b^{4} c d^{4} g^{6} - a^{10} b^{3} d^{5} g^{6} + {\left(b^{13} c^{5} g^{6} - 5 \, a b^{12} c^{4} d g^{6} + 10 \, a^{2} b^{11} c^{3} d^{2} g^{6} - 10 \, a^{3} b^{10} c^{2} d^{3} g^{6} + 5 \, a^{4} b^{9} c d^{4} g^{6} - a^{5} b^{8} d^{5} g^{6}\right)} x^{5} + 5 \, {\left(a b^{12} c^{5} g^{6} - 5 \, a^{2} b^{11} c^{4} d g^{6} + 10 \, a^{3} b^{10} c^{3} d^{2} g^{6} - 10 \, a^{4} b^{9} c^{2} d^{3} g^{6} + 5 \, a^{5} b^{8} c d^{4} g^{6} - a^{6} b^{7} d^{5} g^{6}\right)} x^{4} + 10 \, {\left(a^{2} b^{11} c^{5} g^{6} - 5 \, a^{3} b^{10} c^{4} d g^{6} + 10 \, a^{4} b^{9} c^{3} d^{2} g^{6} - 10 \, a^{5} b^{8} c^{2} d^{3} g^{6} + 5 \, a^{6} b^{7} c d^{4} g^{6} - a^{7} b^{6} d^{5} g^{6}\right)} x^{3} + 10 \, {\left(a^{3} b^{10} c^{5} g^{6} - 5 \, a^{4} b^{9} c^{4} d g^{6} + 10 \, a^{5} b^{8} c^{3} d^{2} g^{6} - 10 \, a^{6} b^{7} c^{2} d^{3} g^{6} + 5 \, a^{7} b^{6} c d^{4} g^{6} - a^{8} b^{5} d^{5} g^{6}\right)} x^{2} + 5 \, {\left(a^{4} b^{9} c^{5} g^{6} - 5 \, a^{5} b^{8} c^{4} d g^{6} + 10 \, a^{6} b^{7} c^{3} d^{2} g^{6} - 10 \, a^{7} b^{6} c^{2} d^{3} g^{6} + 5 \, a^{8} b^{5} c d^{4} g^{6} - a^{9} b^{4} d^{5} g^{6}\right)} x}\right)} B^{2} d^{2} i^{2} - \frac{{\left(5 \, b x + a\right)} A B c d i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{5 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} A B d^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{15 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{B^{2} c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}} - \frac{{\left(5 \, b x + a\right)} A^{2} c d i^{2}}{10 \, {\left(b^{7} g^{6} x^{5} + 5 \, a b^{6} g^{6} x^{4} + 10 \, a^{2} b^{5} g^{6} x^{3} + 10 \, a^{3} b^{4} g^{6} x^{2} + 5 \, a^{4} b^{3} g^{6} x + a^{5} b^{2} g^{6}\right)}} - \frac{{\left(10 \, b^{2} x^{2} + 5 \, a b x + a^{2}\right)} A^{2} d^{2} i^{2}}{30 \, {\left(b^{8} g^{6} x^{5} + 5 \, a b^{7} g^{6} x^{4} + 10 \, a^{2} b^{6} g^{6} x^{3} + 10 \, a^{3} b^{5} g^{6} x^{2} + 5 \, a^{4} b^{4} g^{6} x + a^{5} b^{3} g^{6}\right)}} - \frac{2 \, A B c^{2} i^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}} - \frac{A^{2} c^{2} i^{2}}{5 \, {\left(b^{6} g^{6} x^{5} + 5 \, a b^{5} g^{6} x^{4} + 10 \, a^{2} b^{4} g^{6} x^{3} + 10 \, a^{3} b^{3} g^{6} x^{2} + 5 \, a^{4} b^{2} g^{6} x + a^{5} b g^{6}\right)}}"," ",0,"-1/150*A*B*c^2*i^2*n*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6)) - 1/900*A*B*d^2*i^2*n*((47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6)) - 1/300*A*B*c*d*i^2*n*((27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6)) - 1/10*(5*b*x + a)*B^2*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/30*(10*b^2*x^2 + 5*a*b*x + a^2)*B^2*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/9000*(60*n*((60*b^4*d^4*x^4 + 12*b^4*c^4 - 63*a*b^3*c^3*d + 137*a^2*b^2*c^2*d^2 - 163*a^3*b*c*d^3 + 137*a^4*d^4 - 30*(b^4*c*d^3 - 9*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 - 13*a*b^3*c*d^3 + 47*a^2*b^2*d^4)*x^2 - 5*(3*b^4*c^3*d - 17*a*b^3*c^2*d^2 + 43*a^2*b^2*c*d^3 - 77*a^3*b*d^4)*x)/((b^10*c^4 - 4*a*b^9*c^3*d + 6*a^2*b^8*c^2*d^2 - 4*a^3*b^7*c*d^3 + a^4*b^6*d^4)*g^6*x^5 + 5*(a*b^9*c^4 - 4*a^2*b^8*c^3*d + 6*a^3*b^7*c^2*d^2 - 4*a^4*b^6*c*d^3 + a^5*b^5*d^4)*g^6*x^4 + 10*(a^2*b^8*c^4 - 4*a^3*b^7*c^3*d + 6*a^4*b^6*c^2*d^2 - 4*a^5*b^5*c*d^3 + a^6*b^4*d^4)*g^6*x^3 + 10*(a^3*b^7*c^4 - 4*a^4*b^6*c^3*d + 6*a^5*b^5*c^2*d^2 - 4*a^6*b^4*c*d^3 + a^7*b^3*d^4)*g^6*x^2 + 5*(a^4*b^6*c^4 - 4*a^5*b^5*c^3*d + 6*a^6*b^4*c^2*d^2 - 4*a^7*b^3*c*d^3 + a^8*b^2*d^4)*g^6*x + (a^5*b^5*c^4 - 4*a^6*b^4*c^3*d + 6*a^7*b^3*c^2*d^2 - 4*a^8*b^2*c*d^3 + a^9*b*d^4)*g^6) + 60*d^5*log(b*x + a)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6) - 60*d^5*log(d*x + c)/((b^6*c^5 - 5*a*b^5*c^4*d + 10*a^2*b^4*c^3*d^2 - 10*a^3*b^3*c^2*d^3 + 5*a^4*b^2*c*d^4 - a^5*b*d^5)*g^6))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (144*b^5*c^5 - 1125*a*b^4*c^4*d + 4000*a^2*b^3*c^3*d^2 - 9000*a^3*b^2*c^2*d^3 + 18000*a^4*b*c*d^4 - 12019*a^5*d^5 + 8220*(b^5*c*d^4 - a*b^4*d^5)*x^4 - 30*(77*b^5*c^2*d^3 - 1250*a*b^4*c*d^4 + 1173*a^2*b^3*d^5)*x^3 + 10*(94*b^5*c^3*d^2 - 975*a*b^4*c^2*d^3 + 6600*a^2*b^3*c*d^4 - 5719*a^3*b^2*d^5)*x^2 - 1800*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a)^2 - 1800*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(d*x + c)^2 - 5*(81*b^5*c^4*d - 700*a*b^4*c^3*d^2 + 3000*a^2*b^3*c^2*d^3 - 10800*a^3*b^2*c*d^4 + 8419*a^4*b*d^5)*x + 8220*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a) - 60*(137*b^5*d^5*x^5 + 685*a*b^4*d^5*x^4 + 1370*a^2*b^3*d^5*x^3 + 1370*a^3*b^2*d^5*x^2 + 685*a^4*b*d^5*x + 137*a^5*d^5 - 60*(b^5*d^5*x^5 + 5*a*b^4*d^5*x^4 + 10*a^2*b^3*d^5*x^3 + 10*a^3*b^2*d^5*x^2 + 5*a^4*b*d^5*x + a^5*d^5)*log(b*x + a))*log(d*x + c))*n^2/(a^5*b^6*c^5*g^6 - 5*a^6*b^5*c^4*d*g^6 + 10*a^7*b^4*c^3*d^2*g^6 - 10*a^8*b^3*c^2*d^3*g^6 + 5*a^9*b^2*c*d^4*g^6 - a^10*b*d^5*g^6 + (b^11*c^5*g^6 - 5*a*b^10*c^4*d*g^6 + 10*a^2*b^9*c^3*d^2*g^6 - 10*a^3*b^8*c^2*d^3*g^6 + 5*a^4*b^7*c*d^4*g^6 - a^5*b^6*d^5*g^6)*x^5 + 5*(a*b^10*c^5*g^6 - 5*a^2*b^9*c^4*d*g^6 + 10*a^3*b^8*c^3*d^2*g^6 - 10*a^4*b^7*c^2*d^3*g^6 + 5*a^5*b^6*c*d^4*g^6 - a^6*b^5*d^5*g^6)*x^4 + 10*(a^2*b^9*c^5*g^6 - 5*a^3*b^8*c^4*d*g^6 + 10*a^4*b^7*c^3*d^2*g^6 - 10*a^5*b^6*c^2*d^3*g^6 + 5*a^6*b^5*c*d^4*g^6 - a^7*b^4*d^5*g^6)*x^3 + 10*(a^3*b^8*c^5*g^6 - 5*a^4*b^7*c^4*d*g^6 + 10*a^5*b^6*c^3*d^2*g^6 - 10*a^6*b^5*c^2*d^3*g^6 + 5*a^7*b^4*c*d^4*g^6 - a^8*b^3*d^5*g^6)*x^2 + 5*(a^4*b^7*c^5*g^6 - 5*a^5*b^6*c^4*d*g^6 + 10*a^6*b^5*c^3*d^2*g^6 - 10*a^7*b^4*c^2*d^3*g^6 + 5*a^8*b^3*c*d^4*g^6 - a^9*b^2*d^5*g^6)*x))*B^2*c^2*i^2 - 1/18000*(60*n*((27*a*b^4*c^4 - 148*a^2*b^3*c^3*d + 352*a^3*b^2*c^2*d^2 - 548*a^4*b*c*d^3 + 77*a^5*d^4 - 60*(5*b^5*c*d^3 - a*b^4*d^4)*x^4 + 30*(5*b^5*c^2*d^2 - 46*a*b^4*c*d^3 + 9*a^2*b^3*d^4)*x^3 - 10*(10*b^5*c^3*d - 67*a*b^4*c^2*d^2 + 248*a^2*b^3*c*d^3 - 47*a^3*b^2*d^4)*x^2 + 5*(15*b^5*c^4 - 88*a*b^4*c^3*d + 232*a^2*b^3*c^2*d^2 - 428*a^3*b^2*c*d^3 + 77*a^4*b*d^4)*x)/((b^11*c^4 - 4*a*b^10*c^3*d + 6*a^2*b^9*c^2*d^2 - 4*a^3*b^8*c*d^3 + a^4*b^7*d^4)*g^6*x^5 + 5*(a*b^10*c^4 - 4*a^2*b^9*c^3*d + 6*a^3*b^8*c^2*d^2 - 4*a^4*b^7*c*d^3 + a^5*b^6*d^4)*g^6*x^4 + 10*(a^2*b^9*c^4 - 4*a^3*b^8*c^3*d + 6*a^4*b^7*c^2*d^2 - 4*a^5*b^6*c*d^3 + a^6*b^5*d^4)*g^6*x^3 + 10*(a^3*b^8*c^4 - 4*a^4*b^7*c^3*d + 6*a^5*b^6*c^2*d^2 - 4*a^6*b^5*c*d^3 + a^7*b^4*d^4)*g^6*x^2 + 5*(a^4*b^7*c^4 - 4*a^5*b^6*c^3*d + 6*a^6*b^5*c^2*d^2 - 4*a^7*b^4*c*d^3 + a^8*b^3*d^4)*g^6*x + (a^5*b^6*c^4 - 4*a^6*b^5*c^3*d + 6*a^7*b^4*c^2*d^2 - 4*a^8*b^3*c*d^3 + a^9*b^2*d^4)*g^6) - 60*(5*b*c*d^4 - a*d^5)*log(b*x + a)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6) + 60*(5*b*c*d^4 - a*d^5)*log(d*x + c)/((b^7*c^5 - 5*a*b^6*c^4*d + 10*a^2*b^5*c^3*d^2 - 10*a^3*b^4*c^2*d^3 + 5*a^4*b^3*c*d^4 - a^5*b^2*d^5)*g^6))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (549*a*b^5*c^5 - 4625*a^2*b^4*c^4*d + 19000*a^3*b^3*c^3*d^2 - 63000*a^4*b^2*c^2*d^3 + 51875*a^5*b*c*d^4 - 3799*a^6*d^5 - 60*(625*b^6*c^2*d^3 - 702*a*b^5*c*d^4 + 77*a^2*b^4*d^5)*x^4 + 30*(325*b^6*c^3*d^2 - 5667*a*b^5*c^2*d^3 + 5975*a^2*b^4*c*d^4 - 633*a^3*b^3*d^5)*x^3 - 10*(350*b^6*c^4*d - 3949*a*b^5*c^3*d^2 + 29475*a^2*b^4*c^2*d^3 - 28775*a^3*b^3*c*d^4 + 2899*a^4*b^2*d^5)*x^2 + 1800*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(b*x + a)^2 + 1800*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(d*x + c)^2 + 5*(225*b^6*c^5 - 2201*a*b^5*c^4*d + 10900*a^2*b^4*c^3*d^2 - 46200*a^3*b^3*c^2*d^3 + 41075*a^4*b^2*c*d^4 - 3799*a^5*b*d^5)*x - 60*(625*a^5*b*c*d^4 - 77*a^6*d^5 + (625*b^6*c*d^4 - 77*a*b^5*d^5)*x^5 + 5*(625*a*b^5*c*d^4 - 77*a^2*b^4*d^5)*x^4 + 10*(625*a^2*b^4*c*d^4 - 77*a^3*b^3*d^5)*x^3 + 10*(625*a^3*b^3*c*d^4 - 77*a^4*b^2*d^5)*x^2 + 5*(625*a^4*b^2*c*d^4 - 77*a^5*b*d^5)*x)*log(b*x + a) + 60*(625*a^5*b*c*d^4 - 77*a^6*d^5 + (625*b^6*c*d^4 - 77*a*b^5*d^5)*x^5 + 5*(625*a*b^5*c*d^4 - 77*a^2*b^4*d^5)*x^4 + 10*(625*a^2*b^4*c*d^4 - 77*a^3*b^3*d^5)*x^3 + 10*(625*a^3*b^3*c*d^4 - 77*a^4*b^2*d^5)*x^2 + 5*(625*a^4*b^2*c*d^4 - 77*a^5*b*d^5)*x - 60*(5*a^5*b*c*d^4 - a^6*d^5 + (5*b^6*c*d^4 - a*b^5*d^5)*x^5 + 5*(5*a*b^5*c*d^4 - a^2*b^4*d^5)*x^4 + 10*(5*a^2*b^4*c*d^4 - a^3*b^3*d^5)*x^3 + 10*(5*a^3*b^3*c*d^4 - a^4*b^2*d^5)*x^2 + 5*(5*a^4*b^2*c*d^4 - a^5*b*d^5)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^5*b^7*c^5*g^6 - 5*a^6*b^6*c^4*d*g^6 + 10*a^7*b^5*c^3*d^2*g^6 - 10*a^8*b^4*c^2*d^3*g^6 + 5*a^9*b^3*c*d^4*g^6 - a^10*b^2*d^5*g^6 + (b^12*c^5*g^6 - 5*a*b^11*c^4*d*g^6 + 10*a^2*b^10*c^3*d^2*g^6 - 10*a^3*b^9*c^2*d^3*g^6 + 5*a^4*b^8*c*d^4*g^6 - a^5*b^7*d^5*g^6)*x^5 + 5*(a*b^11*c^5*g^6 - 5*a^2*b^10*c^4*d*g^6 + 10*a^3*b^9*c^3*d^2*g^6 - 10*a^4*b^8*c^2*d^3*g^6 + 5*a^5*b^7*c*d^4*g^6 - a^6*b^6*d^5*g^6)*x^4 + 10*(a^2*b^10*c^5*g^6 - 5*a^3*b^9*c^4*d*g^6 + 10*a^4*b^8*c^3*d^2*g^6 - 10*a^5*b^7*c^2*d^3*g^6 + 5*a^6*b^6*c*d^4*g^6 - a^7*b^5*d^5*g^6)*x^3 + 10*(a^3*b^9*c^5*g^6 - 5*a^4*b^8*c^4*d*g^6 + 10*a^5*b^7*c^3*d^2*g^6 - 10*a^6*b^6*c^2*d^3*g^6 + 5*a^7*b^5*c*d^4*g^6 - a^8*b^4*d^5*g^6)*x^2 + 5*(a^4*b^8*c^5*g^6 - 5*a^5*b^7*c^4*d*g^6 + 10*a^6*b^6*c^3*d^2*g^6 - 10*a^7*b^5*c^2*d^3*g^6 + 5*a^8*b^4*c*d^4*g^6 - a^9*b^3*d^5*g^6)*x))*B^2*c*d*i^2 - 1/54000*(60*n*((47*a^2*b^4*c^4 - 278*a^3*b^3*c^3*d + 822*a^4*b^2*c^2*d^2 - 278*a^5*b*c*d^3 + 47*a^6*d^4 + 60*(10*b^6*c^2*d^2 - 5*a*b^5*c*d^3 + a^2*b^4*d^4)*x^4 - 30*(10*b^6*c^3*d - 95*a*b^5*c^2*d^2 + 46*a^2*b^4*c*d^3 - 9*a^3*b^3*d^4)*x^3 + 10*(20*b^6*c^4 - 140*a*b^5*c^3*d + 537*a^2*b^4*c^2*d^2 - 248*a^3*b^3*c*d^3 + 47*a^4*b^2*d^4)*x^2 + 5*(35*a*b^5*c^4 - 218*a^2*b^4*c^3*d + 702*a^3*b^3*c^2*d^2 - 278*a^4*b^2*c*d^3 + 47*a^5*b*d^4)*x)/((b^12*c^4 - 4*a*b^11*c^3*d + 6*a^2*b^10*c^2*d^2 - 4*a^3*b^9*c*d^3 + a^4*b^8*d^4)*g^6*x^5 + 5*(a*b^11*c^4 - 4*a^2*b^10*c^3*d + 6*a^3*b^9*c^2*d^2 - 4*a^4*b^8*c*d^3 + a^5*b^7*d^4)*g^6*x^4 + 10*(a^2*b^10*c^4 - 4*a^3*b^9*c^3*d + 6*a^4*b^8*c^2*d^2 - 4*a^5*b^7*c*d^3 + a^6*b^6*d^4)*g^6*x^3 + 10*(a^3*b^9*c^4 - 4*a^4*b^8*c^3*d + 6*a^5*b^7*c^2*d^2 - 4*a^6*b^6*c*d^3 + a^7*b^5*d^4)*g^6*x^2 + 5*(a^4*b^8*c^4 - 4*a^5*b^7*c^3*d + 6*a^6*b^6*c^2*d^2 - 4*a^7*b^5*c*d^3 + a^8*b^4*d^4)*g^6*x + (a^5*b^7*c^4 - 4*a^6*b^6*c^3*d + 6*a^7*b^5*c^2*d^2 - 4*a^8*b^4*c*d^3 + a^9*b^3*d^4)*g^6) + 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(b*x + a)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6) - 60*(10*b^2*c^2*d^3 - 5*a*b*c*d^4 + a^2*d^5)*log(d*x + c)/((b^8*c^5 - 5*a*b^7*c^4*d + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 + 5*a^4*b^4*c*d^4 - a^5*b^3*d^5)*g^6))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + (1489*a^2*b^5*c^5 - 14375*a^3*b^4*c^4*d + 85000*a^4*b^3*c^3*d^2 - 85000*a^5*b^2*c^2*d^3 + 14375*a^6*b*c*d^4 - 1489*a^7*d^5 + 60*(1100*b^7*c^3*d^2 - 1425*a*b^6*c^2*d^3 + 372*a^2*b^5*c*d^4 - 47*a^3*b^4*d^5)*x^4 - 30*(500*b^7*c^4*d - 9825*a*b^6*c^3*d^2 + 11937*a^2*b^5*c^2*d^3 - 2975*a^3*b^4*c*d^4 + 363*a^4*b^3*d^5)*x^3 + 10*(400*b^7*c^5 - 5450*a*b^6*c^4*d + 49189*a^2*b^5*c^3*d^2 - 55525*a^3*b^4*c^2*d^3 + 12875*a^4*b^3*c*d^4 - 1489*a^5*b^2*d^5)*x^2 - 1800*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(b*x + a)^2 - 1800*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(d*x + c)^2 + 5*(925*a*b^6*c^5 - 9911*a^2*b^5*c^4*d + 67900*a^3*b^4*c^3*d^2 - 71800*a^4*b^3*c^2*d^3 + 14375*a^5*b^2*c*d^4 - 1489*a^6*b*d^5)*x + 60*(1100*a^5*b^2*c^2*d^3 - 325*a^6*b*c*d^4 + 47*a^7*d^5 + (1100*b^7*c^2*d^3 - 325*a*b^6*c*d^4 + 47*a^2*b^5*d^5)*x^5 + 5*(1100*a*b^6*c^2*d^3 - 325*a^2*b^5*c*d^4 + 47*a^3*b^4*d^5)*x^4 + 10*(1100*a^2*b^5*c^2*d^3 - 325*a^3*b^4*c*d^4 + 47*a^4*b^3*d^5)*x^3 + 10*(1100*a^3*b^4*c^2*d^3 - 325*a^4*b^3*c*d^4 + 47*a^5*b^2*d^5)*x^2 + 5*(1100*a^4*b^3*c^2*d^3 - 325*a^5*b^2*c*d^4 + 47*a^6*b*d^5)*x)*log(b*x + a) - 60*(1100*a^5*b^2*c^2*d^3 - 325*a^6*b*c*d^4 + 47*a^7*d^5 + (1100*b^7*c^2*d^3 - 325*a*b^6*c*d^4 + 47*a^2*b^5*d^5)*x^5 + 5*(1100*a*b^6*c^2*d^3 - 325*a^2*b^5*c*d^4 + 47*a^3*b^4*d^5)*x^4 + 10*(1100*a^2*b^5*c^2*d^3 - 325*a^3*b^4*c*d^4 + 47*a^4*b^3*d^5)*x^3 + 10*(1100*a^3*b^4*c^2*d^3 - 325*a^4*b^3*c*d^4 + 47*a^5*b^2*d^5)*x^2 + 5*(1100*a^4*b^3*c^2*d^3 - 325*a^5*b^2*c*d^4 + 47*a^6*b*d^5)*x - 60*(10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4 + a^7*d^5 + (10*b^7*c^2*d^3 - 5*a*b^6*c*d^4 + a^2*b^5*d^5)*x^5 + 5*(10*a*b^6*c^2*d^3 - 5*a^2*b^5*c*d^4 + a^3*b^4*d^5)*x^4 + 10*(10*a^2*b^5*c^2*d^3 - 5*a^3*b^4*c*d^4 + a^4*b^3*d^5)*x^3 + 10*(10*a^3*b^4*c^2*d^3 - 5*a^4*b^3*c*d^4 + a^5*b^2*d^5)*x^2 + 5*(10*a^4*b^3*c^2*d^3 - 5*a^5*b^2*c*d^4 + a^6*b*d^5)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^5*b^8*c^5*g^6 - 5*a^6*b^7*c^4*d*g^6 + 10*a^7*b^6*c^3*d^2*g^6 - 10*a^8*b^5*c^2*d^3*g^6 + 5*a^9*b^4*c*d^4*g^6 - a^10*b^3*d^5*g^6 + (b^13*c^5*g^6 - 5*a*b^12*c^4*d*g^6 + 10*a^2*b^11*c^3*d^2*g^6 - 10*a^3*b^10*c^2*d^3*g^6 + 5*a^4*b^9*c*d^4*g^6 - a^5*b^8*d^5*g^6)*x^5 + 5*(a*b^12*c^5*g^6 - 5*a^2*b^11*c^4*d*g^6 + 10*a^3*b^10*c^3*d^2*g^6 - 10*a^4*b^9*c^2*d^3*g^6 + 5*a^5*b^8*c*d^4*g^6 - a^6*b^7*d^5*g^6)*x^4 + 10*(a^2*b^11*c^5*g^6 - 5*a^3*b^10*c^4*d*g^6 + 10*a^4*b^9*c^3*d^2*g^6 - 10*a^5*b^8*c^2*d^3*g^6 + 5*a^6*b^7*c*d^4*g^6 - a^7*b^6*d^5*g^6)*x^3 + 10*(a^3*b^10*c^5*g^6 - 5*a^4*b^9*c^4*d*g^6 + 10*a^5*b^8*c^3*d^2*g^6 - 10*a^6*b^7*c^2*d^3*g^6 + 5*a^7*b^6*c*d^4*g^6 - a^8*b^5*d^5*g^6)*x^2 + 5*(a^4*b^9*c^5*g^6 - 5*a^5*b^8*c^4*d*g^6 + 10*a^6*b^7*c^3*d^2*g^6 - 10*a^7*b^6*c^2*d^3*g^6 + 5*a^8*b^5*c*d^4*g^6 - a^9*b^4*d^5*g^6)*x))*B^2*d^2*i^2 - 1/5*(5*b*x + a)*A*B*c*d*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/15*(10*b^2*x^2 + 5*a*b*x + a^2)*A*B*d^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 1/5*B^2*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) - 1/10*(5*b*x + a)*A^2*c*d*i^2/(b^7*g^6*x^5 + 5*a*b^6*g^6*x^4 + 10*a^2*b^5*g^6*x^3 + 10*a^3*b^4*g^6*x^2 + 5*a^4*b^3*g^6*x + a^5*b^2*g^6) - 1/30*(10*b^2*x^2 + 5*a*b*x + a^2)*A^2*d^2*i^2/(b^8*g^6*x^5 + 5*a*b^7*g^6*x^4 + 10*a^2*b^6*g^6*x^3 + 10*a^3*b^5*g^6*x^2 + 5*a^4*b^4*g^6*x + a^5*b^3*g^6) - 2/5*A*B*c^2*i^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6) - 1/5*A^2*c^2*i^2/(b^6*g^6*x^5 + 5*a*b^5*g^6*x^4 + 10*a^2*b^4*g^6*x^3 + 10*a^3*b^3*g^6*x^2 + 5*a^4*b^2*g^6*x + a^5*b*g^6)","B",0
178,1,7845,0,6.360416," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{7} \, A B b^{3} d^{3} g^{3} i^{3} x^{7} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{7} \, A^{2} b^{3} d^{3} g^{3} i^{3} x^{7} + A B b^{3} c d^{2} g^{3} i^{3} x^{6} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A B a b^{2} d^{3} g^{3} i^{3} x^{6} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A^{2} b^{3} c d^{2} g^{3} i^{3} x^{6} + \frac{1}{2} \, A^{2} a b^{2} d^{3} g^{3} i^{3} x^{6} + \frac{6}{5} \, A B b^{3} c^{2} d g^{3} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{18}{5} \, A B a b^{2} c d^{2} g^{3} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{6}{5} \, A B a^{2} b d^{3} g^{3} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{5} \, A^{2} b^{3} c^{2} d g^{3} i^{3} x^{5} + \frac{9}{5} \, A^{2} a b^{2} c d^{2} g^{3} i^{3} x^{5} + \frac{3}{5} \, A^{2} a^{2} b d^{3} g^{3} i^{3} x^{5} + \frac{1}{2} \, A B b^{3} c^{3} g^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{9}{2} \, A B a b^{2} c^{2} d g^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{9}{2} \, A B a^{2} b c d^{2} g^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A B a^{3} d^{3} g^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A^{2} b^{3} c^{3} g^{3} i^{3} x^{4} + \frac{9}{4} \, A^{2} a b^{2} c^{2} d g^{3} i^{3} x^{4} + \frac{9}{4} \, A^{2} a^{2} b c d^{2} g^{3} i^{3} x^{4} + \frac{1}{4} \, A^{2} a^{3} d^{3} g^{3} i^{3} x^{4} + 2 \, A B a b^{2} c^{3} g^{3} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 6 \, A B a^{2} b c^{2} d g^{3} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A B a^{3} c d^{2} g^{3} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a b^{2} c^{3} g^{3} i^{3} x^{3} + 3 \, A^{2} a^{2} b c^{2} d g^{3} i^{3} x^{3} + A^{2} a^{3} c d^{2} g^{3} i^{3} x^{3} + 3 \, A B a^{2} b c^{3} g^{3} i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 3 \, A B a^{3} c^{2} d g^{3} i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A^{2} a^{2} b c^{3} g^{3} i^{3} x^{2} + \frac{3}{2} \, A^{2} a^{3} c^{2} d g^{3} i^{3} x^{2} + \frac{1}{210} \, A B b^{3} d^{3} g^{3} i^{3} n {\left(\frac{60 \, a^{7} \log\left(b x + a\right)}{b^{7}} - \frac{60 \, c^{7} \log\left(d x + c\right)}{d^{7}} - \frac{10 \, {\left(b^{6} c d^{5} - a b^{5} d^{6}\right)} x^{6} - 12 \, {\left(b^{6} c^{2} d^{4} - a^{2} b^{4} d^{6}\right)} x^{5} + 15 \, {\left(b^{6} c^{3} d^{3} - a^{3} b^{3} d^{6}\right)} x^{4} - 20 \, {\left(b^{6} c^{4} d^{2} - a^{4} b^{2} d^{6}\right)} x^{3} + 30 \, {\left(b^{6} c^{5} d - a^{5} b d^{6}\right)} x^{2} - 60 \, {\left(b^{6} c^{6} - a^{6} d^{6}\right)} x}{b^{6} d^{6}}\right)} - \frac{1}{60} \, A B b^{3} c d^{2} g^{3} i^{3} n {\left(\frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} - \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} + \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} - \frac{1}{60} \, A B a b^{2} d^{3} g^{3} i^{3} n {\left(\frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} - \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} + \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} + \frac{1}{10} \, A B b^{3} c^{2} d g^{3} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} + \frac{3}{10} \, A B a b^{2} c d^{2} g^{3} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} + \frac{1}{10} \, A B a^{2} b d^{3} g^{3} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{12} \, A B b^{3} c^{3} g^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{3}{4} \, A B a b^{2} c^{2} d g^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{3}{4} \, A B a^{2} b c d^{2} g^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{12} \, A B a^{3} d^{3} g^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + A B a b^{2} c^{3} g^{3} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + 3 \, A B a^{2} b c^{2} d g^{3} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + A B a^{3} c d^{2} g^{3} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - 3 \, A B a^{2} b c^{3} g^{3} i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - 3 \, A B a^{3} c^{2} d g^{3} i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a^{3} c^{3} g^{3} i^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a^{3} c^{3} g^{3} i^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{3} c^{3} g^{3} i^{3} x - \frac{{\left(107 \, a^{4} b^{2} c^{3} d^{4} g^{3} i^{3} n^{2} - 39 \, a^{5} b c^{2} d^{5} g^{3} i^{3} n^{2} + 6 \, a^{6} c d^{6} g^{3} i^{3} n^{2} - 6 \, b^{6} c^{7} g^{3} i^{3} n \log\left(e\right) - 6 \, {\left(g^{3} i^{3} n^{2} - 7 \, g^{3} i^{3} n \log\left(e\right)\right)} a b^{5} c^{6} d + 3 \, {\left(13 \, g^{3} i^{3} n^{2} - 42 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{2} b^{4} c^{5} d^{2} - {\left(107 \, g^{3} i^{3} n^{2} - 210 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{3} b^{3} c^{4} d^{3}\right)} B^{2} \log\left(d x + c\right)}{420 \, b^{3} d^{4}} + \frac{{\left(b^{7} c^{7} g^{3} i^{3} n^{2} - 7 \, a b^{6} c^{6} d g^{3} i^{3} n^{2} + 21 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} n^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} n^{2} + 35 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} n^{2} - 21 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} n^{2} + 7 \, a^{6} b c d^{6} g^{3} i^{3} n^{2} - a^{7} d^{7} g^{3} i^{3} n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{70 \, b^{4} d^{4}} + \frac{360 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} \log\left(e\right)^{2} - 60 \, {\left({\left(2 \, g^{3} i^{3} n \log\left(e\right) - 21 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} b^{7} c d^{6} - {\left(2 \, g^{3} i^{3} n \log\left(e\right) + 21 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a b^{6} d^{7}\right)} B^{2} x^{6} + 24 \, {\left({\left(g^{3} i^{3} n^{2} - 15 \, g^{3} i^{3} n \log\left(e\right) + 63 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} b^{7} c^{2} d^{5} - {\left(2 \, g^{3} i^{3} n^{2} - 189 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a b^{6} c d^{6} + {\left(g^{3} i^{3} n^{2} + 15 \, g^{3} i^{3} n \log\left(e\right) + 63 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a^{2} b^{5} d^{7}\right)} B^{2} x^{5} + 6 \, {\left({\left(10 \, g^{3} i^{3} n^{2} - 51 \, g^{3} i^{3} n \log\left(e\right) + 105 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} b^{7} c^{3} d^{4} - {\left(10 \, g^{3} i^{3} n^{2} + 147 \, g^{3} i^{3} n \log\left(e\right) - 945 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a b^{6} c^{2} d^{5} - {\left(10 \, g^{3} i^{3} n^{2} - 147 \, g^{3} i^{3} n \log\left(e\right) - 945 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a^{2} b^{5} c d^{6} + {\left(10 \, g^{3} i^{3} n^{2} + 51 \, g^{3} i^{3} n \log\left(e\right) + 105 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a^{3} b^{4} d^{7}\right)} B^{2} x^{4} + 2 \, {\left({\left(11 \, g^{3} i^{3} n^{2} - 6 \, g^{3} i^{3} n \log\left(e\right)\right)} b^{7} c^{4} d^{3} + 4 \, {\left(19 \, g^{3} i^{3} n^{2} - 147 \, g^{3} i^{3} n \log\left(e\right) + 315 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a b^{6} c^{3} d^{4} - 6 \, {\left(29 \, g^{3} i^{3} n^{2} - 630 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a^{2} b^{5} c^{2} d^{5} + 4 \, {\left(19 \, g^{3} i^{3} n^{2} + 147 \, g^{3} i^{3} n \log\left(e\right) + 315 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a^{3} b^{4} c d^{6} + {\left(11 \, g^{3} i^{3} n^{2} + 6 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{4} b^{3} d^{7}\right)} B^{2} x^{3} - 3 \, {\left(3 \, {\left(3 \, g^{3} i^{3} n^{2} - 2 \, g^{3} i^{3} n \log\left(e\right)\right)} b^{7} c^{5} d^{2} - {\left(67 \, g^{3} i^{3} n^{2} - 42 \, g^{3} i^{3} n \log\left(e\right)\right)} a b^{6} c^{4} d^{3} + 2 \, {\left(29 \, g^{3} i^{3} n^{2} + 252 \, g^{3} i^{3} n \log\left(e\right) - 630 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a^{2} b^{5} c^{3} d^{4} + 2 \, {\left(29 \, g^{3} i^{3} n^{2} - 252 \, g^{3} i^{3} n \log\left(e\right) - 630 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a^{3} b^{4} c^{2} d^{5} - {\left(67 \, g^{3} i^{3} n^{2} + 42 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{4} b^{3} c d^{6} + 3 \, {\left(3 \, g^{3} i^{3} n^{2} + 2 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{5} b^{2} d^{7}\right)} B^{2} x^{2} - 18 \, {\left(35 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} n^{2} - 21 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} n^{2} + 7 \, a^{6} b c d^{6} g^{3} i^{3} n^{2} - a^{7} d^{7} g^{3} i^{3} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} - 36 \, {\left(b^{7} c^{7} g^{3} i^{3} n^{2} - 7 \, a b^{6} c^{6} d g^{3} i^{3} n^{2} + 21 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} n^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) + 18 \, {\left(b^{7} c^{7} g^{3} i^{3} n^{2} - 7 \, a b^{6} c^{6} d g^{3} i^{3} n^{2} + 21 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} n^{2} - 35 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + 6 \, {\left(6 \, {\left(g^{3} i^{3} n^{2} - g^{3} i^{3} n \log\left(e\right)\right)} b^{7} c^{6} d - 3 \, {\left(15 \, g^{3} i^{3} n^{2} - 14 \, g^{3} i^{3} n \log\left(e\right)\right)} a b^{6} c^{5} d^{2} + 2 \, {\left(73 \, g^{3} i^{3} n^{2} - 63 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{2} b^{5} c^{4} d^{3} - 2 \, {\left(107 \, g^{3} i^{3} n^{2} - 210 \, g^{3} i^{3} \log\left(e\right)^{2}\right)} a^{3} b^{4} c^{3} d^{4} + 2 \, {\left(73 \, g^{3} i^{3} n^{2} + 63 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{4} b^{3} c^{2} d^{5} - 3 \, {\left(15 \, g^{3} i^{3} n^{2} + 14 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{5} b^{2} c d^{6} + 6 \, {\left(g^{3} i^{3} n^{2} + g^{3} i^{3} n \log\left(e\right)\right)} a^{6} b d^{7}\right)} B^{2} x - 6 \, {\left(6 \, a b^{6} c^{6} d g^{3} i^{3} n^{2} - 39 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} n^{2} + 107 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} n^{2} + 6 \, a^{7} d^{7} g^{3} i^{3} n \log\left(e\right) - {\left(107 \, g^{3} i^{3} n^{2} + 210 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{4} b^{3} c^{3} d^{4} + 3 \, {\left(13 \, g^{3} i^{3} n^{2} + 42 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{5} b^{2} c^{2} d^{5} - 6 \, {\left(g^{3} i^{3} n^{2} + 7 \, g^{3} i^{3} n \log\left(e\right)\right)} a^{6} b c d^{6}\right)} B^{2} \log\left(b x + a\right) + 18 \, {\left(20 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} + 140 \, B^{2} a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} x + 70 \, {\left(b^{7} c d^{6} g^{3} i^{3} + a b^{6} d^{7} g^{3} i^{3}\right)} B^{2} x^{6} + 84 \, {\left(b^{7} c^{2} d^{5} g^{3} i^{3} + 3 \, a b^{6} c d^{6} g^{3} i^{3} + a^{2} b^{5} d^{7} g^{3} i^{3}\right)} B^{2} x^{5} + 35 \, {\left(b^{7} c^{3} d^{4} g^{3} i^{3} + 9 \, a b^{6} c^{2} d^{5} g^{3} i^{3} + 9 \, a^{2} b^{5} c d^{6} g^{3} i^{3} + a^{3} b^{4} d^{7} g^{3} i^{3}\right)} B^{2} x^{4} + 140 \, {\left(a b^{6} c^{3} d^{4} g^{3} i^{3} + 3 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} + a^{3} b^{4} c d^{6} g^{3} i^{3}\right)} B^{2} x^{3} + 210 \, {\left(a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} + a^{3} b^{4} c^{2} d^{5} g^{3} i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 18 \, {\left(20 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} + 140 \, B^{2} a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} x + 70 \, {\left(b^{7} c d^{6} g^{3} i^{3} + a b^{6} d^{7} g^{3} i^{3}\right)} B^{2} x^{6} + 84 \, {\left(b^{7} c^{2} d^{5} g^{3} i^{3} + 3 \, a b^{6} c d^{6} g^{3} i^{3} + a^{2} b^{5} d^{7} g^{3} i^{3}\right)} B^{2} x^{5} + 35 \, {\left(b^{7} c^{3} d^{4} g^{3} i^{3} + 9 \, a b^{6} c^{2} d^{5} g^{3} i^{3} + 9 \, a^{2} b^{5} c d^{6} g^{3} i^{3} + a^{3} b^{4} d^{7} g^{3} i^{3}\right)} B^{2} x^{4} + 140 \, {\left(a b^{6} c^{3} d^{4} g^{3} i^{3} + 3 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} + a^{3} b^{4} c d^{6} g^{3} i^{3}\right)} B^{2} x^{3} + 210 \, {\left(a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} + a^{3} b^{4} c^{2} d^{5} g^{3} i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 6 \, {\left(120 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} \log\left(e\right) - 20 \, {\left({\left(g^{3} i^{3} n - 21 \, g^{3} i^{3} \log\left(e\right)\right)} b^{7} c d^{6} - {\left(g^{3} i^{3} n + 21 \, g^{3} i^{3} \log\left(e\right)\right)} a b^{6} d^{7}\right)} B^{2} x^{6} + 12 \, {\left(126 \, a b^{6} c d^{6} g^{3} i^{3} \log\left(e\right) - {\left(5 \, g^{3} i^{3} n - 42 \, g^{3} i^{3} \log\left(e\right)\right)} b^{7} c^{2} d^{5} + {\left(5 \, g^{3} i^{3} n + 42 \, g^{3} i^{3} \log\left(e\right)\right)} a^{2} b^{5} d^{7}\right)} B^{2} x^{5} - 3 \, {\left({\left(17 \, g^{3} i^{3} n - 70 \, g^{3} i^{3} \log\left(e\right)\right)} b^{7} c^{3} d^{4} + 7 \, {\left(7 \, g^{3} i^{3} n - 90 \, g^{3} i^{3} \log\left(e\right)\right)} a b^{6} c^{2} d^{5} - 7 \, {\left(7 \, g^{3} i^{3} n + 90 \, g^{3} i^{3} \log\left(e\right)\right)} a^{2} b^{5} c d^{6} - {\left(17 \, g^{3} i^{3} n + 70 \, g^{3} i^{3} \log\left(e\right)\right)} a^{3} b^{4} d^{7}\right)} B^{2} x^{4} - 2 \, {\left(b^{7} c^{4} d^{3} g^{3} i^{3} n - a^{4} b^{3} d^{7} g^{3} i^{3} n - 1260 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} \log\left(e\right) + 14 \, {\left(7 \, g^{3} i^{3} n - 30 \, g^{3} i^{3} \log\left(e\right)\right)} a b^{6} c^{3} d^{4} - 14 \, {\left(7 \, g^{3} i^{3} n + 30 \, g^{3} i^{3} \log\left(e\right)\right)} a^{3} b^{4} c d^{6}\right)} B^{2} x^{3} + 3 \, {\left(b^{7} c^{5} d^{2} g^{3} i^{3} n - 7 \, a b^{6} c^{4} d^{3} g^{3} i^{3} n + 7 \, a^{4} b^{3} c d^{6} g^{3} i^{3} n - a^{5} b^{2} d^{7} g^{3} i^{3} n - 84 \, {\left(g^{3} i^{3} n - 5 \, g^{3} i^{3} \log\left(e\right)\right)} a^{2} b^{5} c^{3} d^{4} + 84 \, {\left(g^{3} i^{3} n + 5 \, g^{3} i^{3} \log\left(e\right)\right)} a^{3} b^{4} c^{2} d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{7} c^{6} d g^{3} i^{3} n - 7 \, a b^{6} c^{5} d^{2} g^{3} i^{3} n + 21 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} n - 21 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} n + 7 \, a^{5} b^{2} c d^{6} g^{3} i^{3} n - a^{6} b d^{7} g^{3} i^{3} n - 140 \, a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} \log\left(e\right)\right)} B^{2} x + 6 \, {\left(35 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} n - 21 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} n + 7 \, a^{6} b c d^{6} g^{3} i^{3} n - a^{7} d^{7} g^{3} i^{3} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(b^{7} c^{7} g^{3} i^{3} n - 7 \, a b^{6} c^{6} d g^{3} i^{3} n + 21 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} n - 35 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 6 \, {\left(120 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} \log\left(e\right) - 20 \, {\left({\left(g^{3} i^{3} n - 21 \, g^{3} i^{3} \log\left(e\right)\right)} b^{7} c d^{6} - {\left(g^{3} i^{3} n + 21 \, g^{3} i^{3} \log\left(e\right)\right)} a b^{6} d^{7}\right)} B^{2} x^{6} + 12 \, {\left(126 \, a b^{6} c d^{6} g^{3} i^{3} \log\left(e\right) - {\left(5 \, g^{3} i^{3} n - 42 \, g^{3} i^{3} \log\left(e\right)\right)} b^{7} c^{2} d^{5} + {\left(5 \, g^{3} i^{3} n + 42 \, g^{3} i^{3} \log\left(e\right)\right)} a^{2} b^{5} d^{7}\right)} B^{2} x^{5} - 3 \, {\left({\left(17 \, g^{3} i^{3} n - 70 \, g^{3} i^{3} \log\left(e\right)\right)} b^{7} c^{3} d^{4} + 7 \, {\left(7 \, g^{3} i^{3} n - 90 \, g^{3} i^{3} \log\left(e\right)\right)} a b^{6} c^{2} d^{5} - 7 \, {\left(7 \, g^{3} i^{3} n + 90 \, g^{3} i^{3} \log\left(e\right)\right)} a^{2} b^{5} c d^{6} - {\left(17 \, g^{3} i^{3} n + 70 \, g^{3} i^{3} \log\left(e\right)\right)} a^{3} b^{4} d^{7}\right)} B^{2} x^{4} - 2 \, {\left(b^{7} c^{4} d^{3} g^{3} i^{3} n - a^{4} b^{3} d^{7} g^{3} i^{3} n - 1260 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} \log\left(e\right) + 14 \, {\left(7 \, g^{3} i^{3} n - 30 \, g^{3} i^{3} \log\left(e\right)\right)} a b^{6} c^{3} d^{4} - 14 \, {\left(7 \, g^{3} i^{3} n + 30 \, g^{3} i^{3} \log\left(e\right)\right)} a^{3} b^{4} c d^{6}\right)} B^{2} x^{3} + 3 \, {\left(b^{7} c^{5} d^{2} g^{3} i^{3} n - 7 \, a b^{6} c^{4} d^{3} g^{3} i^{3} n + 7 \, a^{4} b^{3} c d^{6} g^{3} i^{3} n - a^{5} b^{2} d^{7} g^{3} i^{3} n - 84 \, {\left(g^{3} i^{3} n - 5 \, g^{3} i^{3} \log\left(e\right)\right)} a^{2} b^{5} c^{3} d^{4} + 84 \, {\left(g^{3} i^{3} n + 5 \, g^{3} i^{3} \log\left(e\right)\right)} a^{3} b^{4} c^{2} d^{5}\right)} B^{2} x^{2} - 6 \, {\left(b^{7} c^{6} d g^{3} i^{3} n - 7 \, a b^{6} c^{5} d^{2} g^{3} i^{3} n + 21 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} n - 21 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} n + 7 \, a^{5} b^{2} c d^{6} g^{3} i^{3} n - a^{6} b d^{7} g^{3} i^{3} n - 140 \, a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} \log\left(e\right)\right)} B^{2} x + 6 \, {\left(35 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} n - 21 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} n + 7 \, a^{6} b c d^{6} g^{3} i^{3} n - a^{7} d^{7} g^{3} i^{3} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(b^{7} c^{7} g^{3} i^{3} n - 7 \, a b^{6} c^{6} d g^{3} i^{3} n + 21 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} n - 35 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} n\right)} B^{2} \log\left(d x + c\right) + 6 \, {\left(20 \, B^{2} b^{7} d^{7} g^{3} i^{3} x^{7} + 140 \, B^{2} a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} x + 70 \, {\left(b^{7} c d^{6} g^{3} i^{3} + a b^{6} d^{7} g^{3} i^{3}\right)} B^{2} x^{6} + 84 \, {\left(b^{7} c^{2} d^{5} g^{3} i^{3} + 3 \, a b^{6} c d^{6} g^{3} i^{3} + a^{2} b^{5} d^{7} g^{3} i^{3}\right)} B^{2} x^{5} + 35 \, {\left(b^{7} c^{3} d^{4} g^{3} i^{3} + 9 \, a b^{6} c^{2} d^{5} g^{3} i^{3} + 9 \, a^{2} b^{5} c d^{6} g^{3} i^{3} + a^{3} b^{4} d^{7} g^{3} i^{3}\right)} B^{2} x^{4} + 140 \, {\left(a b^{6} c^{3} d^{4} g^{3} i^{3} + 3 \, a^{2} b^{5} c^{2} d^{5} g^{3} i^{3} + a^{3} b^{4} c d^{6} g^{3} i^{3}\right)} B^{2} x^{3} + 210 \, {\left(a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} + a^{3} b^{4} c^{2} d^{5} g^{3} i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2520 \, b^{4} d^{4}}"," ",0,"2/7*A*B*b^3*d^3*g^3*i^3*x^7*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/7*A^2*b^3*d^3*g^3*i^3*x^7 + A*B*b^3*c*d^2*g^3*i^3*x^6*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*B*a*b^2*d^3*g^3*i^3*x^6*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*b^3*c*d^2*g^3*i^3*x^6 + 1/2*A^2*a*b^2*d^3*g^3*i^3*x^6 + 6/5*A*B*b^3*c^2*d*g^3*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 18/5*A*B*a*b^2*c*d^2*g^3*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 6/5*A*B*a^2*b*d^3*g^3*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/5*A^2*b^3*c^2*d*g^3*i^3*x^5 + 9/5*A^2*a*b^2*c*d^2*g^3*i^3*x^5 + 3/5*A^2*a^2*b*d^3*g^3*i^3*x^5 + 1/2*A*B*b^3*c^3*g^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 9/2*A*B*a*b^2*c^2*d*g^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 9/2*A*B*a^2*b*c*d^2*g^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*B*a^3*d^3*g^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*b^3*c^3*g^3*i^3*x^4 + 9/4*A^2*a*b^2*c^2*d*g^3*i^3*x^4 + 9/4*A^2*a^2*b*c*d^2*g^3*i^3*x^4 + 1/4*A^2*a^3*d^3*g^3*i^3*x^4 + 2*A*B*a*b^2*c^3*g^3*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 6*A*B*a^2*b*c^2*d*g^3*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*B*a^3*c*d^2*g^3*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b^2*c^3*g^3*i^3*x^3 + 3*A^2*a^2*b*c^2*d*g^3*i^3*x^3 + A^2*a^3*c*d^2*g^3*i^3*x^3 + 3*A*B*a^2*b*c^3*g^3*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3*A*B*a^3*c^2*d*g^3*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A^2*a^2*b*c^3*g^3*i^3*x^2 + 3/2*A^2*a^3*c^2*d*g^3*i^3*x^2 + 1/210*A*B*b^3*d^3*g^3*i^3*n*(60*a^7*log(b*x + a)/b^7 - 60*c^7*log(d*x + c)/d^7 - (10*(b^6*c*d^5 - a*b^5*d^6)*x^6 - 12*(b^6*c^2*d^4 - a^2*b^4*d^6)*x^5 + 15*(b^6*c^3*d^3 - a^3*b^3*d^6)*x^4 - 20*(b^6*c^4*d^2 - a^4*b^2*d^6)*x^3 + 30*(b^6*c^5*d - a^5*b*d^6)*x^2 - 60*(b^6*c^6 - a^6*d^6)*x)/(b^6*d^6)) - 1/60*A*B*b^3*c*d^2*g^3*i^3*n*(60*a^6*log(b*x + a)/b^6 - 60*c^6*log(d*x + c)/d^6 + (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5)) - 1/60*A*B*a*b^2*d^3*g^3*i^3*n*(60*a^6*log(b*x + a)/b^6 - 60*c^6*log(d*x + c)/d^6 + (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5)) + 1/10*A*B*b^3*c^2*d*g^3*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) + 3/10*A*B*a*b^2*c*d^2*g^3*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) + 1/10*A*B*a^2*b*d^3*g^3*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/12*A*B*b^3*c^3*g^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 3/4*A*B*a*b^2*c^2*d*g^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 3/4*A*B*a^2*b*c*d^2*g^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/12*A*B*a^3*d^3*g^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + A*B*a*b^2*c^3*g^3*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 3*A*B*a^2*b*c^2*d*g^3*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + A*B*a^3*c*d^2*g^3*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 3*A*B*a^2*b*c^3*g^3*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 3*A*B*a^3*c^2*d*g^3*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a^3*c^3*g^3*i^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^3*c^3*g^3*i^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^3*c^3*g^3*i^3*x - 1/420*(107*a^4*b^2*c^3*d^4*g^3*i^3*n^2 - 39*a^5*b*c^2*d^5*g^3*i^3*n^2 + 6*a^6*c*d^6*g^3*i^3*n^2 - 6*b^6*c^7*g^3*i^3*n*log(e) - 6*(g^3*i^3*n^2 - 7*g^3*i^3*n*log(e))*a*b^5*c^6*d + 3*(13*g^3*i^3*n^2 - 42*g^3*i^3*n*log(e))*a^2*b^4*c^5*d^2 - (107*g^3*i^3*n^2 - 210*g^3*i^3*n*log(e))*a^3*b^3*c^4*d^3)*B^2*log(d*x + c)/(b^3*d^4) + 1/70*(b^7*c^7*g^3*i^3*n^2 - 7*a*b^6*c^6*d*g^3*i^3*n^2 + 21*a^2*b^5*c^5*d^2*g^3*i^3*n^2 - 35*a^3*b^4*c^4*d^3*g^3*i^3*n^2 + 35*a^4*b^3*c^3*d^4*g^3*i^3*n^2 - 21*a^5*b^2*c^2*d^5*g^3*i^3*n^2 + 7*a^6*b*c*d^6*g^3*i^3*n^2 - a^7*d^7*g^3*i^3*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^4*d^4) + 1/2520*(360*B^2*b^7*d^7*g^3*i^3*x^7*log(e)^2 - 60*((2*g^3*i^3*n*log(e) - 21*g^3*i^3*log(e)^2)*b^7*c*d^6 - (2*g^3*i^3*n*log(e) + 21*g^3*i^3*log(e)^2)*a*b^6*d^7)*B^2*x^6 + 24*((g^3*i^3*n^2 - 15*g^3*i^3*n*log(e) + 63*g^3*i^3*log(e)^2)*b^7*c^2*d^5 - (2*g^3*i^3*n^2 - 189*g^3*i^3*log(e)^2)*a*b^6*c*d^6 + (g^3*i^3*n^2 + 15*g^3*i^3*n*log(e) + 63*g^3*i^3*log(e)^2)*a^2*b^5*d^7)*B^2*x^5 + 6*((10*g^3*i^3*n^2 - 51*g^3*i^3*n*log(e) + 105*g^3*i^3*log(e)^2)*b^7*c^3*d^4 - (10*g^3*i^3*n^2 + 147*g^3*i^3*n*log(e) - 945*g^3*i^3*log(e)^2)*a*b^6*c^2*d^5 - (10*g^3*i^3*n^2 - 147*g^3*i^3*n*log(e) - 945*g^3*i^3*log(e)^2)*a^2*b^5*c*d^6 + (10*g^3*i^3*n^2 + 51*g^3*i^3*n*log(e) + 105*g^3*i^3*log(e)^2)*a^3*b^4*d^7)*B^2*x^4 + 2*((11*g^3*i^3*n^2 - 6*g^3*i^3*n*log(e))*b^7*c^4*d^3 + 4*(19*g^3*i^3*n^2 - 147*g^3*i^3*n*log(e) + 315*g^3*i^3*log(e)^2)*a*b^6*c^3*d^4 - 6*(29*g^3*i^3*n^2 - 630*g^3*i^3*log(e)^2)*a^2*b^5*c^2*d^5 + 4*(19*g^3*i^3*n^2 + 147*g^3*i^3*n*log(e) + 315*g^3*i^3*log(e)^2)*a^3*b^4*c*d^6 + (11*g^3*i^3*n^2 + 6*g^3*i^3*n*log(e))*a^4*b^3*d^7)*B^2*x^3 - 3*(3*(3*g^3*i^3*n^2 - 2*g^3*i^3*n*log(e))*b^7*c^5*d^2 - (67*g^3*i^3*n^2 - 42*g^3*i^3*n*log(e))*a*b^6*c^4*d^3 + 2*(29*g^3*i^3*n^2 + 252*g^3*i^3*n*log(e) - 630*g^3*i^3*log(e)^2)*a^2*b^5*c^3*d^4 + 2*(29*g^3*i^3*n^2 - 252*g^3*i^3*n*log(e) - 630*g^3*i^3*log(e)^2)*a^3*b^4*c^2*d^5 - (67*g^3*i^3*n^2 + 42*g^3*i^3*n*log(e))*a^4*b^3*c*d^6 + 3*(3*g^3*i^3*n^2 + 2*g^3*i^3*n*log(e))*a^5*b^2*d^7)*B^2*x^2 - 18*(35*a^4*b^3*c^3*d^4*g^3*i^3*n^2 - 21*a^5*b^2*c^2*d^5*g^3*i^3*n^2 + 7*a^6*b*c*d^6*g^3*i^3*n^2 - a^7*d^7*g^3*i^3*n^2)*B^2*log(b*x + a)^2 - 36*(b^7*c^7*g^3*i^3*n^2 - 7*a*b^6*c^6*d*g^3*i^3*n^2 + 21*a^2*b^5*c^5*d^2*g^3*i^3*n^2 - 35*a^3*b^4*c^4*d^3*g^3*i^3*n^2)*B^2*log(b*x + a)*log(d*x + c) + 18*(b^7*c^7*g^3*i^3*n^2 - 7*a*b^6*c^6*d*g^3*i^3*n^2 + 21*a^2*b^5*c^5*d^2*g^3*i^3*n^2 - 35*a^3*b^4*c^4*d^3*g^3*i^3*n^2)*B^2*log(d*x + c)^2 + 6*(6*(g^3*i^3*n^2 - g^3*i^3*n*log(e))*b^7*c^6*d - 3*(15*g^3*i^3*n^2 - 14*g^3*i^3*n*log(e))*a*b^6*c^5*d^2 + 2*(73*g^3*i^3*n^2 - 63*g^3*i^3*n*log(e))*a^2*b^5*c^4*d^3 - 2*(107*g^3*i^3*n^2 - 210*g^3*i^3*log(e)^2)*a^3*b^4*c^3*d^4 + 2*(73*g^3*i^3*n^2 + 63*g^3*i^3*n*log(e))*a^4*b^3*c^2*d^5 - 3*(15*g^3*i^3*n^2 + 14*g^3*i^3*n*log(e))*a^5*b^2*c*d^6 + 6*(g^3*i^3*n^2 + g^3*i^3*n*log(e))*a^6*b*d^7)*B^2*x - 6*(6*a*b^6*c^6*d*g^3*i^3*n^2 - 39*a^2*b^5*c^5*d^2*g^3*i^3*n^2 + 107*a^3*b^4*c^4*d^3*g^3*i^3*n^2 + 6*a^7*d^7*g^3*i^3*n*log(e) - (107*g^3*i^3*n^2 + 210*g^3*i^3*n*log(e))*a^4*b^3*c^3*d^4 + 3*(13*g^3*i^3*n^2 + 42*g^3*i^3*n*log(e))*a^5*b^2*c^2*d^5 - 6*(g^3*i^3*n^2 + 7*g^3*i^3*n*log(e))*a^6*b*c*d^6)*B^2*log(b*x + a) + 18*(20*B^2*b^7*d^7*g^3*i^3*x^7 + 140*B^2*a^3*b^4*c^3*d^4*g^3*i^3*x + 70*(b^7*c*d^6*g^3*i^3 + a*b^6*d^7*g^3*i^3)*B^2*x^6 + 84*(b^7*c^2*d^5*g^3*i^3 + 3*a*b^6*c*d^6*g^3*i^3 + a^2*b^5*d^7*g^3*i^3)*B^2*x^5 + 35*(b^7*c^3*d^4*g^3*i^3 + 9*a*b^6*c^2*d^5*g^3*i^3 + 9*a^2*b^5*c*d^6*g^3*i^3 + a^3*b^4*d^7*g^3*i^3)*B^2*x^4 + 140*(a*b^6*c^3*d^4*g^3*i^3 + 3*a^2*b^5*c^2*d^5*g^3*i^3 + a^3*b^4*c*d^6*g^3*i^3)*B^2*x^3 + 210*(a^2*b^5*c^3*d^4*g^3*i^3 + a^3*b^4*c^2*d^5*g^3*i^3)*B^2*x^2)*log((b*x + a)^n)^2 + 18*(20*B^2*b^7*d^7*g^3*i^3*x^7 + 140*B^2*a^3*b^4*c^3*d^4*g^3*i^3*x + 70*(b^7*c*d^6*g^3*i^3 + a*b^6*d^7*g^3*i^3)*B^2*x^6 + 84*(b^7*c^2*d^5*g^3*i^3 + 3*a*b^6*c*d^6*g^3*i^3 + a^2*b^5*d^7*g^3*i^3)*B^2*x^5 + 35*(b^7*c^3*d^4*g^3*i^3 + 9*a*b^6*c^2*d^5*g^3*i^3 + 9*a^2*b^5*c*d^6*g^3*i^3 + a^3*b^4*d^7*g^3*i^3)*B^2*x^4 + 140*(a*b^6*c^3*d^4*g^3*i^3 + 3*a^2*b^5*c^2*d^5*g^3*i^3 + a^3*b^4*c*d^6*g^3*i^3)*B^2*x^3 + 210*(a^2*b^5*c^3*d^4*g^3*i^3 + a^3*b^4*c^2*d^5*g^3*i^3)*B^2*x^2)*log((d*x + c)^n)^2 + 6*(120*B^2*b^7*d^7*g^3*i^3*x^7*log(e) - 20*((g^3*i^3*n - 21*g^3*i^3*log(e))*b^7*c*d^6 - (g^3*i^3*n + 21*g^3*i^3*log(e))*a*b^6*d^7)*B^2*x^6 + 12*(126*a*b^6*c*d^6*g^3*i^3*log(e) - (5*g^3*i^3*n - 42*g^3*i^3*log(e))*b^7*c^2*d^5 + (5*g^3*i^3*n + 42*g^3*i^3*log(e))*a^2*b^5*d^7)*B^2*x^5 - 3*((17*g^3*i^3*n - 70*g^3*i^3*log(e))*b^7*c^3*d^4 + 7*(7*g^3*i^3*n - 90*g^3*i^3*log(e))*a*b^6*c^2*d^5 - 7*(7*g^3*i^3*n + 90*g^3*i^3*log(e))*a^2*b^5*c*d^6 - (17*g^3*i^3*n + 70*g^3*i^3*log(e))*a^3*b^4*d^7)*B^2*x^4 - 2*(b^7*c^4*d^3*g^3*i^3*n - a^4*b^3*d^7*g^3*i^3*n - 1260*a^2*b^5*c^2*d^5*g^3*i^3*log(e) + 14*(7*g^3*i^3*n - 30*g^3*i^3*log(e))*a*b^6*c^3*d^4 - 14*(7*g^3*i^3*n + 30*g^3*i^3*log(e))*a^3*b^4*c*d^6)*B^2*x^3 + 3*(b^7*c^5*d^2*g^3*i^3*n - 7*a*b^6*c^4*d^3*g^3*i^3*n + 7*a^4*b^3*c*d^6*g^3*i^3*n - a^5*b^2*d^7*g^3*i^3*n - 84*(g^3*i^3*n - 5*g^3*i^3*log(e))*a^2*b^5*c^3*d^4 + 84*(g^3*i^3*n + 5*g^3*i^3*log(e))*a^3*b^4*c^2*d^5)*B^2*x^2 - 6*(b^7*c^6*d*g^3*i^3*n - 7*a*b^6*c^5*d^2*g^3*i^3*n + 21*a^2*b^5*c^4*d^3*g^3*i^3*n - 21*a^4*b^3*c^2*d^5*g^3*i^3*n + 7*a^5*b^2*c*d^6*g^3*i^3*n - a^6*b*d^7*g^3*i^3*n - 140*a^3*b^4*c^3*d^4*g^3*i^3*log(e))*B^2*x + 6*(35*a^4*b^3*c^3*d^4*g^3*i^3*n - 21*a^5*b^2*c^2*d^5*g^3*i^3*n + 7*a^6*b*c*d^6*g^3*i^3*n - a^7*d^7*g^3*i^3*n)*B^2*log(b*x + a) + 6*(b^7*c^7*g^3*i^3*n - 7*a*b^6*c^6*d*g^3*i^3*n + 21*a^2*b^5*c^5*d^2*g^3*i^3*n - 35*a^3*b^4*c^4*d^3*g^3*i^3*n)*B^2*log(d*x + c))*log((b*x + a)^n) - 6*(120*B^2*b^7*d^7*g^3*i^3*x^7*log(e) - 20*((g^3*i^3*n - 21*g^3*i^3*log(e))*b^7*c*d^6 - (g^3*i^3*n + 21*g^3*i^3*log(e))*a*b^6*d^7)*B^2*x^6 + 12*(126*a*b^6*c*d^6*g^3*i^3*log(e) - (5*g^3*i^3*n - 42*g^3*i^3*log(e))*b^7*c^2*d^5 + (5*g^3*i^3*n + 42*g^3*i^3*log(e))*a^2*b^5*d^7)*B^2*x^5 - 3*((17*g^3*i^3*n - 70*g^3*i^3*log(e))*b^7*c^3*d^4 + 7*(7*g^3*i^3*n - 90*g^3*i^3*log(e))*a*b^6*c^2*d^5 - 7*(7*g^3*i^3*n + 90*g^3*i^3*log(e))*a^2*b^5*c*d^6 - (17*g^3*i^3*n + 70*g^3*i^3*log(e))*a^3*b^4*d^7)*B^2*x^4 - 2*(b^7*c^4*d^3*g^3*i^3*n - a^4*b^3*d^7*g^3*i^3*n - 1260*a^2*b^5*c^2*d^5*g^3*i^3*log(e) + 14*(7*g^3*i^3*n - 30*g^3*i^3*log(e))*a*b^6*c^3*d^4 - 14*(7*g^3*i^3*n + 30*g^3*i^3*log(e))*a^3*b^4*c*d^6)*B^2*x^3 + 3*(b^7*c^5*d^2*g^3*i^3*n - 7*a*b^6*c^4*d^3*g^3*i^3*n + 7*a^4*b^3*c*d^6*g^3*i^3*n - a^5*b^2*d^7*g^3*i^3*n - 84*(g^3*i^3*n - 5*g^3*i^3*log(e))*a^2*b^5*c^3*d^4 + 84*(g^3*i^3*n + 5*g^3*i^3*log(e))*a^3*b^4*c^2*d^5)*B^2*x^2 - 6*(b^7*c^6*d*g^3*i^3*n - 7*a*b^6*c^5*d^2*g^3*i^3*n + 21*a^2*b^5*c^4*d^3*g^3*i^3*n - 21*a^4*b^3*c^2*d^5*g^3*i^3*n + 7*a^5*b^2*c*d^6*g^3*i^3*n - a^6*b*d^7*g^3*i^3*n - 140*a^3*b^4*c^3*d^4*g^3*i^3*log(e))*B^2*x + 6*(35*a^4*b^3*c^3*d^4*g^3*i^3*n - 21*a^5*b^2*c^2*d^5*g^3*i^3*n + 7*a^6*b*c*d^6*g^3*i^3*n - a^7*d^7*g^3*i^3*n)*B^2*log(b*x + a) + 6*(b^7*c^7*g^3*i^3*n - 7*a*b^6*c^6*d*g^3*i^3*n + 21*a^2*b^5*c^5*d^2*g^3*i^3*n - 35*a^3*b^4*c^4*d^3*g^3*i^3*n)*B^2*log(d*x + c) + 6*(20*B^2*b^7*d^7*g^3*i^3*x^7 + 140*B^2*a^3*b^4*c^3*d^4*g^3*i^3*x + 70*(b^7*c*d^6*g^3*i^3 + a*b^6*d^7*g^3*i^3)*B^2*x^6 + 84*(b^7*c^2*d^5*g^3*i^3 + 3*a*b^6*c*d^6*g^3*i^3 + a^2*b^5*d^7*g^3*i^3)*B^2*x^5 + 35*(b^7*c^3*d^4*g^3*i^3 + 9*a*b^6*c^2*d^5*g^3*i^3 + 9*a^2*b^5*c*d^6*g^3*i^3 + a^3*b^4*d^7*g^3*i^3)*B^2*x^4 + 140*(a*b^6*c^3*d^4*g^3*i^3 + 3*a^2*b^5*c^2*d^5*g^3*i^3 + a^3*b^4*c*d^6*g^3*i^3)*B^2*x^3 + 210*(a^2*b^5*c^3*d^4*g^3*i^3 + a^3*b^4*c^2*d^5*g^3*i^3)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^4*d^4)","B",0
179,1,5931,0,5.592624," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A B b^{2} d^{3} g^{2} i^{3} x^{6} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{6} \, A^{2} b^{2} d^{3} g^{2} i^{3} x^{6} + \frac{6}{5} \, A B b^{2} c d^{2} g^{2} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{4}{5} \, A B a b d^{3} g^{2} i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{5} \, A^{2} b^{2} c d^{2} g^{2} i^{3} x^{5} + \frac{2}{5} \, A^{2} a b d^{3} g^{2} i^{3} x^{5} + \frac{3}{2} \, A B b^{2} c^{2} d g^{2} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 3 \, A B a b c d^{2} g^{2} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A B a^{2} d^{3} g^{2} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{4} \, A^{2} b^{2} c^{2} d g^{2} i^{3} x^{4} + \frac{3}{2} \, A^{2} a b c d^{2} g^{2} i^{3} x^{4} + \frac{1}{4} \, A^{2} a^{2} d^{3} g^{2} i^{3} x^{4} + \frac{2}{3} \, A B b^{2} c^{3} g^{2} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 4 \, A B a b c^{2} d g^{2} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A B a^{2} c d^{2} g^{2} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, A^{2} b^{2} c^{3} g^{2} i^{3} x^{3} + 2 \, A^{2} a b c^{2} d g^{2} i^{3} x^{3} + A^{2} a^{2} c d^{2} g^{2} i^{3} x^{3} + 2 \, A B a b c^{3} g^{2} i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 3 \, A B a^{2} c^{2} d g^{2} i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a b c^{3} g^{2} i^{3} x^{2} + \frac{3}{2} \, A^{2} a^{2} c^{2} d g^{2} i^{3} x^{2} - \frac{1}{180} \, A B b^{2} d^{3} g^{2} i^{3} n {\left(\frac{60 \, a^{6} \log\left(b x + a\right)}{b^{6}} - \frac{60 \, c^{6} \log\left(d x + c\right)}{d^{6}} + \frac{12 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{5} - 15 \, {\left(b^{5} c^{2} d^{3} - a^{2} b^{3} d^{5}\right)} x^{4} + 20 \, {\left(b^{5} c^{3} d^{2} - a^{3} b^{2} d^{5}\right)} x^{3} - 30 \, {\left(b^{5} c^{4} d - a^{4} b d^{5}\right)} x^{2} + 60 \, {\left(b^{5} c^{5} - a^{5} d^{5}\right)} x}{b^{5} d^{5}}\right)} + \frac{1}{10} \, A B b^{2} c d^{2} g^{2} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} + \frac{1}{15} \, A B a b d^{3} g^{2} i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{4} \, A B b^{2} c^{2} d g^{2} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{2} \, A B a b c d^{2} g^{2} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{12} \, A B a^{2} d^{3} g^{2} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + \frac{1}{3} \, A B b^{2} c^{3} g^{2} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + 2 \, A B a b c^{2} d g^{2} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + A B a^{2} c d^{2} g^{2} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - 2 \, A B a b c^{3} g^{2} i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - 3 \, A B a^{2} c^{2} d g^{2} i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a^{2} c^{3} g^{2} i^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a^{2} c^{3} g^{2} i^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{2} c^{3} g^{2} i^{3} x - \frac{{\left(74 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} n^{2} - 33 \, a^{4} b c^{2} d^{4} g^{2} i^{3} n^{2} + 6 \, a^{5} c d^{5} g^{2} i^{3} n^{2} - 2 \, {\left(g^{2} i^{3} n^{2} - 3 \, g^{2} i^{3} n \log\left(e\right)\right)} b^{5} c^{6} + 18 \, {\left(g^{2} i^{3} n^{2} - 2 \, g^{2} i^{3} n \log\left(e\right)\right)} a b^{4} c^{5} d - 9 \, {\left(7 \, g^{2} i^{3} n^{2} - 10 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{2} b^{3} c^{4} d^{2}\right)} B^{2} \log\left(d x + c\right)}{180 \, b^{3} d^{3}} - \frac{{\left(b^{6} c^{6} g^{2} i^{3} n^{2} - 6 \, a b^{5} c^{5} d g^{2} i^{3} n^{2} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3} n^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} g^{2} i^{3} n^{2} + 15 \, a^{4} b^{2} c^{2} d^{4} g^{2} i^{3} n^{2} - 6 \, a^{5} b c d^{5} g^{2} i^{3} n^{2} + a^{6} d^{6} g^{2} i^{3} n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{30 \, b^{4} d^{3}} + \frac{60 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} \log\left(e\right)^{2} - 24 \, {\left({\left(g^{2} i^{3} n \log\left(e\right) - 9 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} b^{6} c d^{5} - {\left(g^{2} i^{3} n \log\left(e\right) + 6 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} a b^{5} d^{6}\right)} B^{2} x^{5} + 6 \, {\left({\left(g^{2} i^{3} n^{2} - 13 \, g^{2} i^{3} n \log\left(e\right) + 45 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} b^{6} c^{2} d^{4} - 2 \, {\left(g^{2} i^{3} n^{2} - 3 \, g^{2} i^{3} n \log\left(e\right) - 45 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} a b^{5} c d^{5} + {\left(g^{2} i^{3} n^{2} + 7 \, g^{2} i^{3} n \log\left(e\right) + 15 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} + 2 \, {\left({\left(9 \, g^{2} i^{3} n^{2} - 38 \, g^{2} i^{3} n \log\left(e\right) + 60 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} b^{6} c^{3} d^{3} - 3 \, {\left(5 \, g^{2} i^{3} n^{2} + 14 \, g^{2} i^{3} n \log\left(e\right) - 120 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} a b^{5} c^{2} d^{4} + 3 \, {\left(g^{2} i^{3} n^{2} + 26 \, g^{2} i^{3} n \log\left(e\right) + 60 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} a^{2} b^{4} c d^{5} + {\left(3 \, g^{2} i^{3} n^{2} + 2 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{3} b^{3} d^{6}\right)} B^{2} x^{3} + {\left({\left(11 \, g^{2} i^{3} n^{2} - 6 \, g^{2} i^{3} n \log\left(e\right)\right)} b^{6} c^{4} d^{2} + 2 \, {\left(5 \, g^{2} i^{3} n^{2} - 102 \, g^{2} i^{3} n \log\left(e\right) + 180 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} a b^{5} c^{3} d^{3} - 60 \, {\left(g^{2} i^{3} n^{2} - 3 \, g^{2} i^{3} n \log\left(e\right) - 9 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} a^{2} b^{4} c^{2} d^{4} + 2 \, {\left(23 \, g^{2} i^{3} n^{2} + 18 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{3} b^{3} c d^{5} - {\left(7 \, g^{2} i^{3} n^{2} + 6 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{4} b^{2} d^{6}\right)} B^{2} x^{2} - 6 \, {\left(20 \, a^{3} b^{3} c^{3} d^{3} g^{2} i^{3} n^{2} - 15 \, a^{4} b^{2} c^{2} d^{4} g^{2} i^{3} n^{2} + 6 \, a^{5} b c d^{5} g^{2} i^{3} n^{2} - a^{6} d^{6} g^{2} i^{3} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + 12 \, {\left(b^{6} c^{6} g^{2} i^{3} n^{2} - 6 \, a b^{5} c^{5} d g^{2} i^{3} n^{2} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) - 6 \, {\left(b^{6} c^{6} g^{2} i^{3} n^{2} - 6 \, a b^{5} c^{5} d g^{2} i^{3} n^{2} + 15 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(4 \, g^{2} i^{3} n^{2} - 3 \, g^{2} i^{3} n \log\left(e\right)\right)} b^{6} c^{5} d - 3 \, {\left(17 \, g^{2} i^{3} n^{2} - 12 \, g^{2} i^{3} n \log\left(e\right)\right)} a b^{5} c^{4} d^{2} + {\left(97 \, g^{2} i^{3} n^{2} + 30 \, g^{2} i^{3} n \log\left(e\right) - 180 \, g^{2} i^{3} \log\left(e\right)^{2}\right)} a^{2} b^{4} c^{3} d^{3} - {\left(77 \, g^{2} i^{3} n^{2} + 90 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{3} b^{3} c^{2} d^{4} + 9 \, {\left(3 \, g^{2} i^{3} n^{2} + 4 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{4} b^{2} c d^{5} - 2 \, {\left(2 \, g^{2} i^{3} n^{2} + 3 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{5} b d^{6}\right)} B^{2} x + 2 \, {\left(6 \, a b^{5} c^{5} d g^{2} i^{3} n^{2} - 33 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3} n^{2} + 2 \, {\left(17 \, g^{2} i^{3} n^{2} + 60 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{3} b^{3} c^{3} d^{3} - 3 \, {\left(g^{2} i^{3} n^{2} + 30 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{4} b^{2} c^{2} d^{4} - 6 \, {\left(g^{2} i^{3} n^{2} - 6 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{5} b c d^{5} + 2 \, {\left(g^{2} i^{3} n^{2} - 3 \, g^{2} i^{3} n \log\left(e\right)\right)} a^{6} d^{6}\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} + 60 \, B^{2} a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} x + 12 \, {\left(3 \, b^{6} c d^{5} g^{2} i^{3} + 2 \, a b^{5} d^{6} g^{2} i^{3}\right)} B^{2} x^{5} + 15 \, {\left(3 \, b^{6} c^{2} d^{4} g^{2} i^{3} + 6 \, a b^{5} c d^{5} g^{2} i^{3} + a^{2} b^{4} d^{6} g^{2} i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{6} c^{3} d^{3} g^{2} i^{3} + 6 \, a b^{5} c^{2} d^{4} g^{2} i^{3} + 3 \, a^{2} b^{4} c d^{5} g^{2} i^{3}\right)} B^{2} x^{3} + 30 \, {\left(2 \, a b^{5} c^{3} d^{3} g^{2} i^{3} + 3 \, a^{2} b^{4} c^{2} d^{4} g^{2} i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} + 60 \, B^{2} a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} x + 12 \, {\left(3 \, b^{6} c d^{5} g^{2} i^{3} + 2 \, a b^{5} d^{6} g^{2} i^{3}\right)} B^{2} x^{5} + 15 \, {\left(3 \, b^{6} c^{2} d^{4} g^{2} i^{3} + 6 \, a b^{5} c d^{5} g^{2} i^{3} + a^{2} b^{4} d^{6} g^{2} i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{6} c^{3} d^{3} g^{2} i^{3} + 6 \, a b^{5} c^{2} d^{4} g^{2} i^{3} + 3 \, a^{2} b^{4} c d^{5} g^{2} i^{3}\right)} B^{2} x^{3} + 30 \, {\left(2 \, a b^{5} c^{3} d^{3} g^{2} i^{3} + 3 \, a^{2} b^{4} c^{2} d^{4} g^{2} i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(60 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} \log\left(e\right) - 12 \, {\left({\left(g^{2} i^{3} n - 18 \, g^{2} i^{3} \log\left(e\right)\right)} b^{6} c d^{5} - {\left(g^{2} i^{3} n + 12 \, g^{2} i^{3} \log\left(e\right)\right)} a b^{5} d^{6}\right)} B^{2} x^{5} - 3 \, {\left({\left(13 \, g^{2} i^{3} n - 90 \, g^{2} i^{3} \log\left(e\right)\right)} b^{6} c^{2} d^{4} - 6 \, {\left(g^{2} i^{3} n + 30 \, g^{2} i^{3} \log\left(e\right)\right)} a b^{5} c d^{5} - {\left(7 \, g^{2} i^{3} n + 30 \, g^{2} i^{3} \log\left(e\right)\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} + 2 \, {\left(a^{3} b^{3} d^{6} g^{2} i^{3} n - {\left(19 \, g^{2} i^{3} n - 60 \, g^{2} i^{3} \log\left(e\right)\right)} b^{6} c^{3} d^{3} - 3 \, {\left(7 \, g^{2} i^{3} n - 120 \, g^{2} i^{3} \log\left(e\right)\right)} a b^{5} c^{2} d^{4} + 3 \, {\left(13 \, g^{2} i^{3} n + 60 \, g^{2} i^{3} \log\left(e\right)\right)} a^{2} b^{4} c d^{5}\right)} B^{2} x^{3} - 3 \, {\left(b^{6} c^{4} d^{2} g^{2} i^{3} n - 6 \, a^{3} b^{3} c d^{5} g^{2} i^{3} n + a^{4} b^{2} d^{6} g^{2} i^{3} n + 2 \, {\left(17 \, g^{2} i^{3} n - 60 \, g^{2} i^{3} \log\left(e\right)\right)} a b^{5} c^{3} d^{3} - 30 \, {\left(g^{2} i^{3} n + 6 \, g^{2} i^{3} \log\left(e\right)\right)} a^{2} b^{4} c^{2} d^{4}\right)} B^{2} x^{2} + 6 \, {\left(b^{6} c^{5} d g^{2} i^{3} n - 6 \, a b^{5} c^{4} d^{2} g^{2} i^{3} n + 15 \, a^{3} b^{3} c^{2} d^{4} g^{2} i^{3} n - 6 \, a^{4} b^{2} c d^{5} g^{2} i^{3} n + a^{5} b d^{6} g^{2} i^{3} n - 5 \, {\left(g^{2} i^{3} n - 12 \, g^{2} i^{3} \log\left(e\right)\right)} a^{2} b^{4} c^{3} d^{3}\right)} B^{2} x + 6 \, {\left(20 \, a^{3} b^{3} c^{3} d^{3} g^{2} i^{3} n - 15 \, a^{4} b^{2} c^{2} d^{4} g^{2} i^{3} n + 6 \, a^{5} b c d^{5} g^{2} i^{3} n - a^{6} d^{6} g^{2} i^{3} n\right)} B^{2} \log\left(b x + a\right) - 6 \, {\left(b^{6} c^{6} g^{2} i^{3} n - 6 \, a b^{5} c^{5} d g^{2} i^{3} n + 15 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3} n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(60 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} \log\left(e\right) - 12 \, {\left({\left(g^{2} i^{3} n - 18 \, g^{2} i^{3} \log\left(e\right)\right)} b^{6} c d^{5} - {\left(g^{2} i^{3} n + 12 \, g^{2} i^{3} \log\left(e\right)\right)} a b^{5} d^{6}\right)} B^{2} x^{5} - 3 \, {\left({\left(13 \, g^{2} i^{3} n - 90 \, g^{2} i^{3} \log\left(e\right)\right)} b^{6} c^{2} d^{4} - 6 \, {\left(g^{2} i^{3} n + 30 \, g^{2} i^{3} \log\left(e\right)\right)} a b^{5} c d^{5} - {\left(7 \, g^{2} i^{3} n + 30 \, g^{2} i^{3} \log\left(e\right)\right)} a^{2} b^{4} d^{6}\right)} B^{2} x^{4} + 2 \, {\left(a^{3} b^{3} d^{6} g^{2} i^{3} n - {\left(19 \, g^{2} i^{3} n - 60 \, g^{2} i^{3} \log\left(e\right)\right)} b^{6} c^{3} d^{3} - 3 \, {\left(7 \, g^{2} i^{3} n - 120 \, g^{2} i^{3} \log\left(e\right)\right)} a b^{5} c^{2} d^{4} + 3 \, {\left(13 \, g^{2} i^{3} n + 60 \, g^{2} i^{3} \log\left(e\right)\right)} a^{2} b^{4} c d^{5}\right)} B^{2} x^{3} - 3 \, {\left(b^{6} c^{4} d^{2} g^{2} i^{3} n - 6 \, a^{3} b^{3} c d^{5} g^{2} i^{3} n + a^{4} b^{2} d^{6} g^{2} i^{3} n + 2 \, {\left(17 \, g^{2} i^{3} n - 60 \, g^{2} i^{3} \log\left(e\right)\right)} a b^{5} c^{3} d^{3} - 30 \, {\left(g^{2} i^{3} n + 6 \, g^{2} i^{3} \log\left(e\right)\right)} a^{2} b^{4} c^{2} d^{4}\right)} B^{2} x^{2} + 6 \, {\left(b^{6} c^{5} d g^{2} i^{3} n - 6 \, a b^{5} c^{4} d^{2} g^{2} i^{3} n + 15 \, a^{3} b^{3} c^{2} d^{4} g^{2} i^{3} n - 6 \, a^{4} b^{2} c d^{5} g^{2} i^{3} n + a^{5} b d^{6} g^{2} i^{3} n - 5 \, {\left(g^{2} i^{3} n - 12 \, g^{2} i^{3} \log\left(e\right)\right)} a^{2} b^{4} c^{3} d^{3}\right)} B^{2} x + 6 \, {\left(20 \, a^{3} b^{3} c^{3} d^{3} g^{2} i^{3} n - 15 \, a^{4} b^{2} c^{2} d^{4} g^{2} i^{3} n + 6 \, a^{5} b c d^{5} g^{2} i^{3} n - a^{6} d^{6} g^{2} i^{3} n\right)} B^{2} \log\left(b x + a\right) - 6 \, {\left(b^{6} c^{6} g^{2} i^{3} n - 6 \, a b^{5} c^{5} d g^{2} i^{3} n + 15 \, a^{2} b^{4} c^{4} d^{2} g^{2} i^{3} n\right)} B^{2} \log\left(d x + c\right) + 6 \, {\left(10 \, B^{2} b^{6} d^{6} g^{2} i^{3} x^{6} + 60 \, B^{2} a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} x + 12 \, {\left(3 \, b^{6} c d^{5} g^{2} i^{3} + 2 \, a b^{5} d^{6} g^{2} i^{3}\right)} B^{2} x^{5} + 15 \, {\left(3 \, b^{6} c^{2} d^{4} g^{2} i^{3} + 6 \, a b^{5} c d^{5} g^{2} i^{3} + a^{2} b^{4} d^{6} g^{2} i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{6} c^{3} d^{3} g^{2} i^{3} + 6 \, a b^{5} c^{2} d^{4} g^{2} i^{3} + 3 \, a^{2} b^{4} c d^{5} g^{2} i^{3}\right)} B^{2} x^{3} + 30 \, {\left(2 \, a b^{5} c^{3} d^{3} g^{2} i^{3} + 3 \, a^{2} b^{4} c^{2} d^{4} g^{2} i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{360 \, b^{4} d^{3}}"," ",0,"1/3*A*B*b^2*d^3*g^2*i^3*x^6*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/6*A^2*b^2*d^3*g^2*i^3*x^6 + 6/5*A*B*b^2*c*d^2*g^2*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 4/5*A*B*a*b*d^3*g^2*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/5*A^2*b^2*c*d^2*g^2*i^3*x^5 + 2/5*A^2*a*b*d^3*g^2*i^3*x^5 + 3/2*A*B*b^2*c^2*d*g^2*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3*A*B*a*b*c*d^2*g^2*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*B*a^2*d^3*g^2*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/4*A^2*b^2*c^2*d*g^2*i^3*x^4 + 3/2*A^2*a*b*c*d^2*g^2*i^3*x^4 + 1/4*A^2*a^2*d^3*g^2*i^3*x^4 + 2/3*A*B*b^2*c^3*g^2*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 4*A*B*a*b*c^2*d*g^2*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*B*a^2*c*d^2*g^2*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A^2*b^2*c^3*g^2*i^3*x^3 + 2*A^2*a*b*c^2*d*g^2*i^3*x^3 + A^2*a^2*c*d^2*g^2*i^3*x^3 + 2*A*B*a*b*c^3*g^2*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3*A*B*a^2*c^2*d*g^2*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b*c^3*g^2*i^3*x^2 + 3/2*A^2*a^2*c^2*d*g^2*i^3*x^2 - 1/180*A*B*b^2*d^3*g^2*i^3*n*(60*a^6*log(b*x + a)/b^6 - 60*c^6*log(d*x + c)/d^6 + (12*(b^5*c*d^4 - a*b^4*d^5)*x^5 - 15*(b^5*c^2*d^3 - a^2*b^3*d^5)*x^4 + 20*(b^5*c^3*d^2 - a^3*b^2*d^5)*x^3 - 30*(b^5*c^4*d - a^4*b*d^5)*x^2 + 60*(b^5*c^5 - a^5*d^5)*x)/(b^5*d^5)) + 1/10*A*B*b^2*c*d^2*g^2*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) + 1/15*A*B*a*b*d^3*g^2*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/4*A*B*b^2*c^2*d*g^2*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/2*A*B*a*b*c*d^2*g^2*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/12*A*B*a^2*d^3*g^2*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + 1/3*A*B*b^2*c^3*g^2*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + 2*A*B*a*b*c^2*d*g^2*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + A*B*a^2*c*d^2*g^2*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 2*A*B*a*b*c^3*g^2*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 3*A*B*a^2*c^2*d*g^2*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a^2*c^3*g^2*i^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^2*c^3*g^2*i^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^2*c^3*g^2*i^3*x - 1/180*(74*a^3*b^2*c^3*d^3*g^2*i^3*n^2 - 33*a^4*b*c^2*d^4*g^2*i^3*n^2 + 6*a^5*c*d^5*g^2*i^3*n^2 - 2*(g^2*i^3*n^2 - 3*g^2*i^3*n*log(e))*b^5*c^6 + 18*(g^2*i^3*n^2 - 2*g^2*i^3*n*log(e))*a*b^4*c^5*d - 9*(7*g^2*i^3*n^2 - 10*g^2*i^3*n*log(e))*a^2*b^3*c^4*d^2)*B^2*log(d*x + c)/(b^3*d^3) - 1/30*(b^6*c^6*g^2*i^3*n^2 - 6*a*b^5*c^5*d*g^2*i^3*n^2 + 15*a^2*b^4*c^4*d^2*g^2*i^3*n^2 - 20*a^3*b^3*c^3*d^3*g^2*i^3*n^2 + 15*a^4*b^2*c^2*d^4*g^2*i^3*n^2 - 6*a^5*b*c*d^5*g^2*i^3*n^2 + a^6*d^6*g^2*i^3*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^4*d^3) + 1/360*(60*B^2*b^6*d^6*g^2*i^3*x^6*log(e)^2 - 24*((g^2*i^3*n*log(e) - 9*g^2*i^3*log(e)^2)*b^6*c*d^5 - (g^2*i^3*n*log(e) + 6*g^2*i^3*log(e)^2)*a*b^5*d^6)*B^2*x^5 + 6*((g^2*i^3*n^2 - 13*g^2*i^3*n*log(e) + 45*g^2*i^3*log(e)^2)*b^6*c^2*d^4 - 2*(g^2*i^3*n^2 - 3*g^2*i^3*n*log(e) - 45*g^2*i^3*log(e)^2)*a*b^5*c*d^5 + (g^2*i^3*n^2 + 7*g^2*i^3*n*log(e) + 15*g^2*i^3*log(e)^2)*a^2*b^4*d^6)*B^2*x^4 + 2*((9*g^2*i^3*n^2 - 38*g^2*i^3*n*log(e) + 60*g^2*i^3*log(e)^2)*b^6*c^3*d^3 - 3*(5*g^2*i^3*n^2 + 14*g^2*i^3*n*log(e) - 120*g^2*i^3*log(e)^2)*a*b^5*c^2*d^4 + 3*(g^2*i^3*n^2 + 26*g^2*i^3*n*log(e) + 60*g^2*i^3*log(e)^2)*a^2*b^4*c*d^5 + (3*g^2*i^3*n^2 + 2*g^2*i^3*n*log(e))*a^3*b^3*d^6)*B^2*x^3 + ((11*g^2*i^3*n^2 - 6*g^2*i^3*n*log(e))*b^6*c^4*d^2 + 2*(5*g^2*i^3*n^2 - 102*g^2*i^3*n*log(e) + 180*g^2*i^3*log(e)^2)*a*b^5*c^3*d^3 - 60*(g^2*i^3*n^2 - 3*g^2*i^3*n*log(e) - 9*g^2*i^3*log(e)^2)*a^2*b^4*c^2*d^4 + 2*(23*g^2*i^3*n^2 + 18*g^2*i^3*n*log(e))*a^3*b^3*c*d^5 - (7*g^2*i^3*n^2 + 6*g^2*i^3*n*log(e))*a^4*b^2*d^6)*B^2*x^2 - 6*(20*a^3*b^3*c^3*d^3*g^2*i^3*n^2 - 15*a^4*b^2*c^2*d^4*g^2*i^3*n^2 + 6*a^5*b*c*d^5*g^2*i^3*n^2 - a^6*d^6*g^2*i^3*n^2)*B^2*log(b*x + a)^2 + 12*(b^6*c^6*g^2*i^3*n^2 - 6*a*b^5*c^5*d*g^2*i^3*n^2 + 15*a^2*b^4*c^4*d^2*g^2*i^3*n^2)*B^2*log(b*x + a)*log(d*x + c) - 6*(b^6*c^6*g^2*i^3*n^2 - 6*a*b^5*c^5*d*g^2*i^3*n^2 + 15*a^2*b^4*c^4*d^2*g^2*i^3*n^2)*B^2*log(d*x + c)^2 - 2*(2*(4*g^2*i^3*n^2 - 3*g^2*i^3*n*log(e))*b^6*c^5*d - 3*(17*g^2*i^3*n^2 - 12*g^2*i^3*n*log(e))*a*b^5*c^4*d^2 + (97*g^2*i^3*n^2 + 30*g^2*i^3*n*log(e) - 180*g^2*i^3*log(e)^2)*a^2*b^4*c^3*d^3 - (77*g^2*i^3*n^2 + 90*g^2*i^3*n*log(e))*a^3*b^3*c^2*d^4 + 9*(3*g^2*i^3*n^2 + 4*g^2*i^3*n*log(e))*a^4*b^2*c*d^5 - 2*(2*g^2*i^3*n^2 + 3*g^2*i^3*n*log(e))*a^5*b*d^6)*B^2*x + 2*(6*a*b^5*c^5*d*g^2*i^3*n^2 - 33*a^2*b^4*c^4*d^2*g^2*i^3*n^2 + 2*(17*g^2*i^3*n^2 + 60*g^2*i^3*n*log(e))*a^3*b^3*c^3*d^3 - 3*(g^2*i^3*n^2 + 30*g^2*i^3*n*log(e))*a^4*b^2*c^2*d^4 - 6*(g^2*i^3*n^2 - 6*g^2*i^3*n*log(e))*a^5*b*c*d^5 + 2*(g^2*i^3*n^2 - 3*g^2*i^3*n*log(e))*a^6*d^6)*B^2*log(b*x + a) + 6*(10*B^2*b^6*d^6*g^2*i^3*x^6 + 60*B^2*a^2*b^4*c^3*d^3*g^2*i^3*x + 12*(3*b^6*c*d^5*g^2*i^3 + 2*a*b^5*d^6*g^2*i^3)*B^2*x^5 + 15*(3*b^6*c^2*d^4*g^2*i^3 + 6*a*b^5*c*d^5*g^2*i^3 + a^2*b^4*d^6*g^2*i^3)*B^2*x^4 + 20*(b^6*c^3*d^3*g^2*i^3 + 6*a*b^5*c^2*d^4*g^2*i^3 + 3*a^2*b^4*c*d^5*g^2*i^3)*B^2*x^3 + 30*(2*a*b^5*c^3*d^3*g^2*i^3 + 3*a^2*b^4*c^2*d^4*g^2*i^3)*B^2*x^2)*log((b*x + a)^n)^2 + 6*(10*B^2*b^6*d^6*g^2*i^3*x^6 + 60*B^2*a^2*b^4*c^3*d^3*g^2*i^3*x + 12*(3*b^6*c*d^5*g^2*i^3 + 2*a*b^5*d^6*g^2*i^3)*B^2*x^5 + 15*(3*b^6*c^2*d^4*g^2*i^3 + 6*a*b^5*c*d^5*g^2*i^3 + a^2*b^4*d^6*g^2*i^3)*B^2*x^4 + 20*(b^6*c^3*d^3*g^2*i^3 + 6*a*b^5*c^2*d^4*g^2*i^3 + 3*a^2*b^4*c*d^5*g^2*i^3)*B^2*x^3 + 30*(2*a*b^5*c^3*d^3*g^2*i^3 + 3*a^2*b^4*c^2*d^4*g^2*i^3)*B^2*x^2)*log((d*x + c)^n)^2 + 2*(60*B^2*b^6*d^6*g^2*i^3*x^6*log(e) - 12*((g^2*i^3*n - 18*g^2*i^3*log(e))*b^6*c*d^5 - (g^2*i^3*n + 12*g^2*i^3*log(e))*a*b^5*d^6)*B^2*x^5 - 3*((13*g^2*i^3*n - 90*g^2*i^3*log(e))*b^6*c^2*d^4 - 6*(g^2*i^3*n + 30*g^2*i^3*log(e))*a*b^5*c*d^5 - (7*g^2*i^3*n + 30*g^2*i^3*log(e))*a^2*b^4*d^6)*B^2*x^4 + 2*(a^3*b^3*d^6*g^2*i^3*n - (19*g^2*i^3*n - 60*g^2*i^3*log(e))*b^6*c^3*d^3 - 3*(7*g^2*i^3*n - 120*g^2*i^3*log(e))*a*b^5*c^2*d^4 + 3*(13*g^2*i^3*n + 60*g^2*i^3*log(e))*a^2*b^4*c*d^5)*B^2*x^3 - 3*(b^6*c^4*d^2*g^2*i^3*n - 6*a^3*b^3*c*d^5*g^2*i^3*n + a^4*b^2*d^6*g^2*i^3*n + 2*(17*g^2*i^3*n - 60*g^2*i^3*log(e))*a*b^5*c^3*d^3 - 30*(g^2*i^3*n + 6*g^2*i^3*log(e))*a^2*b^4*c^2*d^4)*B^2*x^2 + 6*(b^6*c^5*d*g^2*i^3*n - 6*a*b^5*c^4*d^2*g^2*i^3*n + 15*a^3*b^3*c^2*d^4*g^2*i^3*n - 6*a^4*b^2*c*d^5*g^2*i^3*n + a^5*b*d^6*g^2*i^3*n - 5*(g^2*i^3*n - 12*g^2*i^3*log(e))*a^2*b^4*c^3*d^3)*B^2*x + 6*(20*a^3*b^3*c^3*d^3*g^2*i^3*n - 15*a^4*b^2*c^2*d^4*g^2*i^3*n + 6*a^5*b*c*d^5*g^2*i^3*n - a^6*d^6*g^2*i^3*n)*B^2*log(b*x + a) - 6*(b^6*c^6*g^2*i^3*n - 6*a*b^5*c^5*d*g^2*i^3*n + 15*a^2*b^4*c^4*d^2*g^2*i^3*n)*B^2*log(d*x + c))*log((b*x + a)^n) - 2*(60*B^2*b^6*d^6*g^2*i^3*x^6*log(e) - 12*((g^2*i^3*n - 18*g^2*i^3*log(e))*b^6*c*d^5 - (g^2*i^3*n + 12*g^2*i^3*log(e))*a*b^5*d^6)*B^2*x^5 - 3*((13*g^2*i^3*n - 90*g^2*i^3*log(e))*b^6*c^2*d^4 - 6*(g^2*i^3*n + 30*g^2*i^3*log(e))*a*b^5*c*d^5 - (7*g^2*i^3*n + 30*g^2*i^3*log(e))*a^2*b^4*d^6)*B^2*x^4 + 2*(a^3*b^3*d^6*g^2*i^3*n - (19*g^2*i^3*n - 60*g^2*i^3*log(e))*b^6*c^3*d^3 - 3*(7*g^2*i^3*n - 120*g^2*i^3*log(e))*a*b^5*c^2*d^4 + 3*(13*g^2*i^3*n + 60*g^2*i^3*log(e))*a^2*b^4*c*d^5)*B^2*x^3 - 3*(b^6*c^4*d^2*g^2*i^3*n - 6*a^3*b^3*c*d^5*g^2*i^3*n + a^4*b^2*d^6*g^2*i^3*n + 2*(17*g^2*i^3*n - 60*g^2*i^3*log(e))*a*b^5*c^3*d^3 - 30*(g^2*i^3*n + 6*g^2*i^3*log(e))*a^2*b^4*c^2*d^4)*B^2*x^2 + 6*(b^6*c^5*d*g^2*i^3*n - 6*a*b^5*c^4*d^2*g^2*i^3*n + 15*a^3*b^3*c^2*d^4*g^2*i^3*n - 6*a^4*b^2*c*d^5*g^2*i^3*n + a^5*b*d^6*g^2*i^3*n - 5*(g^2*i^3*n - 12*g^2*i^3*log(e))*a^2*b^4*c^3*d^3)*B^2*x + 6*(20*a^3*b^3*c^3*d^3*g^2*i^3*n - 15*a^4*b^2*c^2*d^4*g^2*i^3*n + 6*a^5*b*c*d^5*g^2*i^3*n - a^6*d^6*g^2*i^3*n)*B^2*log(b*x + a) - 6*(b^6*c^6*g^2*i^3*n - 6*a*b^5*c^5*d*g^2*i^3*n + 15*a^2*b^4*c^4*d^2*g^2*i^3*n)*B^2*log(d*x + c) + 6*(10*B^2*b^6*d^6*g^2*i^3*x^6 + 60*B^2*a^2*b^4*c^3*d^3*g^2*i^3*x + 12*(3*b^6*c*d^5*g^2*i^3 + 2*a*b^5*d^6*g^2*i^3)*B^2*x^5 + 15*(3*b^6*c^2*d^4*g^2*i^3 + 6*a*b^5*c*d^5*g^2*i^3 + a^2*b^4*d^6*g^2*i^3)*B^2*x^4 + 20*(b^6*c^3*d^3*g^2*i^3 + 6*a*b^5*c^2*d^4*g^2*i^3 + 3*a^2*b^4*c*d^5*g^2*i^3)*B^2*x^3 + 30*(2*a*b^5*c^3*d^3*g^2*i^3 + 3*a^2*b^4*c^2*d^4*g^2*i^3)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^4*d^3)","B",0
180,1,3724,0,5.490022," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{5} \, A B b d^{3} g i^{3} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{5} \, A^{2} b d^{3} g i^{3} x^{5} + \frac{3}{2} \, A B b c d^{2} g i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A B a d^{3} g i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{4} \, A^{2} b c d^{2} g i^{3} x^{4} + \frac{1}{4} \, A^{2} a d^{3} g i^{3} x^{4} + 2 \, A B b c^{2} d g i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A B a c d^{2} g i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} b c^{2} d g i^{3} x^{3} + A^{2} a c d^{2} g i^{3} x^{3} + A B b c^{3} g i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 3 \, A B a c^{2} d g i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A^{2} b c^{3} g i^{3} x^{2} + \frac{3}{2} \, A^{2} a c^{2} d g i^{3} x^{2} + \frac{1}{30} \, A B b d^{3} g i^{3} n {\left(\frac{12 \, a^{5} \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} x^{2} - 12 \, {\left(b^{4} c^{4} - a^{4} d^{4}\right)} x}{b^{4} d^{4}}\right)} - \frac{1}{4} \, A B b c d^{2} g i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} - \frac{1}{12} \, A B a d^{3} g i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + A B b c^{2} d g i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} + A B a c d^{2} g i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - A B b c^{3} g i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} - 3 \, A B a c^{2} d g i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B a c^{3} g i^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B a c^{3} g i^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a c^{3} g i^{3} x - \frac{{\left(47 \, a^{2} b^{2} c^{3} d^{2} g i^{3} n^{2} - 27 \, a^{3} b c^{2} d^{3} g i^{3} n^{2} + 6 \, a^{4} c d^{4} g i^{3} n^{2} + {\left(5 \, g i^{3} n^{2} - 6 \, g i^{3} n \log\left(e\right)\right)} b^{4} c^{5} - {\left(31 \, g i^{3} n^{2} - 30 \, g i^{3} n \log\left(e\right)\right)} a b^{3} c^{4} d\right)} B^{2} \log\left(d x + c\right)}{60 \, b^{3} d^{2}} + \frac{{\left(b^{5} c^{5} g i^{3} n^{2} - 5 \, a b^{4} c^{4} d g i^{3} n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g i^{3} n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g i^{3} n^{2} + 5 \, a^{4} b c d^{4} g i^{3} n^{2} - a^{5} d^{5} g i^{3} n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{10 \, b^{4} d^{2}} + \frac{12 \, B^{2} b^{5} d^{5} g i^{3} x^{5} \log\left(e\right)^{2} - 3 \, {\left({\left(2 \, g i^{3} n \log\left(e\right) - 15 \, g i^{3} \log\left(e\right)^{2}\right)} b^{5} c d^{4} - {\left(2 \, g i^{3} n \log\left(e\right) + 5 \, g i^{3} \log\left(e\right)^{2}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left({\left(g i^{3} n^{2} - 11 \, g i^{3} n \log\left(e\right) + 30 \, g i^{3} \log\left(e\right)^{2}\right)} b^{5} c^{2} d^{3} - 2 \, {\left(g i^{3} n^{2} - 5 \, g i^{3} n \log\left(e\right) - 15 \, g i^{3} \log\left(e\right)^{2}\right)} a b^{4} c d^{4} + {\left(g i^{3} n^{2} + g i^{3} n \log\left(e\right)\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + {\left({\left(8 \, g i^{3} n^{2} - 27 \, g i^{3} n \log\left(e\right) + 30 \, g i^{3} \log\left(e\right)^{2}\right)} b^{5} c^{3} d^{2} - 3 \, {\left(6 \, g i^{3} n^{2} - 5 \, g i^{3} n \log\left(e\right) - 30 \, g i^{3} \log\left(e\right)^{2}\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(4 \, g i^{3} n^{2} + 5 \, g i^{3} n \log\left(e\right)\right)} a^{2} b^{3} c d^{4} - {\left(2 \, g i^{3} n^{2} + 3 \, g i^{3} n \log\left(e\right)\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 3 \, {\left(10 \, a^{2} b^{3} c^{3} d^{2} g i^{3} n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g i^{3} n^{2} + 5 \, a^{4} b c d^{4} g i^{3} n^{2} - a^{5} d^{5} g i^{3} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{5} c^{5} g i^{3} n^{2} - 5 \, a b^{4} c^{4} d g i^{3} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) + 3 \, {\left(b^{5} c^{5} g i^{3} n^{2} - 5 \, a b^{4} c^{4} d g i^{3} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + {\left({\left(11 \, g i^{3} n^{2} - 6 \, g i^{3} n \log\left(e\right)\right)} b^{5} c^{4} d - 2 \, {\left(14 \, g i^{3} n^{2} + 15 \, g i^{3} n \log\left(e\right) - 30 \, g i^{3} \log\left(e\right)^{2}\right)} a b^{4} c^{3} d^{2} + 12 \, {\left(2 \, g i^{3} n^{2} + 5 \, g i^{3} n \log\left(e\right)\right)} a^{2} b^{3} c^{2} d^{3} - 2 \, {\left(4 \, g i^{3} n^{2} + 15 \, g i^{3} n \log\left(e\right)\right)} a^{3} b^{2} c d^{4} + {\left(g i^{3} n^{2} + 6 \, g i^{3} n \log\left(e\right)\right)} a^{4} b d^{5}\right)} B^{2} x - {\left(6 \, a b^{4} c^{4} d g i^{3} n^{2} + 3 \, {\left(g i^{3} n^{2} - 20 \, g i^{3} n \log\left(e\right)\right)} a^{2} b^{3} c^{3} d^{2} - {\left(23 \, g i^{3} n^{2} - 60 \, g i^{3} n \log\left(e\right)\right)} a^{3} b^{2} c^{2} d^{3} + {\left(19 \, g i^{3} n^{2} - 30 \, g i^{3} n \log\left(e\right)\right)} a^{4} b c d^{4} - {\left(5 \, g i^{3} n^{2} - 6 \, g i^{3} n \log\left(e\right)\right)} a^{5} d^{5}\right)} B^{2} \log\left(b x + a\right) + 3 \, {\left(4 \, B^{2} b^{5} d^{5} g i^{3} x^{5} + 20 \, B^{2} a b^{4} c^{3} d^{2} g i^{3} x + 5 \, {\left(3 \, b^{5} c d^{4} g i^{3} + a b^{4} d^{5} g i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} g i^{3} + a b^{4} c d^{4} g i^{3}\right)} B^{2} x^{3} + 10 \, {\left(b^{5} c^{3} d^{2} g i^{3} + 3 \, a b^{4} c^{2} d^{3} g i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(4 \, B^{2} b^{5} d^{5} g i^{3} x^{5} + 20 \, B^{2} a b^{4} c^{3} d^{2} g i^{3} x + 5 \, {\left(3 \, b^{5} c d^{4} g i^{3} + a b^{4} d^{5} g i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} g i^{3} + a b^{4} c d^{4} g i^{3}\right)} B^{2} x^{3} + 10 \, {\left(b^{5} c^{3} d^{2} g i^{3} + 3 \, a b^{4} c^{2} d^{3} g i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(24 \, B^{2} b^{5} d^{5} g i^{3} x^{5} \log\left(e\right) - 6 \, {\left({\left(g i^{3} n - 15 \, g i^{3} \log\left(e\right)\right)} b^{5} c d^{4} - {\left(g i^{3} n + 5 \, g i^{3} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left(a^{2} b^{3} d^{5} g i^{3} n - {\left(11 \, g i^{3} n - 60 \, g i^{3} \log\left(e\right)\right)} b^{5} c^{2} d^{3} + 10 \, {\left(g i^{3} n + 6 \, g i^{3} \log\left(e\right)\right)} a b^{4} c d^{4}\right)} B^{2} x^{3} + 3 \, {\left(5 \, a^{2} b^{3} c d^{4} g i^{3} n - a^{3} b^{2} d^{5} g i^{3} n - {\left(9 \, g i^{3} n - 20 \, g i^{3} \log\left(e\right)\right)} b^{5} c^{3} d^{2} + 5 \, {\left(g i^{3} n + 12 \, g i^{3} \log\left(e\right)\right)} a b^{4} c^{2} d^{3}\right)} B^{2} x^{2} - 6 \, {\left(b^{5} c^{4} d g i^{3} n - 10 \, a^{2} b^{3} c^{2} d^{3} g i^{3} n + 5 \, a^{3} b^{2} c d^{4} g i^{3} n - a^{4} b d^{5} g i^{3} n + 5 \, {\left(g i^{3} n - 4 \, g i^{3} \log\left(e\right)\right)} a b^{4} c^{3} d^{2}\right)} B^{2} x + 6 \, {\left(10 \, a^{2} b^{3} c^{3} d^{2} g i^{3} n - 10 \, a^{3} b^{2} c^{2} d^{3} g i^{3} n + 5 \, a^{4} b c d^{4} g i^{3} n - a^{5} d^{5} g i^{3} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(b^{5} c^{5} g i^{3} n - 5 \, a b^{4} c^{4} d g i^{3} n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(24 \, B^{2} b^{5} d^{5} g i^{3} x^{5} \log\left(e\right) - 6 \, {\left({\left(g i^{3} n - 15 \, g i^{3} \log\left(e\right)\right)} b^{5} c d^{4} - {\left(g i^{3} n + 5 \, g i^{3} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left(a^{2} b^{3} d^{5} g i^{3} n - {\left(11 \, g i^{3} n - 60 \, g i^{3} \log\left(e\right)\right)} b^{5} c^{2} d^{3} + 10 \, {\left(g i^{3} n + 6 \, g i^{3} \log\left(e\right)\right)} a b^{4} c d^{4}\right)} B^{2} x^{3} + 3 \, {\left(5 \, a^{2} b^{3} c d^{4} g i^{3} n - a^{3} b^{2} d^{5} g i^{3} n - {\left(9 \, g i^{3} n - 20 \, g i^{3} \log\left(e\right)\right)} b^{5} c^{3} d^{2} + 5 \, {\left(g i^{3} n + 12 \, g i^{3} \log\left(e\right)\right)} a b^{4} c^{2} d^{3}\right)} B^{2} x^{2} - 6 \, {\left(b^{5} c^{4} d g i^{3} n - 10 \, a^{2} b^{3} c^{2} d^{3} g i^{3} n + 5 \, a^{3} b^{2} c d^{4} g i^{3} n - a^{4} b d^{5} g i^{3} n + 5 \, {\left(g i^{3} n - 4 \, g i^{3} \log\left(e\right)\right)} a b^{4} c^{3} d^{2}\right)} B^{2} x + 6 \, {\left(10 \, a^{2} b^{3} c^{3} d^{2} g i^{3} n - 10 \, a^{3} b^{2} c^{2} d^{3} g i^{3} n + 5 \, a^{4} b c d^{4} g i^{3} n - a^{5} d^{5} g i^{3} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(b^{5} c^{5} g i^{3} n - 5 \, a b^{4} c^{4} d g i^{3} n\right)} B^{2} \log\left(d x + c\right) + 6 \, {\left(4 \, B^{2} b^{5} d^{5} g i^{3} x^{5} + 20 \, B^{2} a b^{4} c^{3} d^{2} g i^{3} x + 5 \, {\left(3 \, b^{5} c d^{4} g i^{3} + a b^{4} d^{5} g i^{3}\right)} B^{2} x^{4} + 20 \, {\left(b^{5} c^{2} d^{3} g i^{3} + a b^{4} c d^{4} g i^{3}\right)} B^{2} x^{3} + 10 \, {\left(b^{5} c^{3} d^{2} g i^{3} + 3 \, a b^{4} c^{2} d^{3} g i^{3}\right)} B^{2} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{60 \, b^{4} d^{2}}"," ",0,"2/5*A*B*b*d^3*g*i^3*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A^2*b*d^3*g*i^3*x^5 + 3/2*A*B*b*c*d^2*g*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*B*a*d^3*g*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/4*A^2*b*c*d^2*g*i^3*x^4 + 1/4*A^2*a*d^3*g*i^3*x^4 + 2*A*B*b*c^2*d*g*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*B*a*c*d^2*g*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*b*c^2*d*g*i^3*x^3 + A^2*a*c*d^2*g*i^3*x^3 + A*B*b*c^3*g*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3*A*B*a*c^2*d*g*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*b*c^3*g*i^3*x^2 + 3/2*A^2*a*c^2*d*g*i^3*x^2 + 1/30*A*B*b*d^3*g*i^3*n*(12*a^5*log(b*x + a)/b^5 - 12*c^5*log(d*x + c)/d^5 - (3*(b^4*c*d^3 - a*b^3*d^4)*x^4 - 4*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^3 + 6*(b^4*c^3*d - a^3*b*d^4)*x^2 - 12*(b^4*c^4 - a^4*d^4)*x)/(b^4*d^4)) - 1/4*A*B*b*c*d^2*g*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) - 1/12*A*B*a*d^3*g*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + A*B*b*c^2*d*g*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) + A*B*a*c*d^2*g*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - A*B*b*c^3*g*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) - 3*A*B*a*c^2*d*g*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*a*c^3*g*i^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a*c^3*g*i^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*c^3*g*i^3*x - 1/60*(47*a^2*b^2*c^3*d^2*g*i^3*n^2 - 27*a^3*b*c^2*d^3*g*i^3*n^2 + 6*a^4*c*d^4*g*i^3*n^2 + (5*g*i^3*n^2 - 6*g*i^3*n*log(e))*b^4*c^5 - (31*g*i^3*n^2 - 30*g*i^3*n*log(e))*a*b^3*c^4*d)*B^2*log(d*x + c)/(b^3*d^2) + 1/10*(b^5*c^5*g*i^3*n^2 - 5*a*b^4*c^4*d*g*i^3*n^2 + 10*a^2*b^3*c^3*d^2*g*i^3*n^2 - 10*a^3*b^2*c^2*d^3*g*i^3*n^2 + 5*a^4*b*c*d^4*g*i^3*n^2 - a^5*d^5*g*i^3*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^4*d^2) + 1/60*(12*B^2*b^5*d^5*g*i^3*x^5*log(e)^2 - 3*((2*g*i^3*n*log(e) - 15*g*i^3*log(e)^2)*b^5*c*d^4 - (2*g*i^3*n*log(e) + 5*g*i^3*log(e)^2)*a*b^4*d^5)*B^2*x^4 + 2*((g*i^3*n^2 - 11*g*i^3*n*log(e) + 30*g*i^3*log(e)^2)*b^5*c^2*d^3 - 2*(g*i^3*n^2 - 5*g*i^3*n*log(e) - 15*g*i^3*log(e)^2)*a*b^4*c*d^4 + (g*i^3*n^2 + g*i^3*n*log(e))*a^2*b^3*d^5)*B^2*x^3 + ((8*g*i^3*n^2 - 27*g*i^3*n*log(e) + 30*g*i^3*log(e)^2)*b^5*c^3*d^2 - 3*(6*g*i^3*n^2 - 5*g*i^3*n*log(e) - 30*g*i^3*log(e)^2)*a*b^4*c^2*d^3 + 3*(4*g*i^3*n^2 + 5*g*i^3*n*log(e))*a^2*b^3*c*d^4 - (2*g*i^3*n^2 + 3*g*i^3*n*log(e))*a^3*b^2*d^5)*B^2*x^2 - 3*(10*a^2*b^3*c^3*d^2*g*i^3*n^2 - 10*a^3*b^2*c^2*d^3*g*i^3*n^2 + 5*a^4*b*c*d^4*g*i^3*n^2 - a^5*d^5*g*i^3*n^2)*B^2*log(b*x + a)^2 - 6*(b^5*c^5*g*i^3*n^2 - 5*a*b^4*c^4*d*g*i^3*n^2)*B^2*log(b*x + a)*log(d*x + c) + 3*(b^5*c^5*g*i^3*n^2 - 5*a*b^4*c^4*d*g*i^3*n^2)*B^2*log(d*x + c)^2 + ((11*g*i^3*n^2 - 6*g*i^3*n*log(e))*b^5*c^4*d - 2*(14*g*i^3*n^2 + 15*g*i^3*n*log(e) - 30*g*i^3*log(e)^2)*a*b^4*c^3*d^2 + 12*(2*g*i^3*n^2 + 5*g*i^3*n*log(e))*a^2*b^3*c^2*d^3 - 2*(4*g*i^3*n^2 + 15*g*i^3*n*log(e))*a^3*b^2*c*d^4 + (g*i^3*n^2 + 6*g*i^3*n*log(e))*a^4*b*d^5)*B^2*x - (6*a*b^4*c^4*d*g*i^3*n^2 + 3*(g*i^3*n^2 - 20*g*i^3*n*log(e))*a^2*b^3*c^3*d^2 - (23*g*i^3*n^2 - 60*g*i^3*n*log(e))*a^3*b^2*c^2*d^3 + (19*g*i^3*n^2 - 30*g*i^3*n*log(e))*a^4*b*c*d^4 - (5*g*i^3*n^2 - 6*g*i^3*n*log(e))*a^5*d^5)*B^2*log(b*x + a) + 3*(4*B^2*b^5*d^5*g*i^3*x^5 + 20*B^2*a*b^4*c^3*d^2*g*i^3*x + 5*(3*b^5*c*d^4*g*i^3 + a*b^4*d^5*g*i^3)*B^2*x^4 + 20*(b^5*c^2*d^3*g*i^3 + a*b^4*c*d^4*g*i^3)*B^2*x^3 + 10*(b^5*c^3*d^2*g*i^3 + 3*a*b^4*c^2*d^3*g*i^3)*B^2*x^2)*log((b*x + a)^n)^2 + 3*(4*B^2*b^5*d^5*g*i^3*x^5 + 20*B^2*a*b^4*c^3*d^2*g*i^3*x + 5*(3*b^5*c*d^4*g*i^3 + a*b^4*d^5*g*i^3)*B^2*x^4 + 20*(b^5*c^2*d^3*g*i^3 + a*b^4*c*d^4*g*i^3)*B^2*x^3 + 10*(b^5*c^3*d^2*g*i^3 + 3*a*b^4*c^2*d^3*g*i^3)*B^2*x^2)*log((d*x + c)^n)^2 + (24*B^2*b^5*d^5*g*i^3*x^5*log(e) - 6*((g*i^3*n - 15*g*i^3*log(e))*b^5*c*d^4 - (g*i^3*n + 5*g*i^3*log(e))*a*b^4*d^5)*B^2*x^4 + 2*(a^2*b^3*d^5*g*i^3*n - (11*g*i^3*n - 60*g*i^3*log(e))*b^5*c^2*d^3 + 10*(g*i^3*n + 6*g*i^3*log(e))*a*b^4*c*d^4)*B^2*x^3 + 3*(5*a^2*b^3*c*d^4*g*i^3*n - a^3*b^2*d^5*g*i^3*n - (9*g*i^3*n - 20*g*i^3*log(e))*b^5*c^3*d^2 + 5*(g*i^3*n + 12*g*i^3*log(e))*a*b^4*c^2*d^3)*B^2*x^2 - 6*(b^5*c^4*d*g*i^3*n - 10*a^2*b^3*c^2*d^3*g*i^3*n + 5*a^3*b^2*c*d^4*g*i^3*n - a^4*b*d^5*g*i^3*n + 5*(g*i^3*n - 4*g*i^3*log(e))*a*b^4*c^3*d^2)*B^2*x + 6*(10*a^2*b^3*c^3*d^2*g*i^3*n - 10*a^3*b^2*c^2*d^3*g*i^3*n + 5*a^4*b*c*d^4*g*i^3*n - a^5*d^5*g*i^3*n)*B^2*log(b*x + a) + 6*(b^5*c^5*g*i^3*n - 5*a*b^4*c^4*d*g*i^3*n)*B^2*log(d*x + c))*log((b*x + a)^n) - (24*B^2*b^5*d^5*g*i^3*x^5*log(e) - 6*((g*i^3*n - 15*g*i^3*log(e))*b^5*c*d^4 - (g*i^3*n + 5*g*i^3*log(e))*a*b^4*d^5)*B^2*x^4 + 2*(a^2*b^3*d^5*g*i^3*n - (11*g*i^3*n - 60*g*i^3*log(e))*b^5*c^2*d^3 + 10*(g*i^3*n + 6*g*i^3*log(e))*a*b^4*c*d^4)*B^2*x^3 + 3*(5*a^2*b^3*c*d^4*g*i^3*n - a^3*b^2*d^5*g*i^3*n - (9*g*i^3*n - 20*g*i^3*log(e))*b^5*c^3*d^2 + 5*(g*i^3*n + 12*g*i^3*log(e))*a*b^4*c^2*d^3)*B^2*x^2 - 6*(b^5*c^4*d*g*i^3*n - 10*a^2*b^3*c^2*d^3*g*i^3*n + 5*a^3*b^2*c*d^4*g*i^3*n - a^4*b*d^5*g*i^3*n + 5*(g*i^3*n - 4*g*i^3*log(e))*a*b^4*c^3*d^2)*B^2*x + 6*(10*a^2*b^3*c^3*d^2*g*i^3*n - 10*a^3*b^2*c^2*d^3*g*i^3*n + 5*a^4*b*c*d^4*g*i^3*n - a^5*d^5*g*i^3*n)*B^2*log(b*x + a) + 6*(b^5*c^5*g*i^3*n - 5*a*b^4*c^4*d*g*i^3*n)*B^2*log(d*x + c) + 6*(4*B^2*b^5*d^5*g*i^3*x^5 + 20*B^2*a*b^4*c^3*d^2*g*i^3*x + 5*(3*b^5*c*d^4*g*i^3 + a*b^4*d^5*g*i^3)*B^2*x^4 + 20*(b^5*c^2*d^3*g*i^3 + a*b^4*c*d^4*g*i^3)*B^2*x^3 + 10*(b^5*c^3*d^2*g*i^3 + 3*a*b^4*c^2*d^3*g*i^3)*B^2*x^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b^4*d^2)","B",0
181,1,2129,0,4.976409," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A B d^{3} i^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{4} \, A^{2} d^{3} i^{3} x^{4} + 2 \, A B c d^{2} i^{3} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c d^{2} i^{3} x^{3} + 3 \, A B c^{2} d i^{3} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A^{2} c^{2} d i^{3} x^{2} - \frac{1}{12} \, A B d^{3} i^{3} n {\left(\frac{6 \, a^{4} \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} x^{2} + 6 \, {\left(b^{3} c^{3} - a^{3} d^{3}\right)} x}{b^{3} d^{3}}\right)} + A B c d^{2} i^{3} n {\left(\frac{2 \, a^{3} \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d - a b d^{2}\right)} x^{2} - 2 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} x}{b^{2} d^{2}}\right)} - 3 \, A B c^{2} d i^{3} n {\left(\frac{a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c - a d\right)} x}{b d}\right)} + 2 \, A B c^{3} i^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B c^{3} i^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c^{3} i^{3} x - \frac{{\left(26 \, a b^{2} c^{3} d i^{3} n^{2} - 21 \, a^{2} b c^{2} d^{2} i^{3} n^{2} + 6 \, a^{3} c d^{3} i^{3} n^{2} - {\left(11 \, i^{3} n^{2} - 6 \, i^{3} n \log\left(e\right)\right)} b^{3} c^{4}\right)} B^{2} \log\left(d x + c\right)}{12 \, b^{3} d} - \frac{{\left(b^{4} c^{4} i^{3} n^{2} - 4 \, a b^{3} c^{3} d i^{3} n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} n^{2} - 4 \, a^{3} b c d^{3} i^{3} n^{2} + a^{4} d^{4} i^{3} n^{2}\right)} {\left(\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)\right)} B^{2}}{2 \, b^{4} d} + \frac{3 \, B^{2} b^{4} d^{4} i^{3} x^{4} \log\left(e\right)^{2} + 6 \, B^{2} b^{4} c^{4} i^{3} n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - 3 \, B^{2} b^{4} c^{4} i^{3} n^{2} \log\left(d x + c\right)^{2} + 2 \, {\left(a b^{3} d^{4} i^{3} n \log\left(e\right) - {\left(i^{3} n \log\left(e\right) - 6 \, i^{3} \log\left(e\right)^{2}\right)} b^{4} c d^{3}\right)} B^{2} x^{3} + {\left({\left(i^{3} n^{2} - 9 \, i^{3} n \log\left(e\right) + 18 \, i^{3} \log\left(e\right)^{2}\right)} b^{4} c^{2} d^{2} - 2 \, {\left(i^{3} n^{2} - 6 \, i^{3} n \log\left(e\right)\right)} a b^{3} c d^{3} + {\left(i^{3} n^{2} - 3 \, i^{3} n \log\left(e\right)\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 3 \, {\left(4 \, a b^{3} c^{3} d i^{3} n^{2} - 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} n^{2} + 4 \, a^{3} b c d^{3} i^{3} n^{2} - a^{4} d^{4} i^{3} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + {\left({\left(7 \, i^{3} n^{2} - 18 \, i^{3} n \log\left(e\right) + 12 \, i^{3} \log\left(e\right)^{2}\right)} b^{4} c^{3} d - {\left(19 \, i^{3} n^{2} - 36 \, i^{3} n \log\left(e\right)\right)} a b^{3} c^{2} d^{2} + {\left(17 \, i^{3} n^{2} - 24 \, i^{3} n \log\left(e\right)\right)} a^{2} b^{2} c d^{3} - {\left(5 \, i^{3} n^{2} - 6 \, i^{3} n \log\left(e\right)\right)} a^{3} b d^{4}\right)} B^{2} x - {\left(6 \, {\left(3 \, i^{3} n^{2} - 4 \, i^{3} n \log\left(e\right)\right)} a b^{3} c^{3} d - 9 \, {\left(5 \, i^{3} n^{2} - 4 \, i^{3} n \log\left(e\right)\right)} a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(19 \, i^{3} n^{2} - 12 \, i^{3} n \log\left(e\right)\right)} a^{3} b c d^{3} - {\left(11 \, i^{3} n^{2} - 6 \, i^{3} n \log\left(e\right)\right)} a^{4} d^{4}\right)} B^{2} \log\left(b x + a\right) + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} i^{3} x^{4} \log\left(e\right) - 6 \, B^{2} b^{4} c^{4} i^{3} n \log\left(d x + c\right) + 2 \, {\left(a b^{3} d^{4} i^{3} n - {\left(i^{3} n - 12 \, i^{3} \log\left(e\right)\right)} b^{4} c d^{3}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} c d^{3} i^{3} n - a^{2} b^{2} d^{4} i^{3} n - 3 \, {\left(i^{3} n - 4 \, i^{3} \log\left(e\right)\right)} b^{4} c^{2} d^{2}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} c^{2} d^{2} i^{3} n - 4 \, a^{2} b^{2} c d^{3} i^{3} n + a^{3} b d^{4} i^{3} n - {\left(3 \, i^{3} n - 4 \, i^{3} \log\left(e\right)\right)} b^{4} c^{3} d\right)} B^{2} x + 6 \, {\left(4 \, a b^{3} c^{3} d i^{3} n - 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} n + 4 \, a^{3} b c d^{3} i^{3} n - a^{4} d^{4} i^{3} n\right)} B^{2} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(6 \, B^{2} b^{4} d^{4} i^{3} x^{4} \log\left(e\right) - 6 \, B^{2} b^{4} c^{4} i^{3} n \log\left(d x + c\right) + 2 \, {\left(a b^{3} d^{4} i^{3} n - {\left(i^{3} n - 12 \, i^{3} \log\left(e\right)\right)} b^{4} c d^{3}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} c d^{3} i^{3} n - a^{2} b^{2} d^{4} i^{3} n - 3 \, {\left(i^{3} n - 4 \, i^{3} \log\left(e\right)\right)} b^{4} c^{2} d^{2}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} c^{2} d^{2} i^{3} n - 4 \, a^{2} b^{2} c d^{3} i^{3} n + a^{3} b d^{4} i^{3} n - {\left(3 \, i^{3} n - 4 \, i^{3} \log\left(e\right)\right)} b^{4} c^{3} d\right)} B^{2} x + 6 \, {\left(4 \, a b^{3} c^{3} d i^{3} n - 6 \, a^{2} b^{2} c^{2} d^{2} i^{3} n + 4 \, a^{3} b c d^{3} i^{3} n - a^{4} d^{4} i^{3} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{12 \, b^{4} d}"," ",0,"1/2*A*B*d^3*i^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*d^3*i^3*x^4 + 2*A*B*c*d^2*i^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c*d^2*i^3*x^3 + 3*A*B*c^2*d*i^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A^2*c^2*d*i^3*x^2 - 1/12*A*B*d^3*i^3*n*(6*a^4*log(b*x + a)/b^4 - 6*c^4*log(d*x + c)/d^4 + (2*(b^3*c*d^2 - a*b^2*d^3)*x^3 - 3*(b^3*c^2*d - a^2*b*d^3)*x^2 + 6*(b^3*c^3 - a^3*d^3)*x)/(b^3*d^3)) + A*B*c*d^2*i^3*n*(2*a^3*log(b*x + a)/b^3 - 2*c^3*log(d*x + c)/d^3 - ((b^2*c*d - a*b*d^2)*x^2 - 2*(b^2*c^2 - a^2*d^2)*x)/(b^2*d^2)) - 3*A*B*c^2*d*i^3*n*(a^2*log(b*x + a)/b^2 - c^2*log(d*x + c)/d^2 + (b*c - a*d)*x/(b*d)) + 2*A*B*c^3*i^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*c^3*i^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c^3*i^3*x - 1/12*(26*a*b^2*c^3*d*i^3*n^2 - 21*a^2*b*c^2*d^2*i^3*n^2 + 6*a^3*c*d^3*i^3*n^2 - (11*i^3*n^2 - 6*i^3*n*log(e))*b^3*c^4)*B^2*log(d*x + c)/(b^3*d) - 1/2*(b^4*c^4*i^3*n^2 - 4*a*b^3*c^3*d*i^3*n^2 + 6*a^2*b^2*c^2*d^2*i^3*n^2 - 4*a^3*b*c*d^3*i^3*n^2 + a^4*d^4*i^3*n^2)*(log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))*B^2/(b^4*d) + 1/12*(3*B^2*b^4*d^4*i^3*x^4*log(e)^2 + 6*B^2*b^4*c^4*i^3*n^2*log(b*x + a)*log(d*x + c) - 3*B^2*b^4*c^4*i^3*n^2*log(d*x + c)^2 + 2*(a*b^3*d^4*i^3*n*log(e) - (i^3*n*log(e) - 6*i^3*log(e)^2)*b^4*c*d^3)*B^2*x^3 + ((i^3*n^2 - 9*i^3*n*log(e) + 18*i^3*log(e)^2)*b^4*c^2*d^2 - 2*(i^3*n^2 - 6*i^3*n*log(e))*a*b^3*c*d^3 + (i^3*n^2 - 3*i^3*n*log(e))*a^2*b^2*d^4)*B^2*x^2 - 3*(4*a*b^3*c^3*d*i^3*n^2 - 6*a^2*b^2*c^2*d^2*i^3*n^2 + 4*a^3*b*c*d^3*i^3*n^2 - a^4*d^4*i^3*n^2)*B^2*log(b*x + a)^2 + ((7*i^3*n^2 - 18*i^3*n*log(e) + 12*i^3*log(e)^2)*b^4*c^3*d - (19*i^3*n^2 - 36*i^3*n*log(e))*a*b^3*c^2*d^2 + (17*i^3*n^2 - 24*i^3*n*log(e))*a^2*b^2*c*d^3 - (5*i^3*n^2 - 6*i^3*n*log(e))*a^3*b*d^4)*B^2*x - (6*(3*i^3*n^2 - 4*i^3*n*log(e))*a*b^3*c^3*d - 9*(5*i^3*n^2 - 4*i^3*n*log(e))*a^2*b^2*c^2*d^2 + 2*(19*i^3*n^2 - 12*i^3*n*log(e))*a^3*b*c*d^3 - (11*i^3*n^2 - 6*i^3*n*log(e))*a^4*d^4)*B^2*log(b*x + a) + 3*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x)*log((b*x + a)^n)^2 + 3*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x)*log((d*x + c)^n)^2 + (6*B^2*b^4*d^4*i^3*x^4*log(e) - 6*B^2*b^4*c^4*i^3*n*log(d*x + c) + 2*(a*b^3*d^4*i^3*n - (i^3*n - 12*i^3*log(e))*b^4*c*d^3)*B^2*x^3 + 3*(4*a*b^3*c*d^3*i^3*n - a^2*b^2*d^4*i^3*n - 3*(i^3*n - 4*i^3*log(e))*b^4*c^2*d^2)*B^2*x^2 + 6*(6*a*b^3*c^2*d^2*i^3*n - 4*a^2*b^2*c*d^3*i^3*n + a^3*b*d^4*i^3*n - (3*i^3*n - 4*i^3*log(e))*b^4*c^3*d)*B^2*x + 6*(4*a*b^3*c^3*d*i^3*n - 6*a^2*b^2*c^2*d^2*i^3*n + 4*a^3*b*c*d^3*i^3*n - a^4*d^4*i^3*n)*B^2*log(b*x + a))*log((b*x + a)^n) - (6*B^2*b^4*d^4*i^3*x^4*log(e) - 6*B^2*b^4*c^4*i^3*n*log(d*x + c) + 2*(a*b^3*d^4*i^3*n - (i^3*n - 12*i^3*log(e))*b^4*c*d^3)*B^2*x^3 + 3*(4*a*b^3*c*d^3*i^3*n - a^2*b^2*d^4*i^3*n - 3*(i^3*n - 4*i^3*log(e))*b^4*c^2*d^2)*B^2*x^2 + 6*(6*a*b^3*c^2*d^2*i^3*n - 4*a^2*b^2*c*d^3*i^3*n + a^3*b*d^4*i^3*n - (3*i^3*n - 4*i^3*log(e))*b^4*c^3*d)*B^2*x + 6*(4*a*b^3*c^3*d*i^3*n - 6*a^2*b^2*c^2*d^2*i^3*n + 4*a^3*b*c*d^3*i^3*n - a^4*d^4*i^3*n)*B^2*log(b*x + a) + 6*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^4*d)","B",0
182,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g),x, algorithm=""maxima"")","3 \, A^{2} c^{2} d i^{3} {\left(\frac{x}{b g} - \frac{a \log\left(b x + a\right)}{b^{2} g}\right)} - \frac{1}{6} \, A^{2} d^{3} i^{3} {\left(\frac{6 \, a^{3} \log\left(b x + a\right)}{b^{4} g} - \frac{2 \, b^{2} x^{3} - 3 \, a b x^{2} + 6 \, a^{2} x}{b^{3} g}\right)} + \frac{3}{2} \, A^{2} c d^{2} i^{3} {\left(\frac{2 \, a^{2} \log\left(b x + a\right)}{b^{3} g} + \frac{b x^{2} - 2 \, a x}{b^{2} g}\right)} + \frac{A^{2} c^{3} i^{3} \log\left(b g x + a g\right)}{b g} + \frac{{\left(2 \, B^{2} b^{3} d^{3} i^{3} x^{3} + 3 \, {\left(3 \, b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B^{2} x^{2} + 6 \, {\left(3 \, b^{3} c^{2} d i^{3} - 3 \, a b^{2} c d^{2} i^{3} + a^{2} b d^{3} i^{3}\right)} B^{2} x + 6 \, {\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B^{2} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{6 \, b^{4} g} - \int -\frac{3 \, B^{2} b^{4} c^{4} i^{3} \log\left(e\right)^{2} + 6 \, A B b^{4} c^{4} i^{3} \log\left(e\right) + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} d^{4} i^{3} \log\left(e\right)\right)} x^{4} + 12 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c d^{3} i^{3} \log\left(e\right)\right)} x^{3} + 18 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c^{2} d^{2} i^{3} \log\left(e\right)\right)} x^{2} + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 12 \, {\left(B^{2} b^{4} c^{3} d i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c^{3} d i^{3} \log\left(e\right)\right)} x + 6 \, {\left(B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + A B b^{4} c^{4} i^{3} + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right) + A B b^{4} d^{4} i^{3}\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right) + A B b^{4} c d^{3} i^{3}\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right) + A B b^{4} c^{2} d^{2} i^{3}\right)} x^{2} + 4 \, {\left(B^{2} b^{4} c^{3} d i^{3} \log\left(e\right) + A B b^{4} c^{3} d i^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(6 \, B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + 6 \, A B b^{4} c^{4} i^{3} + 2 \, {\left(3 \, A B b^{4} d^{4} i^{3} + {\left(i^{3} n + 3 \, i^{3} \log\left(e\right)\right)} B^{2} b^{4} d^{4}\right)} x^{4} + {\left(24 \, A B b^{4} c d^{3} i^{3} - {\left(a b^{3} d^{4} i^{3} n - 3 \, {\left(3 \, i^{3} n + 8 \, i^{3} \log\left(e\right)\right)} b^{4} c d^{3}\right)} B^{2}\right)} x^{3} + 3 \, {\left(12 \, A B b^{4} c^{2} d^{2} i^{3} - {\left(3 \, a b^{3} c d^{3} i^{3} n - a^{2} b^{2} d^{4} i^{3} n - 6 \, {\left(i^{3} n + 2 \, i^{3} \log\left(e\right)\right)} b^{4} c^{2} d^{2}\right)} B^{2}\right)} x^{2} + 6 \, {\left(4 \, A B b^{4} c^{3} d i^{3} + {\left(3 \, a b^{3} c^{2} d^{2} i^{3} n - 3 \, a^{2} b^{2} c d^{3} i^{3} n + a^{3} b d^{4} i^{3} n + 4 \, b^{4} c^{3} d i^{3} \log\left(e\right)\right)} B^{2}\right)} x + 6 \, {\left({\left(b^{4} c^{3} d i^{3} n - 3 \, a b^{3} c^{2} d^{2} i^{3} n + 3 \, a^{2} b^{2} c d^{3} i^{3} n - a^{3} b d^{4} i^{3} n\right)} B^{2} x + {\left(a b^{3} c^{3} d i^{3} n - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} n + 3 \, a^{3} b c d^{3} i^{3} n - a^{4} d^{4} i^{3} n\right)} B^{2}\right)} \log\left(b x + a\right) + 6 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{3 \, {\left(b^{5} d g x^{2} + a b^{4} c g + {\left(b^{5} c g + a b^{4} d g\right)} x\right)}}\,{d x}"," ",0,"3*A^2*c^2*d*i^3*(x/(b*g) - a*log(b*x + a)/(b^2*g)) - 1/6*A^2*d^3*i^3*(6*a^3*log(b*x + a)/(b^4*g) - (2*b^2*x^3 - 3*a*b*x^2 + 6*a^2*x)/(b^3*g)) + 3/2*A^2*c*d^2*i^3*(2*a^2*log(b*x + a)/(b^3*g) + (b*x^2 - 2*a*x)/(b^2*g)) + A^2*c^3*i^3*log(b*g*x + a*g)/(b*g) + 1/6*(2*B^2*b^3*d^3*i^3*x^3 + 3*(3*b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B^2*x^2 + 6*(3*b^3*c^2*d*i^3 - 3*a*b^2*c*d^2*i^3 + a^2*b*d^3*i^3)*B^2*x + 6*(b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B^2*log(b*x + a))*log((d*x + c)^n)^2/(b^4*g) - integrate(-1/3*(3*B^2*b^4*c^4*i^3*log(e)^2 + 6*A*B*b^4*c^4*i^3*log(e) + 3*(B^2*b^4*d^4*i^3*log(e)^2 + 2*A*B*b^4*d^4*i^3*log(e))*x^4 + 12*(B^2*b^4*c*d^3*i^3*log(e)^2 + 2*A*B*b^4*c*d^3*i^3*log(e))*x^3 + 18*(B^2*b^4*c^2*d^2*i^3*log(e)^2 + 2*A*B*b^4*c^2*d^2*i^3*log(e))*x^2 + 3*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*x + a)^n)^2 + 12*(B^2*b^4*c^3*d*i^3*log(e)^2 + 2*A*B*b^4*c^3*d*i^3*log(e))*x + 6*(B^2*b^4*c^4*i^3*log(e) + A*B*b^4*c^4*i^3 + (B^2*b^4*d^4*i^3*log(e) + A*B*b^4*d^4*i^3)*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e) + A*B*b^4*c*d^3*i^3)*x^3 + 6*(B^2*b^4*c^2*d^2*i^3*log(e) + A*B*b^4*c^2*d^2*i^3)*x^2 + 4*(B^2*b^4*c^3*d*i^3*log(e) + A*B*b^4*c^3*d*i^3)*x)*log((b*x + a)^n) - (6*B^2*b^4*c^4*i^3*log(e) + 6*A*B*b^4*c^4*i^3 + 2*(3*A*B*b^4*d^4*i^3 + (i^3*n + 3*i^3*log(e))*B^2*b^4*d^4)*x^4 + (24*A*B*b^4*c*d^3*i^3 - (a*b^3*d^4*i^3*n - 3*(3*i^3*n + 8*i^3*log(e))*b^4*c*d^3)*B^2)*x^3 + 3*(12*A*B*b^4*c^2*d^2*i^3 - (3*a*b^3*c*d^3*i^3*n - a^2*b^2*d^4*i^3*n - 6*(i^3*n + 2*i^3*log(e))*b^4*c^2*d^2)*B^2)*x^2 + 6*(4*A*B*b^4*c^3*d*i^3 + (3*a*b^3*c^2*d^2*i^3*n - 3*a^2*b^2*c*d^3*i^3*n + a^3*b*d^4*i^3*n + 4*b^4*c^3*d*i^3*log(e))*B^2)*x + 6*((b^4*c^3*d*i^3*n - 3*a*b^3*c^2*d^2*i^3*n + 3*a^2*b^2*c*d^3*i^3*n - a^3*b*d^4*i^3*n)*B^2*x + (a*b^3*c^3*d*i^3*n - 3*a^2*b^2*c^2*d^2*i^3*n + 3*a^3*b*c*d^3*i^3*n - a^4*d^4*i^3*n)*B^2)*log(b*x + a) + 6*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*x + a)^n))*log((d*x + c)^n))/(b^5*d*g*x^2 + a*b^4*c*g + (b^5*c*g + a*b^4*d*g)*x), x)","F",0
183,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-2 \, A B c^{3} i^{3} n {\left(\frac{1}{b^{2} g^{2} x + a b g^{2}} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - 3 \, A^{2} {\left(\frac{a^{2}}{b^{4} g^{2} x + a b^{3} g^{2}} - \frac{x}{b^{2} g^{2}} + \frac{2 \, a \log\left(b x + a\right)}{b^{3} g^{2}}\right)} c d^{2} i^{3} + \frac{1}{2} \, {\left(\frac{2 \, a^{3}}{b^{5} g^{2} x + a b^{4} g^{2}} + \frac{6 \, a^{2} \log\left(b x + a\right)}{b^{4} g^{2}} + \frac{b x^{2} - 4 \, a x}{b^{3} g^{2}}\right)} A^{2} d^{3} i^{3} + 3 \, A^{2} c^{2} d i^{3} {\left(\frac{a}{b^{3} g^{2} x + a b^{2} g^{2}} + \frac{\log\left(b x + a\right)}{b^{2} g^{2}}\right)} - \frac{2 \, A B c^{3} i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{2} g^{2} x + a b g^{2}} - \frac{A^{2} c^{3} i^{3}}{b^{2} g^{2} x + a b g^{2}} + \frac{{\left(B^{2} b^{3} d^{3} i^{3} x^{3} + 3 \, {\left(2 \, b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} c d^{2} i^{3} - 2 \, a^{2} b d^{3} i^{3}\right)} B^{2} x - 2 \, {\left(b^{3} c^{3} i^{3} - 3 \, a b^{2} c^{2} d i^{3} + 3 \, a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B^{2} + 6 \, {\left({\left(b^{3} c^{2} d i^{3} - 2 \, a b^{2} c d^{2} i^{3} + a^{2} b d^{3} i^{3}\right)} B^{2} x + {\left(a b^{2} c^{2} d i^{3} - 2 \, a^{2} b c d^{2} i^{3} + a^{3} d^{3} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, {\left(b^{5} g^{2} x + a b^{4} g^{2}\right)}} - \int -\frac{B^{2} b^{4} c^{4} i^{3} \log\left(e\right)^{2} + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} d^{4} i^{3} \log\left(e\right)\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c d^{3} i^{3} \log\left(e\right)\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c^{2} d^{2} i^{3} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(2 \, B^{2} b^{4} c^{3} d i^{3} \log\left(e\right)^{2} + 3 \, A B b^{4} c^{3} d i^{3} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right) + A B b^{4} d^{4} i^{3}\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right) + A B b^{4} c d^{3} i^{3}\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right) + A B b^{4} c^{2} d^{2} i^{3}\right)} x^{2} + {\left(4 \, B^{2} b^{4} c^{3} d i^{3} \log\left(e\right) + 3 \, A B b^{4} c^{3} d i^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(2 \, A B b^{4} d^{4} i^{3} + {\left(i^{3} n + 2 \, i^{3} \log\left(e\right)\right)} B^{2} b^{4} d^{4}\right)} x^{4} + 2 \, {\left(4 \, A B b^{4} c d^{3} i^{3} - {\left(a b^{3} d^{4} i^{3} n - {\left(3 \, i^{3} n + 4 \, i^{3} \log\left(e\right)\right)} b^{4} c d^{3}\right)} B^{2}\right)} x^{3} - 2 \, {\left(a b^{3} c^{3} d i^{3} n - 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} n + 3 \, a^{3} b c d^{3} i^{3} n - a^{4} d^{4} i^{3} n - b^{4} c^{4} i^{3} \log\left(e\right)\right)} B^{2} + {\left(12 \, A B b^{4} c^{2} d^{2} i^{3} + {\left(12 \, a b^{3} c d^{3} i^{3} n - 7 \, a^{2} b^{2} d^{4} i^{3} n + 12 \, b^{4} c^{2} d^{2} i^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left(3 \, A B b^{4} c^{3} d i^{3} + {\left(3 \, a b^{3} c^{2} d^{2} i^{3} n - a^{3} b d^{4} i^{3} n - {\left(i^{3} n - 4 \, i^{3} \log\left(e\right)\right)} b^{4} c^{3} d\right)} B^{2}\right)} x + 6 \, {\left({\left(b^{4} c^{2} d^{2} i^{3} n - 2 \, a b^{3} c d^{3} i^{3} n + a^{2} b^{2} d^{4} i^{3} n\right)} B^{2} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} i^{3} n - 2 \, a^{2} b^{2} c d^{3} i^{3} n + a^{3} b d^{4} i^{3} n\right)} B^{2} x + {\left(a^{2} b^{2} c^{2} d^{2} i^{3} n - 2 \, a^{3} b c d^{3} i^{3} n + a^{4} d^{4} i^{3} n\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{6} d g^{2} x^{3} + a^{2} b^{4} c g^{2} + {\left(b^{6} c g^{2} + 2 \, a b^{5} d g^{2}\right)} x^{2} + {\left(2 \, a b^{5} c g^{2} + a^{2} b^{4} d g^{2}\right)} x}\,{d x}"," ",0,"-2*A*B*c^3*i^3*n*(1/(b^2*g^2*x + a*b*g^2) + d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - 3*A^2*(a^2/(b^4*g^2*x + a*b^3*g^2) - x/(b^2*g^2) + 2*a*log(b*x + a)/(b^3*g^2))*c*d^2*i^3 + 1/2*(2*a^3/(b^5*g^2*x + a*b^4*g^2) + 6*a^2*log(b*x + a)/(b^4*g^2) + (b*x^2 - 4*a*x)/(b^3*g^2))*A^2*d^3*i^3 + 3*A^2*c^2*d*i^3*(a/(b^3*g^2*x + a*b^2*g^2) + log(b*x + a)/(b^2*g^2)) - 2*A*B*c^3*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*g^2*x + a*b*g^2) - A^2*c^3*i^3/(b^2*g^2*x + a*b*g^2) + 1/2*(B^2*b^3*d^3*i^3*x^3 + 3*(2*b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B^2*x^2 + 2*(3*a*b^2*c*d^2*i^3 - 2*a^2*b*d^3*i^3)*B^2*x - 2*(b^3*c^3*i^3 - 3*a*b^2*c^2*d*i^3 + 3*a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B^2 + 6*((b^3*c^2*d*i^3 - 2*a*b^2*c*d^2*i^3 + a^2*b*d^3*i^3)*B^2*x + (a*b^2*c^2*d*i^3 - 2*a^2*b*c*d^2*i^3 + a^3*d^3*i^3)*B^2)*log(b*x + a))*log((d*x + c)^n)^2/(b^5*g^2*x + a*b^4*g^2) - integrate(-(B^2*b^4*c^4*i^3*log(e)^2 + (B^2*b^4*d^4*i^3*log(e)^2 + 2*A*B*b^4*d^4*i^3*log(e))*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e)^2 + 2*A*B*b^4*c*d^3*i^3*log(e))*x^3 + 6*(B^2*b^4*c^2*d^2*i^3*log(e)^2 + 2*A*B*b^4*c^2*d^2*i^3*log(e))*x^2 + (B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*x + a)^n)^2 + 2*(2*B^2*b^4*c^3*d*i^3*log(e)^2 + 3*A*B*b^4*c^3*d*i^3*log(e))*x + 2*(B^2*b^4*c^4*i^3*log(e) + (B^2*b^4*d^4*i^3*log(e) + A*B*b^4*d^4*i^3)*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e) + A*B*b^4*c*d^3*i^3)*x^3 + 6*(B^2*b^4*c^2*d^2*i^3*log(e) + A*B*b^4*c^2*d^2*i^3)*x^2 + (4*B^2*b^4*c^3*d*i^3*log(e) + 3*A*B*b^4*c^3*d*i^3)*x)*log((b*x + a)^n) - ((2*A*B*b^4*d^4*i^3 + (i^3*n + 2*i^3*log(e))*B^2*b^4*d^4)*x^4 + 2*(4*A*B*b^4*c*d^3*i^3 - (a*b^3*d^4*i^3*n - (3*i^3*n + 4*i^3*log(e))*b^4*c*d^3)*B^2)*x^3 - 2*(a*b^3*c^3*d*i^3*n - 3*a^2*b^2*c^2*d^2*i^3*n + 3*a^3*b*c*d^3*i^3*n - a^4*d^4*i^3*n - b^4*c^4*i^3*log(e))*B^2 + (12*A*B*b^4*c^2*d^2*i^3 + (12*a*b^3*c*d^3*i^3*n - 7*a^2*b^2*d^4*i^3*n + 12*b^4*c^2*d^2*i^3*log(e))*B^2)*x^2 + 2*(3*A*B*b^4*c^3*d*i^3 + (3*a*b^3*c^2*d^2*i^3*n - a^3*b*d^4*i^3*n - (i^3*n - 4*i^3*log(e))*b^4*c^3*d)*B^2)*x + 6*((b^4*c^2*d^2*i^3*n - 2*a*b^3*c*d^3*i^3*n + a^2*b^2*d^4*i^3*n)*B^2*x^2 + 2*(a*b^3*c^2*d^2*i^3*n - 2*a^2*b^2*c*d^3*i^3*n + a^3*b*d^4*i^3*n)*B^2*x + (a^2*b^2*c^2*d^2*i^3*n - 2*a^3*b*c*d^3*i^3*n + a^4*d^4*i^3*n)*B^2)*log(b*x + a) + 2*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*x + a)^n))*log((d*x + c)^n))/(b^6*d*g^2*x^3 + a^2*b^4*c*g^2 + (b^6*c*g^2 + 2*a*b^5*d*g^2)*x^2 + (2*a*b^5*c*g^2 + a^2*b^4*d*g^2)*x), x)","F",0
184,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{3}{2} \, A B c^{2} d i^{3} n {\left(\frac{3 \, a b c - a^{2} d + 2 \, {\left(2 \, b^{2} c - a b d\right)} x}{{\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}} + \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(b x + a\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}} - \frac{2 \, {\left(2 \, b c d - a d^{2}\right)} \log\left(d x + c\right)}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3}}\right)} + \frac{1}{2} \, A B c^{3} i^{3} n {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c - a b^{3} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} g^{3} x + {\left(a^{2} b^{2} c - a^{3} b d\right)} g^{3}} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{3}}\right)} - \frac{1}{2} \, A^{2} d^{3} i^{3} {\left(\frac{6 \, a^{2} b x + 5 \, a^{3}}{b^{6} g^{3} x^{2} + 2 \, a b^{5} g^{3} x + a^{2} b^{4} g^{3}} - \frac{2 \, x}{b^{3} g^{3}} + \frac{6 \, a \log\left(b x + a\right)}{b^{4} g^{3}}\right)} + \frac{3}{2} \, A^{2} c d^{2} i^{3} {\left(\frac{4 \, a b x + 3 \, a^{2}}{b^{5} g^{3} x^{2} + 2 \, a b^{4} g^{3} x + a^{2} b^{3} g^{3}} + \frac{2 \, \log\left(b x + a\right)}{b^{3} g^{3}}\right)} - \frac{3 \, {\left(2 \, b x + a\right)} A B c^{2} d i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}} - \frac{3 \, {\left(2 \, b x + a\right)} A^{2} c^{2} d i^{3}}{2 \, {\left(b^{4} g^{3} x^{2} + 2 \, a b^{3} g^{3} x + a^{2} b^{2} g^{3}\right)}} - \frac{A B c^{3} i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}} - \frac{A^{2} c^{3} i^{3}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} + \frac{{\left(2 \, B^{2} b^{3} d^{3} i^{3} x^{3} + 4 \, B^{2} a b^{2} d^{3} i^{3} x^{2} - 2 \, {\left(3 \, b^{3} c^{2} d i^{3} - 6 \, a b^{2} c d^{2} i^{3} + 2 \, a^{2} b d^{3} i^{3}\right)} B^{2} x - {\left(b^{3} c^{3} i^{3} + 3 \, a b^{2} c^{2} d i^{3} - 9 \, a^{2} b c d^{2} i^{3} + 5 \, a^{3} d^{3} i^{3}\right)} B^{2} + 6 \, {\left({\left(b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c d^{2} i^{3} - a^{2} b d^{3} i^{3}\right)} B^{2} x + {\left(a^{2} b c d^{2} i^{3} - a^{3} d^{3} i^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, {\left(b^{6} g^{3} x^{2} + 2 \, a b^{5} g^{3} x + a^{2} b^{4} g^{3}\right)}} - \int -\frac{4 \, B^{2} b^{4} c^{3} d i^{3} x \log\left(e\right)^{2} + B^{2} b^{4} c^{4} i^{3} \log\left(e\right)^{2} + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} d^{4} i^{3} \log\left(e\right)\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} c d^{3} i^{3} \log\left(e\right)\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right)^{2} + A B b^{4} c^{2} d^{2} i^{3} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(4 \, B^{2} b^{4} c^{3} d i^{3} x \log\left(e\right) + B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right) + A B b^{4} d^{4} i^{3}\right)} x^{4} + 4 \, {\left(B^{2} b^{4} c d^{3} i^{3} \log\left(e\right) + A B b^{4} c d^{3} i^{3}\right)} x^{3} + 3 \, {\left(2 \, B^{2} b^{4} c^{2} d^{2} i^{3} \log\left(e\right) + A B b^{4} c^{2} d^{2} i^{3}\right)} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, {\left(A B b^{4} d^{4} i^{3} + {\left(i^{3} n + i^{3} \log\left(e\right)\right)} B^{2} b^{4} d^{4}\right)} x^{4} - {\left(9 \, a b^{3} c^{2} d^{2} i^{3} n - 21 \, a^{2} b^{2} c d^{3} i^{3} n + 9 \, a^{3} b d^{4} i^{3} n + {\left(i^{3} n - 8 \, i^{3} \log\left(e\right)\right)} b^{4} c^{3} d\right)} B^{2} x + 2 \, {\left(4 \, A B b^{4} c d^{3} i^{3} + {\left(3 \, a b^{3} d^{4} i^{3} n + 4 \, b^{4} c d^{3} i^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} - {\left(a b^{3} c^{3} d i^{3} n + 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} n - 9 \, a^{3} b c d^{3} i^{3} n + 5 \, a^{4} d^{4} i^{3} n - 2 \, b^{4} c^{4} i^{3} \log\left(e\right)\right)} B^{2} + 6 \, {\left(A B b^{4} c^{2} d^{2} i^{3} + {\left(2 \, a b^{3} c d^{3} i^{3} n - {\left(i^{3} n - 2 \, i^{3} \log\left(e\right)\right)} b^{4} c^{2} d^{2}\right)} B^{2}\right)} x^{2} + 6 \, {\left({\left(b^{4} c d^{3} i^{3} n - a b^{3} d^{4} i^{3} n\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c d^{3} i^{3} n - a^{2} b^{2} d^{4} i^{3} n\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c d^{3} i^{3} n - a^{3} b d^{4} i^{3} n\right)} B^{2} x + {\left(a^{3} b c d^{3} i^{3} n - a^{4} d^{4} i^{3} n\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{7} d g^{3} x^{4} + a^{3} b^{4} c g^{3} + {\left(b^{7} c g^{3} + 3 \, a b^{6} d g^{3}\right)} x^{3} + 3 \, {\left(a b^{6} c g^{3} + a^{2} b^{5} d g^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{5} c g^{3} + a^{3} b^{4} d g^{3}\right)} x}\,{d x}"," ",0,"-3/2*A*B*c^2*d*i^3*n*((3*a*b*c - a^2*d + 2*(2*b^2*c - a*b*d)*x)/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3) + 2*(2*b*c*d - a*d^2)*log(b*x + a)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3) - 2*(2*b*c*d - a*d^2)*log(d*x + c)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3)) + 1/2*A*B*c^3*i^3*n*((2*b*d*x - b*c + 3*a*d)/((b^4*c - a*b^3*d)*g^3*x^2 + 2*(a*b^3*c - a^2*b^2*d)*g^3*x + (a^2*b^2*c - a^3*b*d)*g^3) + 2*d^2*log(b*x + a)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3) - 2*d^2*log(d*x + c)/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^3)) - 1/2*A^2*d^3*i^3*((6*a^2*b*x + 5*a^3)/(b^6*g^3*x^2 + 2*a*b^5*g^3*x + a^2*b^4*g^3) - 2*x/(b^3*g^3) + 6*a*log(b*x + a)/(b^4*g^3)) + 3/2*A^2*c*d^2*i^3*((4*a*b*x + 3*a^2)/(b^5*g^3*x^2 + 2*a*b^4*g^3*x + a^2*b^3*g^3) + 2*log(b*x + a)/(b^3*g^3)) - 3*(2*b*x + a)*A*B*c^2*d*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - 3/2*(2*b*x + a)*A^2*c^2*d*i^3/(b^4*g^3*x^2 + 2*a*b^3*g^3*x + a^2*b^2*g^3) - A*B*c^3*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A^2*c^3*i^3/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) + 1/2*(2*B^2*b^3*d^3*i^3*x^3 + 4*B^2*a*b^2*d^3*i^3*x^2 - 2*(3*b^3*c^2*d*i^3 - 6*a*b^2*c*d^2*i^3 + 2*a^2*b*d^3*i^3)*B^2*x - (b^3*c^3*i^3 + 3*a*b^2*c^2*d*i^3 - 9*a^2*b*c*d^2*i^3 + 5*a^3*d^3*i^3)*B^2 + 6*((b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B^2*x^2 + 2*(a*b^2*c*d^2*i^3 - a^2*b*d^3*i^3)*B^2*x + (a^2*b*c*d^2*i^3 - a^3*d^3*i^3)*B^2)*log(b*x + a))*log((d*x + c)^n)^2/(b^6*g^3*x^2 + 2*a*b^5*g^3*x + a^2*b^4*g^3) - integrate(-(4*B^2*b^4*c^3*d*i^3*x*log(e)^2 + B^2*b^4*c^4*i^3*log(e)^2 + (B^2*b^4*d^4*i^3*log(e)^2 + 2*A*B*b^4*d^4*i^3*log(e))*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e)^2 + 2*A*B*b^4*c*d^3*i^3*log(e))*x^3 + 6*(B^2*b^4*c^2*d^2*i^3*log(e)^2 + A*B*b^4*c^2*d^2*i^3*log(e))*x^2 + (B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*x + a)^n)^2 + 2*(4*B^2*b^4*c^3*d*i^3*x*log(e) + B^2*b^4*c^4*i^3*log(e) + (B^2*b^4*d^4*i^3*log(e) + A*B*b^4*d^4*i^3)*x^4 + 4*(B^2*b^4*c*d^3*i^3*log(e) + A*B*b^4*c*d^3*i^3)*x^3 + 3*(2*B^2*b^4*c^2*d^2*i^3*log(e) + A*B*b^4*c^2*d^2*i^3)*x^2)*log((b*x + a)^n) - (2*(A*B*b^4*d^4*i^3 + (i^3*n + i^3*log(e))*B^2*b^4*d^4)*x^4 - (9*a*b^3*c^2*d^2*i^3*n - 21*a^2*b^2*c*d^3*i^3*n + 9*a^3*b*d^4*i^3*n + (i^3*n - 8*i^3*log(e))*b^4*c^3*d)*B^2*x + 2*(4*A*B*b^4*c*d^3*i^3 + (3*a*b^3*d^4*i^3*n + 4*b^4*c*d^3*i^3*log(e))*B^2)*x^3 - (a*b^3*c^3*d*i^3*n + 3*a^2*b^2*c^2*d^2*i^3*n - 9*a^3*b*c*d^3*i^3*n + 5*a^4*d^4*i^3*n - 2*b^4*c^4*i^3*log(e))*B^2 + 6*(A*B*b^4*c^2*d^2*i^3 + (2*a*b^3*c*d^3*i^3*n - (i^3*n - 2*i^3*log(e))*b^4*c^2*d^2)*B^2)*x^2 + 6*((b^4*c*d^3*i^3*n - a*b^3*d^4*i^3*n)*B^2*x^3 + 3*(a*b^3*c*d^3*i^3*n - a^2*b^2*d^4*i^3*n)*B^2*x^2 + 3*(a^2*b^2*c*d^3*i^3*n - a^3*b*d^4*i^3*n)*B^2*x + (a^3*b*c*d^3*i^3*n - a^4*d^4*i^3*n)*B^2)*log(b*x + a) + 2*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*x + a)^n))*log((d*x + c)^n))/(b^7*d*g^3*x^4 + a^3*b^4*c*g^3 + (b^7*c*g^3 + 3*a*b^6*d*g^3)*x^3 + 3*(a*b^6*c*g^3 + a^2*b^5*d*g^3)*x^2 + (3*a^2*b^5*c*g^3 + a^3*b^4*d*g^3)*x), x)","F",0
185,0,0,0,0.000000," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{3} \, A B c d^{2} i^{3} n {\left(\frac{11 \, a^{2} b^{2} c^{2} - 7 \, a^{3} b c d + 2 \, a^{4} d^{2} + 6 \, {\left(3 \, b^{4} c^{2} - 3 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} c^{2} - 7 \, a^{2} b^{2} c d + 2 \, a^{3} b d^{2}\right)} x}{{\left(b^{8} c^{2} - 2 \, a b^{7} c d + a^{2} b^{6} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{7} c^{2} - 2 \, a^{2} b^{6} c d + a^{3} b^{5} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{6} c^{2} - 2 \, a^{3} b^{5} c d + a^{4} b^{4} d^{2}\right)} g^{4} x + {\left(a^{3} b^{5} c^{2} - 2 \, a^{4} b^{4} c d + a^{5} b^{3} d^{2}\right)} g^{4}} + \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}} - \frac{6 \, {\left(3 \, b^{2} c^{2} d - 3 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4}}\right)} - \frac{1}{9} \, A B c^{3} i^{3} n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} g^{4} x + {\left(a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} g^{4}} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}\right)} g^{4}}\right)} - \frac{1}{6} \, A B c^{2} d i^{3} n {\left(\frac{5 \, a b^{2} c^{2} - 22 \, a^{2} b c d + 5 \, a^{3} d^{2} - 6 \, {\left(3 \, b^{3} c d - a b^{2} d^{2}\right)} x^{2} + 3 \, {\left(3 \, b^{3} c^{2} - 16 \, a b^{2} c d + 5 \, a^{2} b d^{2}\right)} x}{{\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}} - \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(b x + a\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}} + \frac{6 \, {\left(3 \, b c d^{2} - a d^{3}\right)} \log\left(d x + c\right)}{{\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{4}}\right)} + \frac{1}{6} \, A^{2} d^{3} i^{3} {\left(\frac{18 \, a b^{2} x^{2} + 27 \, a^{2} b x + 11 \, a^{3}}{b^{7} g^{4} x^{3} + 3 \, a b^{6} g^{4} x^{2} + 3 \, a^{2} b^{5} g^{4} x + a^{3} b^{4} g^{4}} + \frac{6 \, \log\left(b x + a\right)}{b^{4} g^{4}}\right)} - \frac{{\left(3 \, b x + a\right)} A B c^{2} d i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}} - \frac{2 \, {\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A B c d^{2} i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}} - \frac{{\left(3 \, b x + a\right)} A^{2} c^{2} d i^{3}}{2 \, {\left(b^{5} g^{4} x^{3} + 3 \, a b^{4} g^{4} x^{2} + 3 \, a^{2} b^{3} g^{4} x + a^{3} b^{2} g^{4}\right)}} - \frac{{\left(3 \, b^{2} x^{2} + 3 \, a b x + a^{2}\right)} A^{2} c d^{2} i^{3}}{b^{6} g^{4} x^{3} + 3 \, a b^{5} g^{4} x^{2} + 3 \, a^{2} b^{4} g^{4} x + a^{3} b^{3} g^{4}} - \frac{2 \, A B c^{3} i^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{A^{2} c^{3} i^{3}}{3 \, {\left(b^{4} g^{4} x^{3} + 3 \, a b^{3} g^{4} x^{2} + 3 \, a^{2} b^{2} g^{4} x + a^{3} b g^{4}\right)}} - \frac{{\left(18 \, {\left(b^{3} c d^{2} i^{3} - a b^{2} d^{3} i^{3}\right)} B^{2} x^{2} + 9 \, {\left(b^{3} c^{2} d i^{3} + 2 \, a b^{2} c d^{2} i^{3} - 3 \, a^{2} b d^{3} i^{3}\right)} B^{2} x + {\left(2 \, b^{3} c^{3} i^{3} + 3 \, a b^{2} c^{2} d i^{3} + 6 \, a^{2} b c d^{2} i^{3} - 11 \, a^{3} d^{3} i^{3}\right)} B^{2} - 6 \, {\left(B^{2} b^{3} d^{3} i^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} i^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} i^{3} x + B^{2} a^{3} d^{3} i^{3}\right)} \log\left(b x + a\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{6 \, {\left(b^{7} g^{4} x^{3} + 3 \, a b^{6} g^{4} x^{2} + 3 \, a^{2} b^{5} g^{4} x + a^{3} b^{4} g^{4}\right)}} - \int -\frac{18 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} \log\left(e\right)^{2} + 12 \, B^{2} b^{4} c^{3} d i^{3} x \log\left(e\right)^{2} + 3 \, B^{2} b^{4} c^{4} i^{3} \log\left(e\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right)^{2} + 2 \, A B b^{4} d^{4} i^{3} \log\left(e\right)\right)} x^{4} + 6 \, {\left(2 \, B^{2} b^{4} c d^{3} i^{3} \log\left(e\right)^{2} + A B b^{4} c d^{3} i^{3} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 6 \, {\left(6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} \log\left(e\right) + 4 \, B^{2} b^{4} c^{3} d i^{3} x \log\left(e\right) + B^{2} b^{4} c^{4} i^{3} \log\left(e\right) + {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right) + A B b^{4} d^{4} i^{3}\right)} x^{4} + {\left(4 \, B^{2} b^{4} c d^{3} i^{3} \log\left(e\right) + A B b^{4} c d^{3} i^{3}\right)} x^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right) + {\left(9 \, {\left(4 \, a b^{3} c d^{3} i^{3} n - 5 \, a^{2} b^{2} d^{4} i^{3} n + {\left(i^{3} n - 4 \, i^{3} \log\left(e\right)\right)} b^{4} c^{2} d^{2}\right)} B^{2} x^{2} - 6 \, {\left(B^{2} b^{4} d^{4} i^{3} \log\left(e\right) + A B b^{4} d^{4} i^{3}\right)} x^{4} + 2 \, {\left(6 \, a b^{3} c^{2} d^{2} i^{3} n + 12 \, a^{2} b^{2} c d^{3} i^{3} n - 19 \, a^{3} b d^{4} i^{3} n + {\left(i^{3} n - 12 \, i^{3} \log\left(e\right)\right)} b^{4} c^{3} d\right)} B^{2} x - 6 \, {\left(A B b^{4} c d^{3} i^{3} + {\left(3 \, a b^{3} d^{4} i^{3} n - {\left(3 \, i^{3} n - 4 \, i^{3} \log\left(e\right)\right)} b^{4} c d^{3}\right)} B^{2}\right)} x^{3} + {\left(2 \, a b^{3} c^{3} d i^{3} n + 3 \, a^{2} b^{2} c^{2} d^{2} i^{3} n + 6 \, a^{3} b c d^{3} i^{3} n - 11 \, a^{4} d^{4} i^{3} n - 6 \, b^{4} c^{4} i^{3} \log\left(e\right)\right)} B^{2} - 6 \, {\left(B^{2} b^{4} d^{4} i^{3} n x^{4} + 4 \, B^{2} a b^{3} d^{4} i^{3} n x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} i^{3} n x^{2} + 4 \, B^{2} a^{3} b d^{4} i^{3} n x + B^{2} a^{4} d^{4} i^{3} n\right)} \log\left(b x + a\right) - 6 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{3 \, {\left(b^{8} d g^{4} x^{5} + a^{4} b^{4} c g^{4} + {\left(b^{8} c g^{4} + 4 \, a b^{7} d g^{4}\right)} x^{4} + 2 \, {\left(2 \, a b^{7} c g^{4} + 3 \, a^{2} b^{6} d g^{4}\right)} x^{3} + 2 \, {\left(3 \, a^{2} b^{6} c g^{4} + 2 \, a^{3} b^{5} d g^{4}\right)} x^{2} + {\left(4 \, a^{3} b^{5} c g^{4} + a^{4} b^{4} d g^{4}\right)} x\right)}}\,{d x}"," ",0,"-1/3*A*B*c*d^2*i^3*n*((11*a^2*b^2*c^2 - 7*a^3*b*c*d + 2*a^4*d^2 + 6*(3*b^4*c^2 - 3*a*b^3*c*d + a^2*b^2*d^2)*x^2 + 3*(9*a*b^3*c^2 - 7*a^2*b^2*c*d + 2*a^3*b*d^2)*x)/((b^8*c^2 - 2*a*b^7*c*d + a^2*b^6*d^2)*g^4*x^3 + 3*(a*b^7*c^2 - 2*a^2*b^6*c*d + a^3*b^5*d^2)*g^4*x^2 + 3*(a^2*b^6*c^2 - 2*a^3*b^5*c*d + a^4*b^4*d^2)*g^4*x + (a^3*b^5*c^2 - 2*a^4*b^4*c*d + a^5*b^3*d^2)*g^4) + 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(b*x + a)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4) - 6*(3*b^2*c^2*d - 3*a*b*c*d^2 + a^2*d^3)*log(d*x + c)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4)) - 1/9*A*B*c^3*i^3*n*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*g^4*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*g^4*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*g^4*x + (a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2)*g^4) + 6*d^3*log(b*x + a)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4) - 6*d^3*log(d*x + c)/((b^4*c^3 - 3*a*b^3*c^2*d + 3*a^2*b^2*c*d^2 - a^3*b*d^3)*g^4)) - 1/6*A*B*c^2*d*i^3*n*((5*a*b^2*c^2 - 22*a^2*b*c*d + 5*a^3*d^2 - 6*(3*b^3*c*d - a*b^2*d^2)*x^2 + 3*(3*b^3*c^2 - 16*a*b^2*c*d + 5*a^2*b*d^2)*x)/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4) - 6*(3*b*c*d^2 - a*d^3)*log(b*x + a)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4) + 6*(3*b*c*d^2 - a*d^3)*log(d*x + c)/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^4)) + 1/6*A^2*d^3*i^3*((18*a*b^2*x^2 + 27*a^2*b*x + 11*a^3)/(b^7*g^4*x^3 + 3*a*b^6*g^4*x^2 + 3*a^2*b^5*g^4*x + a^3*b^4*g^4) + 6*log(b*x + a)/(b^4*g^4)) - (3*b*x + a)*A*B*c^2*d*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - 2*(3*b^2*x^2 + 3*a*b*x + a^2)*A*B*c*d^2*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 1/2*(3*b*x + a)*A^2*c^2*d*i^3/(b^5*g^4*x^3 + 3*a*b^4*g^4*x^2 + 3*a^2*b^3*g^4*x + a^3*b^2*g^4) - (3*b^2*x^2 + 3*a*b*x + a^2)*A^2*c*d^2*i^3/(b^6*g^4*x^3 + 3*a*b^5*g^4*x^2 + 3*a^2*b^4*g^4*x + a^3*b^3*g^4) - 2/3*A*B*c^3*i^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/3*A^2*c^3*i^3/(b^4*g^4*x^3 + 3*a*b^3*g^4*x^2 + 3*a^2*b^2*g^4*x + a^3*b*g^4) - 1/6*(18*(b^3*c*d^2*i^3 - a*b^2*d^3*i^3)*B^2*x^2 + 9*(b^3*c^2*d*i^3 + 2*a*b^2*c*d^2*i^3 - 3*a^2*b*d^3*i^3)*B^2*x + (2*b^3*c^3*i^3 + 3*a*b^2*c^2*d*i^3 + 6*a^2*b*c*d^2*i^3 - 11*a^3*d^3*i^3)*B^2 - 6*(B^2*b^3*d^3*i^3*x^3 + 3*B^2*a*b^2*d^3*i^3*x^2 + 3*B^2*a^2*b*d^3*i^3*x + B^2*a^3*d^3*i^3)*log(b*x + a))*log((d*x + c)^n)^2/(b^7*g^4*x^3 + 3*a*b^6*g^4*x^2 + 3*a^2*b^5*g^4*x + a^3*b^4*g^4) - integrate(-1/3*(18*B^2*b^4*c^2*d^2*i^3*x^2*log(e)^2 + 12*B^2*b^4*c^3*d*i^3*x*log(e)^2 + 3*B^2*b^4*c^4*i^3*log(e)^2 + 3*(B^2*b^4*d^4*i^3*log(e)^2 + 2*A*B*b^4*d^4*i^3*log(e))*x^4 + 6*(2*B^2*b^4*c*d^3*i^3*log(e)^2 + A*B*b^4*c*d^3*i^3*log(e))*x^3 + 3*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*x + a)^n)^2 + 6*(6*B^2*b^4*c^2*d^2*i^3*x^2*log(e) + 4*B^2*b^4*c^3*d*i^3*x*log(e) + B^2*b^4*c^4*i^3*log(e) + (B^2*b^4*d^4*i^3*log(e) + A*B*b^4*d^4*i^3)*x^4 + (4*B^2*b^4*c*d^3*i^3*log(e) + A*B*b^4*c*d^3*i^3)*x^3)*log((b*x + a)^n) + (9*(4*a*b^3*c*d^3*i^3*n - 5*a^2*b^2*d^4*i^3*n + (i^3*n - 4*i^3*log(e))*b^4*c^2*d^2)*B^2*x^2 - 6*(B^2*b^4*d^4*i^3*log(e) + A*B*b^4*d^4*i^3)*x^4 + 2*(6*a*b^3*c^2*d^2*i^3*n + 12*a^2*b^2*c*d^3*i^3*n - 19*a^3*b*d^4*i^3*n + (i^3*n - 12*i^3*log(e))*b^4*c^3*d)*B^2*x - 6*(A*B*b^4*c*d^3*i^3 + (3*a*b^3*d^4*i^3*n - (3*i^3*n - 4*i^3*log(e))*b^4*c*d^3)*B^2)*x^3 + (2*a*b^3*c^3*d*i^3*n + 3*a^2*b^2*c^2*d^2*i^3*n + 6*a^3*b*c*d^3*i^3*n - 11*a^4*d^4*i^3*n - 6*b^4*c^4*i^3*log(e))*B^2 - 6*(B^2*b^4*d^4*i^3*n*x^4 + 4*B^2*a*b^3*d^4*i^3*n*x^3 + 6*B^2*a^2*b^2*d^4*i^3*n*x^2 + 4*B^2*a^3*b*d^4*i^3*n*x + B^2*a^4*d^4*i^3*n)*log(b*x + a) - 6*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*x + a)^n))*log((d*x + c)^n))/(b^8*d*g^4*x^5 + a^4*b^4*c*g^4 + (b^8*c*g^4 + 4*a*b^7*d*g^4)*x^4 + 2*(2*a*b^7*c*g^4 + 3*a^2*b^6*d*g^4)*x^3 + 2*(3*a^2*b^6*c*g^4 + 2*a^3*b^5*d*g^4)*x^2 + (4*a^3*b^5*c*g^4 + a^4*b^4*d*g^4)*x), x)","F",0
186,0,0,0,0.000000," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i),x, algorithm=""maxima"")","3 \, A^{2} a^{2} b g^{3} {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} - \frac{1}{6} \, A^{2} b^{3} g^{3} {\left(\frac{6 \, c^{3} \log\left(d x + c\right)}{d^{4} i} - \frac{2 \, d^{2} x^{3} - 3 \, c d x^{2} + 6 \, c^{2} x}{d^{3} i}\right)} + \frac{3}{2} \, A^{2} a b^{2} g^{3} {\left(\frac{2 \, c^{2} \log\left(d x + c\right)}{d^{3} i} + \frac{d x^{2} - 2 \, c x}{d^{2} i}\right)} + \frac{A^{2} a^{3} g^{3} \log\left(d i x + c i\right)}{d i} + \frac{{\left(2 \, B^{2} b^{3} d^{3} g^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} g^{3} - 3 \, a b^{2} d^{3} g^{3}\right)} B^{2} x^{2} + 6 \, {\left(b^{3} c^{2} d g^{3} - 3 \, a b^{2} c d^{2} g^{3} + 3 \, a^{2} b d^{3} g^{3}\right)} B^{2} x - 6 \, {\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - a^{3} d^{3} g^{3}\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{6 \, d^{4} i} - \int -\frac{3 \, B^{2} a^{3} d^{3} g^{3} \log\left(e\right)^{2} + 6 \, A B a^{3} d^{3} g^{3} \log\left(e\right) + 3 \, {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} g^{3} \log\left(e\right)\right)} x^{3} + 9 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B a b^{2} d^{3} g^{3} \log\left(e\right)\right)} x^{2} + 3 \, {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 9 \, {\left(B^{2} a^{2} b d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B a^{2} b d^{3} g^{3} \log\left(e\right)\right)} x + 6 \, {\left(B^{2} a^{3} d^{3} g^{3} \log\left(e\right) + A B a^{3} d^{3} g^{3} + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right) + A B b^{3} d^{3} g^{3}\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right) + A B a b^{2} d^{3} g^{3}\right)} x^{2} + 3 \, {\left(B^{2} a^{2} b d^{3} g^{3} \log\left(e\right) + A B a^{2} b d^{3} g^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(6 \, B^{2} a^{3} d^{3} g^{3} \log\left(e\right) + 6 \, A B a^{3} d^{3} g^{3} + 2 \, {\left(3 \, A B b^{3} d^{3} g^{3} + {\left(g^{3} n + 3 \, g^{3} \log\left(e\right)\right)} B^{2} b^{3} d^{3}\right)} x^{3} - 6 \, {\left(b^{3} c^{3} g^{3} n - 3 \, a b^{2} c^{2} d g^{3} n + 3 \, a^{2} b c d^{2} g^{3} n - a^{3} d^{3} g^{3} n\right)} B^{2} \log\left(d x + c\right) + 3 \, {\left(6 \, A B a b^{2} d^{3} g^{3} - {\left(b^{3} c d^{2} g^{3} n - 3 \, {\left(g^{3} n + 2 \, g^{3} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2}\right)} x^{2} + 6 \, {\left(3 \, A B a^{2} b d^{3} g^{3} + {\left(b^{3} c^{2} d g^{3} n - 3 \, a b^{2} c d^{2} g^{3} n + 3 \, {\left(g^{3} n + g^{3} \log\left(e\right)\right)} a^{2} b d^{3}\right)} B^{2}\right)} x + 6 \, {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{3 \, {\left(d^{4} i x + c d^{3} i\right)}}\,{d x}"," ",0,"3*A^2*a^2*b*g^3*(x/(d*i) - c*log(d*x + c)/(d^2*i)) - 1/6*A^2*b^3*g^3*(6*c^3*log(d*x + c)/(d^4*i) - (2*d^2*x^3 - 3*c*d*x^2 + 6*c^2*x)/(d^3*i)) + 3/2*A^2*a*b^2*g^3*(2*c^2*log(d*x + c)/(d^3*i) + (d*x^2 - 2*c*x)/(d^2*i)) + A^2*a^3*g^3*log(d*i*x + c*i)/(d*i) + 1/6*(2*B^2*b^3*d^3*g^3*x^3 - 3*(b^3*c*d^2*g^3 - 3*a*b^2*d^3*g^3)*B^2*x^2 + 6*(b^3*c^2*d*g^3 - 3*a*b^2*c*d^2*g^3 + 3*a^2*b*d^3*g^3)*B^2*x - 6*(b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - a^3*d^3*g^3)*B^2*log(d*x + c))*log((d*x + c)^n)^2/(d^4*i) - integrate(-1/3*(3*B^2*a^3*d^3*g^3*log(e)^2 + 6*A*B*a^3*d^3*g^3*log(e) + 3*(B^2*b^3*d^3*g^3*log(e)^2 + 2*A*B*b^3*d^3*g^3*log(e))*x^3 + 9*(B^2*a*b^2*d^3*g^3*log(e)^2 + 2*A*B*a*b^2*d^3*g^3*log(e))*x^2 + 3*(B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log((b*x + a)^n)^2 + 9*(B^2*a^2*b*d^3*g^3*log(e)^2 + 2*A*B*a^2*b*d^3*g^3*log(e))*x + 6*(B^2*a^3*d^3*g^3*log(e) + A*B*a^3*d^3*g^3 + (B^2*b^3*d^3*g^3*log(e) + A*B*b^3*d^3*g^3)*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e) + A*B*a*b^2*d^3*g^3)*x^2 + 3*(B^2*a^2*b*d^3*g^3*log(e) + A*B*a^2*b*d^3*g^3)*x)*log((b*x + a)^n) - (6*B^2*a^3*d^3*g^3*log(e) + 6*A*B*a^3*d^3*g^3 + 2*(3*A*B*b^3*d^3*g^3 + (g^3*n + 3*g^3*log(e))*B^2*b^3*d^3)*x^3 - 6*(b^3*c^3*g^3*n - 3*a*b^2*c^2*d*g^3*n + 3*a^2*b*c*d^2*g^3*n - a^3*d^3*g^3*n)*B^2*log(d*x + c) + 3*(6*A*B*a*b^2*d^3*g^3 - (b^3*c*d^2*g^3*n - 3*(g^3*n + 2*g^3*log(e))*a*b^2*d^3)*B^2)*x^2 + 6*(3*A*B*a^2*b*d^3*g^3 + (b^3*c^2*d*g^3*n - 3*a*b^2*c*d^2*g^3*n + 3*(g^3*n + g^3*log(e))*a^2*b*d^3)*B^2)*x + 6*(B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log((b*x + a)^n))*log((d*x + c)^n))/(d^4*i*x + c*d^3*i), x)","F",0
187,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i),x, algorithm=""maxima"")","2 \, A^{2} a b g^{2} {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} + \frac{1}{2} \, A^{2} b^{2} g^{2} {\left(\frac{2 \, c^{2} \log\left(d x + c\right)}{d^{3} i} + \frac{d x^{2} - 2 \, c x}{d^{2} i}\right)} + \frac{A^{2} a^{2} g^{2} \log\left(d i x + c i\right)}{d i} + \frac{{\left(B^{2} b^{2} d^{2} g^{2} x^{2} - 2 \, {\left(b^{2} c d g^{2} - 2 \, a b d^{2} g^{2}\right)} B^{2} x + 2 \, {\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + a^{2} d^{2} g^{2}\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, d^{3} i} - \int -\frac{B^{2} a^{2} d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B a^{2} d^{2} g^{2} \log\left(e\right) + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} g^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(B^{2} a b d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B a b d^{2} g^{2} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a^{2} d^{2} g^{2} \log\left(e\right) + A B a^{2} d^{2} g^{2} + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right) + A B b^{2} d^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} a b d^{2} g^{2} \log\left(e\right) + A B a b d^{2} g^{2}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, B^{2} a^{2} d^{2} g^{2} \log\left(e\right) + 2 \, A B a^{2} d^{2} g^{2} + 2 \, {\left(b^{2} c^{2} g^{2} n - 2 \, a b c d g^{2} n + a^{2} d^{2} g^{2} n\right)} B^{2} \log\left(d x + c\right) + {\left(2 \, A B b^{2} d^{2} g^{2} + {\left(g^{2} n + 2 \, g^{2} \log\left(e\right)\right)} B^{2} b^{2} d^{2}\right)} x^{2} + 2 \, {\left(2 \, A B a b d^{2} g^{2} - {\left(b^{2} c d g^{2} n - 2 \, {\left(g^{2} n + g^{2} \log\left(e\right)\right)} a b d^{2}\right)} B^{2}\right)} x + 2 \, {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{3} i x + c d^{2} i}\,{d x}"," ",0,"2*A^2*a*b*g^2*(x/(d*i) - c*log(d*x + c)/(d^2*i)) + 1/2*A^2*b^2*g^2*(2*c^2*log(d*x + c)/(d^3*i) + (d*x^2 - 2*c*x)/(d^2*i)) + A^2*a^2*g^2*log(d*i*x + c*i)/(d*i) + 1/2*(B^2*b^2*d^2*g^2*x^2 - 2*(b^2*c*d*g^2 - 2*a*b*d^2*g^2)*B^2*x + 2*(b^2*c^2*g^2 - 2*a*b*c*d*g^2 + a^2*d^2*g^2)*B^2*log(d*x + c))*log((d*x + c)^n)^2/(d^3*i) - integrate(-(B^2*a^2*d^2*g^2*log(e)^2 + 2*A*B*a^2*d^2*g^2*log(e) + (B^2*b^2*d^2*g^2*log(e)^2 + 2*A*B*b^2*d^2*g^2*log(e))*x^2 + (B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log((b*x + a)^n)^2 + 2*(B^2*a*b*d^2*g^2*log(e)^2 + 2*A*B*a*b*d^2*g^2*log(e))*x + 2*(B^2*a^2*d^2*g^2*log(e) + A*B*a^2*d^2*g^2 + (B^2*b^2*d^2*g^2*log(e) + A*B*b^2*d^2*g^2)*x^2 + 2*(B^2*a*b*d^2*g^2*log(e) + A*B*a*b*d^2*g^2)*x)*log((b*x + a)^n) - (2*B^2*a^2*d^2*g^2*log(e) + 2*A*B*a^2*d^2*g^2 + 2*(b^2*c^2*g^2*n - 2*a*b*c*d*g^2*n + a^2*d^2*g^2*n)*B^2*log(d*x + c) + (2*A*B*b^2*d^2*g^2 + (g^2*n + 2*g^2*log(e))*B^2*b^2*d^2)*x^2 + 2*(2*A*B*a*b*d^2*g^2 - (b^2*c*d*g^2*n - 2*(g^2*n + g^2*log(e))*a*b*d^2)*B^2)*x + 2*(B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log((b*x + a)^n))*log((d*x + c)^n))/(d^3*i*x + c*d^2*i), x)","F",0
188,0,0,0,0.000000," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i),x, algorithm=""maxima"")","A^{2} b g {\left(\frac{x}{d i} - \frac{c \log\left(d x + c\right)}{d^{2} i}\right)} + \frac{A^{2} a g \log\left(d i x + c i\right)}{d i} + \frac{{\left(B^{2} b d g x - {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{d^{2} i} - \int -\frac{B^{2} a d g \log\left(e\right)^{2} + 2 \, A B a d g \log\left(e\right) + {\left(B^{2} b d g x + B^{2} a d g\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b d g \log\left(e\right)^{2} + 2 \, A B b d g \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a d g \log\left(e\right) + A B a d g + {\left(B^{2} b d g \log\left(e\right) + A B b d g\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B^{2} a d g \log\left(e\right) + A B a d g - {\left(b c g n - a d g n\right)} B^{2} \log\left(d x + c\right) + {\left({\left(g n + g \log\left(e\right)\right)} B^{2} b d + A B b d g\right)} x + {\left(B^{2} b d g x + B^{2} a d g\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{2} i x + c d i}\,{d x}"," ",0,"A^2*b*g*(x/(d*i) - c*log(d*x + c)/(d^2*i)) + A^2*a*g*log(d*i*x + c*i)/(d*i) + (B^2*b*d*g*x - (b*c*g - a*d*g)*B^2*log(d*x + c))*log((d*x + c)^n)^2/(d^2*i) - integrate(-(B^2*a*d*g*log(e)^2 + 2*A*B*a*d*g*log(e) + (B^2*b*d*g*x + B^2*a*d*g)*log((b*x + a)^n)^2 + (B^2*b*d*g*log(e)^2 + 2*A*B*b*d*g*log(e))*x + 2*(B^2*a*d*g*log(e) + A*B*a*d*g + (B^2*b*d*g*log(e) + A*B*b*d*g)*x)*log((b*x + a)^n) - 2*(B^2*a*d*g*log(e) + A*B*a*d*g - (b*c*g*n - a*d*g*n)*B^2*log(d*x + c) + ((g*n + g*log(e))*B^2*b*d + A*B*b*d*g)*x + (B^2*b*d*g*x + B^2*a*d*g)*log((b*x + a)^n))*log((d*x + c)^n))/(d^2*i*x + c*d*i), x)","F",0
189,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i),x, algorithm=""maxima"")","\frac{B^{2} \log\left(d x + c\right) \log\left({\left(d x + c\right)}^{n}\right)^{2}}{d i} + \frac{A^{2} \log\left(d i x + c i\right)}{d i} - \int -\frac{B^{2} \log\left({\left(b x + a\right)}^{n}\right)^{2} + B^{2} \log\left(e\right)^{2} + 2 \, A B \log\left(e\right) + 2 \, {\left(B^{2} \log\left(e\right) + A B\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B^{2} n \log\left(d x + c\right) + B^{2} \log\left({\left(b x + a\right)}^{n}\right) + B^{2} \log\left(e\right) + A B\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d i x + c i}\,{d x}"," ",0,"B^2*log(d*x + c)*log((d*x + c)^n)^2/(d*i) + A^2*log(d*i*x + c*i)/(d*i) - integrate(-(B^2*log((b*x + a)^n)^2 + B^2*log(e)^2 + 2*A*B*log(e) + 2*(B^2*log(e) + A*B)*log((b*x + a)^n) - 2*(B^2*n*log(d*x + c) + B^2*log((b*x + a)^n) + B^2*log(e) + A*B)*log((d*x + c)^n))/(d*i*x + c*i), x)","F",0
190,1,407,0,1.192289," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)/(d*i*x+c*i),x, algorithm=""maxima"")","B^{2} {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} + 2 \, A B {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, {\left(\frac{{\left(\log\left(b x + a\right)^{3} - 3 \, \log\left(b x + a\right)^{2} \log\left(d x + c\right) + 3 \, \log\left(b x + a\right) \log\left(d x + c\right)^{2} - \log\left(d x + c\right)^{3}\right)} n^{2}}{b c g i - a d g i} - \frac{3 \, {\left(\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right) + \log\left(d x + c\right)^{2}\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b c g i - a d g i}\right)} B^{2} - \frac{{\left(\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right) + \log\left(d x + c\right)^{2}\right)} A B n}{b c g i - a d g i} + A^{2} {\left(\frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} g i} - \frac{\log\left(d x + c\right)}{{\left(b c - a d\right)} g i}\right)}"," ",0,"B^2*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 + 2*A*B*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*((log(b*x + a)^3 - 3*log(b*x + a)^2*log(d*x + c) + 3*log(b*x + a)*log(d*x + c)^2 - log(d*x + c)^3)*n^2/(b*c*g*i - a*d*g*i) - 3*(log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c) + log(d*x + c)^2)*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b*c*g*i - a*d*g*i))*B^2 - (log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c) + log(d*x + c)^2)*A*B*n/(b*c*g*i - a*d*g*i) + A^2*(log(b*x + a)/((b*c - a*d)*g*i) - log(d*x + c)/((b*c - a*d)*g*i))","B",0
191,1,1018,0,1.222445," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2/(d*i*x+c*i),x, algorithm=""maxima"")","-B^{2} {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} - 2 \, A B {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{1}{3} \, {\left(\frac{{\left({\left(b d x + a d\right)} \log\left(b x + a\right)^{3} - {\left(b d x + a d\right)} \log\left(d x + c\right)^{3} - 3 \, {\left(b d x + a d\right)} \log\left(b x + a\right)^{2} - 3 \, {\left(b d x + a d - {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 6 \, b c - 6 \, a d + 6 \, {\left(b d x + a d\right)} \log\left(b x + a\right) - 3 \, {\left(2 \, b d x + {\left(b d x + a d\right)} \log\left(b x + a\right)^{2} + 2 \, a d - 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a b^{2} c^{2} g^{2} i - 2 \, a^{2} b c d g^{2} i + a^{3} d^{2} g^{2} i + {\left(b^{3} c^{2} g^{2} i - 2 \, a b^{2} c d g^{2} i + a^{2} b d^{2} g^{2} i\right)} x} - \frac{3 \, {\left({\left(b d x + a d\right)} \log\left(b x + a\right)^{2} + {\left(b d x + a d\right)} \log\left(d x + c\right)^{2} - 2 \, b c + 2 \, a d - 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right) + 2 \, {\left(b d x + a d - {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a b^{2} c^{2} g^{2} i - 2 \, a^{2} b c d g^{2} i + a^{3} d^{2} g^{2} i + {\left(b^{3} c^{2} g^{2} i - 2 \, a b^{2} c d g^{2} i + a^{2} b d^{2} g^{2} i\right)} x}\right)} B^{2} + \frac{{\left({\left(b d x + a d\right)} \log\left(b x + a\right)^{2} + {\left(b d x + a d\right)} \log\left(d x + c\right)^{2} - 2 \, b c + 2 \, a d - 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right) + 2 \, {\left(b d x + a d - {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{a b^{2} c^{2} g^{2} i - 2 \, a^{2} b c d g^{2} i + a^{3} d^{2} g^{2} i + {\left(b^{3} c^{2} g^{2} i - 2 \, a b^{2} c d g^{2} i + a^{2} b d^{2} g^{2} i\right)} x} - A^{2} {\left(\frac{1}{{\left(b^{2} c - a b d\right)} g^{2} i x + {\left(a b c - a^{2} d\right)} g^{2} i} + \frac{d \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i} - \frac{d \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g^{2} i}\right)}"," ",0,"-B^2*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 - 2*A*B*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/3*(((b*d*x + a*d)*log(b*x + a)^3 - (b*d*x + a*d)*log(d*x + c)^3 - 3*(b*d*x + a*d)*log(b*x + a)^2 - 3*(b*d*x + a*d - (b*d*x + a*d)*log(b*x + a))*log(d*x + c)^2 + 6*b*c - 6*a*d + 6*(b*d*x + a*d)*log(b*x + a) - 3*(2*b*d*x + (b*d*x + a*d)*log(b*x + a)^2 + 2*a*d - 2*(b*d*x + a*d)*log(b*x + a))*log(d*x + c))*n^2/(a*b^2*c^2*g^2*i - 2*a^2*b*c*d*g^2*i + a^3*d^2*g^2*i + (b^3*c^2*g^2*i - 2*a*b^2*c*d*g^2*i + a^2*b*d^2*g^2*i)*x) - 3*((b*d*x + a*d)*log(b*x + a)^2 + (b*d*x + a*d)*log(d*x + c)^2 - 2*b*c + 2*a*d - 2*(b*d*x + a*d)*log(b*x + a) + 2*(b*d*x + a*d - (b*d*x + a*d)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a*b^2*c^2*g^2*i - 2*a^2*b*c*d*g^2*i + a^3*d^2*g^2*i + (b^3*c^2*g^2*i - 2*a*b^2*c*d*g^2*i + a^2*b*d^2*g^2*i)*x))*B^2 + ((b*d*x + a*d)*log(b*x + a)^2 + (b*d*x + a*d)*log(d*x + c)^2 - 2*b*c + 2*a*d - 2*(b*d*x + a*d)*log(b*x + a) + 2*(b*d*x + a*d - (b*d*x + a*d)*log(b*x + a))*log(d*x + c))*A*B*n/(a*b^2*c^2*g^2*i - 2*a^2*b*c*d*g^2*i + a^3*d^2*g^2*i + (b^3*c^2*g^2*i - 2*a*b^2*c*d*g^2*i + a^2*b*d^2*g^2*i)*x) - A^2*(1/((b^2*c - a*b*d)*g^2*i*x + (a*b*c - a^2*d)*g^2*i) + d*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i) - d*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g^2*i))","B",0
192,1,2126,0,2.116161," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3/(d*i*x+c*i),x, algorithm=""maxima"")","\frac{1}{2} \, B^{2} {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} + A B {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{1}{12} \, {\left(\frac{{\left(3 \, b^{2} c^{2} - 48 \, a b c d + 45 \, a^{2} d^{2} - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{3} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{3} + 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 42 \, {\left(b^{2} c d - a b d^{2}\right)} x - 42 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 6 \, {\left(7 \, b^{2} d^{2} x^{2} + 14 \, a b d^{2} x + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{2} b^{3} c^{3} g^{3} i - 3 \, a^{3} b^{2} c^{2} d g^{3} i + 3 \, a^{4} b c d^{2} g^{3} i - a^{5} d^{3} g^{3} i + {\left(b^{5} c^{3} g^{3} i - 3 \, a b^{4} c^{2} d g^{3} i + 3 \, a^{2} b^{3} c d^{2} g^{3} i - a^{3} b^{2} d^{3} g^{3} i\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} g^{3} i - 3 \, a^{2} b^{3} c^{2} d g^{3} i + 3 \, a^{3} b^{2} c d^{2} g^{3} i - a^{4} b d^{3} g^{3} i\right)} x} + \frac{6 \, {\left(b^{2} c^{2} - 8 \, a b c d + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d - a b d^{2}\right)} x - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a^{2} b^{3} c^{3} g^{3} i - 3 \, a^{3} b^{2} c^{2} d g^{3} i + 3 \, a^{4} b c d^{2} g^{3} i - a^{5} d^{3} g^{3} i + {\left(b^{5} c^{3} g^{3} i - 3 \, a b^{4} c^{2} d g^{3} i + 3 \, a^{2} b^{3} c d^{2} g^{3} i - a^{3} b^{2} d^{3} g^{3} i\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} g^{3} i - 3 \, a^{2} b^{3} c^{2} d g^{3} i + 3 \, a^{3} b^{2} c d^{2} g^{3} i - a^{4} b d^{3} g^{3} i\right)} x}\right)} B^{2} - \frac{{\left(b^{2} c^{2} - 8 \, a b c d + 7 \, a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d - a b d^{2}\right)} x - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, a b d^{2} x + 3 \, a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{2 \, {\left(a^{2} b^{3} c^{3} g^{3} i - 3 \, a^{3} b^{2} c^{2} d g^{3} i + 3 \, a^{4} b c d^{2} g^{3} i - a^{5} d^{3} g^{3} i + {\left(b^{5} c^{3} g^{3} i - 3 \, a b^{4} c^{2} d g^{3} i + 3 \, a^{2} b^{3} c d^{2} g^{3} i - a^{3} b^{2} d^{3} g^{3} i\right)} x^{2} + 2 \, {\left(a b^{4} c^{3} g^{3} i - 3 \, a^{2} b^{3} c^{2} d g^{3} i + 3 \, a^{3} b^{2} c d^{2} g^{3} i - a^{4} b d^{3} g^{3} i\right)} x\right)}} + \frac{1}{2} \, A^{2} {\left(\frac{2 \, b d x - b c + 3 \, a d}{{\left(b^{4} c^{2} - 2 \, a b^{3} c d + a^{2} b^{2} d^{2}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b^{2} c d + a^{3} b d^{2}\right)} g^{3} i x + {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} g^{3} i} + \frac{2 \, d^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i} - \frac{2 \, d^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{3} i}\right)}"," ",0,"1/2*B^2*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 + A*B*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/12*((3*b^2*c^2 - 48*a*b*c*d + 45*a^2*d^2 - 4*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^3 + 4*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^3 + 18*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 6*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c)^2 - 42*(b^2*c*d - a*b*d^2)*x - 42*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 6*(7*b^2*d^2*x^2 + 14*a*b*d^2*x + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))*n^2/(a^2*b^3*c^3*g^3*i - 3*a^3*b^2*c^2*d*g^3*i + 3*a^4*b*c*d^2*g^3*i - a^5*d^3*g^3*i + (b^5*c^3*g^3*i - 3*a*b^4*c^2*d*g^3*i + 3*a^2*b^3*c*d^2*g^3*i - a^3*b^2*d^3*g^3*i)*x^2 + 2*(a*b^4*c^3*g^3*i - 3*a^2*b^3*c^2*d*g^3*i + 3*a^3*b^2*c*d^2*g^3*i - a^4*b*d^3*g^3*i)*x) + 6*(b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^2 - 6*(b^2*c*d - a*b*d^2)*x - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a^2*b^3*c^3*g^3*i - 3*a^3*b^2*c^2*d*g^3*i + 3*a^4*b*c*d^2*g^3*i - a^5*d^3*g^3*i + (b^5*c^3*g^3*i - 3*a*b^4*c^2*d*g^3*i + 3*a^2*b^3*c*d^2*g^3*i - a^3*b^2*d^3*g^3*i)*x^2 + 2*(a*b^4*c^3*g^3*i - 3*a^2*b^3*c^2*d*g^3*i + 3*a^3*b^2*c*d^2*g^3*i - a^4*b*d^3*g^3*i)*x))*B^2 - 1/2*(b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(d*x + c)^2 - 6*(b^2*c*d - a*b*d^2)*x - 6*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a) + 2*(3*b^2*d^2*x^2 + 6*a*b*d^2*x + 3*a^2*d^2 - 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*log(b*x + a))*log(d*x + c))*A*B*n/(a^2*b^3*c^3*g^3*i - 3*a^3*b^2*c^2*d*g^3*i + 3*a^4*b*c*d^2*g^3*i - a^5*d^3*g^3*i + (b^5*c^3*g^3*i - 3*a*b^4*c^2*d*g^3*i + 3*a^2*b^3*c*d^2*g^3*i - a^3*b^2*d^3*g^3*i)*x^2 + 2*(a*b^4*c^3*g^3*i - 3*a^2*b^3*c^2*d*g^3*i + 3*a^3*b^2*c*d^2*g^3*i - a^4*b*d^3*g^3*i)*x) + 1/2*A^2*((2*b*d*x - b*c + 3*a*d)/((b^4*c^2 - 2*a*b^3*c*d + a^2*b^2*d^2)*g^3*i*x^2 + 2*(a*b^3*c^2 - 2*a^2*b^2*c*d + a^3*b*d^2)*g^3*i*x + (a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*g^3*i) + 2*d^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i) - 2*d^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^3*i))","B",0
193,1,3445,0,2.977617," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4/(d*i*x+c*i),x, algorithm=""maxima"")","-\frac{1}{6} \, B^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} - \frac{1}{3} \, A B {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{1}{108} \, {\left(\frac{{\left(8 \, b^{3} c^{3} - 81 \, a b^{2} c^{2} d + 648 \, a^{2} b c d^{2} - 575 \, a^{3} d^{3} + 36 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{3} - 36 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{3} + 510 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 198 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(19 \, b^{3} c^{2} d - 378 \, a b^{2} c d^{2} + 359 \, a^{2} b d^{3}\right)} x + 510 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(85 \, b^{3} d^{3} x^{3} + 255 \, a b^{2} d^{3} x^{2} + 255 \, a^{2} b d^{3} x + 85 \, a^{3} d^{3} + 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{3} b^{4} c^{4} g^{4} i - 4 \, a^{4} b^{3} c^{3} d g^{4} i + 6 \, a^{5} b^{2} c^{2} d^{2} g^{4} i - 4 \, a^{6} b c d^{3} g^{4} i + a^{7} d^{4} g^{4} i + {\left(b^{7} c^{4} g^{4} i - 4 \, a b^{6} c^{3} d g^{4} i + 6 \, a^{2} b^{5} c^{2} d^{2} g^{4} i - 4 \, a^{3} b^{4} c d^{3} g^{4} i + a^{4} b^{3} d^{4} g^{4} i\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} g^{4} i - 4 \, a^{2} b^{5} c^{3} d g^{4} i + 6 \, a^{3} b^{4} c^{2} d^{2} g^{4} i - 4 \, a^{4} b^{3} c d^{3} g^{4} i + a^{5} b^{2} d^{4} g^{4} i\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} g^{4} i - 4 \, a^{3} b^{4} c^{3} d g^{4} i + 6 \, a^{4} b^{3} c^{2} d^{2} g^{4} i - 4 \, a^{5} b^{2} c d^{3} g^{4} i + a^{6} b d^{4} g^{4} i\right)} x} + \frac{6 \, {\left(4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a^{3} b^{4} c^{4} g^{4} i - 4 \, a^{4} b^{3} c^{3} d g^{4} i + 6 \, a^{5} b^{2} c^{2} d^{2} g^{4} i - 4 \, a^{6} b c d^{3} g^{4} i + a^{7} d^{4} g^{4} i + {\left(b^{7} c^{4} g^{4} i - 4 \, a b^{6} c^{3} d g^{4} i + 6 \, a^{2} b^{5} c^{2} d^{2} g^{4} i - 4 \, a^{3} b^{4} c d^{3} g^{4} i + a^{4} b^{3} d^{4} g^{4} i\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} g^{4} i - 4 \, a^{2} b^{5} c^{3} d g^{4} i + 6 \, a^{3} b^{4} c^{2} d^{2} g^{4} i - 4 \, a^{4} b^{3} c d^{3} g^{4} i + a^{5} b^{2} d^{4} g^{4} i\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} g^{4} i - 4 \, a^{3} b^{4} c^{3} d g^{4} i + 6 \, a^{4} b^{3} c^{2} d^{2} g^{4} i - 4 \, a^{5} b^{2} c d^{3} g^{4} i + a^{6} b d^{4} g^{4} i\right)} x}\right)} B^{2} - \frac{{\left(4 \, b^{3} c^{3} - 27 \, a b^{2} c^{2} d + 108 \, a^{2} b c d^{2} - 85 \, a^{3} d^{3} + 66 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 49 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, a b^{2} d^{3} x^{2} + 33 \, a^{2} b d^{3} x + 11 \, a^{3} d^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, a b^{2} d^{3} x^{2} + 3 \, a^{2} b d^{3} x + a^{3} d^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{18 \, {\left(a^{3} b^{4} c^{4} g^{4} i - 4 \, a^{4} b^{3} c^{3} d g^{4} i + 6 \, a^{5} b^{2} c^{2} d^{2} g^{4} i - 4 \, a^{6} b c d^{3} g^{4} i + a^{7} d^{4} g^{4} i + {\left(b^{7} c^{4} g^{4} i - 4 \, a b^{6} c^{3} d g^{4} i + 6 \, a^{2} b^{5} c^{2} d^{2} g^{4} i - 4 \, a^{3} b^{4} c d^{3} g^{4} i + a^{4} b^{3} d^{4} g^{4} i\right)} x^{3} + 3 \, {\left(a b^{6} c^{4} g^{4} i - 4 \, a^{2} b^{5} c^{3} d g^{4} i + 6 \, a^{3} b^{4} c^{2} d^{2} g^{4} i - 4 \, a^{4} b^{3} c d^{3} g^{4} i + a^{5} b^{2} d^{4} g^{4} i\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} g^{4} i - 4 \, a^{3} b^{4} c^{3} d g^{4} i + 6 \, a^{4} b^{3} c^{2} d^{2} g^{4} i - 4 \, a^{5} b^{2} c d^{3} g^{4} i + a^{6} b d^{4} g^{4} i\right)} x\right)}} - \frac{1}{6} \, A^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} - 7 \, a b c d + 11 \, a^{2} d^{2} - 3 \, {\left(b^{2} c d - 5 \, a b d^{2}\right)} x}{{\left(b^{6} c^{3} - 3 \, a b^{5} c^{2} d + 3 \, a^{2} b^{4} c d^{2} - a^{3} b^{3} d^{3}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{5} c^{3} - 3 \, a^{2} b^{4} c^{2} d + 3 \, a^{3} b^{3} c d^{2} - a^{4} b^{2} d^{3}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{4} c^{3} - 3 \, a^{3} b^{3} c^{2} d + 3 \, a^{4} b^{2} c d^{2} - a^{5} b d^{3}\right)} g^{4} i x + {\left(a^{3} b^{3} c^{3} - 3 \, a^{4} b^{2} c^{2} d + 3 \, a^{5} b c d^{2} - a^{6} d^{3}\right)} g^{4} i} + \frac{6 \, d^{3} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i} - \frac{6 \, d^{3} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{4} i}\right)}"," ",0,"-1/6*B^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 - 1/3*A*B*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/108*((8*b^3*c^3 - 81*a*b^2*c^2*d + 648*a^2*b*c*d^2 - 575*a^3*d^3 + 36*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^3 - 36*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^3 + 510*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 198*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c)^2 - 3*(19*b^3*c^2*d - 378*a*b^2*c*d^2 + 359*a^2*b*d^3)*x + 510*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(85*b^3*d^3*x^3 + 255*a*b^2*d^3*x^2 + 255*a^2*b*d^3*x + 85*a^3*d^3 + 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*n^2/(a^3*b^4*c^4*g^4*i - 4*a^4*b^3*c^3*d*g^4*i + 6*a^5*b^2*c^2*d^2*g^4*i - 4*a^6*b*c*d^3*g^4*i + a^7*d^4*g^4*i + (b^7*c^4*g^4*i - 4*a*b^6*c^3*d*g^4*i + 6*a^2*b^5*c^2*d^2*g^4*i - 4*a^3*b^4*c*d^3*g^4*i + a^4*b^3*d^4*g^4*i)*x^3 + 3*(a*b^6*c^4*g^4*i - 4*a^2*b^5*c^3*d*g^4*i + 6*a^3*b^4*c^2*d^2*g^4*i - 4*a^4*b^3*c*d^3*g^4*i + a^5*b^2*d^4*g^4*i)*x^2 + 3*(a^2*b^5*c^4*g^4*i - 4*a^3*b^4*c^3*d*g^4*i + 6*a^4*b^3*c^2*d^2*g^4*i - 4*a^5*b^2*c*d^3*g^4*i + a^6*b*d^4*g^4*i)*x) + 6*(4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a^3*b^4*c^4*g^4*i - 4*a^4*b^3*c^3*d*g^4*i + 6*a^5*b^2*c^2*d^2*g^4*i - 4*a^6*b*c*d^3*g^4*i + a^7*d^4*g^4*i + (b^7*c^4*g^4*i - 4*a*b^6*c^3*d*g^4*i + 6*a^2*b^5*c^2*d^2*g^4*i - 4*a^3*b^4*c*d^3*g^4*i + a^4*b^3*d^4*g^4*i)*x^3 + 3*(a*b^6*c^4*g^4*i - 4*a^2*b^5*c^3*d*g^4*i + 6*a^3*b^4*c^2*d^2*g^4*i - 4*a^4*b^3*c*d^3*g^4*i + a^5*b^2*d^4*g^4*i)*x^2 + 3*(a^2*b^5*c^4*g^4*i - 4*a^3*b^4*c^3*d*g^4*i + 6*a^4*b^3*c^2*d^2*g^4*i - 4*a^5*b^2*c*d^3*g^4*i + a^6*b*d^4*g^4*i)*x))*B^2 - 1/18*(4*b^3*c^3 - 27*a*b^2*c^2*d + 108*a^2*b*c*d^2 - 85*a^3*d^3 + 66*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a)^2 - 18*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(d*x + c)^2 - 3*(5*b^3*c^2*d - 54*a*b^2*c*d^2 + 49*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*a*b^2*d^3*x^2 + 33*a^2*b*d^3*x + 11*a^3*d^3 - 6*(b^3*d^3*x^3 + 3*a*b^2*d^3*x^2 + 3*a^2*b*d^3*x + a^3*d^3)*log(b*x + a))*log(d*x + c))*A*B*n/(a^3*b^4*c^4*g^4*i - 4*a^4*b^3*c^3*d*g^4*i + 6*a^5*b^2*c^2*d^2*g^4*i - 4*a^6*b*c*d^3*g^4*i + a^7*d^4*g^4*i + (b^7*c^4*g^4*i - 4*a*b^6*c^3*d*g^4*i + 6*a^2*b^5*c^2*d^2*g^4*i - 4*a^3*b^4*c*d^3*g^4*i + a^4*b^3*d^4*g^4*i)*x^3 + 3*(a*b^6*c^4*g^4*i - 4*a^2*b^5*c^3*d*g^4*i + 6*a^3*b^4*c^2*d^2*g^4*i - 4*a^4*b^3*c*d^3*g^4*i + a^5*b^2*d^4*g^4*i)*x^2 + 3*(a^2*b^5*c^4*g^4*i - 4*a^3*b^4*c^3*d*g^4*i + 6*a^4*b^3*c^2*d^2*g^4*i - 4*a^5*b^2*c*d^3*g^4*i + a^6*b*d^4*g^4*i)*x) - 1/6*A^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 - 7*a*b*c*d + 11*a^2*d^2 - 3*(b^2*c*d - 5*a*b*d^2)*x)/((b^6*c^3 - 3*a*b^5*c^2*d + 3*a^2*b^4*c*d^2 - a^3*b^3*d^3)*g^4*i*x^3 + 3*(a*b^5*c^3 - 3*a^2*b^4*c^2*d + 3*a^3*b^3*c*d^2 - a^4*b^2*d^3)*g^4*i*x^2 + 3*(a^2*b^4*c^3 - 3*a^3*b^3*c^2*d + 3*a^4*b^2*c*d^2 - a^5*b*d^3)*g^4*i*x + (a^3*b^3*c^3 - 3*a^4*b^2*c^2*d + 3*a^5*b*c*d^2 - a^6*d^3)*g^4*i) + 6*d^3*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i) - 6*d^3*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^4*i))","B",0
194,0,0,0,0.000000," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","2 \, A B a^{3} g^{3} n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} + \frac{1}{2} \, {\left(\frac{2 \, c^{3}}{d^{5} i^{2} x + c d^{4} i^{2}} + \frac{6 \, c^{2} \log\left(d x + c\right)}{d^{4} i^{2}} + \frac{d x^{2} - 4 \, c x}{d^{3} i^{2}}\right)} A^{2} b^{3} g^{3} - 3 \, A^{2} a b^{2} {\left(\frac{c^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \frac{x}{d^{2} i^{2}} + \frac{2 \, c \log\left(d x + c\right)}{d^{3} i^{2}}\right)} g^{3} + 3 \, A^{2} a^{2} b g^{3} {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - \frac{2 \, A B a^{3} g^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{A^{2} a^{3} g^{3}}{d^{2} i^{2} x + c d i^{2}} + \frac{{\left(B^{2} b^{3} d^{3} g^{3} x^{3} - 3 \, {\left(b^{3} c d^{2} g^{3} - 2 \, a b^{2} d^{3} g^{3}\right)} B^{2} x^{2} - 2 \, {\left(2 \, b^{3} c^{2} d g^{3} - 3 \, a b^{2} c d^{2} g^{3}\right)} B^{2} x + 2 \, {\left(b^{3} c^{3} g^{3} - 3 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} - a^{3} d^{3} g^{3}\right)} B^{2} + 6 \, {\left({\left(b^{3} c^{2} d g^{3} - 2 \, a b^{2} c d^{2} g^{3} + a^{2} b d^{3} g^{3}\right)} B^{2} x + {\left(b^{3} c^{3} g^{3} - 2 \, a b^{2} c^{2} d g^{3} + a^{2} b c d^{2} g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, {\left(d^{5} i^{2} x + c d^{4} i^{2}\right)}} - \int -\frac{B^{2} a^{3} d^{3} g^{3} \log\left(e\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} g^{3} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B a b^{2} d^{3} g^{3} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{2} a^{2} b d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B a^{2} b d^{3} g^{3} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a^{3} d^{3} g^{3} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right) + A B b^{3} d^{3} g^{3}\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right) + A B a b^{2} d^{3} g^{3}\right)} x^{2} + 3 \, {\left(B^{2} a^{2} b d^{3} g^{3} \log\left(e\right) + A B a^{2} b d^{3} g^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(2 \, A B b^{3} d^{3} g^{3} + {\left(g^{3} n + 2 \, g^{3} \log\left(e\right)\right)} B^{2} b^{3} d^{3}\right)} x^{3} + 2 \, {\left(b^{3} c^{3} g^{3} n - 3 \, a b^{2} c^{2} d g^{3} n + 3 \, a^{2} b c d^{2} g^{3} n - {\left(g^{3} n - g^{3} \log\left(e\right)\right)} a^{3} d^{3}\right)} B^{2} + 3 \, {\left(2 \, A B a b^{2} d^{3} g^{3} - {\left(b^{3} c d^{2} g^{3} n - 2 \, {\left(g^{3} n + g^{3} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2}\right)} x^{2} + 2 \, {\left(3 \, A B a^{2} b d^{3} g^{3} - {\left(2 \, b^{3} c^{2} d g^{3} n - 3 \, a b^{2} c d^{2} g^{3} n - 3 \, a^{2} b d^{3} g^{3} \log\left(e\right)\right)} B^{2}\right)} x + 6 \, {\left({\left(b^{3} c^{2} d g^{3} n - 2 \, a b^{2} c d^{2} g^{3} n + a^{2} b d^{3} g^{3} n\right)} B^{2} x + {\left(b^{3} c^{3} g^{3} n - 2 \, a b^{2} c^{2} d g^{3} n + a^{2} b c d^{2} g^{3} n\right)} B^{2}\right)} \log\left(d x + c\right) + 2 \, {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{5} i^{2} x^{2} + 2 \, c d^{4} i^{2} x + c^{2} d^{3} i^{2}}\,{d x}"," ",0,"2*A*B*a^3*g^3*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) + 1/2*(2*c^3/(d^5*i^2*x + c*d^4*i^2) + 6*c^2*log(d*x + c)/(d^4*i^2) + (d*x^2 - 4*c*x)/(d^3*i^2))*A^2*b^3*g^3 - 3*A^2*a*b^2*(c^2/(d^4*i^2*x + c*d^3*i^2) - x/(d^2*i^2) + 2*c*log(d*x + c)/(d^3*i^2))*g^3 + 3*A^2*a^2*b*g^3*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - 2*A*B*a^3*g^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*i^2*x + c*d*i^2) - A^2*a^3*g^3/(d^2*i^2*x + c*d*i^2) + 1/2*(B^2*b^3*d^3*g^3*x^3 - 3*(b^3*c*d^2*g^3 - 2*a*b^2*d^3*g^3)*B^2*x^2 - 2*(2*b^3*c^2*d*g^3 - 3*a*b^2*c*d^2*g^3)*B^2*x + 2*(b^3*c^3*g^3 - 3*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 - a^3*d^3*g^3)*B^2 + 6*((b^3*c^2*d*g^3 - 2*a*b^2*c*d^2*g^3 + a^2*b*d^3*g^3)*B^2*x + (b^3*c^3*g^3 - 2*a*b^2*c^2*d*g^3 + a^2*b*c*d^2*g^3)*B^2)*log(d*x + c))*log((d*x + c)^n)^2/(d^5*i^2*x + c*d^4*i^2) - integrate(-(B^2*a^3*d^3*g^3*log(e)^2 + (B^2*b^3*d^3*g^3*log(e)^2 + 2*A*B*b^3*d^3*g^3*log(e))*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e)^2 + 2*A*B*a*b^2*d^3*g^3*log(e))*x^2 + (B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log((b*x + a)^n)^2 + 3*(B^2*a^2*b*d^3*g^3*log(e)^2 + 2*A*B*a^2*b*d^3*g^3*log(e))*x + 2*(B^2*a^3*d^3*g^3*log(e) + (B^2*b^3*d^3*g^3*log(e) + A*B*b^3*d^3*g^3)*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e) + A*B*a*b^2*d^3*g^3)*x^2 + 3*(B^2*a^2*b*d^3*g^3*log(e) + A*B*a^2*b*d^3*g^3)*x)*log((b*x + a)^n) - ((2*A*B*b^3*d^3*g^3 + (g^3*n + 2*g^3*log(e))*B^2*b^3*d^3)*x^3 + 2*(b^3*c^3*g^3*n - 3*a*b^2*c^2*d*g^3*n + 3*a^2*b*c*d^2*g^3*n - (g^3*n - g^3*log(e))*a^3*d^3)*B^2 + 3*(2*A*B*a*b^2*d^3*g^3 - (b^3*c*d^2*g^3*n - 2*(g^3*n + g^3*log(e))*a*b^2*d^3)*B^2)*x^2 + 2*(3*A*B*a^2*b*d^3*g^3 - (2*b^3*c^2*d*g^3*n - 3*a*b^2*c*d^2*g^3*n - 3*a^2*b*d^3*g^3*log(e))*B^2)*x + 6*((b^3*c^2*d*g^3*n - 2*a*b^2*c*d^2*g^3*n + a^2*b*d^3*g^3*n)*B^2*x + (b^3*c^3*g^3*n - 2*a*b^2*c^2*d*g^3*n + a^2*b*c*d^2*g^3*n)*B^2)*log(d*x + c) + 2*(B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log((b*x + a)^n))*log((d*x + c)^n))/(d^5*i^2*x^2 + 2*c*d^4*i^2*x + c^2*d^3*i^2), x)","F",0
195,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","2 \, A B a^{2} g^{2} n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} - A^{2} b^{2} {\left(\frac{c^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \frac{x}{d^{2} i^{2}} + \frac{2 \, c \log\left(d x + c\right)}{d^{3} i^{2}}\right)} g^{2} + 2 \, A^{2} a b g^{2} {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - \frac{2 \, A B a^{2} g^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{A^{2} a^{2} g^{2}}{d^{2} i^{2} x + c d i^{2}} + \frac{{\left(B^{2} b^{2} d^{2} g^{2} x^{2} + B^{2} b^{2} c d g^{2} x - {\left(b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} + a^{2} d^{2} g^{2}\right)} B^{2} - 2 \, {\left({\left(b^{2} c d g^{2} - a b d^{2} g^{2}\right)} B^{2} x + {\left(b^{2} c^{2} g^{2} - a b c d g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{d^{4} i^{2} x + c d^{3} i^{2}} - \int -\frac{B^{2} a^{2} d^{2} g^{2} \log\left(e\right)^{2} + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} g^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(B^{2} a b d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B a b d^{2} g^{2} \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a^{2} d^{2} g^{2} \log\left(e\right) + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right) + A B b^{2} d^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} a b d^{2} g^{2} \log\left(e\right) + A B a b d^{2} g^{2}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) + 2 \, {\left({\left(b^{2} c^{2} g^{2} n - 2 \, a b c d g^{2} n + {\left(g^{2} n - g^{2} \log\left(e\right)\right)} a^{2} d^{2}\right)} B^{2} - {\left(A B b^{2} d^{2} g^{2} + {\left(g^{2} n + g^{2} \log\left(e\right)\right)} B^{2} b^{2} d^{2}\right)} x^{2} - {\left(2 \, A B a b d^{2} g^{2} + {\left(b^{2} c d g^{2} n + 2 \, a b d^{2} g^{2} \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b^{2} c d g^{2} n - a b d^{2} g^{2} n\right)} B^{2} x + {\left(b^{2} c^{2} g^{2} n - a b c d g^{2} n\right)} B^{2}\right)} \log\left(d x + c\right) - {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{4} i^{2} x^{2} + 2 \, c d^{3} i^{2} x + c^{2} d^{2} i^{2}}\,{d x}"," ",0,"2*A*B*a^2*g^2*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) - A^2*b^2*(c^2/(d^4*i^2*x + c*d^3*i^2) - x/(d^2*i^2) + 2*c*log(d*x + c)/(d^3*i^2))*g^2 + 2*A^2*a*b*g^2*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - 2*A*B*a^2*g^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*i^2*x + c*d*i^2) - A^2*a^2*g^2/(d^2*i^2*x + c*d*i^2) + (B^2*b^2*d^2*g^2*x^2 + B^2*b^2*c*d*g^2*x - (b^2*c^2*g^2 - 2*a*b*c*d*g^2 + a^2*d^2*g^2)*B^2 - 2*((b^2*c*d*g^2 - a*b*d^2*g^2)*B^2*x + (b^2*c^2*g^2 - a*b*c*d*g^2)*B^2)*log(d*x + c))*log((d*x + c)^n)^2/(d^4*i^2*x + c*d^3*i^2) - integrate(-(B^2*a^2*d^2*g^2*log(e)^2 + (B^2*b^2*d^2*g^2*log(e)^2 + 2*A*B*b^2*d^2*g^2*log(e))*x^2 + (B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log((b*x + a)^n)^2 + 2*(B^2*a*b*d^2*g^2*log(e)^2 + 2*A*B*a*b*d^2*g^2*log(e))*x + 2*(B^2*a^2*d^2*g^2*log(e) + (B^2*b^2*d^2*g^2*log(e) + A*B*b^2*d^2*g^2)*x^2 + 2*(B^2*a*b*d^2*g^2*log(e) + A*B*a*b*d^2*g^2)*x)*log((b*x + a)^n) + 2*((b^2*c^2*g^2*n - 2*a*b*c*d*g^2*n + (g^2*n - g^2*log(e))*a^2*d^2)*B^2 - (A*B*b^2*d^2*g^2 + (g^2*n + g^2*log(e))*B^2*b^2*d^2)*x^2 - (2*A*B*a*b*d^2*g^2 + (b^2*c*d*g^2*n + 2*a*b*d^2*g^2*log(e))*B^2)*x + 2*((b^2*c*d*g^2*n - a*b*d^2*g^2*n)*B^2*x + (b^2*c^2*g^2*n - a*b*c*d*g^2*n)*B^2)*log(d*x + c) - (B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log((b*x + a)^n))*log((d*x + c)^n))/(d^4*i^2*x^2 + 2*c*d^3*i^2*x + c^2*d^2*i^2), x)","F",0
196,0,0,0,0.000000," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","2 \, A B a g n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} + A^{2} b g {\left(\frac{c}{d^{3} i^{2} x + c d^{2} i^{2}} + \frac{\log\left(d x + c\right)}{d^{2} i^{2}}\right)} - \frac{2 \, A B a g \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{A^{2} a g}{d^{2} i^{2} x + c d i^{2}} + \frac{{\left({\left(b c g - a d g\right)} B^{2} + {\left(B^{2} b d g x + B^{2} b c g\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{d^{3} i^{2} x + c d^{2} i^{2}} - \int -\frac{B^{2} a d g \log\left(e\right)^{2} + {\left(B^{2} b d g x + B^{2} a d g\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b d g \log\left(e\right)^{2} + 2 \, A B b d g \log\left(e\right)\right)} x + 2 \, {\left(B^{2} a d g \log\left(e\right) + {\left(B^{2} b d g \log\left(e\right) + A B b d g\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left({\left(b c g n - {\left(g n - g \log\left(e\right)\right)} a d\right)} B^{2} + {\left(B^{2} b d g \log\left(e\right) + A B b d g\right)} x + {\left(B^{2} b d g n x + B^{2} b c g n\right)} \log\left(d x + c\right) + {\left(B^{2} b d g x + B^{2} a d g\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{3} i^{2} x^{2} + 2 \, c d^{2} i^{2} x + c^{2} d i^{2}}\,{d x}"," ",0,"2*A*B*a*g*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) + A^2*b*g*(c/(d^3*i^2*x + c*d^2*i^2) + log(d*x + c)/(d^2*i^2)) - 2*A*B*a*g*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*i^2*x + c*d*i^2) - A^2*a*g/(d^2*i^2*x + c*d*i^2) + ((b*c*g - a*d*g)*B^2 + (B^2*b*d*g*x + B^2*b*c*g)*log(d*x + c))*log((d*x + c)^n)^2/(d^3*i^2*x + c*d^2*i^2) - integrate(-(B^2*a*d*g*log(e)^2 + (B^2*b*d*g*x + B^2*a*d*g)*log((b*x + a)^n)^2 + (B^2*b*d*g*log(e)^2 + 2*A*B*b*d*g*log(e))*x + 2*(B^2*a*d*g*log(e) + (B^2*b*d*g*log(e) + A*B*b*d*g)*x)*log((b*x + a)^n) - 2*((b*c*g*n - (g*n - g*log(e))*a*d)*B^2 + (B^2*b*d*g*log(e) + A*B*b*d*g)*x + (B^2*b*d*g*n*x + B^2*b*c*g*n)*log(d*x + c) + (B^2*b*d*g*x + B^2*a*d*g)*log((b*x + a)^n))*log((d*x + c)^n))/(d^3*i^2*x^2 + 2*c*d^2*i^2*x + c^2*d*i^2), x)","F",0
197,1,428,0,0.922419," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","2 \, A B n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} + {\left(2 \, n {\left(\frac{1}{d^{2} i^{2} x + c d i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left({\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} + 2 \, b c - 2 \, a d + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 2 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{b c^{2} d i^{2} - a c d^{2} i^{2} + {\left(b c d^{2} i^{2} - a d^{3} i^{2}\right)} x}\right)} B^{2} - \frac{B^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{d^{2} i^{2} x + c d i^{2}} - \frac{2 \, A B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} i^{2} x + c d i^{2}} - \frac{A^{2}}{d^{2} i^{2} x + c d i^{2}}"," ",0,"2*A*B*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2)) + (2*n*(1/(d^2*i^2*x + c*d*i^2) + b*log(b*x + a)/((b*c*d - a*d^2)*i^2) - b*log(d*x + c)/((b*c*d - a*d^2)*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - ((b*d*x + b*c)*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 + 2*b*c - 2*a*d + 2*(b*d*x + b*c)*log(b*x + a) - 2*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c))*n^2/(b*c^2*d*i^2 - a*c*d^2*i^2 + (b*c*d^2*i^2 - a*d^3*i^2)*x))*B^2 - B^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(d^2*i^2*x + c*d*i^2) - 2*A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*i^2*x + c*d*i^2) - A^2/(d^2*i^2*x + c*d*i^2)","B",0
198,1,1014,0,1.288907," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)/(d*i*x+c*i)^2,x, algorithm=""maxima"")","B^{2} {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} + 2 \, A B {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{3} \, {\left(\frac{{\left({\left(b d x + b c\right)} \log\left(b x + a\right)^{3} - {\left(b d x + b c\right)} \log\left(d x + c\right)^{3} + 3 \, {\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 6 \, b c - 6 \, a d + 6 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 3 \, {\left(2 \, b d x + {\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + 2 \, b c + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{b^{2} c^{3} g i^{2} - 2 \, a b c^{2} d g i^{2} + a^{2} c d^{2} g i^{2} + {\left(b^{2} c^{2} d g i^{2} - 2 \, a b c d^{2} g i^{2} + a^{2} d^{3} g i^{2}\right)} x} - \frac{3 \, {\left({\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} + 2 \, b c - 2 \, a d + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 2 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{2} c^{3} g i^{2} - 2 \, a b c^{2} d g i^{2} + a^{2} c d^{2} g i^{2} + {\left(b^{2} c^{2} d g i^{2} - 2 \, a b c d^{2} g i^{2} + a^{2} d^{3} g i^{2}\right)} x}\right)} B^{2} - \frac{{\left({\left(b d x + b c\right)} \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} + 2 \, b c - 2 \, a d + 2 \, {\left(b d x + b c\right)} \log\left(b x + a\right) - 2 \, {\left(b d x + b c + {\left(b d x + b c\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{b^{2} c^{3} g i^{2} - 2 \, a b c^{2} d g i^{2} + a^{2} c d^{2} g i^{2} + {\left(b^{2} c^{2} d g i^{2} - 2 \, a b c d^{2} g i^{2} + a^{2} d^{3} g i^{2}\right)} x} + A^{2} {\left(\frac{1}{{\left(b c d - a d^{2}\right)} g i^{2} x + {\left(b c^{2} - a c d\right)} g i^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} g i^{2}}\right)}"," ",0,"B^2*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 + 2*A*B*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*(((b*d*x + b*c)*log(b*x + a)^3 - (b*d*x + b*c)*log(d*x + c)^3 + 3*(b*d*x + b*c)*log(b*x + a)^2 + 3*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c)^2 + 6*b*c - 6*a*d + 6*(b*d*x + b*c)*log(b*x + a) - 3*(2*b*d*x + (b*d*x + b*c)*log(b*x + a)^2 + 2*b*c + 2*(b*d*x + b*c)*log(b*x + a))*log(d*x + c))*n^2/(b^2*c^3*g*i^2 - 2*a*b*c^2*d*g*i^2 + a^2*c*d^2*g*i^2 + (b^2*c^2*d*g*i^2 - 2*a*b*c*d^2*g*i^2 + a^2*d^3*g*i^2)*x) - 3*((b*d*x + b*c)*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 + 2*b*c - 2*a*d + 2*(b*d*x + b*c)*log(b*x + a) - 2*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*c^3*g*i^2 - 2*a*b*c^2*d*g*i^2 + a^2*c*d^2*g*i^2 + (b^2*c^2*d*g*i^2 - 2*a*b*c*d^2*g*i^2 + a^2*d^3*g*i^2)*x))*B^2 - ((b*d*x + b*c)*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 + 2*b*c - 2*a*d + 2*(b*d*x + b*c)*log(b*x + a) - 2*(b*d*x + b*c + (b*d*x + b*c)*log(b*x + a))*log(d*x + c))*A*B*n/(b^2*c^3*g*i^2 - 2*a*b*c^2*d*g*i^2 + a^2*c*d^2*g*i^2 + (b^2*c^2*d*g*i^2 - 2*a*b*c*d^2*g*i^2 + a^2*d^3*g*i^2)*x) + A^2*(1/((b*c*d - a*d^2)*g*i^2*x + (b*c^2 - a*c*d)*g*i^2) + b*log(b*x + a)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2) - b*log(d*x + c)/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*g*i^2))","B",0
199,1,2006,0,1.803194," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-B^{2} {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} - 2 \, A B {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{2}{3} \, {\left(\frac{{\left(3 \, b^{2} c^{2} - 3 \, a^{2} d^{2} + {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{3} + 3 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right)^{2} - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)^{3} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) - 3 \, {\left(2 \, b^{2} d^{2} x^{2} + 2 \, a b c d + {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)\right)} n^{2}}{a b^{3} c^{4} g^{2} i^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} i^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} i^{2} - a^{4} c d^{3} g^{2} i^{2} + {\left(b^{4} c^{3} d g^{2} i^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} i^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} i^{2} - a^{3} b d^{4} g^{2} i^{2}\right)} x^{2} + {\left(b^{4} c^{4} g^{2} i^{2} - 2 \, a b^{3} c^{3} d g^{2} i^{2} + 2 \, a^{3} b c d^{3} g^{2} i^{2} - a^{4} d^{4} g^{2} i^{2}\right)} x} + \frac{3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)^{2}\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a b^{3} c^{4} g^{2} i^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} i^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} i^{2} - a^{4} c d^{3} g^{2} i^{2} + {\left(b^{4} c^{3} d g^{2} i^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} i^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} i^{2} - a^{3} b d^{4} g^{2} i^{2}\right)} x^{2} + {\left(b^{4} c^{4} g^{2} i^{2} - 2 \, a b^{3} c^{3} d g^{2} i^{2} + 2 \, a^{3} b c d^{3} g^{2} i^{2} - a^{4} d^{4} g^{2} i^{2}\right)} x}\right)} B^{2} - \frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{2} d^{2} x^{2} + a b c d + {\left(b^{2} c d + a b d^{2}\right)} x\right)} \log\left(d x + c\right)^{2}\right)} A B n}{a b^{3} c^{4} g^{2} i^{2} - 3 \, a^{2} b^{2} c^{3} d g^{2} i^{2} + 3 \, a^{3} b c^{2} d^{2} g^{2} i^{2} - a^{4} c d^{3} g^{2} i^{2} + {\left(b^{4} c^{3} d g^{2} i^{2} - 3 \, a b^{3} c^{2} d^{2} g^{2} i^{2} + 3 \, a^{2} b^{2} c d^{3} g^{2} i^{2} - a^{3} b d^{4} g^{2} i^{2}\right)} x^{2} + {\left(b^{4} c^{4} g^{2} i^{2} - 2 \, a b^{3} c^{3} d g^{2} i^{2} + 2 \, a^{3} b c d^{3} g^{2} i^{2} - a^{4} d^{4} g^{2} i^{2}\right)} x} - A^{2} {\left(\frac{2 \, b d x + b c + a d}{{\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} g^{2} i^{2} x^{2} + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} g^{2} i^{2} x + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} g^{2} i^{2}} + \frac{2 \, b d \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}} - \frac{2 \, b d \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g^{2} i^{2}}\right)}"," ",0,"-B^2*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 - 2*A*B*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 2/3*((3*b^2*c^2 - 3*a^2*d^2 + (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^3 + 3*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)*log(d*x + c)^2 - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c)^3 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a) - 3*(2*b^2*d^2*x^2 + 2*a*b*c*d + (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^2 + 2*(b^2*c*d + a*b*d^2)*x)*log(d*x + c))*n^2/(a*b^3*c^4*g^2*i^2 - 3*a^2*b^2*c^3*d*g^2*i^2 + 3*a^3*b*c^2*d^2*g^2*i^2 - a^4*c*d^3*g^2*i^2 + (b^4*c^3*d*g^2*i^2 - 3*a*b^3*c^2*d^2*g^2*i^2 + 3*a^2*b^2*c*d^3*g^2*i^2 - a^3*b*d^4*g^2*i^2)*x^2 + (b^4*c^4*g^2*i^2 - 2*a*b^3*c^3*d*g^2*i^2 + 2*a^3*b*c*d^3*g^2*i^2 - a^4*d^4*g^2*i^2)*x) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)*log(d*x + c) - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c)^2)*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a*b^3*c^4*g^2*i^2 - 3*a^2*b^2*c^3*d*g^2*i^2 + 3*a^3*b*c^2*d^2*g^2*i^2 - a^4*c*d^3*g^2*i^2 + (b^4*c^3*d*g^2*i^2 - 3*a*b^3*c^2*d^2*g^2*i^2 + 3*a^2*b^2*c*d^3*g^2*i^2 - a^3*b*d^4*g^2*i^2)*x^2 + (b^4*c^4*g^2*i^2 - 2*a*b^3*c^3*d*g^2*i^2 + 2*a^3*b*c*d^3*g^2*i^2 - a^4*d^4*g^2*i^2)*x))*B^2 - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(b*x + a)*log(d*x + c) - (b^2*d^2*x^2 + a*b*c*d + (b^2*c*d + a*b*d^2)*x)*log(d*x + c)^2)*A*B*n/(a*b^3*c^4*g^2*i^2 - 3*a^2*b^2*c^3*d*g^2*i^2 + 3*a^3*b*c^2*d^2*g^2*i^2 - a^4*c*d^3*g^2*i^2 + (b^4*c^3*d*g^2*i^2 - 3*a*b^3*c^2*d^2*g^2*i^2 + 3*a^2*b^2*c*d^3*g^2*i^2 - a^3*b*d^4*g^2*i^2)*x^2 + (b^4*c^4*g^2*i^2 - 2*a*b^3*c^3*d*g^2*i^2 + 2*a^3*b*c*d^3*g^2*i^2 - a^4*d^4*g^2*i^2)*x) - A^2*((2*b*d*x + b*c + a*d)/((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*g^2*i^2*x^2 + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*g^2*i^2*x + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*g^2*i^2) + 2*b*d*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2) - 2*b*d*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g^2*i^2))","B",0
200,1,4198,0,4.813679," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3/(d*i*x+c*i)^2,x, algorithm=""maxima"")","\frac{1}{2} \, B^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} + A B {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{1}{4} \, {\left(\frac{{\left(b^{3} c^{3} - 24 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} + 8 \, a^{3} d^{3} - 4 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{3} + 4 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{3} - 30 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(7 \, b^{3} c^{2} d + 6 \, a b^{2} c d^{2} - 13 \, a^{2} b d^{3}\right)} x - 30 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(5 \, b^{3} d^{3} x^{3} + 5 \, a^{2} b c d^{2} + 5 \, {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 5 \, {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{2} b^{4} c^{5} g^{3} i^{2} - 4 \, a^{3} b^{3} c^{4} d g^{3} i^{2} + 6 \, a^{4} b^{2} c^{3} d^{2} g^{3} i^{2} - 4 \, a^{5} b c^{2} d^{3} g^{3} i^{2} + a^{6} c d^{4} g^{3} i^{2} + {\left(b^{6} c^{4} d g^{3} i^{2} - 4 \, a b^{5} c^{3} d^{2} g^{3} i^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} g^{3} i^{2} - 4 \, a^{3} b^{3} c d^{4} g^{3} i^{2} + a^{4} b^{2} d^{5} g^{3} i^{2}\right)} x^{3} + {\left(b^{6} c^{5} g^{3} i^{2} - 2 \, a b^{5} c^{4} d g^{3} i^{2} - 2 \, a^{2} b^{4} c^{3} d^{2} g^{3} i^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} g^{3} i^{2} - 7 \, a^{4} b^{2} c d^{4} g^{3} i^{2} + 2 \, a^{5} b d^{5} g^{3} i^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} g^{3} i^{2} - 7 \, a^{2} b^{4} c^{4} d g^{3} i^{2} + 8 \, a^{3} b^{3} c^{3} d^{2} g^{3} i^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} g^{3} i^{2} - 2 \, a^{5} b c d^{4} g^{3} i^{2} + a^{6} d^{5} g^{3} i^{2}\right)} x} + \frac{2 \, {\left(b^{3} c^{3} - 12 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a^{2} b^{4} c^{5} g^{3} i^{2} - 4 \, a^{3} b^{3} c^{4} d g^{3} i^{2} + 6 \, a^{4} b^{2} c^{3} d^{2} g^{3} i^{2} - 4 \, a^{5} b c^{2} d^{3} g^{3} i^{2} + a^{6} c d^{4} g^{3} i^{2} + {\left(b^{6} c^{4} d g^{3} i^{2} - 4 \, a b^{5} c^{3} d^{2} g^{3} i^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} g^{3} i^{2} - 4 \, a^{3} b^{3} c d^{4} g^{3} i^{2} + a^{4} b^{2} d^{5} g^{3} i^{2}\right)} x^{3} + {\left(b^{6} c^{5} g^{3} i^{2} - 2 \, a b^{5} c^{4} d g^{3} i^{2} - 2 \, a^{2} b^{4} c^{3} d^{2} g^{3} i^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} g^{3} i^{2} - 7 \, a^{4} b^{2} c d^{4} g^{3} i^{2} + 2 \, a^{5} b d^{5} g^{3} i^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} g^{3} i^{2} - 7 \, a^{2} b^{4} c^{4} d g^{3} i^{2} + 8 \, a^{3} b^{3} c^{3} d^{2} g^{3} i^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} g^{3} i^{2} - 2 \, a^{5} b c d^{4} g^{3} i^{2} + a^{6} d^{5} g^{3} i^{2}\right)} x}\right)} B^{2} - \frac{{\left(b^{3} c^{3} - 12 \, a b^{2} c^{2} d + 15 \, a^{2} b c d^{2} - 4 \, a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(3 \, b^{3} c^{2} d - 2 \, a b^{2} c d^{2} - a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x - 2 \, {\left(b^{3} d^{3} x^{3} + a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{2 \, {\left(a^{2} b^{4} c^{5} g^{3} i^{2} - 4 \, a^{3} b^{3} c^{4} d g^{3} i^{2} + 6 \, a^{4} b^{2} c^{3} d^{2} g^{3} i^{2} - 4 \, a^{5} b c^{2} d^{3} g^{3} i^{2} + a^{6} c d^{4} g^{3} i^{2} + {\left(b^{6} c^{4} d g^{3} i^{2} - 4 \, a b^{5} c^{3} d^{2} g^{3} i^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} g^{3} i^{2} - 4 \, a^{3} b^{3} c d^{4} g^{3} i^{2} + a^{4} b^{2} d^{5} g^{3} i^{2}\right)} x^{3} + {\left(b^{6} c^{5} g^{3} i^{2} - 2 \, a b^{5} c^{4} d g^{3} i^{2} - 2 \, a^{2} b^{4} c^{3} d^{2} g^{3} i^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} g^{3} i^{2} - 7 \, a^{4} b^{2} c d^{4} g^{3} i^{2} + 2 \, a^{5} b d^{5} g^{3} i^{2}\right)} x^{2} + {\left(2 \, a b^{5} c^{5} g^{3} i^{2} - 7 \, a^{2} b^{4} c^{4} d g^{3} i^{2} + 8 \, a^{3} b^{3} c^{3} d^{2} g^{3} i^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} g^{3} i^{2} - 2 \, a^{5} b c d^{4} g^{3} i^{2} + a^{6} d^{5} g^{3} i^{2}\right)} x\right)}} + \frac{1}{2} \, A^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} - b^{2} c^{2} + 5 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(b^{2} c d + 3 \, a b d^{2}\right)} x}{{\left(b^{5} c^{3} d - 3 \, a b^{4} c^{2} d^{2} + 3 \, a^{2} b^{3} c d^{3} - a^{3} b^{2} d^{4}\right)} g^{3} i^{2} x^{3} + {\left(b^{5} c^{4} - a b^{4} c^{3} d - 3 \, a^{2} b^{3} c^{2} d^{2} + 5 \, a^{3} b^{2} c d^{3} - 2 \, a^{4} b d^{4}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{4} c^{4} - 5 \, a^{2} b^{3} c^{3} d + 3 \, a^{3} b^{2} c^{2} d^{2} + a^{4} b c d^{3} - a^{5} d^{4}\right)} g^{3} i^{2} x + {\left(a^{2} b^{3} c^{4} - 3 \, a^{3} b^{2} c^{3} d + 3 \, a^{4} b c^{2} d^{2} - a^{5} c d^{3}\right)} g^{3} i^{2}} + \frac{6 \, b d^{2} \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}} - \frac{6 \, b d^{2} \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{3} i^{2}}\right)}"," ",0,"1/2*B^2*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 + A*B*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/4*((b^3*c^3 - 24*a*b^2*c^2*d + 15*a^2*b*c*d^2 + 8*a^3*d^3 - 4*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^3 + 4*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c)^3 - 30*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c)^2 - 3*(7*b^3*c^2*d + 6*a*b^2*c*d^2 - 13*a^2*b*d^3)*x - 30*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(5*b^3*d^3*x^3 + 5*a^2*b*c*d^2 + 5*(b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 5*(2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^2*b^4*c^5*g^3*i^2 - 4*a^3*b^3*c^4*d*g^3*i^2 + 6*a^4*b^2*c^3*d^2*g^3*i^2 - 4*a^5*b*c^2*d^3*g^3*i^2 + a^6*c*d^4*g^3*i^2 + (b^6*c^4*d*g^3*i^2 - 4*a*b^5*c^3*d^2*g^3*i^2 + 6*a^2*b^4*c^2*d^3*g^3*i^2 - 4*a^3*b^3*c*d^4*g^3*i^2 + a^4*b^2*d^5*g^3*i^2)*x^3 + (b^6*c^5*g^3*i^2 - 2*a*b^5*c^4*d*g^3*i^2 - 2*a^2*b^4*c^3*d^2*g^3*i^2 + 8*a^3*b^3*c^2*d^3*g^3*i^2 - 7*a^4*b^2*c*d^4*g^3*i^2 + 2*a^5*b*d^5*g^3*i^2)*x^2 + (2*a*b^5*c^5*g^3*i^2 - 7*a^2*b^4*c^4*d*g^3*i^2 + 8*a^3*b^3*c^3*d^2*g^3*i^2 - 2*a^4*b^2*c^2*d^3*g^3*i^2 - 2*a^5*b*c*d^4*g^3*i^2 + a^6*d^5*g^3*i^2)*x) + 2*(b^3*c^3 - 12*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c)^2 - 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a^2*b^4*c^5*g^3*i^2 - 4*a^3*b^3*c^4*d*g^3*i^2 + 6*a^4*b^2*c^3*d^2*g^3*i^2 - 4*a^5*b*c^2*d^3*g^3*i^2 + a^6*c*d^4*g^3*i^2 + (b^6*c^4*d*g^3*i^2 - 4*a*b^5*c^3*d^2*g^3*i^2 + 6*a^2*b^4*c^2*d^3*g^3*i^2 - 4*a^3*b^3*c*d^4*g^3*i^2 + a^4*b^2*d^5*g^3*i^2)*x^3 + (b^6*c^5*g^3*i^2 - 2*a*b^5*c^4*d*g^3*i^2 - 2*a^2*b^4*c^3*d^2*g^3*i^2 + 8*a^3*b^3*c^2*d^3*g^3*i^2 - 7*a^4*b^2*c*d^4*g^3*i^2 + 2*a^5*b*d^5*g^3*i^2)*x^2 + (2*a*b^5*c^5*g^3*i^2 - 7*a^2*b^4*c^4*d*g^3*i^2 + 8*a^3*b^3*c^3*d^2*g^3*i^2 - 2*a^4*b^2*c^2*d^3*g^3*i^2 - 2*a^5*b*c*d^4*g^3*i^2 + a^6*d^5*g^3*i^2)*x))*B^2 - 1/2*(b^3*c^3 - 12*a*b^2*c^2*d + 15*a^2*b*c*d^2 - 4*a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(d*x + c)^2 - 3*(3*b^3*c^2*d - 2*a*b^2*c*d^2 - a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x - 2*(b^3*d^3*x^3 + a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*x)*log(b*x + a))*log(d*x + c))*A*B*n/(a^2*b^4*c^5*g^3*i^2 - 4*a^3*b^3*c^4*d*g^3*i^2 + 6*a^4*b^2*c^3*d^2*g^3*i^2 - 4*a^5*b*c^2*d^3*g^3*i^2 + a^6*c*d^4*g^3*i^2 + (b^6*c^4*d*g^3*i^2 - 4*a*b^5*c^3*d^2*g^3*i^2 + 6*a^2*b^4*c^2*d^3*g^3*i^2 - 4*a^3*b^3*c*d^4*g^3*i^2 + a^4*b^2*d^5*g^3*i^2)*x^3 + (b^6*c^5*g^3*i^2 - 2*a*b^5*c^4*d*g^3*i^2 - 2*a^2*b^4*c^3*d^2*g^3*i^2 + 8*a^3*b^3*c^2*d^3*g^3*i^2 - 7*a^4*b^2*c*d^4*g^3*i^2 + 2*a^5*b*d^5*g^3*i^2)*x^2 + (2*a*b^5*c^5*g^3*i^2 - 7*a^2*b^4*c^4*d*g^3*i^2 + 8*a^3*b^3*c^3*d^2*g^3*i^2 - 2*a^4*b^2*c^2*d^3*g^3*i^2 - 2*a^5*b*c*d^4*g^3*i^2 + a^6*d^5*g^3*i^2)*x) + 1/2*A^2*((6*b^2*d^2*x^2 - b^2*c^2 + 5*a*b*c*d + 2*a^2*d^2 + 3*(b^2*c*d + 3*a*b*d^2)*x)/((b^5*c^3*d - 3*a*b^4*c^2*d^2 + 3*a^2*b^3*c*d^3 - a^3*b^2*d^4)*g^3*i^2*x^3 + (b^5*c^4 - a*b^4*c^3*d - 3*a^2*b^3*c^2*d^2 + 5*a^3*b^2*c*d^3 - 2*a^4*b*d^4)*g^3*i^2*x^2 + (2*a*b^4*c^4 - 5*a^2*b^3*c^3*d + 3*a^3*b^2*c^2*d^2 + a^4*b*c*d^3 - a^5*d^4)*g^3*i^2*x + (a^2*b^3*c^4 - 3*a^3*b^2*c^3*d + 3*a^4*b*c^2*d^2 - a^5*c*d^3)*g^3*i^2) + 6*b*d^2*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2) - 6*b*d^2*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^3*i^2))","B",0
201,1,6171,0,7.494569," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4/(d*i*x+c*i)^2,x, algorithm=""maxima"")","-\frac{1}{3} \, B^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} - \frac{2}{3} \, A B {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{1}{27} \, {\left(\frac{{\left(2 \, b^{4} c^{4} - 27 \, a b^{3} c^{3} d + 324 \, a^{2} b^{2} c^{2} d^{2} - 245 \, a^{3} b c d^{3} - 54 \, a^{4} d^{4} + 330 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 36 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{3} - 36 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{3} + 15 \, {\left(17 \, b^{4} c^{2} d^{2} + 32 \, a b^{3} c d^{3} - 49 \, a^{2} b^{2} d^{4}\right)} x^{2} - 90 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{3} b c d^{3} + 5 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 15 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 6 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - {\left(19 \, b^{4} c^{3} d - 567 \, a b^{3} c^{2} d^{2} + 87 \, a^{2} b^{2} c d^{3} + 461 \, a^{3} b d^{4}\right)} x + 330 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(55 \, b^{4} d^{4} x^{4} + 55 \, a^{3} b c d^{3} + 55 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 165 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} + 55 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 30 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{3} b^{5} c^{6} g^{4} i^{2} - 5 \, a^{4} b^{4} c^{5} d g^{4} i^{2} + 10 \, a^{5} b^{3} c^{4} d^{2} g^{4} i^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{7} b c^{2} d^{4} g^{4} i^{2} - a^{8} c d^{5} g^{4} i^{2} + {\left(b^{8} c^{5} d g^{4} i^{2} - 5 \, a b^{7} c^{4} d^{2} g^{4} i^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} g^{4} i^{2} - 10 \, a^{3} b^{5} c^{2} d^{4} g^{4} i^{2} + 5 \, a^{4} b^{4} c d^{5} g^{4} i^{2} - a^{5} b^{3} d^{6} g^{4} i^{2}\right)} x^{4} + {\left(b^{8} c^{6} g^{4} i^{2} - 2 \, a b^{7} c^{5} d g^{4} i^{2} - 5 \, a^{2} b^{6} c^{4} d^{2} g^{4} i^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} g^{4} i^{2} - 25 \, a^{4} b^{4} c^{2} d^{4} g^{4} i^{2} + 14 \, a^{5} b^{3} c d^{5} g^{4} i^{2} - 3 \, a^{6} b^{2} d^{6} g^{4} i^{2}\right)} x^{3} + 3 \, {\left(a b^{7} c^{6} g^{4} i^{2} - 4 \, a^{2} b^{6} c^{5} d g^{4} i^{2} + 5 \, a^{3} b^{5} c^{4} d^{2} g^{4} i^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} g^{4} i^{2} + 4 \, a^{6} b^{2} c d^{5} g^{4} i^{2} - a^{7} b d^{6} g^{4} i^{2}\right)} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} g^{4} i^{2} - 14 \, a^{3} b^{5} c^{5} d g^{4} i^{2} + 25 \, a^{4} b^{4} c^{4} d^{2} g^{4} i^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{6} b^{2} c^{2} d^{4} g^{4} i^{2} + 2 \, a^{7} b c d^{5} g^{4} i^{2} - a^{8} d^{6} g^{4} i^{2}\right)} x} + \frac{6 \, {\left(b^{4} c^{4} - 9 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} - 55 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4} + 30 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(11 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} - 19 \, a^{2} b^{2} d^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - {\left(5 \, b^{4} c^{3} d - 81 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} + 19 \, a^{3} b d^{4}\right)} x + 30 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{3} b c d^{3} + 5 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 15 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 6 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a^{3} b^{5} c^{6} g^{4} i^{2} - 5 \, a^{4} b^{4} c^{5} d g^{4} i^{2} + 10 \, a^{5} b^{3} c^{4} d^{2} g^{4} i^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{7} b c^{2} d^{4} g^{4} i^{2} - a^{8} c d^{5} g^{4} i^{2} + {\left(b^{8} c^{5} d g^{4} i^{2} - 5 \, a b^{7} c^{4} d^{2} g^{4} i^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} g^{4} i^{2} - 10 \, a^{3} b^{5} c^{2} d^{4} g^{4} i^{2} + 5 \, a^{4} b^{4} c d^{5} g^{4} i^{2} - a^{5} b^{3} d^{6} g^{4} i^{2}\right)} x^{4} + {\left(b^{8} c^{6} g^{4} i^{2} - 2 \, a b^{7} c^{5} d g^{4} i^{2} - 5 \, a^{2} b^{6} c^{4} d^{2} g^{4} i^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} g^{4} i^{2} - 25 \, a^{4} b^{4} c^{2} d^{4} g^{4} i^{2} + 14 \, a^{5} b^{3} c d^{5} g^{4} i^{2} - 3 \, a^{6} b^{2} d^{6} g^{4} i^{2}\right)} x^{3} + 3 \, {\left(a b^{7} c^{6} g^{4} i^{2} - 4 \, a^{2} b^{6} c^{5} d g^{4} i^{2} + 5 \, a^{3} b^{5} c^{4} d^{2} g^{4} i^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} g^{4} i^{2} + 4 \, a^{6} b^{2} c d^{5} g^{4} i^{2} - a^{7} b d^{6} g^{4} i^{2}\right)} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} g^{4} i^{2} - 14 \, a^{3} b^{5} c^{5} d g^{4} i^{2} + 25 \, a^{4} b^{4} c^{4} d^{2} g^{4} i^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{6} b^{2} c^{2} d^{4} g^{4} i^{2} + 2 \, a^{7} b c d^{5} g^{4} i^{2} - a^{8} d^{6} g^{4} i^{2}\right)} x}\right)} B^{2} - \frac{2 \, {\left(b^{4} c^{4} - 9 \, a b^{3} c^{3} d + 54 \, a^{2} b^{2} c^{2} d^{2} - 55 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4} + 30 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(11 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} - 19 \, a^{2} b^{2} d^{4}\right)} x^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - {\left(5 \, b^{4} c^{3} d - 81 \, a b^{3} c^{2} d^{2} + 57 \, a^{2} b^{2} c d^{3} + 19 \, a^{3} b d^{4}\right)} x + 30 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{3} b c d^{3} + 5 \, {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 15 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 5 \, {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x - 6 \, {\left(b^{4} d^{4} x^{4} + a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{9 \, {\left(a^{3} b^{5} c^{6} g^{4} i^{2} - 5 \, a^{4} b^{4} c^{5} d g^{4} i^{2} + 10 \, a^{5} b^{3} c^{4} d^{2} g^{4} i^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{7} b c^{2} d^{4} g^{4} i^{2} - a^{8} c d^{5} g^{4} i^{2} + {\left(b^{8} c^{5} d g^{4} i^{2} - 5 \, a b^{7} c^{4} d^{2} g^{4} i^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} g^{4} i^{2} - 10 \, a^{3} b^{5} c^{2} d^{4} g^{4} i^{2} + 5 \, a^{4} b^{4} c d^{5} g^{4} i^{2} - a^{5} b^{3} d^{6} g^{4} i^{2}\right)} x^{4} + {\left(b^{8} c^{6} g^{4} i^{2} - 2 \, a b^{7} c^{5} d g^{4} i^{2} - 5 \, a^{2} b^{6} c^{4} d^{2} g^{4} i^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} g^{4} i^{2} - 25 \, a^{4} b^{4} c^{2} d^{4} g^{4} i^{2} + 14 \, a^{5} b^{3} c d^{5} g^{4} i^{2} - 3 \, a^{6} b^{2} d^{6} g^{4} i^{2}\right)} x^{3} + 3 \, {\left(a b^{7} c^{6} g^{4} i^{2} - 4 \, a^{2} b^{6} c^{5} d g^{4} i^{2} + 5 \, a^{3} b^{5} c^{4} d^{2} g^{4} i^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} g^{4} i^{2} + 4 \, a^{6} b^{2} c d^{5} g^{4} i^{2} - a^{7} b d^{6} g^{4} i^{2}\right)} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} g^{4} i^{2} - 14 \, a^{3} b^{5} c^{5} d g^{4} i^{2} + 25 \, a^{4} b^{4} c^{4} d^{2} g^{4} i^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} g^{4} i^{2} + 5 \, a^{6} b^{2} c^{2} d^{4} g^{4} i^{2} + 2 \, a^{7} b c d^{5} g^{4} i^{2} - a^{8} d^{6} g^{4} i^{2}\right)} x\right)}} - \frac{1}{3} \, A^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} + b^{3} c^{3} - 5 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3} + 6 \, {\left(b^{3} c d^{2} + 5 \, a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(b^{3} c^{2} d - 8 \, a b^{2} c d^{2} - 11 \, a^{2} b d^{3}\right)} x}{{\left(b^{7} c^{4} d - 4 \, a b^{6} c^{3} d^{2} + 6 \, a^{2} b^{5} c^{2} d^{3} - 4 \, a^{3} b^{4} c d^{4} + a^{4} b^{3} d^{5}\right)} g^{4} i^{2} x^{4} + {\left(b^{7} c^{5} - a b^{6} c^{4} d - 6 \, a^{2} b^{5} c^{3} d^{2} + 14 \, a^{3} b^{4} c^{2} d^{3} - 11 \, a^{4} b^{3} c d^{4} + 3 \, a^{5} b^{2} d^{5}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{6} c^{5} - 3 \, a^{2} b^{5} c^{4} d + 2 \, a^{3} b^{4} c^{3} d^{2} + 2 \, a^{4} b^{3} c^{2} d^{3} - 3 \, a^{5} b^{2} c d^{4} + a^{6} b d^{5}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{5} c^{5} - 11 \, a^{3} b^{4} c^{4} d + 14 \, a^{4} b^{3} c^{3} d^{2} - 6 \, a^{5} b^{2} c^{2} d^{3} - a^{6} b c d^{4} + a^{7} d^{5}\right)} g^{4} i^{2} x + {\left(a^{3} b^{4} c^{5} - 4 \, a^{4} b^{3} c^{4} d + 6 \, a^{5} b^{2} c^{3} d^{2} - 4 \, a^{6} b c^{2} d^{3} + a^{7} c d^{4}\right)} g^{4} i^{2}} + \frac{12 \, b d^{3} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}} - \frac{12 \, b d^{3} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{4} i^{2}}\right)}"," ",0,"-1/3*B^2*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 - 2/3*A*B*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/27*((2*b^4*c^4 - 27*a*b^3*c^3*d + 324*a^2*b^2*c^2*d^2 - 245*a^3*b*c*d^3 - 54*a^4*d^4 + 330*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 36*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^3 - 36*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(d*x + c)^3 + 15*(17*b^4*c^2*d^2 + 32*a*b^3*c*d^3 - 49*a^2*b^2*d^4)*x^2 - 90*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 - 18*(5*b^4*d^4*x^4 + 5*a^3*b*c*d^3 + 5*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 15*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 5*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 6*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c)^2 - (19*b^4*c^3*d - 567*a*b^3*c^2*d^2 + 87*a^2*b^2*c*d^3 + 461*a^3*b*d^4)*x + 330*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a) - 6*(55*b^4*d^4*x^4 + 55*a^3*b*c*d^3 + 55*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 165*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 + 55*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 30*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^3*b^5*c^6*g^4*i^2 - 5*a^4*b^4*c^5*d*g^4*i^2 + 10*a^5*b^3*c^4*d^2*g^4*i^2 - 10*a^6*b^2*c^3*d^3*g^4*i^2 + 5*a^7*b*c^2*d^4*g^4*i^2 - a^8*c*d^5*g^4*i^2 + (b^8*c^5*d*g^4*i^2 - 5*a*b^7*c^4*d^2*g^4*i^2 + 10*a^2*b^6*c^3*d^3*g^4*i^2 - 10*a^3*b^5*c^2*d^4*g^4*i^2 + 5*a^4*b^4*c*d^5*g^4*i^2 - a^5*b^3*d^6*g^4*i^2)*x^4 + (b^8*c^6*g^4*i^2 - 2*a*b^7*c^5*d*g^4*i^2 - 5*a^2*b^6*c^4*d^2*g^4*i^2 + 20*a^3*b^5*c^3*d^3*g^4*i^2 - 25*a^4*b^4*c^2*d^4*g^4*i^2 + 14*a^5*b^3*c*d^5*g^4*i^2 - 3*a^6*b^2*d^6*g^4*i^2)*x^3 + 3*(a*b^7*c^6*g^4*i^2 - 4*a^2*b^6*c^5*d*g^4*i^2 + 5*a^3*b^5*c^4*d^2*g^4*i^2 - 5*a^5*b^3*c^2*d^4*g^4*i^2 + 4*a^6*b^2*c*d^5*g^4*i^2 - a^7*b*d^6*g^4*i^2)*x^2 + (3*a^2*b^6*c^6*g^4*i^2 - 14*a^3*b^5*c^5*d*g^4*i^2 + 25*a^4*b^4*c^4*d^2*g^4*i^2 - 20*a^5*b^3*c^3*d^3*g^4*i^2 + 5*a^6*b^2*c^2*d^4*g^4*i^2 + 2*a^7*b*c*d^5*g^4*i^2 - a^8*d^6*g^4*i^2)*x) + 6*(b^4*c^4 - 9*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 - 55*a^3*b*c*d^3 + 9*a^4*d^4 + 30*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 3*(11*b^4*c^2*d^2 + 8*a*b^3*c*d^3 - 19*a^2*b^2*d^4)*x^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(d*x + c)^2 - (5*b^4*c^3*d - 81*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 + 19*a^3*b*d^4)*x + 30*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a) - 6*(5*b^4*d^4*x^4 + 5*a^3*b*c*d^3 + 5*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 15*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 5*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 6*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a^3*b^5*c^6*g^4*i^2 - 5*a^4*b^4*c^5*d*g^4*i^2 + 10*a^5*b^3*c^4*d^2*g^4*i^2 - 10*a^6*b^2*c^3*d^3*g^4*i^2 + 5*a^7*b*c^2*d^4*g^4*i^2 - a^8*c*d^5*g^4*i^2 + (b^8*c^5*d*g^4*i^2 - 5*a*b^7*c^4*d^2*g^4*i^2 + 10*a^2*b^6*c^3*d^3*g^4*i^2 - 10*a^3*b^5*c^2*d^4*g^4*i^2 + 5*a^4*b^4*c*d^5*g^4*i^2 - a^5*b^3*d^6*g^4*i^2)*x^4 + (b^8*c^6*g^4*i^2 - 2*a*b^7*c^5*d*g^4*i^2 - 5*a^2*b^6*c^4*d^2*g^4*i^2 + 20*a^3*b^5*c^3*d^3*g^4*i^2 - 25*a^4*b^4*c^2*d^4*g^4*i^2 + 14*a^5*b^3*c*d^5*g^4*i^2 - 3*a^6*b^2*d^6*g^4*i^2)*x^3 + 3*(a*b^7*c^6*g^4*i^2 - 4*a^2*b^6*c^5*d*g^4*i^2 + 5*a^3*b^5*c^4*d^2*g^4*i^2 - 5*a^5*b^3*c^2*d^4*g^4*i^2 + 4*a^6*b^2*c*d^5*g^4*i^2 - a^7*b*d^6*g^4*i^2)*x^2 + (3*a^2*b^6*c^6*g^4*i^2 - 14*a^3*b^5*c^5*d*g^4*i^2 + 25*a^4*b^4*c^4*d^2*g^4*i^2 - 20*a^5*b^3*c^3*d^3*g^4*i^2 + 5*a^6*b^2*c^2*d^4*g^4*i^2 + 2*a^7*b*c*d^5*g^4*i^2 - a^8*d^6*g^4*i^2)*x))*B^2 - 2/9*(b^4*c^4 - 9*a*b^3*c^3*d + 54*a^2*b^2*c^2*d^2 - 55*a^3*b*c*d^3 + 9*a^4*d^4 + 30*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 3*(11*b^4*c^2*d^2 + 8*a*b^3*c*d^3 - 19*a^2*b^2*d^4)*x^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a)^2 - 18*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(d*x + c)^2 - (5*b^4*c^3*d - 81*a*b^3*c^2*d^2 + 57*a^2*b^2*c*d^3 + 19*a^3*b*d^4)*x + 30*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a) - 6*(5*b^4*d^4*x^4 + 5*a^3*b*c*d^3 + 5*(b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 15*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 5*(3*a^2*b^2*c*d^3 + a^3*b*d^4)*x - 6*(b^4*d^4*x^4 + a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*x)*log(b*x + a))*log(d*x + c))*A*B*n/(a^3*b^5*c^6*g^4*i^2 - 5*a^4*b^4*c^5*d*g^4*i^2 + 10*a^5*b^3*c^4*d^2*g^4*i^2 - 10*a^6*b^2*c^3*d^3*g^4*i^2 + 5*a^7*b*c^2*d^4*g^4*i^2 - a^8*c*d^5*g^4*i^2 + (b^8*c^5*d*g^4*i^2 - 5*a*b^7*c^4*d^2*g^4*i^2 + 10*a^2*b^6*c^3*d^3*g^4*i^2 - 10*a^3*b^5*c^2*d^4*g^4*i^2 + 5*a^4*b^4*c*d^5*g^4*i^2 - a^5*b^3*d^6*g^4*i^2)*x^4 + (b^8*c^6*g^4*i^2 - 2*a*b^7*c^5*d*g^4*i^2 - 5*a^2*b^6*c^4*d^2*g^4*i^2 + 20*a^3*b^5*c^3*d^3*g^4*i^2 - 25*a^4*b^4*c^2*d^4*g^4*i^2 + 14*a^5*b^3*c*d^5*g^4*i^2 - 3*a^6*b^2*d^6*g^4*i^2)*x^3 + 3*(a*b^7*c^6*g^4*i^2 - 4*a^2*b^6*c^5*d*g^4*i^2 + 5*a^3*b^5*c^4*d^2*g^4*i^2 - 5*a^5*b^3*c^2*d^4*g^4*i^2 + 4*a^6*b^2*c*d^5*g^4*i^2 - a^7*b*d^6*g^4*i^2)*x^2 + (3*a^2*b^6*c^6*g^4*i^2 - 14*a^3*b^5*c^5*d*g^4*i^2 + 25*a^4*b^4*c^4*d^2*g^4*i^2 - 20*a^5*b^3*c^3*d^3*g^4*i^2 + 5*a^6*b^2*c^2*d^4*g^4*i^2 + 2*a^7*b*c*d^5*g^4*i^2 - a^8*d^6*g^4*i^2)*x) - 1/3*A^2*((12*b^3*d^3*x^3 + b^3*c^3 - 5*a*b^2*c^2*d + 13*a^2*b*c*d^2 + 3*a^3*d^3 + 6*(b^3*c*d^2 + 5*a*b^2*d^3)*x^2 - 2*(b^3*c^2*d - 8*a*b^2*c*d^2 - 11*a^2*b*d^3)*x)/((b^7*c^4*d - 4*a*b^6*c^3*d^2 + 6*a^2*b^5*c^2*d^3 - 4*a^3*b^4*c*d^4 + a^4*b^3*d^5)*g^4*i^2*x^4 + (b^7*c^5 - a*b^6*c^4*d - 6*a^2*b^5*c^3*d^2 + 14*a^3*b^4*c^2*d^3 - 11*a^4*b^3*c*d^4 + 3*a^5*b^2*d^5)*g^4*i^2*x^3 + 3*(a*b^6*c^5 - 3*a^2*b^5*c^4*d + 2*a^3*b^4*c^3*d^2 + 2*a^4*b^3*c^2*d^3 - 3*a^5*b^2*c*d^4 + a^6*b*d^5)*g^4*i^2*x^2 + (3*a^2*b^5*c^5 - 11*a^3*b^4*c^4*d + 14*a^4*b^3*c^3*d^2 - 6*a^5*b^2*c^2*d^3 - a^6*b*c*d^4 + a^7*d^5)*g^4*i^2*x + (a^3*b^4*c^5 - 4*a^4*b^3*c^4*d + 6*a^5*b^2*c^3*d^2 - 4*a^6*b*c^2*d^3 + a^7*c*d^4)*g^4*i^2) + 12*b*d^3*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2) - 12*b*d^3*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^4*i^2))","B",0
202,0,0,0,0.000000," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{3}{2} \, A B a^{2} b g^{3} n {\left(\frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{2} \, A B a^{3} g^{3} n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{1}{2} \, A^{2} b^{3} g^{3} {\left(\frac{6 \, c^{2} d x + 5 \, c^{3}}{d^{6} i^{3} x^{2} + 2 \, c d^{5} i^{3} x + c^{2} d^{4} i^{3}} - \frac{2 \, x}{d^{3} i^{3}} + \frac{6 \, c \log\left(d x + c\right)}{d^{4} i^{3}}\right)} + \frac{3}{2} \, A^{2} a b^{2} g^{3} {\left(\frac{4 \, c d x + 3 \, c^{2}}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} + \frac{2 \, \log\left(d x + c\right)}{d^{3} i^{3}}\right)} - \frac{3 \, {\left(2 \, d x + c\right)} A B a^{2} b g^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{3 \, {\left(2 \, d x + c\right)} A^{2} a^{2} b g^{3}}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{A B a^{3} g^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} - \frac{A^{2} a^{3} g^{3}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} + \frac{{\left(2 \, B^{2} b^{3} d^{3} g^{3} x^{3} + 4 \, B^{2} b^{3} c d^{2} g^{3} x^{2} - 2 \, {\left(2 \, b^{3} c^{2} d g^{3} - 6 \, a b^{2} c d^{2} g^{3} + 3 \, a^{2} b d^{3} g^{3}\right)} B^{2} x - {\left(5 \, b^{3} c^{3} g^{3} - 9 \, a b^{2} c^{2} d g^{3} + 3 \, a^{2} b c d^{2} g^{3} + a^{3} d^{3} g^{3}\right)} B^{2} - 6 \, {\left({\left(b^{3} c d^{2} g^{3} - a b^{2} d^{3} g^{3}\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{2} d g^{3} - a b^{2} c d^{2} g^{3}\right)} B^{2} x + {\left(b^{3} c^{3} g^{3} - a b^{2} c^{2} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, {\left(d^{6} i^{3} x^{2} + 2 \, c d^{5} i^{3} x + c^{2} d^{4} i^{3}\right)}} - \int -\frac{3 \, B^{2} a^{2} b d^{3} g^{3} x \log\left(e\right)^{2} + B^{2} a^{3} d^{3} g^{3} \log\left(e\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B b^{3} d^{3} g^{3} \log\left(e\right)\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right)^{2} + 2 \, A B a b^{2} d^{3} g^{3} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(3 \, B^{2} a^{2} b d^{3} g^{3} x \log\left(e\right) + B^{2} a^{3} d^{3} g^{3} \log\left(e\right) + {\left(B^{2} b^{3} d^{3} g^{3} \log\left(e\right) + A B b^{3} d^{3} g^{3}\right)} x^{3} + 3 \, {\left(B^{2} a b^{2} d^{3} g^{3} \log\left(e\right) + A B a b^{2} d^{3} g^{3}\right)} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) + {\left(2 \, {\left(2 \, b^{3} c^{2} d g^{3} n - 6 \, a b^{2} c d^{2} g^{3} n + 3 \, {\left(g^{3} n - g^{3} \log\left(e\right)\right)} a^{2} b d^{3}\right)} B^{2} x - 2 \, {\left(A B b^{3} d^{3} g^{3} + {\left(g^{3} n + g^{3} \log\left(e\right)\right)} B^{2} b^{3} d^{3}\right)} x^{3} + {\left(5 \, b^{3} c^{3} g^{3} n - 9 \, a b^{2} c^{2} d g^{3} n + 3 \, a^{2} b c d^{2} g^{3} n + {\left(g^{3} n - 2 \, g^{3} \log\left(e\right)\right)} a^{3} d^{3}\right)} B^{2} - 2 \, {\left(3 \, A B a b^{2} d^{3} g^{3} + {\left(2 \, b^{3} c d^{2} g^{3} n + 3 \, a b^{2} d^{3} g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 6 \, {\left({\left(b^{3} c d^{2} g^{3} n - a b^{2} d^{3} g^{3} n\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{2} d g^{3} n - a b^{2} c d^{2} g^{3} n\right)} B^{2} x + {\left(b^{3} c^{3} g^{3} n - a b^{2} c^{2} d g^{3} n\right)} B^{2}\right)} \log\left(d x + c\right) - 2 \, {\left(B^{2} b^{3} d^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{3} x + B^{2} a^{3} d^{3} g^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{6} i^{3} x^{3} + 3 \, c d^{5} i^{3} x^{2} + 3 \, c^{2} d^{4} i^{3} x + c^{3} d^{3} i^{3}}\,{d x}"," ",0,"3/2*A*B*a^2*b*g^3*n*((b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) + 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) - 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/2*A*B*a^3*g^3*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*A^2*b^3*g^3*((6*c^2*d*x + 5*c^3)/(d^6*i^3*x^2 + 2*c*d^5*i^3*x + c^2*d^4*i^3) - 2*x/(d^3*i^3) + 6*c*log(d*x + c)/(d^4*i^3)) + 3/2*A^2*a*b^2*g^3*((4*c*d*x + 3*c^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) + 2*log(d*x + c)/(d^3*i^3)) - 3*(2*d*x + c)*A*B*a^2*b*g^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 3/2*(2*d*x + c)*A^2*a^2*b*g^3/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - A*B*a^3*g^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A^2*a^3*g^3/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 1/2*(2*B^2*b^3*d^3*g^3*x^3 + 4*B^2*b^3*c*d^2*g^3*x^2 - 2*(2*b^3*c^2*d*g^3 - 6*a*b^2*c*d^2*g^3 + 3*a^2*b*d^3*g^3)*B^2*x - (5*b^3*c^3*g^3 - 9*a*b^2*c^2*d*g^3 + 3*a^2*b*c*d^2*g^3 + a^3*d^3*g^3)*B^2 - 6*((b^3*c*d^2*g^3 - a*b^2*d^3*g^3)*B^2*x^2 + 2*(b^3*c^2*d*g^3 - a*b^2*c*d^2*g^3)*B^2*x + (b^3*c^3*g^3 - a*b^2*c^2*d*g^3)*B^2)*log(d*x + c))*log((d*x + c)^n)^2/(d^6*i^3*x^2 + 2*c*d^5*i^3*x + c^2*d^4*i^3) - integrate(-(3*B^2*a^2*b*d^3*g^3*x*log(e)^2 + B^2*a^3*d^3*g^3*log(e)^2 + (B^2*b^3*d^3*g^3*log(e)^2 + 2*A*B*b^3*d^3*g^3*log(e))*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e)^2 + 2*A*B*a*b^2*d^3*g^3*log(e))*x^2 + (B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log((b*x + a)^n)^2 + 2*(3*B^2*a^2*b*d^3*g^3*x*log(e) + B^2*a^3*d^3*g^3*log(e) + (B^2*b^3*d^3*g^3*log(e) + A*B*b^3*d^3*g^3)*x^3 + 3*(B^2*a*b^2*d^3*g^3*log(e) + A*B*a*b^2*d^3*g^3)*x^2)*log((b*x + a)^n) + (2*(2*b^3*c^2*d*g^3*n - 6*a*b^2*c*d^2*g^3*n + 3*(g^3*n - g^3*log(e))*a^2*b*d^3)*B^2*x - 2*(A*B*b^3*d^3*g^3 + (g^3*n + g^3*log(e))*B^2*b^3*d^3)*x^3 + (5*b^3*c^3*g^3*n - 9*a*b^2*c^2*d*g^3*n + 3*a^2*b*c*d^2*g^3*n + (g^3*n - 2*g^3*log(e))*a^3*d^3)*B^2 - 2*(3*A*B*a*b^2*d^3*g^3 + (2*b^3*c*d^2*g^3*n + 3*a*b^2*d^3*g^3*log(e))*B^2)*x^2 + 6*((b^3*c*d^2*g^3*n - a*b^2*d^3*g^3*n)*B^2*x^2 + 2*(b^3*c^2*d*g^3*n - a*b^2*c*d^2*g^3*n)*B^2*x + (b^3*c^3*g^3*n - a*b^2*c^2*d*g^3*n)*B^2)*log(d*x + c) - 2*(B^2*b^3*d^3*g^3*x^3 + 3*B^2*a*b^2*d^3*g^3*x^2 + 3*B^2*a^2*b*d^3*g^3*x + B^2*a^3*d^3*g^3)*log((b*x + a)^n))*log((d*x + c)^n))/(d^6*i^3*x^3 + 3*c*d^5*i^3*x^2 + 3*c^2*d^4*i^3*x + c^3*d^3*i^3), x)","F",0
203,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","A B a b g^{2} n {\left(\frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{2} \, A B a^{2} g^{2} n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} + \frac{1}{2} \, A^{2} b^{2} g^{2} {\left(\frac{4 \, c d x + 3 \, c^{2}}{d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}} + \frac{2 \, \log\left(d x + c\right)}{d^{3} i^{3}}\right)} - \frac{2 \, {\left(2 \, d x + c\right)} A B a b g^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{{\left(2 \, d x + c\right)} A^{2} a b g^{2}}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{A B a^{2} g^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} - \frac{A^{2} a^{2} g^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} + \frac{{\left(4 \, {\left(b^{2} c d g^{2} - a b d^{2} g^{2}\right)} B^{2} x + {\left(3 \, b^{2} c^{2} g^{2} - 2 \, a b c d g^{2} - a^{2} d^{2} g^{2}\right)} B^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} b^{2} c d g^{2} x + B^{2} b^{2} c^{2} g^{2}\right)} \log\left(d x + c\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, {\left(d^{5} i^{3} x^{2} + 2 \, c d^{4} i^{3} x + c^{2} d^{3} i^{3}\right)}} - \int -\frac{2 \, B^{2} a b d^{2} g^{2} x \log\left(e\right)^{2} + B^{2} a^{2} d^{2} g^{2} \log\left(e\right)^{2} + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B b^{2} d^{2} g^{2} \log\left(e\right)\right)} x^{2} + {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(2 \, B^{2} a b d^{2} g^{2} x \log\left(e\right) + B^{2} a^{2} d^{2} g^{2} \log\left(e\right) + {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right) + A B b^{2} d^{2} g^{2}\right)} x^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(4 \, {\left(b^{2} c d g^{2} n - {\left(g^{2} n - g^{2} \log\left(e\right)\right)} a b d^{2}\right)} B^{2} x + {\left(3 \, b^{2} c^{2} g^{2} n - 2 \, a b c d g^{2} n - {\left(g^{2} n - 2 \, g^{2} \log\left(e\right)\right)} a^{2} d^{2}\right)} B^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g^{2} \log\left(e\right) + A B b^{2} d^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g^{2} n x^{2} + 2 \, B^{2} b^{2} c d g^{2} n x + B^{2} b^{2} c^{2} g^{2} n\right)} \log\left(d x + c\right) + 2 \, {\left(B^{2} b^{2} d^{2} g^{2} x^{2} + 2 \, B^{2} a b d^{2} g^{2} x + B^{2} a^{2} d^{2} g^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d^{5} i^{3} x^{3} + 3 \, c d^{4} i^{3} x^{2} + 3 \, c^{2} d^{3} i^{3} x + c^{3} d^{2} i^{3}}\,{d x}"," ",0,"A*B*a*b*g^2*n*((b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) + 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) - 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/2*A*B*a^2*g^2*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) + 1/2*A^2*b^2*g^2*((4*c*d*x + 3*c^2)/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) + 2*log(d*x + c)/(d^3*i^3)) - 2*(2*d*x + c)*A*B*a*b*g^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - (2*d*x + c)*A^2*a*b*g^2/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - A*B*a^2*g^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A^2*a^2*g^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) + 1/2*(4*(b^2*c*d*g^2 - a*b*d^2*g^2)*B^2*x + (3*b^2*c^2*g^2 - 2*a*b*c*d*g^2 - a^2*d^2*g^2)*B^2 + 2*(B^2*b^2*d^2*g^2*x^2 + 2*B^2*b^2*c*d*g^2*x + B^2*b^2*c^2*g^2)*log(d*x + c))*log((d*x + c)^n)^2/(d^5*i^3*x^2 + 2*c*d^4*i^3*x + c^2*d^3*i^3) - integrate(-(2*B^2*a*b*d^2*g^2*x*log(e)^2 + B^2*a^2*d^2*g^2*log(e)^2 + (B^2*b^2*d^2*g^2*log(e)^2 + 2*A*B*b^2*d^2*g^2*log(e))*x^2 + (B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log((b*x + a)^n)^2 + 2*(2*B^2*a*b*d^2*g^2*x*log(e) + B^2*a^2*d^2*g^2*log(e) + (B^2*b^2*d^2*g^2*log(e) + A*B*b^2*d^2*g^2)*x^2)*log((b*x + a)^n) - (4*(b^2*c*d*g^2*n - (g^2*n - g^2*log(e))*a*b*d^2)*B^2*x + (3*b^2*c^2*g^2*n - 2*a*b*c*d*g^2*n - (g^2*n - 2*g^2*log(e))*a^2*d^2)*B^2 + 2*(B^2*b^2*d^2*g^2*log(e) + A*B*b^2*d^2*g^2)*x^2 + 2*(B^2*b^2*d^2*g^2*n*x^2 + 2*B^2*b^2*c*d*g^2*n*x + B^2*b^2*c^2*g^2*n)*log(d*x + c) + 2*(B^2*b^2*d^2*g^2*x^2 + 2*B^2*a*b*d^2*g^2*x + B^2*a^2*d^2*g^2)*log((b*x + a)^n))*log((d*x + c)^n))/(d^5*i^3*x^3 + 3*c*d^4*i^3*x^2 + 3*c^2*d^3*i^3*x + c^3*d^2*i^3), x)","F",0
204,1,1995,0,2.349922," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, A B b g n {\left(\frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} + \frac{1}{2} \, A B a g n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} - \frac{{\left(2 \, d x + c\right)} B^{2} b g \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} + \frac{1}{4} \, {\left(2 \, n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{b^{2} c^{4} d i^{3} - 2 \, a b c^{3} d^{2} i^{3} + a^{2} c^{2} d^{3} i^{3} + {\left(b^{2} c^{2} d^{3} i^{3} - 2 \, a b c d^{4} i^{3} + a^{2} d^{5} i^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} i^{3} - 2 \, a b c^{2} d^{3} i^{3} + a^{2} c d^{4} i^{3}\right)} x}\right)} B^{2} a g + \frac{1}{4} \, {\left(2 \, n {\left(\frac{b c^{2} - 3 \, a c d + 2 \, {\left(b c d - 2 \, a d^{2}\right)} x}{{\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}} + \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}} - \frac{2 \, {\left(b^{2} c - 2 \, a b d\right)} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(b^{2} c^{3} - 8 \, a b c^{2} d + 7 \, a^{2} c d^{2} + 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(b^{2} c^{2} d - 5 \, a b c d^{2} + 4 \, a^{2} d^{3}\right)} x + 2 \, {\left(b^{2} c^{3} - 4 \, a b c^{2} d + {\left(b^{2} c d^{2} - 4 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(b^{2} c^{3} - 4 \, a b c^{2} d + {\left(b^{2} c d^{2} - 4 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 4 \, a b c d^{2}\right)} x + 2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + {\left(b^{2} c d^{2} - 2 \, a b d^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{b^{2} c^{4} d^{2} i^{3} - 2 \, a b c^{3} d^{3} i^{3} + a^{2} c^{2} d^{4} i^{3} + {\left(b^{2} c^{2} d^{4} i^{3} - 2 \, a b c d^{5} i^{3} + a^{2} d^{6} i^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{3} i^{3} - 2 \, a b c^{2} d^{4} i^{3} + a^{2} c d^{5} i^{3}\right)} x}\right)} B^{2} b g - \frac{{\left(2 \, d x + c\right)} A B b g \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}} - \frac{B^{2} a g \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{{\left(2 \, d x + c\right)} A^{2} b g}{2 \, {\left(d^{4} i^{3} x^{2} + 2 \, c d^{3} i^{3} x + c^{2} d^{2} i^{3}\right)}} - \frac{A B a g \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} - \frac{A^{2} a g}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"1/2*A*B*b*g*n*((b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) + 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) - 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3)) + 1/2*A*B*a*g*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) - 1/2*(2*d*x + c)*B^2*b*g*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) + 1/4*(2*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*n^2/(b^2*c^4*d*i^3 - 2*a*b*c^3*d^2*i^3 + a^2*c^2*d^3*i^3 + (b^2*c^2*d^3*i^3 - 2*a*b*c*d^4*i^3 + a^2*d^5*i^3)*x^2 + 2*(b^2*c^3*d^2*i^3 - 2*a*b*c^2*d^3*i^3 + a^2*c*d^4*i^3)*x))*B^2*a*g + 1/4*(2*n*((b*c^2 - 3*a*c*d + 2*(b*c*d - 2*a*d^2)*x)/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3) + 2*(b^2*c - 2*a*b*d)*log(b*x + a)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3) - 2*(b^2*c - 2*a*b*d)*log(d*x + c)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (b^2*c^3 - 8*a*b*c^2*d + 7*a^2*c*d^2 + 2*(b^2*c^3 - 2*a*b*c^2*d + (b^2*c*d^2 - 2*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 2*a*b*c*d^2)*x)*log(b*x + a)^2 + 2*(b^2*c^3 - 2*a*b*c^2*d + (b^2*c*d^2 - 2*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 2*a*b*c*d^2)*x)*log(d*x + c)^2 + 2*(b^2*c^2*d - 5*a*b*c*d^2 + 4*a^2*d^3)*x + 2*(b^2*c^3 - 4*a*b*c^2*d + (b^2*c*d^2 - 4*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 4*a*b*c*d^2)*x)*log(b*x + a) - 2*(b^2*c^3 - 4*a*b*c^2*d + (b^2*c*d^2 - 4*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 4*a*b*c*d^2)*x + 2*(b^2*c^3 - 2*a*b*c^2*d + (b^2*c*d^2 - 2*a*b*d^3)*x^2 + 2*(b^2*c^2*d - 2*a*b*c*d^2)*x)*log(b*x + a))*log(d*x + c))*n^2/(b^2*c^4*d^2*i^3 - 2*a*b*c^3*d^3*i^3 + a^2*c^2*d^4*i^3 + (b^2*c^2*d^4*i^3 - 2*a*b*c*d^5*i^3 + a^2*d^6*i^3)*x^2 + 2*(b^2*c^3*d^3*i^3 - 2*a*b*c^2*d^4*i^3 + a^2*c*d^5*i^3)*x))*B^2*b*g - (2*d*x + c)*A*B*b*g*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - 1/2*B^2*a*g*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*(2*d*x + c)*A^2*b*g/(d^4*i^3*x^2 + 2*c*d^3*i^3*x + c^2*d^2*i^3) - A*B*a*g*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A^2*a*g/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","B",0
205,1,861,0,1.560399," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, A B n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} + \frac{1}{4} \, {\left(2 \, n {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b c d^{3} - a d^{4}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} i^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{b^{2} c^{4} d i^{3} - 2 \, a b c^{3} d^{2} i^{3} + a^{2} c^{2} d^{3} i^{3} + {\left(b^{2} c^{2} d^{3} i^{3} - 2 \, a b c d^{4} i^{3} + a^{2} d^{5} i^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} i^{3} - 2 \, a b c^{2} d^{3} i^{3} + a^{2} c d^{4} i^{3}\right)} x}\right)} B^{2} - \frac{B^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}} - \frac{A B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}} - \frac{A^{2}}{2 \, {\left(d^{3} i^{3} x^{2} + 2 \, c d^{2} i^{3} x + c^{2} d i^{3}\right)}}"," ",0,"1/2*A*B*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3)) + 1/4*(2*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*i^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*i^3*x + (b*c^3*d - a*c^2*d^2)*i^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*n^2/(b^2*c^4*d*i^3 - 2*a*b*c^3*d^2*i^3 + a^2*c^2*d^3*i^3 + (b^2*c^2*d^3*i^3 - 2*a*b*c*d^4*i^3 + a^2*d^5*i^3)*x^2 + 2*(b^2*c^3*d^2*i^3 - 2*a*b*c^2*d^3*i^3 + a^2*c*d^4*i^3)*x))*B^2 - 1/2*B^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3) - 1/2*A^2/(d^3*i^3*x^2 + 2*c*d^2*i^3*x + c^2*d*i^3)","B",0
206,1,2126,0,2.747016," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B^{2} {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} + A B {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{12} \, {\left(\frac{{\left(45 \, b^{2} c^{2} - 48 \, a b c d + 3 \, a^{2} d^{2} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{3} - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{3} + 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 42 \, {\left(b^{2} c d - a b d^{2}\right)} x + 42 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 6 \, {\left(7 \, b^{2} d^{2} x^{2} + 14 \, b^{2} c d x + 7 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{b^{3} c^{5} g i^{3} - 3 \, a b^{2} c^{4} d g i^{3} + 3 \, a^{2} b c^{3} d^{2} g i^{3} - a^{3} c^{2} d^{3} g i^{3} + {\left(b^{3} c^{3} d^{2} g i^{3} - 3 \, a b^{2} c^{2} d^{3} g i^{3} + 3 \, a^{2} b c d^{4} g i^{3} - a^{3} d^{5} g i^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d g i^{3} - 3 \, a b^{2} c^{3} d^{2} g i^{3} + 3 \, a^{2} b c^{2} d^{3} g i^{3} - a^{3} c d^{4} g i^{3}\right)} x} - \frac{6 \, {\left(7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{b^{3} c^{5} g i^{3} - 3 \, a b^{2} c^{4} d g i^{3} + 3 \, a^{2} b c^{3} d^{2} g i^{3} - a^{3} c^{2} d^{3} g i^{3} + {\left(b^{3} c^{3} d^{2} g i^{3} - 3 \, a b^{2} c^{2} d^{3} g i^{3} + 3 \, a^{2} b c d^{4} g i^{3} - a^{3} d^{5} g i^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d g i^{3} - 3 \, a b^{2} c^{3} d^{2} g i^{3} + 3 \, a^{2} b c^{2} d^{3} g i^{3} - a^{3} c d^{4} g i^{3}\right)} x}\right)} B^{2} - \frac{{\left(7 \, b^{2} c^{2} - 8 \, a b c d + a^{2} d^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b^{2} c d - a b d^{2}\right)} x + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{2 \, {\left(b^{3} c^{5} g i^{3} - 3 \, a b^{2} c^{4} d g i^{3} + 3 \, a^{2} b c^{3} d^{2} g i^{3} - a^{3} c^{2} d^{3} g i^{3} + {\left(b^{3} c^{3} d^{2} g i^{3} - 3 \, a b^{2} c^{2} d^{3} g i^{3} + 3 \, a^{2} b c d^{4} g i^{3} - a^{3} d^{5} g i^{3}\right)} x^{2} + 2 \, {\left(b^{3} c^{4} d g i^{3} - 3 \, a b^{2} c^{3} d^{2} g i^{3} + 3 \, a^{2} b c^{2} d^{3} g i^{3} - a^{3} c d^{4} g i^{3}\right)} x\right)}} + \frac{1}{2} \, A^{2} {\left(\frac{2 \, b d x + 3 \, b c - a d}{{\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} g i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d - 2 \, a b c^{2} d^{2} + a^{2} c d^{3}\right)} g i^{3} x + {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} g i^{3}} + \frac{2 \, b^{2} \log\left(b x + a\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}} - \frac{2 \, b^{2} \log\left(d x + c\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} g i^{3}}\right)}"," ",0,"1/2*B^2*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 + A*B*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/12*((45*b^2*c^2 - 48*a*b*c*d + 3*a^2*d^2 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^3 - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^3 + 18*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 6*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c)^2 + 42*(b^2*c*d - a*b*d^2)*x + 42*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 6*(7*b^2*d^2*x^2 + 14*b^2*c*d*x + 7*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*n^2/(b^3*c^5*g*i^3 - 3*a*b^2*c^4*d*g*i^3 + 3*a^2*b*c^3*d^2*g*i^3 - a^3*c^2*d^3*g*i^3 + (b^3*c^3*d^2*g*i^3 - 3*a*b^2*c^2*d^3*g*i^3 + 3*a^2*b*c*d^4*g*i^3 - a^3*d^5*g*i^3)*x^2 + 2*(b^3*c^4*d*g*i^3 - 3*a*b^2*c^3*d^2*g*i^3 + 3*a^2*b*c^2*d^3*g*i^3 - a^3*c*d^4*g*i^3)*x) - 6*(7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^3*c^5*g*i^3 - 3*a*b^2*c^4*d*g*i^3 + 3*a^2*b*c^3*d^2*g*i^3 - a^3*c^2*d^3*g*i^3 + (b^3*c^3*d^2*g*i^3 - 3*a*b^2*c^2*d^3*g*i^3 + 3*a^2*b*c*d^4*g*i^3 - a^3*d^5*g*i^3)*x^2 + 2*(b^3*c^4*d*g*i^3 - 3*a*b^2*c^3*d^2*g*i^3 + 3*a^2*b*c^2*d^3*g*i^3 - a^3*c*d^4*g*i^3)*x))*B^2 - 1/2*(7*b^2*c^2 - 8*a*b*c*d + a^2*d^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(d*x + c)^2 + 6*(b^2*c*d - a*b*d^2)*x + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(b*x + a))*log(d*x + c))*A*B*n/(b^3*c^5*g*i^3 - 3*a*b^2*c^4*d*g*i^3 + 3*a^2*b*c^3*d^2*g*i^3 - a^3*c^2*d^3*g*i^3 + (b^3*c^3*d^2*g*i^3 - 3*a*b^2*c^2*d^3*g*i^3 + 3*a^2*b*c*d^4*g*i^3 - a^3*d^5*g*i^3)*x^2 + 2*(b^3*c^4*d*g*i^3 - 3*a*b^2*c^3*d^2*g*i^3 + 3*a^2*b*c^2*d^3*g*i^3 - a^3*c*d^4*g*i^3)*x) + 1/2*A^2*((2*b*d*x + 3*b*c - a*d)/((b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*g*i^3*x^2 + 2*(b^2*c^3*d - 2*a*b*c^2*d^2 + a^2*c*d^3)*g*i^3*x + (b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*g*i^3) + 2*b^2*log(b*x + a)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3) - 2*b^2*log(d*x + c)/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*g*i^3))","B",0
207,1,4199,0,4.833207," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} - A B {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{1}{4} \, {\left(\frac{{\left(8 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 24 \, a^{2} b c d^{2} + a^{3} d^{3} + 4 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{3} - 4 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)^{3} + 30 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(13 \, b^{3} c^{2} d - 6 \, a b^{2} c d^{2} - 7 \, a^{2} b d^{3}\right)} x + 30 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) - 6 \, {\left(5 \, b^{3} d^{3} x^{3} + 5 \, a b^{2} c^{2} d + 5 \, {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} + 5 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a b^{4} c^{6} g^{2} i^{3} - 4 \, a^{2} b^{3} c^{5} d g^{2} i^{3} + 6 \, a^{3} b^{2} c^{4} d^{2} g^{2} i^{3} - 4 \, a^{4} b c^{3} d^{3} g^{2} i^{3} + a^{5} c^{2} d^{4} g^{2} i^{3} + {\left(b^{5} c^{4} d^{2} g^{2} i^{3} - 4 \, a b^{4} c^{3} d^{3} g^{2} i^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} g^{2} i^{3} - 4 \, a^{3} b^{2} c d^{5} g^{2} i^{3} + a^{4} b d^{6} g^{2} i^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d g^{2} i^{3} - 7 \, a b^{4} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{2} b^{3} c^{3} d^{3} g^{2} i^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} g^{2} i^{3} - 2 \, a^{4} b c d^{5} g^{2} i^{3} + a^{5} d^{6} g^{2} i^{3}\right)} x^{2} + {\left(b^{5} c^{6} g^{2} i^{3} - 2 \, a b^{4} c^{5} d g^{2} i^{3} - 2 \, a^{2} b^{3} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 7 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 2 \, a^{5} c d^{5} g^{2} i^{3}\right)} x} + \frac{2 \, {\left(4 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} - a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a b^{4} c^{6} g^{2} i^{3} - 4 \, a^{2} b^{3} c^{5} d g^{2} i^{3} + 6 \, a^{3} b^{2} c^{4} d^{2} g^{2} i^{3} - 4 \, a^{4} b c^{3} d^{3} g^{2} i^{3} + a^{5} c^{2} d^{4} g^{2} i^{3} + {\left(b^{5} c^{4} d^{2} g^{2} i^{3} - 4 \, a b^{4} c^{3} d^{3} g^{2} i^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} g^{2} i^{3} - 4 \, a^{3} b^{2} c d^{5} g^{2} i^{3} + a^{4} b d^{6} g^{2} i^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d g^{2} i^{3} - 7 \, a b^{4} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{2} b^{3} c^{3} d^{3} g^{2} i^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} g^{2} i^{3} - 2 \, a^{4} b c d^{5} g^{2} i^{3} + a^{5} d^{6} g^{2} i^{3}\right)} x^{2} + {\left(b^{5} c^{6} g^{2} i^{3} - 2 \, a b^{4} c^{5} d g^{2} i^{3} - 2 \, a^{2} b^{3} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 7 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 2 \, a^{5} c d^{5} g^{2} i^{3}\right)} x}\right)} B^{2} - \frac{{\left(4 \, b^{3} c^{3} - 15 \, a b^{2} c^{2} d + 12 \, a^{2} b c d^{2} - a^{3} d^{3} - 6 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3}\right)} x - 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right) + 6 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x + 2 \, {\left(b^{3} d^{3} x^{3} + a b^{2} c^{2} d + {\left(2 \, b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + {\left(b^{3} c^{2} d + 2 \, a b^{2} c d^{2}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{2 \, {\left(a b^{4} c^{6} g^{2} i^{3} - 4 \, a^{2} b^{3} c^{5} d g^{2} i^{3} + 6 \, a^{3} b^{2} c^{4} d^{2} g^{2} i^{3} - 4 \, a^{4} b c^{3} d^{3} g^{2} i^{3} + a^{5} c^{2} d^{4} g^{2} i^{3} + {\left(b^{5} c^{4} d^{2} g^{2} i^{3} - 4 \, a b^{4} c^{3} d^{3} g^{2} i^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} g^{2} i^{3} - 4 \, a^{3} b^{2} c d^{5} g^{2} i^{3} + a^{4} b d^{6} g^{2} i^{3}\right)} x^{3} + {\left(2 \, b^{5} c^{5} d g^{2} i^{3} - 7 \, a b^{4} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{2} b^{3} c^{3} d^{3} g^{2} i^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} g^{2} i^{3} - 2 \, a^{4} b c d^{5} g^{2} i^{3} + a^{5} d^{6} g^{2} i^{3}\right)} x^{2} + {\left(b^{5} c^{6} g^{2} i^{3} - 2 \, a b^{4} c^{5} d g^{2} i^{3} - 2 \, a^{2} b^{3} c^{4} d^{2} g^{2} i^{3} + 8 \, a^{3} b^{2} c^{3} d^{3} g^{2} i^{3} - 7 \, a^{4} b c^{2} d^{4} g^{2} i^{3} + 2 \, a^{5} c d^{5} g^{2} i^{3}\right)} x\right)}} - \frac{1}{2} \, A^{2} {\left(\frac{6 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{2} + 5 \, a b c d - a^{2} d^{2} + 3 \, {\left(3 \, b^{2} c d + a b d^{2}\right)} x}{{\left(b^{4} c^{3} d^{2} - 3 \, a b^{3} c^{2} d^{3} + 3 \, a^{2} b^{2} c d^{4} - a^{3} b d^{5}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{4} c^{4} d - 5 \, a b^{3} c^{3} d^{2} + 3 \, a^{2} b^{2} c^{2} d^{3} + a^{3} b c d^{4} - a^{4} d^{5}\right)} g^{2} i^{3} x^{2} + {\left(b^{4} c^{5} - a b^{3} c^{4} d - 3 \, a^{2} b^{2} c^{3} d^{2} + 5 \, a^{3} b c^{2} d^{3} - 2 \, a^{4} c d^{4}\right)} g^{2} i^{3} x + {\left(a b^{3} c^{5} - 3 \, a^{2} b^{2} c^{4} d + 3 \, a^{3} b c^{3} d^{2} - a^{4} c^{2} d^{3}\right)} g^{2} i^{3}} + \frac{6 \, b^{2} d \log\left(b x + a\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}} - \frac{6 \, b^{2} d \log\left(d x + c\right)}{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} g^{2} i^{3}}\right)}"," ",0,"-1/2*B^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 - A*B*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/4*((8*b^3*c^3 + 15*a*b^2*c^2*d - 24*a^2*b*c*d^2 + a^3*d^3 + 4*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^3 - 4*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c)^3 + 30*(b^3*c*d^2 - a*b^2*d^3)*x^2 + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c)^2 + 3*(13*b^3*c^2*d - 6*a*b^2*c*d^2 - 7*a^2*b*d^3)*x + 30*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) - 6*(5*b^3*d^3*x^3 + 5*a*b^2*c^2*d + 5*(2*b^3*c*d^2 + a*b^2*d^3)*x^2 + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 + 5*(b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c))*n^2/(a*b^4*c^6*g^2*i^3 - 4*a^2*b^3*c^5*d*g^2*i^3 + 6*a^3*b^2*c^4*d^2*g^2*i^3 - 4*a^4*b*c^3*d^3*g^2*i^3 + a^5*c^2*d^4*g^2*i^3 + (b^5*c^4*d^2*g^2*i^3 - 4*a*b^4*c^3*d^3*g^2*i^3 + 6*a^2*b^3*c^2*d^4*g^2*i^3 - 4*a^3*b^2*c*d^5*g^2*i^3 + a^4*b*d^6*g^2*i^3)*x^3 + (2*b^5*c^5*d*g^2*i^3 - 7*a*b^4*c^4*d^2*g^2*i^3 + 8*a^2*b^3*c^3*d^3*g^2*i^3 - 2*a^3*b^2*c^2*d^4*g^2*i^3 - 2*a^4*b*c*d^5*g^2*i^3 + a^5*d^6*g^2*i^3)*x^2 + (b^5*c^6*g^2*i^3 - 2*a*b^4*c^5*d*g^2*i^3 - 2*a^2*b^3*c^4*d^2*g^2*i^3 + 8*a^3*b^2*c^3*d^3*g^2*i^3 - 7*a^4*b*c^2*d^4*g^2*i^3 + 2*a^5*c*d^5*g^2*i^3)*x) + 2*(4*b^3*c^3 - 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 - a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c)^2 - 3*(b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a*b^4*c^6*g^2*i^3 - 4*a^2*b^3*c^5*d*g^2*i^3 + 6*a^3*b^2*c^4*d^2*g^2*i^3 - 4*a^4*b*c^3*d^3*g^2*i^3 + a^5*c^2*d^4*g^2*i^3 + (b^5*c^4*d^2*g^2*i^3 - 4*a*b^4*c^3*d^3*g^2*i^3 + 6*a^2*b^3*c^2*d^4*g^2*i^3 - 4*a^3*b^2*c*d^5*g^2*i^3 + a^4*b*d^6*g^2*i^3)*x^3 + (2*b^5*c^5*d*g^2*i^3 - 7*a*b^4*c^4*d^2*g^2*i^3 + 8*a^2*b^3*c^3*d^3*g^2*i^3 - 2*a^3*b^2*c^2*d^4*g^2*i^3 - 2*a^4*b*c*d^5*g^2*i^3 + a^5*d^6*g^2*i^3)*x^2 + (b^5*c^6*g^2*i^3 - 2*a*b^4*c^5*d*g^2*i^3 - 2*a^2*b^3*c^4*d^2*g^2*i^3 + 8*a^3*b^2*c^3*d^3*g^2*i^3 - 7*a^4*b*c^2*d^4*g^2*i^3 + 2*a^5*c*d^5*g^2*i^3)*x))*B^2 - 1/2*(4*b^3*c^3 - 15*a*b^2*c^2*d + 12*a^2*b*c*d^2 - a^3*d^3 - 6*(b^3*c*d^2 - a*b^2*d^3)*x^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a)^2 - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(d*x + c)^2 - 3*(b^3*c^2*d + 2*a*b^2*c*d^2 - 3*a^2*b*d^3)*x - 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a) + 6*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x + 2*(b^3*d^3*x^3 + a*b^2*c^2*d + (2*b^3*c*d^2 + a*b^2*d^3)*x^2 + (b^3*c^2*d + 2*a*b^2*c*d^2)*x)*log(b*x + a))*log(d*x + c))*A*B*n/(a*b^4*c^6*g^2*i^3 - 4*a^2*b^3*c^5*d*g^2*i^3 + 6*a^3*b^2*c^4*d^2*g^2*i^3 - 4*a^4*b*c^3*d^3*g^2*i^3 + a^5*c^2*d^4*g^2*i^3 + (b^5*c^4*d^2*g^2*i^3 - 4*a*b^4*c^3*d^3*g^2*i^3 + 6*a^2*b^3*c^2*d^4*g^2*i^3 - 4*a^3*b^2*c*d^5*g^2*i^3 + a^4*b*d^6*g^2*i^3)*x^3 + (2*b^5*c^5*d*g^2*i^3 - 7*a*b^4*c^4*d^2*g^2*i^3 + 8*a^2*b^3*c^3*d^3*g^2*i^3 - 2*a^3*b^2*c^2*d^4*g^2*i^3 - 2*a^4*b*c*d^5*g^2*i^3 + a^5*d^6*g^2*i^3)*x^2 + (b^5*c^6*g^2*i^3 - 2*a*b^4*c^5*d*g^2*i^3 - 2*a^2*b^3*c^4*d^2*g^2*i^3 + 8*a^3*b^2*c^3*d^3*g^2*i^3 - 7*a^4*b*c^2*d^4*g^2*i^3 + 2*a^5*c*d^5*g^2*i^3)*x) - 1/2*A^2*((6*b^2*d^2*x^2 + 2*b^2*c^2 + 5*a*b*c*d - a^2*d^2 + 3*(3*b^2*c*d + a*b*d^2)*x)/((b^4*c^3*d^2 - 3*a*b^3*c^2*d^3 + 3*a^2*b^2*c*d^4 - a^3*b*d^5)*g^2*i^3*x^3 + (2*b^4*c^4*d - 5*a*b^3*c^3*d^2 + 3*a^2*b^2*c^2*d^3 + a^3*b*c*d^4 - a^4*d^5)*g^2*i^3*x^2 + (b^4*c^5 - a*b^3*c^4*d - 3*a^2*b^2*c^3*d^2 + 5*a^3*b*c^2*d^3 - 2*a^4*c*d^4)*g^2*i^3*x + (a*b^3*c^5 - 3*a^2*b^2*c^4*d + 3*a^3*b*c^3*d^2 - a^4*c^2*d^3)*g^2*i^3) + 6*b^2*d*log(b*x + a)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3) - 6*b^2*d*log(d*x + c)/((b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*g^2*i^3))","B",0
208,1,5594,0,5.556461," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3/(d*i*x+c*i)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} + A B {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{1}{4} \, {\left(\frac{{\left(b^{4} c^{4} - 32 \, a b^{3} c^{3} d + 32 \, a^{3} b c d^{3} - a^{4} d^{4} - 60 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} - 8 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{3} - 24 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right)^{2} + 8 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)^{3} - 90 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} x^{2} - 4 \, {\left(7 \, b^{4} c^{3} d + 24 \, a b^{3} c^{2} d^{2} - 24 \, a^{2} b^{2} c d^{3} - 7 \, a^{3} b d^{4}\right)} x - 60 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) + 12 \, {\left(5 \, b^{4} d^{4} x^{4} + 5 \, a^{2} b^{2} c^{2} d^{2} + 10 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + 5 \, {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} + 10 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{2} b^{5} c^{7} g^{3} i^{3} - 5 \, a^{3} b^{4} c^{6} d g^{3} i^{3} + 10 \, a^{4} b^{3} c^{5} d^{2} g^{3} i^{3} - 10 \, a^{5} b^{2} c^{4} d^{3} g^{3} i^{3} + 5 \, a^{6} b c^{3} d^{4} g^{3} i^{3} - a^{7} c^{2} d^{5} g^{3} i^{3} + {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 5 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} - 10 \, a^{3} b^{4} c^{2} d^{5} g^{3} i^{3} + 5 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d g^{3} i^{3} - 4 \, a b^{6} c^{5} d^{2} g^{3} i^{3} + 5 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} + 4 \, a^{5} b^{2} c d^{6} g^{3} i^{3} - a^{6} b d^{7} g^{3} i^{3}\right)} x^{3} + {\left(b^{7} c^{7} g^{3} i^{3} - a b^{6} c^{6} d g^{3} i^{3} - 9 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 25 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} + 9 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} g^{3} i^{3} - 4 \, a^{2} b^{5} c^{6} d g^{3} i^{3} + 5 \, a^{3} b^{4} c^{5} d^{2} g^{3} i^{3} - 5 \, a^{5} b^{2} c^{3} d^{4} g^{3} i^{3} + 4 \, a^{6} b c^{2} d^{5} g^{3} i^{3} - a^{7} c d^{6} g^{3} i^{3}\right)} x} + \frac{2 \, {\left(b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} - 16 \, a^{3} b c d^{3} + a^{4} d^{4} - 12 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} - 24 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 12 \, {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a^{2} b^{5} c^{7} g^{3} i^{3} - 5 \, a^{3} b^{4} c^{6} d g^{3} i^{3} + 10 \, a^{4} b^{3} c^{5} d^{2} g^{3} i^{3} - 10 \, a^{5} b^{2} c^{4} d^{3} g^{3} i^{3} + 5 \, a^{6} b c^{3} d^{4} g^{3} i^{3} - a^{7} c^{2} d^{5} g^{3} i^{3} + {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 5 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} - 10 \, a^{3} b^{4} c^{2} d^{5} g^{3} i^{3} + 5 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d g^{3} i^{3} - 4 \, a b^{6} c^{5} d^{2} g^{3} i^{3} + 5 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} + 4 \, a^{5} b^{2} c d^{6} g^{3} i^{3} - a^{6} b d^{7} g^{3} i^{3}\right)} x^{3} + {\left(b^{7} c^{7} g^{3} i^{3} - a b^{6} c^{6} d g^{3} i^{3} - 9 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 25 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} + 9 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} g^{3} i^{3} - 4 \, a^{2} b^{5} c^{6} d g^{3} i^{3} + 5 \, a^{3} b^{4} c^{5} d^{2} g^{3} i^{3} - 5 \, a^{5} b^{2} c^{3} d^{4} g^{3} i^{3} + 4 \, a^{6} b c^{2} d^{5} g^{3} i^{3} - a^{7} c d^{6} g^{3} i^{3}\right)} x}\right)} B^{2} - \frac{{\left(b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 30 \, a^{2} b^{2} c^{2} d^{2} - 16 \, a^{3} b c d^{3} + a^{4} d^{4} - 12 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right)^{2} - 24 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(b x + a\right) \log\left(d x + c\right) + 12 \, {\left(b^{4} d^{4} x^{4} + a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} x^{3} + {\left(b^{4} c^{2} d^{2} + 4 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(a b^{3} c^{2} d^{2} + a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(d x + c\right)^{2} - 12 \, {\left(b^{4} c^{3} d - a b^{3} c^{2} d^{2} - a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} x\right)} A B n}{2 \, {\left(a^{2} b^{5} c^{7} g^{3} i^{3} - 5 \, a^{3} b^{4} c^{6} d g^{3} i^{3} + 10 \, a^{4} b^{3} c^{5} d^{2} g^{3} i^{3} - 10 \, a^{5} b^{2} c^{4} d^{3} g^{3} i^{3} + 5 \, a^{6} b c^{3} d^{4} g^{3} i^{3} - a^{7} c^{2} d^{5} g^{3} i^{3} + {\left(b^{7} c^{5} d^{2} g^{3} i^{3} - 5 \, a b^{6} c^{4} d^{3} g^{3} i^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} g^{3} i^{3} - 10 \, a^{3} b^{4} c^{2} d^{5} g^{3} i^{3} + 5 \, a^{4} b^{3} c d^{6} g^{3} i^{3} - a^{5} b^{2} d^{7} g^{3} i^{3}\right)} x^{4} + 2 \, {\left(b^{7} c^{6} d g^{3} i^{3} - 4 \, a b^{6} c^{5} d^{2} g^{3} i^{3} + 5 \, a^{2} b^{5} c^{4} d^{3} g^{3} i^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} g^{3} i^{3} + 4 \, a^{5} b^{2} c d^{6} g^{3} i^{3} - a^{6} b d^{7} g^{3} i^{3}\right)} x^{3} + {\left(b^{7} c^{7} g^{3} i^{3} - a b^{6} c^{6} d g^{3} i^{3} - 9 \, a^{2} b^{5} c^{5} d^{2} g^{3} i^{3} + 25 \, a^{3} b^{4} c^{4} d^{3} g^{3} i^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} g^{3} i^{3} + 9 \, a^{5} b^{2} c^{2} d^{5} g^{3} i^{3} + a^{6} b c d^{6} g^{3} i^{3} - a^{7} d^{7} g^{3} i^{3}\right)} x^{2} + 2 \, {\left(a b^{6} c^{7} g^{3} i^{3} - 4 \, a^{2} b^{5} c^{6} d g^{3} i^{3} + 5 \, a^{3} b^{4} c^{5} d^{2} g^{3} i^{3} - 5 \, a^{5} b^{2} c^{3} d^{4} g^{3} i^{3} + 4 \, a^{6} b c^{2} d^{5} g^{3} i^{3} - a^{7} c d^{6} g^{3} i^{3}\right)} x\right)}} + \frac{1}{2} \, A^{2} {\left(\frac{12 \, b^{3} d^{3} x^{3} - b^{3} c^{3} + 7 \, a b^{2} c^{2} d + 7 \, a^{2} b c d^{2} - a^{3} d^{3} + 18 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d + 7 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right)} g^{3} i^{3} x^{3} + {\left(b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right)} g^{3} i^{3} x + {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} g^{3} i^{3}} + \frac{12 \, b^{2} d^{2} \log\left(b x + a\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}} - \frac{12 \, b^{2} d^{2} \log\left(d x + c\right)}{{\left(b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}\right)} g^{3} i^{3}}\right)}"," ",0,"1/2*B^2*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 + A*B*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/4*((b^4*c^4 - 32*a*b^3*c^3*d + 32*a^3*b*c*d^3 - a^4*d^4 - 60*(b^4*c*d^3 - a*b^3*d^4)*x^3 - 8*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^3 - 24*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)*log(d*x + c)^2 + 8*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c)^3 - 90*(b^4*c^2*d^2 - a^2*b^2*d^4)*x^2 - 4*(7*b^4*c^3*d + 24*a*b^3*c^2*d^2 - 24*a^2*b^2*c*d^3 - 7*a^3*b*d^4)*x - 60*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a) + 12*(5*b^4*d^4*x^4 + 5*a^2*b^2*c^2*d^2 + 10*(b^4*c*d^3 + a*b^3*d^4)*x^3 + 5*(b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^2 + 10*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c))*n^2/(a^2*b^5*c^7*g^3*i^3 - 5*a^3*b^4*c^6*d*g^3*i^3 + 10*a^4*b^3*c^5*d^2*g^3*i^3 - 10*a^5*b^2*c^4*d^3*g^3*i^3 + 5*a^6*b*c^3*d^4*g^3*i^3 - a^7*c^2*d^5*g^3*i^3 + (b^7*c^5*d^2*g^3*i^3 - 5*a*b^6*c^4*d^3*g^3*i^3 + 10*a^2*b^5*c^3*d^4*g^3*i^3 - 10*a^3*b^4*c^2*d^5*g^3*i^3 + 5*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3)*x^4 + 2*(b^7*c^6*d*g^3*i^3 - 4*a*b^6*c^5*d^2*g^3*i^3 + 5*a^2*b^5*c^4*d^3*g^3*i^3 - 5*a^4*b^3*c^2*d^5*g^3*i^3 + 4*a^5*b^2*c*d^6*g^3*i^3 - a^6*b*d^7*g^3*i^3)*x^3 + (b^7*c^7*g^3*i^3 - a*b^6*c^6*d*g^3*i^3 - 9*a^2*b^5*c^5*d^2*g^3*i^3 + 25*a^3*b^4*c^4*d^3*g^3*i^3 - 25*a^4*b^3*c^3*d^4*g^3*i^3 + 9*a^5*b^2*c^2*d^5*g^3*i^3 + a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*x^2 + 2*(a*b^6*c^7*g^3*i^3 - 4*a^2*b^5*c^6*d*g^3*i^3 + 5*a^3*b^4*c^5*d^2*g^3*i^3 - 5*a^5*b^2*c^3*d^4*g^3*i^3 + 4*a^6*b*c^2*d^5*g^3*i^3 - a^7*c*d^6*g^3*i^3)*x) + 2*(b^4*c^4 - 16*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 - 16*a^3*b*c*d^3 + a^4*d^4 - 12*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^2 - 24*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)*log(d*x + c) + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c)^2 - 12*(b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x)*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a^2*b^5*c^7*g^3*i^3 - 5*a^3*b^4*c^6*d*g^3*i^3 + 10*a^4*b^3*c^5*d^2*g^3*i^3 - 10*a^5*b^2*c^4*d^3*g^3*i^3 + 5*a^6*b*c^3*d^4*g^3*i^3 - a^7*c^2*d^5*g^3*i^3 + (b^7*c^5*d^2*g^3*i^3 - 5*a*b^6*c^4*d^3*g^3*i^3 + 10*a^2*b^5*c^3*d^4*g^3*i^3 - 10*a^3*b^4*c^2*d^5*g^3*i^3 + 5*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3)*x^4 + 2*(b^7*c^6*d*g^3*i^3 - 4*a*b^6*c^5*d^2*g^3*i^3 + 5*a^2*b^5*c^4*d^3*g^3*i^3 - 5*a^4*b^3*c^2*d^5*g^3*i^3 + 4*a^5*b^2*c*d^6*g^3*i^3 - a^6*b*d^7*g^3*i^3)*x^3 + (b^7*c^7*g^3*i^3 - a*b^6*c^6*d*g^3*i^3 - 9*a^2*b^5*c^5*d^2*g^3*i^3 + 25*a^3*b^4*c^4*d^3*g^3*i^3 - 25*a^4*b^3*c^3*d^4*g^3*i^3 + 9*a^5*b^2*c^2*d^5*g^3*i^3 + a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*x^2 + 2*(a*b^6*c^7*g^3*i^3 - 4*a^2*b^5*c^6*d*g^3*i^3 + 5*a^3*b^4*c^5*d^2*g^3*i^3 - 5*a^5*b^2*c^3*d^4*g^3*i^3 + 4*a^6*b*c^2*d^5*g^3*i^3 - a^7*c*d^6*g^3*i^3)*x))*B^2 - 1/2*(b^4*c^4 - 16*a*b^3*c^3*d + 30*a^2*b^2*c^2*d^2 - 16*a^3*b*c*d^3 + a^4*d^4 - 12*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)^2 - 24*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(b*x + a)*log(d*x + c) + 12*(b^4*d^4*x^4 + a^2*b^2*c^2*d^2 + 2*(b^4*c*d^3 + a*b^3*d^4)*x^3 + (b^4*c^2*d^2 + 4*a*b^3*c*d^3 + a^2*b^2*d^4)*x^2 + 2*(a*b^3*c^2*d^2 + a^2*b^2*c*d^3)*x)*log(d*x + c)^2 - 12*(b^4*c^3*d - a*b^3*c^2*d^2 - a^2*b^2*c*d^3 + a^3*b*d^4)*x)*A*B*n/(a^2*b^5*c^7*g^3*i^3 - 5*a^3*b^4*c^6*d*g^3*i^3 + 10*a^4*b^3*c^5*d^2*g^3*i^3 - 10*a^5*b^2*c^4*d^3*g^3*i^3 + 5*a^6*b*c^3*d^4*g^3*i^3 - a^7*c^2*d^5*g^3*i^3 + (b^7*c^5*d^2*g^3*i^3 - 5*a*b^6*c^4*d^3*g^3*i^3 + 10*a^2*b^5*c^3*d^4*g^3*i^3 - 10*a^3*b^4*c^2*d^5*g^3*i^3 + 5*a^4*b^3*c*d^6*g^3*i^3 - a^5*b^2*d^7*g^3*i^3)*x^4 + 2*(b^7*c^6*d*g^3*i^3 - 4*a*b^6*c^5*d^2*g^3*i^3 + 5*a^2*b^5*c^4*d^3*g^3*i^3 - 5*a^4*b^3*c^2*d^5*g^3*i^3 + 4*a^5*b^2*c*d^6*g^3*i^3 - a^6*b*d^7*g^3*i^3)*x^3 + (b^7*c^7*g^3*i^3 - a*b^6*c^6*d*g^3*i^3 - 9*a^2*b^5*c^5*d^2*g^3*i^3 + 25*a^3*b^4*c^4*d^3*g^3*i^3 - 25*a^4*b^3*c^3*d^4*g^3*i^3 + 9*a^5*b^2*c^2*d^5*g^3*i^3 + a^6*b*c*d^6*g^3*i^3 - a^7*d^7*g^3*i^3)*x^2 + 2*(a*b^6*c^7*g^3*i^3 - 4*a^2*b^5*c^6*d*g^3*i^3 + 5*a^3*b^4*c^5*d^2*g^3*i^3 - 5*a^5*b^2*c^3*d^4*g^3*i^3 + 4*a^6*b*c^2*d^5*g^3*i^3 - a^7*c*d^6*g^3*i^3)*x) + 1/2*A^2*((12*b^3*d^3*x^3 - b^3*c^3 + 7*a*b^2*c^2*d + 7*a^2*b*c*d^2 - a^3*d^3 + 18*(b^3*c*d^2 + a*b^2*d^3)*x^2 + 4*(b^3*c^2*d + 7*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^6*c^4*d^2 - 4*a*b^5*c^3*d^3 + 6*a^2*b^4*c^2*d^4 - 4*a^3*b^3*c*d^5 + a^4*b^2*d^6)*g^3*i^3*x^4 + 2*(b^6*c^5*d - 3*a*b^5*c^4*d^2 + 2*a^2*b^4*c^3*d^3 + 2*a^3*b^3*c^2*d^4 - 3*a^4*b^2*c*d^5 + a^5*b*d^6)*g^3*i^3*x^3 + (b^6*c^6 - 9*a^2*b^4*c^4*d^2 + 16*a^3*b^3*c^3*d^3 - 9*a^4*b^2*c^2*d^4 + a^6*d^6)*g^3*i^3*x^2 + 2*(a*b^5*c^6 - 3*a^2*b^4*c^5*d + 2*a^3*b^3*c^4*d^2 + 2*a^4*b^2*c^3*d^3 - 3*a^5*b*c^2*d^4 + a^6*c*d^5)*g^3*i^3*x + (a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*g^3*i^3) + 12*b^2*d^2*log(b*x + a)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3) - 12*b^2*d^2*log(d*x + c)/((b^5*c^5 - 5*a*b^4*c^4*d + 10*a^2*b^3*c^3*d^2 - 10*a^3*b^2*c^2*d^3 + 5*a^4*b*c*d^4 - a^5*d^5)*g^3*i^3))","B",0
209,1,9293,0,11.575356," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4/(d*i*x+c*i)^3,x, algorithm=""maxima"")","-\frac{1}{6} \, B^{2} {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)^{2} - \frac{1}{3} \, A B {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{1}{108} \, {\left(\frac{{\left(8 \, b^{5} c^{5} - 135 \, a b^{4} c^{4} d + 2160 \, a^{2} b^{3} c^{3} d^{2} - 980 \, a^{3} b^{2} c^{2} d^{3} - 1080 \, a^{4} b c d^{4} + 27 \, a^{5} d^{5} + 2940 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 30 \, {\left(159 \, b^{5} c^{2} d^{3} + 74 \, a b^{4} c d^{4} - 233 \, a^{2} b^{3} d^{5}\right)} x^{3} + 360 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{3} - 360 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)^{3} + 10 \, {\left(170 \, b^{5} c^{3} d^{2} + 921 \, a b^{4} c^{2} d^{3} - 588 \, a^{2} b^{3} c d^{4} - 503 \, a^{3} b^{2} d^{5}\right)} x^{2} - 360 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 360 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 3 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(19 \, b^{5} c^{4} d - 756 \, a b^{4} c^{3} d^{2} - 708 \, a^{2} b^{3} c^{2} d^{3} + 1256 \, a^{3} b^{2} c d^{4} + 189 \, a^{4} b d^{5}\right)} x + 2940 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 60 \, {\left(49 \, b^{5} d^{5} x^{5} + 49 \, a^{3} b^{2} c^{2} d^{3} + 49 \, {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + 49 \, {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + 49 \, {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + 18 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} + 49 \, {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 12 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{a^{3} b^{6} c^{8} g^{4} i^{3} - 6 \, a^{4} b^{5} c^{7} d g^{4} i^{3} + 15 \, a^{5} b^{4} c^{6} d^{2} g^{4} i^{3} - 20 \, a^{6} b^{3} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} g^{4} i^{3} - 6 \, a^{8} b c^{3} d^{5} g^{4} i^{3} + a^{9} c^{2} d^{6} g^{4} i^{3} + {\left(b^{9} c^{6} d^{2} g^{4} i^{3} - 6 \, a b^{8} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} g^{4} i^{3} - 20 \, a^{3} b^{6} c^{3} d^{5} g^{4} i^{3} + 15 \, a^{4} b^{5} c^{2} d^{6} g^{4} i^{3} - 6 \, a^{5} b^{4} c d^{7} g^{4} i^{3} + a^{6} b^{3} d^{8} g^{4} i^{3}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d g^{4} i^{3} - 9 \, a b^{8} c^{6} d^{2} g^{4} i^{3} + 12 \, a^{2} b^{7} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} g^{4} i^{3} - 30 \, a^{4} b^{5} c^{3} d^{5} g^{4} i^{3} + 33 \, a^{5} b^{4} c^{2} d^{6} g^{4} i^{3} - 16 \, a^{6} b^{3} c d^{7} g^{4} i^{3} + 3 \, a^{7} b^{2} d^{8} g^{4} i^{3}\right)} x^{4} + {\left(b^{9} c^{8} g^{4} i^{3} - 18 \, a^{2} b^{7} c^{6} d^{2} g^{4} i^{3} + 52 \, a^{3} b^{6} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} g^{4} i^{3} + 24 \, a^{5} b^{4} c^{3} d^{5} g^{4} i^{3} + 10 \, a^{6} b^{3} c^{2} d^{6} g^{4} i^{3} - 12 \, a^{7} b^{2} c d^{7} g^{4} i^{3} + 3 \, a^{8} b d^{8} g^{4} i^{3}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} g^{4} i^{3} - 12 \, a^{2} b^{7} c^{7} d g^{4} i^{3} + 10 \, a^{3} b^{6} c^{6} d^{2} g^{4} i^{3} + 24 \, a^{4} b^{5} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} g^{4} i^{3} + 52 \, a^{6} b^{3} c^{3} d^{5} g^{4} i^{3} - 18 \, a^{7} b^{2} c^{2} d^{6} g^{4} i^{3} + a^{9} d^{8} g^{4} i^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} g^{4} i^{3} - 16 \, a^{3} b^{6} c^{7} d g^{4} i^{3} + 33 \, a^{4} b^{5} c^{6} d^{2} g^{4} i^{3} - 30 \, a^{5} b^{4} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} g^{4} i^{3} + 12 \, a^{7} b^{2} c^{3} d^{5} g^{4} i^{3} - 9 \, a^{8} b c^{2} d^{6} g^{4} i^{3} + 2 \, a^{9} c d^{7} g^{4} i^{3}\right)} x} + \frac{6 \, {\left(4 \, b^{5} c^{5} - 45 \, a b^{4} c^{4} d + 360 \, a^{2} b^{3} c^{3} d^{2} - 490 \, a^{3} b^{2} c^{2} d^{3} + 180 \, a^{4} b c d^{4} - 9 \, a^{5} d^{5} + 120 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 120 \, {\left(3 \, b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} - a^{2} b^{3} d^{5}\right)} x^{3} + 20 \, {\left(11 \, b^{5} c^{3} d^{2} + 21 \, a b^{4} c^{2} d^{3} - 39 \, a^{2} b^{3} c d^{4} + 7 \, a^{3} b^{2} d^{5}\right)} x^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(5 \, b^{5} c^{4} d - 108 \, a b^{4} c^{3} d^{2} + 78 \, a^{2} b^{3} c^{2} d^{3} + 52 \, a^{3} b^{2} c d^{4} - 27 \, a^{4} b d^{5}\right)} x + 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 3 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{a^{3} b^{6} c^{8} g^{4} i^{3} - 6 \, a^{4} b^{5} c^{7} d g^{4} i^{3} + 15 \, a^{5} b^{4} c^{6} d^{2} g^{4} i^{3} - 20 \, a^{6} b^{3} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} g^{4} i^{3} - 6 \, a^{8} b c^{3} d^{5} g^{4} i^{3} + a^{9} c^{2} d^{6} g^{4} i^{3} + {\left(b^{9} c^{6} d^{2} g^{4} i^{3} - 6 \, a b^{8} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} g^{4} i^{3} - 20 \, a^{3} b^{6} c^{3} d^{5} g^{4} i^{3} + 15 \, a^{4} b^{5} c^{2} d^{6} g^{4} i^{3} - 6 \, a^{5} b^{4} c d^{7} g^{4} i^{3} + a^{6} b^{3} d^{8} g^{4} i^{3}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d g^{4} i^{3} - 9 \, a b^{8} c^{6} d^{2} g^{4} i^{3} + 12 \, a^{2} b^{7} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} g^{4} i^{3} - 30 \, a^{4} b^{5} c^{3} d^{5} g^{4} i^{3} + 33 \, a^{5} b^{4} c^{2} d^{6} g^{4} i^{3} - 16 \, a^{6} b^{3} c d^{7} g^{4} i^{3} + 3 \, a^{7} b^{2} d^{8} g^{4} i^{3}\right)} x^{4} + {\left(b^{9} c^{8} g^{4} i^{3} - 18 \, a^{2} b^{7} c^{6} d^{2} g^{4} i^{3} + 52 \, a^{3} b^{6} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} g^{4} i^{3} + 24 \, a^{5} b^{4} c^{3} d^{5} g^{4} i^{3} + 10 \, a^{6} b^{3} c^{2} d^{6} g^{4} i^{3} - 12 \, a^{7} b^{2} c d^{7} g^{4} i^{3} + 3 \, a^{8} b d^{8} g^{4} i^{3}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} g^{4} i^{3} - 12 \, a^{2} b^{7} c^{7} d g^{4} i^{3} + 10 \, a^{3} b^{6} c^{6} d^{2} g^{4} i^{3} + 24 \, a^{4} b^{5} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} g^{4} i^{3} + 52 \, a^{6} b^{3} c^{3} d^{5} g^{4} i^{3} - 18 \, a^{7} b^{2} c^{2} d^{6} g^{4} i^{3} + a^{9} d^{8} g^{4} i^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} g^{4} i^{3} - 16 \, a^{3} b^{6} c^{7} d g^{4} i^{3} + 33 \, a^{4} b^{5} c^{6} d^{2} g^{4} i^{3} - 30 \, a^{5} b^{4} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} g^{4} i^{3} + 12 \, a^{7} b^{2} c^{3} d^{5} g^{4} i^{3} - 9 \, a^{8} b c^{2} d^{6} g^{4} i^{3} + 2 \, a^{9} c d^{7} g^{4} i^{3}\right)} x}\right)} B^{2} - \frac{{\left(4 \, b^{5} c^{5} - 45 \, a b^{4} c^{4} d + 360 \, a^{2} b^{3} c^{3} d^{2} - 490 \, a^{3} b^{2} c^{2} d^{3} + 180 \, a^{4} b c d^{4} - 9 \, a^{5} d^{5} + 120 \, {\left(b^{5} c d^{4} - a b^{4} d^{5}\right)} x^{4} + 120 \, {\left(3 \, b^{5} c^{2} d^{3} - 2 \, a b^{4} c d^{4} - a^{2} b^{3} d^{5}\right)} x^{3} + 20 \, {\left(11 \, b^{5} c^{3} d^{2} + 21 \, a b^{4} c^{2} d^{3} - 39 \, a^{2} b^{3} c d^{4} + 7 \, a^{3} b^{2} d^{5}\right)} x^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)^{2} - 180 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(d x + c\right)^{2} - 5 \, {\left(5 \, b^{5} c^{4} d - 108 \, a b^{4} c^{3} d^{2} + 78 \, a^{2} b^{3} c^{2} d^{3} + 52 \, a^{3} b^{2} c d^{4} - 27 \, a^{4} b d^{5}\right)} x + 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right) - 120 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x - 3 \, {\left(b^{5} d^{5} x^{5} + a^{3} b^{2} c^{2} d^{3} + {\left(2 \, b^{5} c d^{4} + 3 \, a b^{4} d^{5}\right)} x^{4} + {\left(b^{5} c^{2} d^{3} + 6 \, a b^{4} c d^{4} + 3 \, a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, a b^{4} c^{2} d^{3} + 6 \, a^{2} b^{3} c d^{4} + a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, a^{2} b^{3} c^{2} d^{3} + 2 \, a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} A B n}{18 \, {\left(a^{3} b^{6} c^{8} g^{4} i^{3} - 6 \, a^{4} b^{5} c^{7} d g^{4} i^{3} + 15 \, a^{5} b^{4} c^{6} d^{2} g^{4} i^{3} - 20 \, a^{6} b^{3} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} g^{4} i^{3} - 6 \, a^{8} b c^{3} d^{5} g^{4} i^{3} + a^{9} c^{2} d^{6} g^{4} i^{3} + {\left(b^{9} c^{6} d^{2} g^{4} i^{3} - 6 \, a b^{8} c^{5} d^{3} g^{4} i^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} g^{4} i^{3} - 20 \, a^{3} b^{6} c^{3} d^{5} g^{4} i^{3} + 15 \, a^{4} b^{5} c^{2} d^{6} g^{4} i^{3} - 6 \, a^{5} b^{4} c d^{7} g^{4} i^{3} + a^{6} b^{3} d^{8} g^{4} i^{3}\right)} x^{5} + {\left(2 \, b^{9} c^{7} d g^{4} i^{3} - 9 \, a b^{8} c^{6} d^{2} g^{4} i^{3} + 12 \, a^{2} b^{7} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} g^{4} i^{3} - 30 \, a^{4} b^{5} c^{3} d^{5} g^{4} i^{3} + 33 \, a^{5} b^{4} c^{2} d^{6} g^{4} i^{3} - 16 \, a^{6} b^{3} c d^{7} g^{4} i^{3} + 3 \, a^{7} b^{2} d^{8} g^{4} i^{3}\right)} x^{4} + {\left(b^{9} c^{8} g^{4} i^{3} - 18 \, a^{2} b^{7} c^{6} d^{2} g^{4} i^{3} + 52 \, a^{3} b^{6} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} g^{4} i^{3} + 24 \, a^{5} b^{4} c^{3} d^{5} g^{4} i^{3} + 10 \, a^{6} b^{3} c^{2} d^{6} g^{4} i^{3} - 12 \, a^{7} b^{2} c d^{7} g^{4} i^{3} + 3 \, a^{8} b d^{8} g^{4} i^{3}\right)} x^{3} + {\left(3 \, a b^{8} c^{8} g^{4} i^{3} - 12 \, a^{2} b^{7} c^{7} d g^{4} i^{3} + 10 \, a^{3} b^{6} c^{6} d^{2} g^{4} i^{3} + 24 \, a^{4} b^{5} c^{5} d^{3} g^{4} i^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} g^{4} i^{3} + 52 \, a^{6} b^{3} c^{3} d^{5} g^{4} i^{3} - 18 \, a^{7} b^{2} c^{2} d^{6} g^{4} i^{3} + a^{9} d^{8} g^{4} i^{3}\right)} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} g^{4} i^{3} - 16 \, a^{3} b^{6} c^{7} d g^{4} i^{3} + 33 \, a^{4} b^{5} c^{6} d^{2} g^{4} i^{3} - 30 \, a^{5} b^{4} c^{5} d^{3} g^{4} i^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} g^{4} i^{3} + 12 \, a^{7} b^{2} c^{3} d^{5} g^{4} i^{3} - 9 \, a^{8} b c^{2} d^{6} g^{4} i^{3} + 2 \, a^{9} c d^{7} g^{4} i^{3}\right)} x\right)}} - \frac{1}{6} \, A^{2} {\left(\frac{60 \, b^{4} d^{4} x^{4} + 2 \, b^{4} c^{4} - 13 \, a b^{3} c^{3} d + 47 \, a^{2} b^{2} c^{2} d^{2} + 27 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4} + 30 \, {\left(3 \, b^{4} c d^{3} + 5 \, a b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, b^{4} c^{2} d^{2} + 23 \, a b^{3} c d^{3} + 11 \, a^{2} b^{2} d^{4}\right)} x^{2} - 5 \, {\left(b^{4} c^{3} d - 11 \, a b^{3} c^{2} d^{2} - 35 \, a^{2} b^{2} c d^{3} - 3 \, a^{3} b d^{4}\right)} x}{{\left(b^{8} c^{5} d^{2} - 5 \, a b^{7} c^{4} d^{3} + 10 \, a^{2} b^{6} c^{3} d^{4} - 10 \, a^{3} b^{5} c^{2} d^{5} + 5 \, a^{4} b^{4} c d^{6} - a^{5} b^{3} d^{7}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{8} c^{6} d - 7 \, a b^{7} c^{5} d^{2} + 5 \, a^{2} b^{6} c^{4} d^{3} + 10 \, a^{3} b^{5} c^{3} d^{4} - 20 \, a^{4} b^{4} c^{2} d^{5} + 13 \, a^{5} b^{3} c d^{6} - 3 \, a^{6} b^{2} d^{7}\right)} g^{4} i^{3} x^{4} + {\left(b^{8} c^{7} + a b^{7} c^{6} d - 17 \, a^{2} b^{6} c^{5} d^{2} + 35 \, a^{3} b^{5} c^{4} d^{3} - 25 \, a^{4} b^{4} c^{3} d^{4} - a^{5} b^{3} c^{2} d^{5} + 9 \, a^{6} b^{2} c d^{6} - 3 \, a^{7} b d^{7}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{7} c^{7} - 9 \, a^{2} b^{6} c^{6} d + a^{3} b^{5} c^{5} d^{2} + 25 \, a^{4} b^{4} c^{4} d^{3} - 35 \, a^{5} b^{3} c^{3} d^{4} + 17 \, a^{6} b^{2} c^{2} d^{5} - a^{7} b c d^{6} - a^{8} d^{7}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{6} c^{7} - 13 \, a^{3} b^{5} c^{6} d + 20 \, a^{4} b^{4} c^{5} d^{2} - 10 \, a^{5} b^{3} c^{4} d^{3} - 5 \, a^{6} b^{2} c^{3} d^{4} + 7 \, a^{7} b c^{2} d^{5} - 2 \, a^{8} c d^{6}\right)} g^{4} i^{3} x + {\left(a^{3} b^{5} c^{7} - 5 \, a^{4} b^{4} c^{6} d + 10 \, a^{5} b^{3} c^{5} d^{2} - 10 \, a^{6} b^{2} c^{4} d^{3} + 5 \, a^{7} b c^{3} d^{4} - a^{8} c^{2} d^{5}\right)} g^{4} i^{3}} + \frac{60 \, b^{2} d^{3} \log\left(b x + a\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}} - \frac{60 \, b^{2} d^{3} \log\left(d x + c\right)}{{\left(b^{6} c^{6} - 6 \, a b^{5} c^{5} d + 15 \, a^{2} b^{4} c^{4} d^{2} - 20 \, a^{3} b^{3} c^{3} d^{3} + 15 \, a^{4} b^{2} c^{2} d^{4} - 6 \, a^{5} b c d^{5} + a^{6} d^{6}\right)} g^{4} i^{3}}\right)}"," ",0,"-1/6*B^2*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2 - 1/3*A*B*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - 1/108*((8*b^5*c^5 - 135*a*b^4*c^4*d + 2160*a^2*b^3*c^3*d^2 - 980*a^3*b^2*c^2*d^3 - 1080*a^4*b*c*d^4 + 27*a^5*d^5 + 2940*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 30*(159*b^5*c^2*d^3 + 74*a*b^4*c*d^4 - 233*a^2*b^3*d^5)*x^3 + 360*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^3 - 360*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c)^3 + 10*(170*b^5*c^3*d^2 + 921*a*b^4*c^2*d^3 - 588*a^2*b^3*c*d^4 - 503*a^3*b^2*d^5)*x^2 - 360*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 - 360*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 3*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c)^2 - 5*(19*b^5*c^4*d - 756*a*b^4*c^3*d^2 - 708*a^2*b^3*c^2*d^3 + 1256*a^3*b^2*c*d^4 + 189*a^4*b*d^5)*x + 2940*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 60*(49*b^5*d^5*x^5 + 49*a^3*b^2*c^2*d^3 + 49*(2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + 49*(b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + 49*(3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + 18*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 + 49*(3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 12*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c))*n^2/(a^3*b^6*c^8*g^4*i^3 - 6*a^4*b^5*c^7*d*g^4*i^3 + 15*a^5*b^4*c^6*d^2*g^4*i^3 - 20*a^6*b^3*c^5*d^3*g^4*i^3 + 15*a^7*b^2*c^4*d^4*g^4*i^3 - 6*a^8*b*c^3*d^5*g^4*i^3 + a^9*c^2*d^6*g^4*i^3 + (b^9*c^6*d^2*g^4*i^3 - 6*a*b^8*c^5*d^3*g^4*i^3 + 15*a^2*b^7*c^4*d^4*g^4*i^3 - 20*a^3*b^6*c^3*d^5*g^4*i^3 + 15*a^4*b^5*c^2*d^6*g^4*i^3 - 6*a^5*b^4*c*d^7*g^4*i^3 + a^6*b^3*d^8*g^4*i^3)*x^5 + (2*b^9*c^7*d*g^4*i^3 - 9*a*b^8*c^6*d^2*g^4*i^3 + 12*a^2*b^7*c^5*d^3*g^4*i^3 + 5*a^3*b^6*c^4*d^4*g^4*i^3 - 30*a^4*b^5*c^3*d^5*g^4*i^3 + 33*a^5*b^4*c^2*d^6*g^4*i^3 - 16*a^6*b^3*c*d^7*g^4*i^3 + 3*a^7*b^2*d^8*g^4*i^3)*x^4 + (b^9*c^8*g^4*i^3 - 18*a^2*b^7*c^6*d^2*g^4*i^3 + 52*a^3*b^6*c^5*d^3*g^4*i^3 - 60*a^4*b^5*c^4*d^4*g^4*i^3 + 24*a^5*b^4*c^3*d^5*g^4*i^3 + 10*a^6*b^3*c^2*d^6*g^4*i^3 - 12*a^7*b^2*c*d^7*g^4*i^3 + 3*a^8*b*d^8*g^4*i^3)*x^3 + (3*a*b^8*c^8*g^4*i^3 - 12*a^2*b^7*c^7*d*g^4*i^3 + 10*a^3*b^6*c^6*d^2*g^4*i^3 + 24*a^4*b^5*c^5*d^3*g^4*i^3 - 60*a^5*b^4*c^4*d^4*g^4*i^3 + 52*a^6*b^3*c^3*d^5*g^4*i^3 - 18*a^7*b^2*c^2*d^6*g^4*i^3 + a^9*d^8*g^4*i^3)*x^2 + (3*a^2*b^7*c^8*g^4*i^3 - 16*a^3*b^6*c^7*d*g^4*i^3 + 33*a^4*b^5*c^6*d^2*g^4*i^3 - 30*a^5*b^4*c^5*d^3*g^4*i^3 + 5*a^6*b^3*c^4*d^4*g^4*i^3 + 12*a^7*b^2*c^3*d^5*g^4*i^3 - 9*a^8*b*c^2*d^6*g^4*i^3 + 2*a^9*c*d^7*g^4*i^3)*x) + 6*(4*b^5*c^5 - 45*a*b^4*c^4*d + 360*a^2*b^3*c^3*d^2 - 490*a^3*b^2*c^2*d^3 + 180*a^4*b*c*d^4 - 9*a^5*d^5 + 120*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 120*(3*b^5*c^2*d^3 - 2*a*b^4*c*d^4 - a^2*b^3*d^5)*x^3 + 20*(11*b^5*c^3*d^2 + 21*a*b^4*c^2*d^3 - 39*a^2*b^3*c*d^4 + 7*a^3*b^2*d^5)*x^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c)^2 - 5*(5*b^5*c^4*d - 108*a*b^4*c^3*d^2 + 78*a^2*b^3*c^2*d^3 + 52*a^3*b^2*c*d^4 - 27*a^4*b*d^5)*x + 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 3*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c))*n*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(a^3*b^6*c^8*g^4*i^3 - 6*a^4*b^5*c^7*d*g^4*i^3 + 15*a^5*b^4*c^6*d^2*g^4*i^3 - 20*a^6*b^3*c^5*d^3*g^4*i^3 + 15*a^7*b^2*c^4*d^4*g^4*i^3 - 6*a^8*b*c^3*d^5*g^4*i^3 + a^9*c^2*d^6*g^4*i^3 + (b^9*c^6*d^2*g^4*i^3 - 6*a*b^8*c^5*d^3*g^4*i^3 + 15*a^2*b^7*c^4*d^4*g^4*i^3 - 20*a^3*b^6*c^3*d^5*g^4*i^3 + 15*a^4*b^5*c^2*d^6*g^4*i^3 - 6*a^5*b^4*c*d^7*g^4*i^3 + a^6*b^3*d^8*g^4*i^3)*x^5 + (2*b^9*c^7*d*g^4*i^3 - 9*a*b^8*c^6*d^2*g^4*i^3 + 12*a^2*b^7*c^5*d^3*g^4*i^3 + 5*a^3*b^6*c^4*d^4*g^4*i^3 - 30*a^4*b^5*c^3*d^5*g^4*i^3 + 33*a^5*b^4*c^2*d^6*g^4*i^3 - 16*a^6*b^3*c*d^7*g^4*i^3 + 3*a^7*b^2*d^8*g^4*i^3)*x^4 + (b^9*c^8*g^4*i^3 - 18*a^2*b^7*c^6*d^2*g^4*i^3 + 52*a^3*b^6*c^5*d^3*g^4*i^3 - 60*a^4*b^5*c^4*d^4*g^4*i^3 + 24*a^5*b^4*c^3*d^5*g^4*i^3 + 10*a^6*b^3*c^2*d^6*g^4*i^3 - 12*a^7*b^2*c*d^7*g^4*i^3 + 3*a^8*b*d^8*g^4*i^3)*x^3 + (3*a*b^8*c^8*g^4*i^3 - 12*a^2*b^7*c^7*d*g^4*i^3 + 10*a^3*b^6*c^6*d^2*g^4*i^3 + 24*a^4*b^5*c^5*d^3*g^4*i^3 - 60*a^5*b^4*c^4*d^4*g^4*i^3 + 52*a^6*b^3*c^3*d^5*g^4*i^3 - 18*a^7*b^2*c^2*d^6*g^4*i^3 + a^9*d^8*g^4*i^3)*x^2 + (3*a^2*b^7*c^8*g^4*i^3 - 16*a^3*b^6*c^7*d*g^4*i^3 + 33*a^4*b^5*c^6*d^2*g^4*i^3 - 30*a^5*b^4*c^5*d^3*g^4*i^3 + 5*a^6*b^3*c^4*d^4*g^4*i^3 + 12*a^7*b^2*c^3*d^5*g^4*i^3 - 9*a^8*b*c^2*d^6*g^4*i^3 + 2*a^9*c*d^7*g^4*i^3)*x))*B^2 - 1/18*(4*b^5*c^5 - 45*a*b^4*c^4*d + 360*a^2*b^3*c^3*d^2 - 490*a^3*b^2*c^2*d^3 + 180*a^4*b*c*d^4 - 9*a^5*d^5 + 120*(b^5*c*d^4 - a*b^4*d^5)*x^4 + 120*(3*b^5*c^2*d^3 - 2*a*b^4*c*d^4 - a^2*b^3*d^5)*x^3 + 20*(11*b^5*c^3*d^2 + 21*a*b^4*c^2*d^3 - 39*a^2*b^3*c*d^4 + 7*a^3*b^2*d^5)*x^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a)^2 - 180*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(d*x + c)^2 - 5*(5*b^5*c^4*d - 108*a*b^4*c^3*d^2 + 78*a^2*b^3*c^2*d^3 + 52*a^3*b^2*c*d^4 - 27*a^4*b*d^5)*x + 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a) - 120*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x - 3*(b^5*d^5*x^5 + a^3*b^2*c^2*d^3 + (2*b^5*c*d^4 + 3*a*b^4*d^5)*x^4 + (b^5*c^2*d^3 + 6*a*b^4*c*d^4 + 3*a^2*b^3*d^5)*x^3 + (3*a*b^4*c^2*d^3 + 6*a^2*b^3*c*d^4 + a^3*b^2*d^5)*x^2 + (3*a^2*b^3*c^2*d^3 + 2*a^3*b^2*c*d^4)*x)*log(b*x + a))*log(d*x + c))*A*B*n/(a^3*b^6*c^8*g^4*i^3 - 6*a^4*b^5*c^7*d*g^4*i^3 + 15*a^5*b^4*c^6*d^2*g^4*i^3 - 20*a^6*b^3*c^5*d^3*g^4*i^3 + 15*a^7*b^2*c^4*d^4*g^4*i^3 - 6*a^8*b*c^3*d^5*g^4*i^3 + a^9*c^2*d^6*g^4*i^3 + (b^9*c^6*d^2*g^4*i^3 - 6*a*b^8*c^5*d^3*g^4*i^3 + 15*a^2*b^7*c^4*d^4*g^4*i^3 - 20*a^3*b^6*c^3*d^5*g^4*i^3 + 15*a^4*b^5*c^2*d^6*g^4*i^3 - 6*a^5*b^4*c*d^7*g^4*i^3 + a^6*b^3*d^8*g^4*i^3)*x^5 + (2*b^9*c^7*d*g^4*i^3 - 9*a*b^8*c^6*d^2*g^4*i^3 + 12*a^2*b^7*c^5*d^3*g^4*i^3 + 5*a^3*b^6*c^4*d^4*g^4*i^3 - 30*a^4*b^5*c^3*d^5*g^4*i^3 + 33*a^5*b^4*c^2*d^6*g^4*i^3 - 16*a^6*b^3*c*d^7*g^4*i^3 + 3*a^7*b^2*d^8*g^4*i^3)*x^4 + (b^9*c^8*g^4*i^3 - 18*a^2*b^7*c^6*d^2*g^4*i^3 + 52*a^3*b^6*c^5*d^3*g^4*i^3 - 60*a^4*b^5*c^4*d^4*g^4*i^3 + 24*a^5*b^4*c^3*d^5*g^4*i^3 + 10*a^6*b^3*c^2*d^6*g^4*i^3 - 12*a^7*b^2*c*d^7*g^4*i^3 + 3*a^8*b*d^8*g^4*i^3)*x^3 + (3*a*b^8*c^8*g^4*i^3 - 12*a^2*b^7*c^7*d*g^4*i^3 + 10*a^3*b^6*c^6*d^2*g^4*i^3 + 24*a^4*b^5*c^5*d^3*g^4*i^3 - 60*a^5*b^4*c^4*d^4*g^4*i^3 + 52*a^6*b^3*c^3*d^5*g^4*i^3 - 18*a^7*b^2*c^2*d^6*g^4*i^3 + a^9*d^8*g^4*i^3)*x^2 + (3*a^2*b^7*c^8*g^4*i^3 - 16*a^3*b^6*c^7*d*g^4*i^3 + 33*a^4*b^5*c^6*d^2*g^4*i^3 - 30*a^5*b^4*c^5*d^3*g^4*i^3 + 5*a^6*b^3*c^4*d^4*g^4*i^3 + 12*a^7*b^2*c^3*d^5*g^4*i^3 - 9*a^8*b*c^2*d^6*g^4*i^3 + 2*a^9*c*d^7*g^4*i^3)*x) - 1/6*A^2*((60*b^4*d^4*x^4 + 2*b^4*c^4 - 13*a*b^3*c^3*d + 47*a^2*b^2*c^2*d^2 + 27*a^3*b*c*d^3 - 3*a^4*d^4 + 30*(3*b^4*c*d^3 + 5*a*b^3*d^4)*x^3 + 10*(2*b^4*c^2*d^2 + 23*a*b^3*c*d^3 + 11*a^2*b^2*d^4)*x^2 - 5*(b^4*c^3*d - 11*a*b^3*c^2*d^2 - 35*a^2*b^2*c*d^3 - 3*a^3*b*d^4)*x)/((b^8*c^5*d^2 - 5*a*b^7*c^4*d^3 + 10*a^2*b^6*c^3*d^4 - 10*a^3*b^5*c^2*d^5 + 5*a^4*b^4*c*d^6 - a^5*b^3*d^7)*g^4*i^3*x^5 + (2*b^8*c^6*d - 7*a*b^7*c^5*d^2 + 5*a^2*b^6*c^4*d^3 + 10*a^3*b^5*c^3*d^4 - 20*a^4*b^4*c^2*d^5 + 13*a^5*b^3*c*d^6 - 3*a^6*b^2*d^7)*g^4*i^3*x^4 + (b^8*c^7 + a*b^7*c^6*d - 17*a^2*b^6*c^5*d^2 + 35*a^3*b^5*c^4*d^3 - 25*a^4*b^4*c^3*d^4 - a^5*b^3*c^2*d^5 + 9*a^6*b^2*c*d^6 - 3*a^7*b*d^7)*g^4*i^3*x^3 + (3*a*b^7*c^7 - 9*a^2*b^6*c^6*d + a^3*b^5*c^5*d^2 + 25*a^4*b^4*c^4*d^3 - 35*a^5*b^3*c^3*d^4 + 17*a^6*b^2*c^2*d^5 - a^7*b*c*d^6 - a^8*d^7)*g^4*i^3*x^2 + (3*a^2*b^6*c^7 - 13*a^3*b^5*c^6*d + 20*a^4*b^4*c^5*d^2 - 10*a^5*b^3*c^4*d^3 - 5*a^6*b^2*c^3*d^4 + 7*a^7*b*c^2*d^5 - 2*a^8*c*d^6)*g^4*i^3*x + (a^3*b^5*c^7 - 5*a^4*b^4*c^6*d + 10*a^5*b^3*c^5*d^2 - 10*a^6*b^2*c^4*d^3 + 5*a^7*b*c^3*d^4 - a^8*c^2*d^5)*g^4*i^3) + 60*b^2*d^3*log(b*x + a)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3) - 60*b^2*d^3*log(d*x + c)/((b^6*c^6 - 6*a*b^5*c^5*d + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a^5*b*c*d^5 + a^6*d^6)*g^4*i^3))","B",0
210,0,0,0,0.000000," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^p,x, algorithm=""maxima"")","\int {\left(b g x + a g\right)}^{m} {\left(d i x + c i\right)}^{-m - 2} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}^{p}\,{d x}"," ",0,"integrate((b*g*x + a*g)^m*(d*i*x + c*i)^(-m - 2)*(B*log(e*((b*x + a)/(d*x + c))^n) + A)^p, x)","F",0
211,0,0,0,0.000000," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*((b*x+a)/(d*x+c))^n))^p,x, algorithm=""maxima"")","\int {\left(b g x + a g\right)}^{-m - 2} {\left(d i x + c i\right)}^{m} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}^{p}\,{d x}"," ",0,"integrate((b*g*x + a*g)^(-m - 2)*(d*i*x + c*i)^m*(B*log(e*((b*x + a)/(d*x + c))^n) + A)^p, x)","F",0
212,0,0,0,0.000000," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^3,x, algorithm=""maxima"")","\int {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}^{3} {\left(b g x + a g\right)}^{m} {\left(d i x + c i\right)}^{-m - 2}\,{d x}"," ",0,"integrate((B*log(e*((b*x + a)/(d*x + c))^n) + A)^3*(b*g*x + a*g)^m*(d*i*x + c*i)^(-m - 2), x)","F",0
213,0,0,0,0.000000," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\int {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}^{2} {\left(b g x + a g\right)}^{m} {\left(d i x + c i\right)}^{-m - 2}\,{d x}"," ",0,"integrate((B*log(e*((b*x + a)/(d*x + c))^n) + A)^2*(b*g*x + a*g)^m*(d*i*x + c*i)^(-m - 2), x)","F",0
214,0,0,0,0.000000," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)} {\left(b g x + a g\right)}^{m} {\left(d i x + c i\right)}^{-m - 2}\,{d x}"," ",0,"integrate((B*log(e*((b*x + a)/(d*x + c))^n) + A)*(b*g*x + a*g)^m*(d*i*x + c*i)^(-m - 2), x)","F",0
215,0,0,0,0.000000," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{{\left(b g x + a g\right)}^{m} {\left(d i x + c i\right)}^{-m - 2}}{B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)^m*(d*i*x + c*i)^(-m - 2)/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
216,0,0,0,0.000000," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-g^{m} {\left(m + 1\right)} \int -\frac{{\left(b x + a\right)}^{m}}{{\left(B^{2} d^{2} i^{m + 2} n x^{2} + 2 \, B^{2} c d i^{m + 2} n x + B^{2} c^{2} i^{m + 2} n\right)} {\left(d x + c\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B^{2} d^{2} i^{m + 2} n x^{2} + 2 \, B^{2} c d i^{m + 2} n x + B^{2} c^{2} i^{m + 2} n\right)} {\left(d x + c\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right) + {\left(B^{2} c^{2} i^{m + 2} n \log\left(e\right) + A B c^{2} i^{m + 2} n + {\left(B^{2} d^{2} i^{m + 2} n \log\left(e\right) + A B d^{2} i^{m + 2} n\right)} x^{2} + 2 \, {\left(B^{2} c d i^{m + 2} n \log\left(e\right) + A B c d i^{m + 2} n\right)} x\right)} {\left(d x + c\right)}^{m}}\,{d x} - \frac{{\left(b g^{m} x + a g^{m}\right)} {\left(b x + a\right)}^{m}}{{\left({\left(b c d i^{m + 2} n - a d^{2} i^{m + 2} n\right)} B^{2} x + {\left(b c^{2} i^{m + 2} n - a c d i^{m + 2} n\right)} B^{2}\right)} {\left(d x + c\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c d i^{m + 2} n - a d^{2} i^{m + 2} n\right)} B^{2} x + {\left(b c^{2} i^{m + 2} n - a c d i^{m + 2} n\right)} B^{2}\right)} {\left(d x + c\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right) + {\left({\left(b c^{2} i^{m + 2} n - a c d i^{m + 2} n\right)} A B + {\left(b c^{2} i^{m + 2} n \log\left(e\right) - a c d i^{m + 2} n \log\left(e\right)\right)} B^{2} + {\left({\left(b c d i^{m + 2} n - a d^{2} i^{m + 2} n\right)} A B + {\left(b c d i^{m + 2} n \log\left(e\right) - a d^{2} i^{m + 2} n \log\left(e\right)\right)} B^{2}\right)} x\right)} {\left(d x + c\right)}^{m}}"," ",0,"-g^m*(m + 1)*integrate(-(b*x + a)^m/((B^2*d^2*i^(m + 2)*n*x^2 + 2*B^2*c*d*i^(m + 2)*n*x + B^2*c^2*i^(m + 2)*n)*(d*x + c)^m*log((b*x + a)^n) - (B^2*d^2*i^(m + 2)*n*x^2 + 2*B^2*c*d*i^(m + 2)*n*x + B^2*c^2*i^(m + 2)*n)*(d*x + c)^m*log((d*x + c)^n) + (B^2*c^2*i^(m + 2)*n*log(e) + A*B*c^2*i^(m + 2)*n + (B^2*d^2*i^(m + 2)*n*log(e) + A*B*d^2*i^(m + 2)*n)*x^2 + 2*(B^2*c*d*i^(m + 2)*n*log(e) + A*B*c*d*i^(m + 2)*n)*x)*(d*x + c)^m), x) - (b*g^m*x + a*g^m)*(b*x + a)^m/(((b*c*d*i^(m + 2)*n - a*d^2*i^(m + 2)*n)*B^2*x + (b*c^2*i^(m + 2)*n - a*c*d*i^(m + 2)*n)*B^2)*(d*x + c)^m*log((b*x + a)^n) - ((b*c*d*i^(m + 2)*n - a*d^2*i^(m + 2)*n)*B^2*x + (b*c^2*i^(m + 2)*n - a*c*d*i^(m + 2)*n)*B^2)*(d*x + c)^m*log((d*x + c)^n) + ((b*c^2*i^(m + 2)*n - a*c*d*i^(m + 2)*n)*A*B + (b*c^2*i^(m + 2)*n*log(e) - a*c*d*i^(m + 2)*n*log(e))*B^2 + ((b*c*d*i^(m + 2)*n - a*d^2*i^(m + 2)*n)*A*B + (b*c*d*i^(m + 2)*n*log(e) - a*d^2*i^(m + 2)*n*log(e))*B^2)*x)*(d*x + c)^m)","F",0
217,0,0,0,0.000000," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^3,x, algorithm=""maxima"")","-{\left(m^{2} + 2 \, m + 1\right)} g^{m} \int -\frac{{\left(b x + a\right)}^{m}}{2 \, {\left({\left(B^{3} d^{2} i^{m + 2} n^{2} x^{2} + 2 \, B^{3} c d i^{m + 2} n^{2} x + B^{3} c^{2} i^{m + 2} n^{2}\right)} {\left(d x + c\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B^{3} d^{2} i^{m + 2} n^{2} x^{2} + 2 \, B^{3} c d i^{m + 2} n^{2} x + B^{3} c^{2} i^{m + 2} n^{2}\right)} {\left(d x + c\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right) + {\left(B^{3} c^{2} i^{m + 2} n^{2} \log\left(e\right) + A B^{2} c^{2} i^{m + 2} n^{2} + {\left(B^{3} d^{2} i^{m + 2} n^{2} \log\left(e\right) + A B^{2} d^{2} i^{m + 2} n^{2}\right)} x^{2} + 2 \, {\left(B^{3} c d i^{m + 2} n^{2} \log\left(e\right) + A B^{2} c d i^{m + 2} n^{2}\right)} x\right)} {\left(d x + c\right)}^{m}\right)}}\,{d x} - \frac{{\left(B b g^{m} {\left(m + 1\right)} x + B a g^{m} {\left(m + 1\right)}\right)} {\left(b x + a\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B b g^{m} {\left(m + 1\right)} x + B a g^{m} {\left(m + 1\right)}\right)} {\left(b x + a\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right) + {\left(A a g^{m} {\left(m + 1\right)} + {\left(g^{m} {\left(m + 1\right)} \log\left(e\right) + g^{m} n\right)} B a + {\left(A b g^{m} {\left(m + 1\right)} + {\left(g^{m} {\left(m + 1\right)} \log\left(e\right) + g^{m} n\right)} B b\right)} x\right)} {\left(b x + a\right)}^{m}}{2 \, {\left({\left({\left(b c d i^{m + 2} n^{2} - a d^{2} i^{m + 2} n^{2}\right)} B^{4} x + {\left(b c^{2} i^{m + 2} n^{2} - a c d i^{m + 2} n^{2}\right)} B^{4}\right)} {\left(d x + c\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left({\left(b c d i^{m + 2} n^{2} - a d^{2} i^{m + 2} n^{2}\right)} B^{4} x + {\left(b c^{2} i^{m + 2} n^{2} - a c d i^{m + 2} n^{2}\right)} B^{4}\right)} {\left(d x + c\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left({\left(b c^{2} i^{m + 2} n^{2} - a c d i^{m + 2} n^{2}\right)} A B^{3} + {\left(b c^{2} i^{m + 2} n^{2} \log\left(e\right) - a c d i^{m + 2} n^{2} \log\left(e\right)\right)} B^{4} + {\left({\left(b c d i^{m + 2} n^{2} - a d^{2} i^{m + 2} n^{2}\right)} A B^{3} + {\left(b c d i^{m + 2} n^{2} \log\left(e\right) - a d^{2} i^{m + 2} n^{2} \log\left(e\right)\right)} B^{4}\right)} x\right)} {\left(d x + c\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) + {\left({\left(b c^{2} i^{m + 2} n^{2} - a c d i^{m + 2} n^{2}\right)} A^{2} B^{2} + 2 \, {\left(b c^{2} i^{m + 2} n^{2} \log\left(e\right) - a c d i^{m + 2} n^{2} \log\left(e\right)\right)} A B^{3} + {\left(b c^{2} i^{m + 2} n^{2} \log\left(e\right)^{2} - a c d i^{m + 2} n^{2} \log\left(e\right)^{2}\right)} B^{4} + {\left({\left(b c d i^{m + 2} n^{2} - a d^{2} i^{m + 2} n^{2}\right)} A^{2} B^{2} + 2 \, {\left(b c d i^{m + 2} n^{2} \log\left(e\right) - a d^{2} i^{m + 2} n^{2} \log\left(e\right)\right)} A B^{3} + {\left(b c d i^{m + 2} n^{2} \log\left(e\right)^{2} - a d^{2} i^{m + 2} n^{2} \log\left(e\right)^{2}\right)} B^{4}\right)} x\right)} {\left(d x + c\right)}^{m} - 2 \, {\left({\left({\left(b c d i^{m + 2} n^{2} - a d^{2} i^{m + 2} n^{2}\right)} B^{4} x + {\left(b c^{2} i^{m + 2} n^{2} - a c d i^{m + 2} n^{2}\right)} B^{4}\right)} {\left(d x + c\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) + {\left({\left(b c^{2} i^{m + 2} n^{2} - a c d i^{m + 2} n^{2}\right)} A B^{3} + {\left(b c^{2} i^{m + 2} n^{2} \log\left(e\right) - a c d i^{m + 2} n^{2} \log\left(e\right)\right)} B^{4} + {\left({\left(b c d i^{m + 2} n^{2} - a d^{2} i^{m + 2} n^{2}\right)} A B^{3} + {\left(b c d i^{m + 2} n^{2} \log\left(e\right) - a d^{2} i^{m + 2} n^{2} \log\left(e\right)\right)} B^{4}\right)} x\right)} {\left(d x + c\right)}^{m}\right)} \log\left({\left(d x + c\right)}^{n}\right)\right)}}"," ",0,"-(m^2 + 2*m + 1)*g^m*integrate(-1/2*(b*x + a)^m/((B^3*d^2*i^(m + 2)*n^2*x^2 + 2*B^3*c*d*i^(m + 2)*n^2*x + B^3*c^2*i^(m + 2)*n^2)*(d*x + c)^m*log((b*x + a)^n) - (B^3*d^2*i^(m + 2)*n^2*x^2 + 2*B^3*c*d*i^(m + 2)*n^2*x + B^3*c^2*i^(m + 2)*n^2)*(d*x + c)^m*log((d*x + c)^n) + (B^3*c^2*i^(m + 2)*n^2*log(e) + A*B^2*c^2*i^(m + 2)*n^2 + (B^3*d^2*i^(m + 2)*n^2*log(e) + A*B^2*d^2*i^(m + 2)*n^2)*x^2 + 2*(B^3*c*d*i^(m + 2)*n^2*log(e) + A*B^2*c*d*i^(m + 2)*n^2)*x)*(d*x + c)^m), x) - 1/2*((B*b*g^m*(m + 1)*x + B*a*g^m*(m + 1))*(b*x + a)^m*log((b*x + a)^n) - (B*b*g^m*(m + 1)*x + B*a*g^m*(m + 1))*(b*x + a)^m*log((d*x + c)^n) + (A*a*g^m*(m + 1) + (g^m*(m + 1)*log(e) + g^m*n)*B*a + (A*b*g^m*(m + 1) + (g^m*(m + 1)*log(e) + g^m*n)*B*b)*x)*(b*x + a)^m)/(((b*c*d*i^(m + 2)*n^2 - a*d^2*i^(m + 2)*n^2)*B^4*x + (b*c^2*i^(m + 2)*n^2 - a*c*d*i^(m + 2)*n^2)*B^4)*(d*x + c)^m*log((b*x + a)^n)^2 + ((b*c*d*i^(m + 2)*n^2 - a*d^2*i^(m + 2)*n^2)*B^4*x + (b*c^2*i^(m + 2)*n^2 - a*c*d*i^(m + 2)*n^2)*B^4)*(d*x + c)^m*log((d*x + c)^n)^2 + 2*((b*c^2*i^(m + 2)*n^2 - a*c*d*i^(m + 2)*n^2)*A*B^3 + (b*c^2*i^(m + 2)*n^2*log(e) - a*c*d*i^(m + 2)*n^2*log(e))*B^4 + ((b*c*d*i^(m + 2)*n^2 - a*d^2*i^(m + 2)*n^2)*A*B^3 + (b*c*d*i^(m + 2)*n^2*log(e) - a*d^2*i^(m + 2)*n^2*log(e))*B^4)*x)*(d*x + c)^m*log((b*x + a)^n) + ((b*c^2*i^(m + 2)*n^2 - a*c*d*i^(m + 2)*n^2)*A^2*B^2 + 2*(b*c^2*i^(m + 2)*n^2*log(e) - a*c*d*i^(m + 2)*n^2*log(e))*A*B^3 + (b*c^2*i^(m + 2)*n^2*log(e)^2 - a*c*d*i^(m + 2)*n^2*log(e)^2)*B^4 + ((b*c*d*i^(m + 2)*n^2 - a*d^2*i^(m + 2)*n^2)*A^2*B^2 + 2*(b*c*d*i^(m + 2)*n^2*log(e) - a*d^2*i^(m + 2)*n^2*log(e))*A*B^3 + (b*c*d*i^(m + 2)*n^2*log(e)^2 - a*d^2*i^(m + 2)*n^2*log(e)^2)*B^4)*x)*(d*x + c)^m - 2*(((b*c*d*i^(m + 2)*n^2 - a*d^2*i^(m + 2)*n^2)*B^4*x + (b*c^2*i^(m + 2)*n^2 - a*c*d*i^(m + 2)*n^2)*B^4)*(d*x + c)^m*log((b*x + a)^n) + ((b*c^2*i^(m + 2)*n^2 - a*c*d*i^(m + 2)*n^2)*A*B^3 + (b*c^2*i^(m + 2)*n^2*log(e) - a*c*d*i^(m + 2)*n^2*log(e))*B^4 + ((b*c*d*i^(m + 2)*n^2 - a*d^2*i^(m + 2)*n^2)*A*B^3 + (b*c*d*i^(m + 2)*n^2*log(e) - a*d^2*i^(m + 2)*n^2*log(e))*B^4)*x)*(d*x + c)^m)*log((d*x + c)^n))","F",0
218,0,0,0,0.000000," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*((b*x+a)/(d*x+c))^n))^3,x, algorithm=""maxima"")","\int {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}^{3} {\left(b g x + a g\right)}^{-m - 2} {\left(d i x + c i\right)}^{m}\,{d x}"," ",0,"integrate((B*log(e*((b*x + a)/(d*x + c))^n) + A)^3*(b*g*x + a*g)^(-m - 2)*(d*i*x + c*i)^m, x)","F",0
219,0,0,0,0.000000," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\int {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}^{2} {\left(b g x + a g\right)}^{-m - 2} {\left(d i x + c i\right)}^{m}\,{d x}"," ",0,"integrate((B*log(e*((b*x + a)/(d*x + c))^n) + A)^2*(b*g*x + a*g)^(-m - 2)*(d*i*x + c*i)^m, x)","F",0
220,0,0,0,0.000000," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)} {\left(b g x + a g\right)}^{-m - 2} {\left(d i x + c i\right)}^{m}\,{d x}"," ",0,"integrate((B*log(e*((b*x + a)/(d*x + c))^n) + A)*(b*g*x + a*g)^(-m - 2)*(d*i*x + c*i)^m, x)","F",0
221,0,0,0,0.000000," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{{\left(b g x + a g\right)}^{-m - 2} {\left(d i x + c i\right)}^{m}}{B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)^(-m - 2)*(d*i*x + c*i)^m/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
222,0,0,0,0.000000," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","i^{m} {\left(m + 1\right)} \int -\frac{{\left(d x + c\right)}^{m}}{{\left(B^{2} b^{2} g^{m + 2} n x^{2} + 2 \, B^{2} a b g^{m + 2} n x + B^{2} a^{2} g^{m + 2} n\right)} {\left(b x + a\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B^{2} b^{2} g^{m + 2} n x^{2} + 2 \, B^{2} a b g^{m + 2} n x + B^{2} a^{2} g^{m + 2} n\right)} {\left(b x + a\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right) + {\left(B^{2} a^{2} g^{m + 2} n \log\left(e\right) + A B a^{2} g^{m + 2} n + {\left(B^{2} b^{2} g^{m + 2} n \log\left(e\right) + A B b^{2} g^{m + 2} n\right)} x^{2} + 2 \, {\left(B^{2} a b g^{m + 2} n \log\left(e\right) + A B a b g^{m + 2} n\right)} x\right)} {\left(b x + a\right)}^{m}}\,{d x} - \frac{{\left(d i^{m} x + c i^{m}\right)} {\left(d x + c\right)}^{m}}{{\left({\left(b^{2} c g^{m + 2} n - a b d g^{m + 2} n\right)} B^{2} x + {\left(a b c g^{m + 2} n - a^{2} d g^{m + 2} n\right)} B^{2}\right)} {\left(b x + a\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b^{2} c g^{m + 2} n - a b d g^{m + 2} n\right)} B^{2} x + {\left(a b c g^{m + 2} n - a^{2} d g^{m + 2} n\right)} B^{2}\right)} {\left(b x + a\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right) + {\left({\left(a b c g^{m + 2} n - a^{2} d g^{m + 2} n\right)} A B + {\left(a b c g^{m + 2} n \log\left(e\right) - a^{2} d g^{m + 2} n \log\left(e\right)\right)} B^{2} + {\left({\left(b^{2} c g^{m + 2} n - a b d g^{m + 2} n\right)} A B + {\left(b^{2} c g^{m + 2} n \log\left(e\right) - a b d g^{m + 2} n \log\left(e\right)\right)} B^{2}\right)} x\right)} {\left(b x + a\right)}^{m}}"," ",0,"i^m*(m + 1)*integrate(-(d*x + c)^m/((B^2*b^2*g^(m + 2)*n*x^2 + 2*B^2*a*b*g^(m + 2)*n*x + B^2*a^2*g^(m + 2)*n)*(b*x + a)^m*log((b*x + a)^n) - (B^2*b^2*g^(m + 2)*n*x^2 + 2*B^2*a*b*g^(m + 2)*n*x + B^2*a^2*g^(m + 2)*n)*(b*x + a)^m*log((d*x + c)^n) + (B^2*a^2*g^(m + 2)*n*log(e) + A*B*a^2*g^(m + 2)*n + (B^2*b^2*g^(m + 2)*n*log(e) + A*B*b^2*g^(m + 2)*n)*x^2 + 2*(B^2*a*b*g^(m + 2)*n*log(e) + A*B*a*b*g^(m + 2)*n)*x)*(b*x + a)^m), x) - (d*i^m*x + c*i^m)*(d*x + c)^m/(((b^2*c*g^(m + 2)*n - a*b*d*g^(m + 2)*n)*B^2*x + (a*b*c*g^(m + 2)*n - a^2*d*g^(m + 2)*n)*B^2)*(b*x + a)^m*log((b*x + a)^n) - ((b^2*c*g^(m + 2)*n - a*b*d*g^(m + 2)*n)*B^2*x + (a*b*c*g^(m + 2)*n - a^2*d*g^(m + 2)*n)*B^2)*(b*x + a)^m*log((d*x + c)^n) + ((a*b*c*g^(m + 2)*n - a^2*d*g^(m + 2)*n)*A*B + (a*b*c*g^(m + 2)*n*log(e) - a^2*d*g^(m + 2)*n*log(e))*B^2 + ((b^2*c*g^(m + 2)*n - a*b*d*g^(m + 2)*n)*A*B + (b^2*c*g^(m + 2)*n*log(e) - a*b*d*g^(m + 2)*n*log(e))*B^2)*x)*(b*x + a)^m)","F",0
223,0,0,0,0.000000," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m/(A+B*log(e*((b*x+a)/(d*x+c))^n))^3,x, algorithm=""maxima"")","-{\left(m^{2} + 2 \, m + 1\right)} i^{m} \int -\frac{{\left(d x + c\right)}^{m}}{2 \, {\left({\left(B^{3} b^{2} g^{m + 2} n^{2} x^{2} + 2 \, B^{3} a b g^{m + 2} n^{2} x + B^{3} a^{2} g^{m + 2} n^{2}\right)} {\left(b x + a\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B^{3} b^{2} g^{m + 2} n^{2} x^{2} + 2 \, B^{3} a b g^{m + 2} n^{2} x + B^{3} a^{2} g^{m + 2} n^{2}\right)} {\left(b x + a\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right) + {\left(B^{3} a^{2} g^{m + 2} n^{2} \log\left(e\right) + A B^{2} a^{2} g^{m + 2} n^{2} + {\left(B^{3} b^{2} g^{m + 2} n^{2} \log\left(e\right) + A B^{2} b^{2} g^{m + 2} n^{2}\right)} x^{2} + 2 \, {\left(B^{3} a b g^{m + 2} n^{2} \log\left(e\right) + A B^{2} a b g^{m + 2} n^{2}\right)} x\right)} {\left(b x + a\right)}^{m}\right)}}\,{d x} + \frac{{\left(B d i^{m} {\left(m + 1\right)} x + B c i^{m} {\left(m + 1\right)}\right)} {\left(d x + c\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B d i^{m} {\left(m + 1\right)} x + B c i^{m} {\left(m + 1\right)}\right)} {\left(d x + c\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right) + {\left(A c i^{m} {\left(m + 1\right)} + {\left(i^{m} {\left(m + 1\right)} \log\left(e\right) - i^{m} n\right)} B c + {\left(A d i^{m} {\left(m + 1\right)} + {\left(i^{m} {\left(m + 1\right)} \log\left(e\right) - i^{m} n\right)} B d\right)} x\right)} {\left(d x + c\right)}^{m}}{2 \, {\left({\left({\left(b^{2} c g^{m + 2} n^{2} - a b d g^{m + 2} n^{2}\right)} B^{4} x + {\left(a b c g^{m + 2} n^{2} - a^{2} d g^{m + 2} n^{2}\right)} B^{4}\right)} {\left(b x + a\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left({\left(b^{2} c g^{m + 2} n^{2} - a b d g^{m + 2} n^{2}\right)} B^{4} x + {\left(a b c g^{m + 2} n^{2} - a^{2} d g^{m + 2} n^{2}\right)} B^{4}\right)} {\left(b x + a\right)}^{m} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left({\left(a b c g^{m + 2} n^{2} - a^{2} d g^{m + 2} n^{2}\right)} A B^{3} + {\left(a b c g^{m + 2} n^{2} \log\left(e\right) - a^{2} d g^{m + 2} n^{2} \log\left(e\right)\right)} B^{4} + {\left({\left(b^{2} c g^{m + 2} n^{2} - a b d g^{m + 2} n^{2}\right)} A B^{3} + {\left(b^{2} c g^{m + 2} n^{2} \log\left(e\right) - a b d g^{m + 2} n^{2} \log\left(e\right)\right)} B^{4}\right)} x\right)} {\left(b x + a\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) + {\left({\left(a b c g^{m + 2} n^{2} - a^{2} d g^{m + 2} n^{2}\right)} A^{2} B^{2} + 2 \, {\left(a b c g^{m + 2} n^{2} \log\left(e\right) - a^{2} d g^{m + 2} n^{2} \log\left(e\right)\right)} A B^{3} + {\left(a b c g^{m + 2} n^{2} \log\left(e\right)^{2} - a^{2} d g^{m + 2} n^{2} \log\left(e\right)^{2}\right)} B^{4} + {\left({\left(b^{2} c g^{m + 2} n^{2} - a b d g^{m + 2} n^{2}\right)} A^{2} B^{2} + 2 \, {\left(b^{2} c g^{m + 2} n^{2} \log\left(e\right) - a b d g^{m + 2} n^{2} \log\left(e\right)\right)} A B^{3} + {\left(b^{2} c g^{m + 2} n^{2} \log\left(e\right)^{2} - a b d g^{m + 2} n^{2} \log\left(e\right)^{2}\right)} B^{4}\right)} x\right)} {\left(b x + a\right)}^{m} - 2 \, {\left({\left({\left(b^{2} c g^{m + 2} n^{2} - a b d g^{m + 2} n^{2}\right)} B^{4} x + {\left(a b c g^{m + 2} n^{2} - a^{2} d g^{m + 2} n^{2}\right)} B^{4}\right)} {\left(b x + a\right)}^{m} \log\left({\left(b x + a\right)}^{n}\right) + {\left({\left(a b c g^{m + 2} n^{2} - a^{2} d g^{m + 2} n^{2}\right)} A B^{3} + {\left(a b c g^{m + 2} n^{2} \log\left(e\right) - a^{2} d g^{m + 2} n^{2} \log\left(e\right)\right)} B^{4} + {\left({\left(b^{2} c g^{m + 2} n^{2} - a b d g^{m + 2} n^{2}\right)} A B^{3} + {\left(b^{2} c g^{m + 2} n^{2} \log\left(e\right) - a b d g^{m + 2} n^{2} \log\left(e\right)\right)} B^{4}\right)} x\right)} {\left(b x + a\right)}^{m}\right)} \log\left({\left(d x + c\right)}^{n}\right)\right)}}"," ",0,"-(m^2 + 2*m + 1)*i^m*integrate(-1/2*(d*x + c)^m/((B^3*b^2*g^(m + 2)*n^2*x^2 + 2*B^3*a*b*g^(m + 2)*n^2*x + B^3*a^2*g^(m + 2)*n^2)*(b*x + a)^m*log((b*x + a)^n) - (B^3*b^2*g^(m + 2)*n^2*x^2 + 2*B^3*a*b*g^(m + 2)*n^2*x + B^3*a^2*g^(m + 2)*n^2)*(b*x + a)^m*log((d*x + c)^n) + (B^3*a^2*g^(m + 2)*n^2*log(e) + A*B^2*a^2*g^(m + 2)*n^2 + (B^3*b^2*g^(m + 2)*n^2*log(e) + A*B^2*b^2*g^(m + 2)*n^2)*x^2 + 2*(B^3*a*b*g^(m + 2)*n^2*log(e) + A*B^2*a*b*g^(m + 2)*n^2)*x)*(b*x + a)^m), x) + 1/2*((B*d*i^m*(m + 1)*x + B*c*i^m*(m + 1))*(d*x + c)^m*log((b*x + a)^n) - (B*d*i^m*(m + 1)*x + B*c*i^m*(m + 1))*(d*x + c)^m*log((d*x + c)^n) + (A*c*i^m*(m + 1) + (i^m*(m + 1)*log(e) - i^m*n)*B*c + (A*d*i^m*(m + 1) + (i^m*(m + 1)*log(e) - i^m*n)*B*d)*x)*(d*x + c)^m)/(((b^2*c*g^(m + 2)*n^2 - a*b*d*g^(m + 2)*n^2)*B^4*x + (a*b*c*g^(m + 2)*n^2 - a^2*d*g^(m + 2)*n^2)*B^4)*(b*x + a)^m*log((b*x + a)^n)^2 + ((b^2*c*g^(m + 2)*n^2 - a*b*d*g^(m + 2)*n^2)*B^4*x + (a*b*c*g^(m + 2)*n^2 - a^2*d*g^(m + 2)*n^2)*B^4)*(b*x + a)^m*log((d*x + c)^n)^2 + 2*((a*b*c*g^(m + 2)*n^2 - a^2*d*g^(m + 2)*n^2)*A*B^3 + (a*b*c*g^(m + 2)*n^2*log(e) - a^2*d*g^(m + 2)*n^2*log(e))*B^4 + ((b^2*c*g^(m + 2)*n^2 - a*b*d*g^(m + 2)*n^2)*A*B^3 + (b^2*c*g^(m + 2)*n^2*log(e) - a*b*d*g^(m + 2)*n^2*log(e))*B^4)*x)*(b*x + a)^m*log((b*x + a)^n) + ((a*b*c*g^(m + 2)*n^2 - a^2*d*g^(m + 2)*n^2)*A^2*B^2 + 2*(a*b*c*g^(m + 2)*n^2*log(e) - a^2*d*g^(m + 2)*n^2*log(e))*A*B^3 + (a*b*c*g^(m + 2)*n^2*log(e)^2 - a^2*d*g^(m + 2)*n^2*log(e)^2)*B^4 + ((b^2*c*g^(m + 2)*n^2 - a*b*d*g^(m + 2)*n^2)*A^2*B^2 + 2*(b^2*c*g^(m + 2)*n^2*log(e) - a*b*d*g^(m + 2)*n^2*log(e))*A*B^3 + (b^2*c*g^(m + 2)*n^2*log(e)^2 - a*b*d*g^(m + 2)*n^2*log(e)^2)*B^4)*x)*(b*x + a)^m - 2*(((b^2*c*g^(m + 2)*n^2 - a*b*d*g^(m + 2)*n^2)*B^4*x + (a*b*c*g^(m + 2)*n^2 - a^2*d*g^(m + 2)*n^2)*B^4)*(b*x + a)^m*log((b*x + a)^n) + ((a*b*c*g^(m + 2)*n^2 - a^2*d*g^(m + 2)*n^2)*A*B^3 + (a*b*c*g^(m + 2)*n^2*log(e) - a^2*d*g^(m + 2)*n^2*log(e))*B^4 + ((b^2*c*g^(m + 2)*n^2 - a*b*d*g^(m + 2)*n^2)*A*B^3 + (b^2*c*g^(m + 2)*n^2*log(e) - a*b*d*g^(m + 2)*n^2*log(e))*B^4)*x)*(b*x + a)^m)*log((d*x + c)^n))","F",0
224,0,0,0,0.000000," ","integrate(log(e*((b*x+a)/(d*x+c))^n)^p/(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\int \frac{\log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{p}}{{\left(b x + a\right)} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate(log(e*((b*x + a)/(d*x + c))^n)^p/((b*x + a)*(d*x + c)), x)","F",0
225,0,0,0,0.000000," ","integrate(log(e*((b*x+a)/(d*x+c))^n)^p/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""maxima"")","\int \frac{\log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{p}}{b d x^{2} + a c + {\left(b c + a d\right)} x}\,{d x}"," ",0,"integrate(log(e*((b*x + a)/(d*x + c))^n)^p/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
226,0,0,0,0.000000," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p,x, algorithm=""maxima"")","\int {\left(b g x + a g\right)}^{m} {\left(d i x + c i\right)}^{-m - 2} {\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}^{p}\,{d x}"," ",0,"integrate((b*g*x + a*g)^m*(d*i*x + c*i)^(-m - 2)*(B*log((b*x + a)^n*e/(d*x + c)^n) + A)^p, x)","F",0
227,0,0,0,0.000000," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p,x, algorithm=""maxima"")","\int {\left(b g x + a g\right)}^{-m - 2} {\left(d i x + c i\right)}^{m} {\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}^{p}\,{d x}"," ",0,"integrate((b*g*x + a*g)^(-m - 2)*(d*i*x + c*i)^m*(B*log((b*x + a)^n*e/(d*x + c)^n) + A)^p, x)","F",0
228,1,766,0,1.778149," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(b*x+a)/(d*x+c),x, algorithm=""maxima"")","B^{3} {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{3} + 3 \, A B^{2} {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 3 \, A^{2} B {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) - \frac{1}{4} \, B^{3} {\left(\frac{6 \, {\left(e n \log\left(b x + a\right)^{2} - 2 \, e n \log\left(b x + a\right) \log\left(d x + c\right) + e n \log\left(d x + c\right)^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{{\left(b c - a d\right)} e} - \frac{\frac{4 \, {\left(e^{2} n^{2} \log\left(b x + a\right)^{3} - 3 \, e^{2} n^{2} \log\left(b x + a\right)^{2} \log\left(d x + c\right) + 3 \, e^{2} n^{2} \log\left(b x + a\right) \log\left(d x + c\right)^{2} - e^{2} n^{2} \log\left(d x + c\right)^{3}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{{\left(b c - a d\right)} e} - \frac{e^{3} n^{3} \log\left(b x + a\right)^{4} - 4 \, e^{3} n^{3} \log\left(b x + a\right)^{3} \log\left(d x + c\right) + 6 \, e^{3} n^{3} \log\left(b x + a\right)^{2} \log\left(d x + c\right)^{2} - 4 \, e^{3} n^{3} \log\left(b x + a\right) \log\left(d x + c\right)^{3} + e^{3} n^{3} \log\left(d x + c\right)^{4}}{{\left(b c - a d\right)} e^{2}}}{e}\right)} + A^{3} {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} - A B^{2} {\left(\frac{3 \, {\left(e n \log\left(b x + a\right)^{2} - 2 \, e n \log\left(b x + a\right) \log\left(d x + c\right) + e n \log\left(d x + c\right)^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{{\left(b c - a d\right)} e} - \frac{e^{2} n^{2} \log\left(b x + a\right)^{3} - 3 \, e^{2} n^{2} \log\left(b x + a\right)^{2} \log\left(d x + c\right) + 3 \, e^{2} n^{2} \log\left(b x + a\right) \log\left(d x + c\right)^{2} - e^{2} n^{2} \log\left(d x + c\right)^{3}}{{\left(b c - a d\right)} e^{2}}\right)} - \frac{3 \, {\left(e n \log\left(b x + a\right)^{2} - 2 \, e n \log\left(b x + a\right) \log\left(d x + c\right) + e n \log\left(d x + c\right)^{2}\right)} A^{2} B}{2 \, {\left(b c - a d\right)} e}"," ",0,"B^3*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log((b*x + a)^n*e/(d*x + c)^n)^3 + 3*A*B^2*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log((b*x + a)^n*e/(d*x + c)^n)^2 + 3*A^2*B*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log((b*x + a)^n*e/(d*x + c)^n) - 1/4*B^3*(6*(e*n*log(b*x + a)^2 - 2*e*n*log(b*x + a)*log(d*x + c) + e*n*log(d*x + c)^2)*log((b*x + a)^n*e/(d*x + c)^n)^2/((b*c - a*d)*e) - (4*(e^2*n^2*log(b*x + a)^3 - 3*e^2*n^2*log(b*x + a)^2*log(d*x + c) + 3*e^2*n^2*log(b*x + a)*log(d*x + c)^2 - e^2*n^2*log(d*x + c)^3)*log((b*x + a)^n*e/(d*x + c)^n)/((b*c - a*d)*e) - (e^3*n^3*log(b*x + a)^4 - 4*e^3*n^3*log(b*x + a)^3*log(d*x + c) + 6*e^3*n^3*log(b*x + a)^2*log(d*x + c)^2 - 4*e^3*n^3*log(b*x + a)*log(d*x + c)^3 + e^3*n^3*log(d*x + c)^4)/((b*c - a*d)*e^2))/e) + A^3*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d)) - A*B^2*(3*(e*n*log(b*x + a)^2 - 2*e*n*log(b*x + a)*log(d*x + c) + e*n*log(d*x + c)^2)*log((b*x + a)^n*e/(d*x + c)^n)/((b*c - a*d)*e) - (e^2*n^2*log(b*x + a)^3 - 3*e^2*n^2*log(b*x + a)^2*log(d*x + c) + 3*e^2*n^2*log(b*x + a)*log(d*x + c)^2 - e^2*n^2*log(d*x + c)^3)/((b*c - a*d)*e^2)) - 3/2*(e*n*log(b*x + a)^2 - 2*e*n*log(b*x + a)*log(d*x + c) + e*n*log(d*x + c)^2)*A^2*B/((b*c - a*d)*e)","B",0
229,1,387,0,1.465441," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(b*x+a)/(d*x+c),x, algorithm=""maxima"")","B^{2} {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 2 \, A B {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} - \frac{1}{3} \, B^{2} {\left(\frac{3 \, {\left(e n \log\left(b x + a\right)^{2} - 2 \, e n \log\left(b x + a\right) \log\left(d x + c\right) + e n \log\left(d x + c\right)^{2}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{{\left(b c - a d\right)} e} - \frac{e^{2} n^{2} \log\left(b x + a\right)^{3} - 3 \, e^{2} n^{2} \log\left(b x + a\right)^{2} \log\left(d x + c\right) + 3 \, e^{2} n^{2} \log\left(b x + a\right) \log\left(d x + c\right)^{2} - e^{2} n^{2} \log\left(d x + c\right)^{3}}{{\left(b c - a d\right)} e^{2}}\right)} - \frac{{\left(e n \log\left(b x + a\right)^{2} - 2 \, e n \log\left(b x + a\right) \log\left(d x + c\right) + e n \log\left(d x + c\right)^{2}\right)} A B}{{\left(b c - a d\right)} e}"," ",0,"B^2*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log((b*x + a)^n*e/(d*x + c)^n)^2 + 2*A*B*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log((b*x + a)^n*e/(d*x + c)^n) + A^2*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d)) - 1/3*B^2*(3*(e*n*log(b*x + a)^2 - 2*e*n*log(b*x + a)*log(d*x + c) + e*n*log(d*x + c)^2)*log((b*x + a)^n*e/(d*x + c)^n)/((b*c - a*d)*e) - (e^2*n^2*log(b*x + a)^3 - 3*e^2*n^2*log(b*x + a)^2*log(d*x + c) + 3*e^2*n^2*log(b*x + a)*log(d*x + c)^2 - e^2*n^2*log(d*x + c)^3)/((b*c - a*d)*e^2)) - (e*n*log(b*x + a)^2 - 2*e*n*log(b*x + a)*log(d*x + c) + e*n*log(d*x + c)^2)*A*B/((b*c - a*d)*e)","B",0
230,1,151,0,1.202591," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(b*x+a)/(d*x+c),x, algorithm=""maxima"")","B {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A {\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} - \frac{{\left(e n \log\left(b x + a\right)^{2} - 2 \, e n \log\left(b x + a\right) \log\left(d x + c\right) + e n \log\left(d x + c\right)^{2}\right)} B}{2 \, {\left(b c - a d\right)} e}"," ",0,"B*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log((b*x + a)^n*e/(d*x + c)^n) + A*(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d)) - 1/2*(e*n*log(b*x + a)^2 - 2*e*n*log(b*x + a)*log(d*x + c) + e*n*log(d*x + c)^2)*B/((b*c - a*d)*e)","B",0
231,1,49,0,2.328181," ","integrate(1/(b*x+a)/(d*x+c)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{\log\left(-\frac{B \log\left({\left(b x + a\right)}^{n}\right) - B \log\left({\left(d x + c\right)}^{n}\right) + B \log\left(e\right) + A}{B}\right)}{{\left(b c n - a d n\right)} B}"," ",0,"log(-(B*log((b*x + a)^n) - B*log((d*x + c)^n) + B*log(e) + A)/B)/((b*c*n - a*d*n)*B)","A",0
232,1,81,0,2.470621," ","integrate(1/(b*x+a)/(d*x+c)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","-\frac{1}{{\left(b c n - a d n\right)} B^{2} \log\left({\left(b x + a\right)}^{n}\right) - {\left(b c n - a d n\right)} B^{2} \log\left({\left(d x + c\right)}^{n}\right) + {\left(b c n - a d n\right)} A B + {\left(b c n \log\left(e\right) - a d n \log\left(e\right)\right)} B^{2}}"," ",0,"-1/((b*c*n - a*d*n)*B^2*log((b*x + a)^n) - (b*c*n - a*d*n)*B^2*log((d*x + c)^n) + (b*c*n - a*d*n)*A*B + (b*c*n*log(e) - a*d*n*log(e))*B^2)","A",0
233,1,220,0,3.186949," ","integrate(1/(b*x+a)/(d*x+c)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3,x, algorithm=""maxima"")","-\frac{1}{2 \, {\left({\left(b c n - a d n\right)} B^{3} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(b c n - a d n\right)} B^{3} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(b c n - a d n\right)} A^{2} B + 2 \, {\left(b c n \log\left(e\right) - a d n \log\left(e\right)\right)} A B^{2} + {\left(b c n \log\left(e\right)^{2} - a d n \log\left(e\right)^{2}\right)} B^{3} + 2 \, {\left({\left(b c n - a d n\right)} A B^{2} + {\left(b c n \log\left(e\right) - a d n \log\left(e\right)\right)} B^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left({\left(b c n - a d n\right)} B^{3} \log\left({\left(b x + a\right)}^{n}\right) + {\left(b c n - a d n\right)} A B^{2} + {\left(b c n \log\left(e\right) - a d n \log\left(e\right)\right)} B^{3}\right)} \log\left({\left(d x + c\right)}^{n}\right)\right)}}"," ",0,"-1/2/((b*c*n - a*d*n)*B^3*log((b*x + a)^n)^2 + (b*c*n - a*d*n)*B^3*log((d*x + c)^n)^2 + (b*c*n - a*d*n)*A^2*B + 2*(b*c*n*log(e) - a*d*n*log(e))*A*B^2 + (b*c*n*log(e)^2 - a*d*n*log(e)^2)*B^3 + 2*((b*c*n - a*d*n)*A*B^2 + (b*c*n*log(e) - a*d*n*log(e))*B^3)*log((b*x + a)^n) - 2*((b*c*n - a*d*n)*B^3*log((b*x + a)^n) + (b*c*n - a*d*n)*A*B^2 + (b*c*n*log(e) - a*d*n*log(e))*B^3)*log((d*x + c)^n))","B",0
234,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p/(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\int \frac{{\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}^{p}}{{\left(b x + a\right)} {\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*log((b*x + a)^n*e/(d*x + c)^n) + A)^p/((b*x + a)*(d*x + c)), x)","F",0
235,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p/(b*f*x+a*f)/(d*g*x+c*g),x, algorithm=""maxima"")","\int \frac{{\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}^{p}}{{\left(b f x + a f\right)} {\left(d g x + c g\right)}}\,{d x}"," ",0,"integrate((B*log((b*x + a)^n*e/(d*x + c)^n) + A)^p/((b*f*x + a*f)*(d*g*x + c*g)), x)","F",0
236,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p/(a*c*f+(a*d+b*c)*f*x+b*d*f*x^2),x, algorithm=""maxima"")","\int \frac{{\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}^{p}}{b d f x^{2} + a c f + {\left(b c + a d\right)} f x}\,{d x}"," ",0,"integrate((B*log((b*x + a)^n*e/(d*x + c)^n) + A)^p/(b*d*f*x^2 + a*c*f + (b*c + a*d)*f*x), x)","F",0
237,1,49,0,2.293344," ","integrate(1/(b*x+a)/(d*x+c)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{\log\left(-\frac{B \log\left({\left(b x + a\right)}^{n}\right) - B \log\left({\left(d x + c\right)}^{n}\right) + B \log\left(e\right) + A}{B}\right)}{{\left(b c n - a d n\right)} B}"," ",0,"log(-(B*log((b*x + a)^n) - B*log((d*x + c)^n) + B*log(e) + A)/B)/((b*c*n - a*d*n)*B)","A",0
238,1,53,0,1.690011," ","integrate(1/(b*f*x+a*f)/(d*g*x+c*g)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{\log\left(-\frac{B \log\left({\left(b x + a\right)}^{n}\right) - B \log\left({\left(d x + c\right)}^{n}\right) + B \log\left(e\right) + A}{B}\right)}{{\left(b c f g n - a d f g n\right)} B}"," ",0,"log(-(B*log((b*x + a)^n) - B*log((d*x + c)^n) + B*log(e) + A)/B)/((b*c*f*g*n - a*d*f*g*n)*B)","A",0
239,1,51,0,1.583207," ","integrate(1/(a*c*f+(a*d+b*c)*f*x+b*d*f*x^2)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{\log\left(-\frac{B \log\left({\left(b x + a\right)}^{n}\right) - B \log\left({\left(d x + c\right)}^{n}\right) + B \log\left(e\right) + A}{B}\right)}{{\left(b c f n - a d f n\right)} B}"," ",0,"log(-(B*log((b*x + a)^n) - B*log((d*x + c)^n) + B*log(e) + A)/B)/((b*c*f*n - a*d*f*n)*B)","A",0
240,0,0,0,0.000000," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)/log(e*(b*x+a)^n/((d*x+c)^n)),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}}{\log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}\,{d x}"," ",0,"integrate((b*x + a)^m*(d*x + c)^(-m - 2)/log((b*x + a)^n*e/(d*x + c)^n), x)","F",0
241,0,0,0,0.000000," ","integrate((b*x+a)^3/(d*x+c)^5/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{3}}{{\left(d x + c\right)}^{5} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}\,{d x}"," ",0,"integrate((b*x + a)^3/((d*x + c)^5*log(e*((b*x + a)/(d*x + c))^n)), x)","F",0
242,0,0,0,0.000000," ","integrate((b*x+a)^2/(d*x+c)^4/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{2}}{{\left(d x + c\right)}^{4} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}\,{d x}"," ",0,"integrate((b*x + a)^2/((d*x + c)^4*log(e*((b*x + a)/(d*x + c))^n)), x)","F",0
243,0,0,0,0.000000," ","integrate((b*x+a)/(d*x+c)^3/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","\int \frac{b x + a}{{\left(d x + c\right)}^{3} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}\,{d x}"," ",0,"integrate((b*x + a)/((d*x + c)^3*log(e*((b*x + a)/(d*x + c))^n)), x)","F",0
244,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","\int \frac{1}{{\left(d x + c\right)}^{2} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}\,{d x}"," ",0,"integrate(1/((d*x + c)^2*log(e*((b*x + a)/(d*x + c))^n)), x)","F",0
245,1,37,0,1.687431," ","integrate(1/(b*x+a)/(d*x+c)/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","\frac{\log\left(-\log\left({\left(b x + a\right)}^{n}\right) + \log\left({\left(d x + c\right)}^{n}\right) - \log\left(e\right)\right)}{b c n - a d n}"," ",0,"log(-log((b*x + a)^n) + log((d*x + c)^n) - log(e))/(b*c*n - a*d*n)","A",0
246,0,0,0,0.000000," ","integrate(1/(b*x+a)^2/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","\int \frac{1}{{\left(b x + a\right)}^{2} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}\,{d x}"," ",0,"integrate(1/((b*x + a)^2*log(e*((b*x + a)/(d*x + c))^n)), x)","F",0
247,0,0,0,0.000000," ","integrate((d*x+c)/(b*x+a)^3/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","\int \frac{d x + c}{{\left(b x + a\right)}^{3} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}\,{d x}"," ",0,"integrate((d*x + c)/((b*x + a)^3*log(e*((b*x + a)/(d*x + c))^n)), x)","F",0
248,0,0,0,0.000000," ","integrate((d*x+c)^2/(b*x+a)^4/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{2}}{{\left(b x + a\right)}^{4} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}\,{d x}"," ",0,"integrate((d*x + c)^2/((b*x + a)^4*log(e*((b*x + a)/(d*x + c))^n)), x)","F",0
249,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^4/(g*x+f)/(b*h*x+a*h),x, algorithm=""maxima"")","A^{4} {\left(\frac{\log\left(b x + a\right)}{{\left(b f - a g\right)} h} - \frac{\log\left(g x + f\right)}{{\left(b f - a g\right)} h}\right)} + \int \frac{B^{4} \log\left({\left(b x + a\right)}^{n}\right)^{4} + B^{4} \log\left({\left(d x + c\right)}^{n}\right)^{4} + B^{4} \log\left(e\right)^{4} + 4 \, A B^{3} \log\left(e\right)^{3} + 6 \, A^{2} B^{2} \log\left(e\right)^{2} + 4 \, A^{3} B \log\left(e\right) + 4 \, {\left(B^{4} \log\left(e\right) + A B^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} - 4 \, {\left(B^{4} \log\left({\left(b x + a\right)}^{n}\right) + B^{4} \log\left(e\right) + A B^{3}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{3} + 6 \, {\left(B^{4} \log\left(e\right)^{2} + 2 \, A B^{3} \log\left(e\right) + A^{2} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 6 \, {\left(B^{4} \log\left({\left(b x + a\right)}^{n}\right)^{2} + B^{4} \log\left(e\right)^{2} + 2 \, A B^{3} \log\left(e\right) + A^{2} B^{2} + 2 \, {\left(B^{4} \log\left(e\right) + A B^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 4 \, {\left(B^{4} \log\left(e\right)^{3} + 3 \, A B^{3} \log\left(e\right)^{2} + 3 \, A^{2} B^{2} \log\left(e\right) + A^{3} B\right)} \log\left({\left(b x + a\right)}^{n}\right) - 4 \, {\left(B^{4} \log\left({\left(b x + a\right)}^{n}\right)^{3} + B^{4} \log\left(e\right)^{3} + 3 \, A B^{3} \log\left(e\right)^{2} + 3 \, A^{2} B^{2} \log\left(e\right) + A^{3} B + 3 \, {\left(B^{4} \log\left(e\right) + A B^{3}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{4} \log\left(e\right)^{2} + 2 \, A B^{3} \log\left(e\right) + A^{2} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b g h x^{2} + a f h + {\left(b f h + a g h\right)} x}\,{d x}"," ",0,"A^4*(log(b*x + a)/((b*f - a*g)*h) - log(g*x + f)/((b*f - a*g)*h)) + integrate((B^4*log((b*x + a)^n)^4 + B^4*log((d*x + c)^n)^4 + B^4*log(e)^4 + 4*A*B^3*log(e)^3 + 6*A^2*B^2*log(e)^2 + 4*A^3*B*log(e) + 4*(B^4*log(e) + A*B^3)*log((b*x + a)^n)^3 - 4*(B^4*log((b*x + a)^n) + B^4*log(e) + A*B^3)*log((d*x + c)^n)^3 + 6*(B^4*log(e)^2 + 2*A*B^3*log(e) + A^2*B^2)*log((b*x + a)^n)^2 + 6*(B^4*log((b*x + a)^n)^2 + B^4*log(e)^2 + 2*A*B^3*log(e) + A^2*B^2 + 2*(B^4*log(e) + A*B^3)*log((b*x + a)^n))*log((d*x + c)^n)^2 + 4*(B^4*log(e)^3 + 3*A*B^3*log(e)^2 + 3*A^2*B^2*log(e) + A^3*B)*log((b*x + a)^n) - 4*(B^4*log((b*x + a)^n)^3 + B^4*log(e)^3 + 3*A*B^3*log(e)^2 + 3*A^2*B^2*log(e) + A^3*B + 3*(B^4*log(e) + A*B^3)*log((b*x + a)^n)^2 + 3*(B^4*log(e)^2 + 2*A*B^3*log(e) + A^2*B^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b*g*h*x^2 + a*f*h + (b*f*h + a*g*h)*x), x)","F",0
250,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(g*x+f)/(b*h*x+a*h),x, algorithm=""maxima"")","A^{3} {\left(\frac{\log\left(b x + a\right)}{{\left(b f - a g\right)} h} - \frac{\log\left(g x + f\right)}{{\left(b f - a g\right)} h}\right)} - \int -\frac{B^{3} \log\left({\left(b x + a\right)}^{n}\right)^{3} - B^{3} \log\left({\left(d x + c\right)}^{n}\right)^{3} + B^{3} \log\left(e\right)^{3} + 3 \, A B^{2} \log\left(e\right)^{2} + 3 \, A^{2} B \log\left(e\right) + 3 \, {\left(B^{3} \log\left(e\right) + A B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{3} \log\left({\left(b x + a\right)}^{n}\right) + B^{3} \log\left(e\right) + A B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 3 \, {\left(B^{3} \log\left(e\right)^{2} + 2 \, A B^{2} \log\left(e\right) + A^{2} B\right)} \log\left({\left(b x + a\right)}^{n}\right) - 3 \, {\left(B^{3} \log\left({\left(b x + a\right)}^{n}\right)^{2} + B^{3} \log\left(e\right)^{2} + 2 \, A B^{2} \log\left(e\right) + A^{2} B + 2 \, {\left(B^{3} \log\left(e\right) + A B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b g h x^{2} + a f h + {\left(b f h + a g h\right)} x}\,{d x}"," ",0,"A^3*(log(b*x + a)/((b*f - a*g)*h) - log(g*x + f)/((b*f - a*g)*h)) - integrate(-(B^3*log((b*x + a)^n)^3 - B^3*log((d*x + c)^n)^3 + B^3*log(e)^3 + 3*A*B^2*log(e)^2 + 3*A^2*B*log(e) + 3*(B^3*log(e) + A*B^2)*log((b*x + a)^n)^2 + 3*(B^3*log((b*x + a)^n) + B^3*log(e) + A*B^2)*log((d*x + c)^n)^2 + 3*(B^3*log(e)^2 + 2*A*B^2*log(e) + A^2*B)*log((b*x + a)^n) - 3*(B^3*log((b*x + a)^n)^2 + B^3*log(e)^2 + 2*A*B^2*log(e) + A^2*B + 2*(B^3*log(e) + A*B^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b*g*h*x^2 + a*f*h + (b*f*h + a*g*h)*x), x)","F",0
251,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(g*x+f)/(b*h*x+a*h),x, algorithm=""maxima"")","A^{2} {\left(\frac{\log\left(b x + a\right)}{{\left(b f - a g\right)} h} - \frac{\log\left(g x + f\right)}{{\left(b f - a g\right)} h}\right)} + \int \frac{B^{2} \log\left({\left(b x + a\right)}^{n}\right)^{2} + B^{2} \log\left({\left(d x + c\right)}^{n}\right)^{2} + B^{2} \log\left(e\right)^{2} + 2 \, A B \log\left(e\right) + 2 \, {\left(B^{2} \log\left(e\right) + A B\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B^{2} \log\left({\left(b x + a\right)}^{n}\right) + B^{2} \log\left(e\right) + A B\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b g h x^{2} + a f h + {\left(b f h + a g h\right)} x}\,{d x}"," ",0,"A^2*(log(b*x + a)/((b*f - a*g)*h) - log(g*x + f)/((b*f - a*g)*h)) + integrate((B^2*log((b*x + a)^n)^2 + B^2*log((d*x + c)^n)^2 + B^2*log(e)^2 + 2*A*B*log(e) + 2*(B^2*log(e) + A*B)*log((b*x + a)^n) - 2*(B^2*log((b*x + a)^n) + B^2*log(e) + A*B)*log((d*x + c)^n))/(b*g*h*x^2 + a*f*h + (b*f*h + a*g*h)*x), x)","F",0
252,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(g*x+f)/(b*h*x+a*h),x, algorithm=""maxima"")","A {\left(\frac{\log\left(b x + a\right)}{{\left(b f - a g\right)} h} - \frac{\log\left(g x + f\right)}{{\left(b f - a g\right)} h}\right)} - B \int -\frac{\log\left({\left(b x + a\right)}^{n}\right) - \log\left({\left(d x + c\right)}^{n}\right) + \log\left(e\right)}{b g h x^{2} + a f h + {\left(b f h + a g h\right)} x}\,{d x}"," ",0,"A*(log(b*x + a)/((b*f - a*g)*h) - log(g*x + f)/((b*f - a*g)*h)) - B*integrate(-(log((b*x + a)^n) - log((d*x + c)^n) + log(e))/(b*g*h*x^2 + a*f*h + (b*f*h + a*g*h)*x), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(g*x+f)/(b*h*x+a*h)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b h x + a h\right)} {\left(g x + f\right)} {\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*h*x + a*h)*(g*x + f)*(B*log((b*x + a)^n*e/(d*x + c)^n) + A)), x)","F",0
254,0,0,0,0.000000," ","integrate(1/(g*x+f)/(b*h*x+a*h)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","{\left(d f - c g\right)} \int \frac{1}{{\left(b c f^{2} h n - a d f^{2} h n\right)} A B + {\left(b c f^{2} h n \log\left(e\right) - a d f^{2} h n \log\left(e\right)\right)} B^{2} + {\left({\left(b c g^{2} h n - a d g^{2} h n\right)} A B + {\left(b c g^{2} h n \log\left(e\right) - a d g^{2} h n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c f g h n - a d f g h n\right)} A B + {\left(b c f g h n \log\left(e\right) - a d f g h n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{2} h n - a d g^{2} h n\right)} B^{2} x^{2} + 2 \, {\left(b c f g h n - a d f g h n\right)} B^{2} x + {\left(b c f^{2} h n - a d f^{2} h n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g^{2} h n - a d g^{2} h n\right)} B^{2} x^{2} + 2 \, {\left(b c f g h n - a d f g h n\right)} B^{2} x + {\left(b c f^{2} h n - a d f^{2} h n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x} - \frac{d x + c}{{\left(b c f h n - a d f h n\right)} A B + {\left(b c f h n \log\left(e\right) - a d f h n \log\left(e\right)\right)} B^{2} + {\left({\left(b c g h n - a d g h n\right)} A B + {\left(b c g h n \log\left(e\right) - a d g h n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g h n - a d g h n\right)} B^{2} x + {\left(b c f h n - a d f h n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g h n - a d g h n\right)} B^{2} x + {\left(b c f h n - a d f h n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}"," ",0,"(d*f - c*g)*integrate(1/((b*c*f^2*h*n - a*d*f^2*h*n)*A*B + (b*c*f^2*h*n*log(e) - a*d*f^2*h*n*log(e))*B^2 + ((b*c*g^2*h*n - a*d*g^2*h*n)*A*B + (b*c*g^2*h*n*log(e) - a*d*g^2*h*n*log(e))*B^2)*x^2 + 2*((b*c*f*g*h*n - a*d*f*g*h*n)*A*B + (b*c*f*g*h*n*log(e) - a*d*f*g*h*n*log(e))*B^2)*x + ((b*c*g^2*h*n - a*d*g^2*h*n)*B^2*x^2 + 2*(b*c*f*g*h*n - a*d*f*g*h*n)*B^2*x + (b*c*f^2*h*n - a*d*f^2*h*n)*B^2)*log((b*x + a)^n) - ((b*c*g^2*h*n - a*d*g^2*h*n)*B^2*x^2 + 2*(b*c*f*g*h*n - a*d*f*g*h*n)*B^2*x + (b*c*f^2*h*n - a*d*f^2*h*n)*B^2)*log((d*x + c)^n)), x) - (d*x + c)/((b*c*f*h*n - a*d*f*h*n)*A*B + (b*c*f*h*n*log(e) - a*d*f*h*n*log(e))*B^2 + ((b*c*g*h*n - a*d*g*h*n)*A*B + (b*c*g*h*n*log(e) - a*d*g*h*n*log(e))*B^2)*x + ((b*c*g*h*n - a*d*g*h*n)*B^2*x + (b*c*f*h*n - a*d*f*h*n)*B^2)*log((b*x + a)^n) - ((b*c*g*h*n - a*d*g*h*n)*B^2*x + (b*c*f*h*n - a*d*f*h*n)*B^2)*log((d*x + c)^n))","F",0
255,1,357,0,0.852544," ","integrate(log((d*x+c)/(b*x+a))/(b*x+a)/((a-c)*h+(b-d)*h*x),x, algorithm=""maxima"")","{\left(\frac{\log\left(-{\left(b - d\right)} x - a + c\right)}{{\left(b c - a d\right)} h} - \frac{\log\left(b x + a\right)}{{\left(b c - a d\right)} h}\right)} \log\left(\frac{d x + c}{b x + a}\right) + \frac{2 \, \log\left(-{\left(b - d\right)} x - a + c\right) \log\left(b x + a\right) - \log\left(b x + a\right)^{2}}{2 \, {\left(b c h - a d h\right)}} + \frac{\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)}{b c h - a d h} - \frac{\log\left(b x + a\right) \log\left(-\frac{a {\left(b - d\right)} + {\left(b^{2} - b d\right)} x}{b c - a d} + 1\right) + {\rm Li}_2\left(\frac{a {\left(b - d\right)} + {\left(b^{2} - b d\right)} x}{b c - a d}\right)}{b c h - a d h} - \frac{\log\left(-{\left(b - d\right)} x - a + c\right) \log\left(\frac{a d - c d + {\left(b d - d^{2}\right)} x}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{a d - c d + {\left(b d - d^{2}\right)} x}{b c - a d}\right)}{b c h - a d h}"," ",0,"(log(-(b - d)*x - a + c)/((b*c - a*d)*h) - log(b*x + a)/((b*c - a*d)*h))*log((d*x + c)/(b*x + a)) + 1/2*(2*log(-(b - d)*x - a + c)*log(b*x + a) - log(b*x + a)^2)/(b*c*h - a*d*h) + (log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))/(b*c*h - a*d*h) - (log(b*x + a)*log(-(a*(b - d) + (b^2 - b*d)*x)/(b*c - a*d) + 1) + dilog((a*(b - d) + (b^2 - b*d)*x)/(b*c - a*d)))/(b*c*h - a*d*h) - (log(-(b - d)*x - a + c)*log((a*d - c*d + (b*d - d^2)*x)/(b*c - a*d) + 1) + dilog(-(a*d - c*d + (b*d - d^2)*x)/(b*c - a*d)))/(b*c*h - a*d*h)","B",0
256,1,344,0,0.762813," ","integrate(log((a-c*g+(-d*g+b)*x)/(b*x+a))/(b*x+a)/(d*x+c),x, algorithm=""maxima"")","{\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(-\frac{c g + {\left(d g - b\right)} x - a}{b x + a}\right) + \frac{\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right)}{2 \, {\left(b c - a d\right)}} - \frac{\log\left(b x + a\right) \log\left(\frac{{\left(d g - b\right)} a + {\left(b d g - b^{2}\right)} x}{b c g - a d g} + 1\right) + {\rm Li}_2\left(-\frac{{\left(d g - b\right)} a + {\left(b d g - b^{2}\right)} x}{b c g - a d g}\right)}{b c - a d} + \frac{\log\left(d x + c\right) \log\left(\frac{c d g - b c + {\left(d^{2} g - b d\right)} x}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{c d g - b c + {\left(d^{2} g - b d\right)} x}{b c - a d}\right)}{b c - a d} + \frac{\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)}{b c - a d}"," ",0,"(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log(-(c*g + (d*g - b)*x - a)/(b*x + a)) + 1/2*(log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c))/(b*c - a*d) - (log(b*x + a)*log(((d*g - b)*a + (b*d*g - b^2)*x)/(b*c*g - a*d*g) + 1) + dilog(-((d*g - b)*a + (b*d*g - b^2)*x)/(b*c*g - a*d*g)))/(b*c - a*d) + (log(d*x + c)*log((c*d*g - b*c + (d^2*g - b*d)*x)/(b*c - a*d) + 1) + dilog(-(c*d*g - b*c + (d^2*g - b*d)*x)/(b*c - a*d)))/(b*c - a*d) + (log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))/(b*c - a*d)","B",0
257,1,336,0,0.813175," ","integrate(log(1-g*(d*x+c)/(b*x+a))/(b*x+a)/(d*x+c),x, algorithm=""maxima"")","{\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(-\frac{{\left(d x + c\right)} g}{b x + a} + 1\right) + \frac{\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right)}{2 \, {\left(b c - a d\right)}} - \frac{\log\left(b x + a\right) \log\left(\frac{{\left(d g - b\right)} a + {\left(b d g - b^{2}\right)} x}{b c g - a d g} + 1\right) + {\rm Li}_2\left(-\frac{{\left(d g - b\right)} a + {\left(b d g - b^{2}\right)} x}{b c g - a d g}\right)}{b c - a d} + \frac{\log\left(d x + c\right) \log\left(\frac{c d g - b c + {\left(d^{2} g - b d\right)} x}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{c d g - b c + {\left(d^{2} g - b d\right)} x}{b c - a d}\right)}{b c - a d} + \frac{\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)}{b c - a d}"," ",0,"(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log(-(d*x + c)*g/(b*x + a) + 1) + 1/2*(log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c))/(b*c - a*d) - (log(b*x + a)*log(((d*g - b)*a + (b*d*g - b^2)*x)/(b*c*g - a*d*g) + 1) + dilog(-((d*g - b)*a + (b*d*g - b^2)*x)/(b*c*g - a*d*g)))/(b*c - a*d) + (log(d*x + c)*log((c*d*g - b*c + (d^2*g - b*d)*x)/(b*c - a*d) + 1) + dilog(-(c*d*g - b*c + (d^2*g - b*d)*x)/(b*c - a*d)))/(b*c - a*d) + (log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))/(b*c - a*d)","B",0
258,1,343,0,0.823436," ","integrate(log((-d*g*x+b*x-c*g+a)/(b*x+a))/(b*x+a)/(d*x+c),x, algorithm=""maxima"")","{\left(\frac{\log\left(b x + a\right)}{b c - a d} - \frac{\log\left(d x + c\right)}{b c - a d}\right)} \log\left(-\frac{d g x + c g - b x - a}{b x + a}\right) + \frac{\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(d x + c\right)}{2 \, {\left(b c - a d\right)}} - \frac{\log\left(b x + a\right) \log\left(\frac{{\left(d g - b\right)} a + {\left(b d g - b^{2}\right)} x}{b c g - a d g} + 1\right) + {\rm Li}_2\left(-\frac{{\left(d g - b\right)} a + {\left(b d g - b^{2}\right)} x}{b c g - a d g}\right)}{b c - a d} + \frac{\log\left(d x + c\right) \log\left(\frac{c d g - b c + {\left(d^{2} g - b d\right)} x}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{c d g - b c + {\left(d^{2} g - b d\right)} x}{b c - a d}\right)}{b c - a d} + \frac{\log\left(b x + a\right) \log\left(\frac{b d x + a d}{b c - a d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d}{b c - a d}\right)}{b c - a d}"," ",0,"(log(b*x + a)/(b*c - a*d) - log(d*x + c)/(b*c - a*d))*log(-(d*g*x + c*g - b*x - a)/(b*x + a)) + 1/2*(log(b*x + a)^2 - 2*log(b*x + a)*log(d*x + c))/(b*c - a*d) - (log(b*x + a)*log(((d*g - b)*a + (b*d*g - b^2)*x)/(b*c*g - a*d*g) + 1) + dilog(-((d*g - b)*a + (b*d*g - b^2)*x)/(b*c*g - a*d*g)))/(b*c - a*d) + (log(d*x + c)*log((c*d*g - b*c + (d^2*g - b*d)*x)/(b*c - a*d) + 1) + dilog(-(c*d*g - b*c + (d^2*g - b*d)*x)/(b*c - a*d)))/(b*c - a*d) + (log(b*x + a)*log((b*d*x + a*d)/(b*c - a*d) + 1) + dilog(-(b*d*x + a*d)/(b*c - a*d)))/(b*c - a*d)","B",0
259,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x)),x, algorithm=""maxima"")","A^{3} {\left(\frac{\log\left(b x + a\right)}{{\left(b f - a g\right)} h} - \frac{\log\left(g x + f\right)}{{\left(b f - a g\right)} h}\right)} - \int -\frac{B^{3} \log\left({\left(b x + a\right)}^{n}\right)^{3} - B^{3} \log\left({\left(d x + c\right)}^{n}\right)^{3} + B^{3} \log\left(e\right)^{3} + 3 \, A B^{2} \log\left(e\right)^{2} + 3 \, A^{2} B \log\left(e\right) + 3 \, {\left(B^{3} \log\left(e\right) + A B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{3} \log\left({\left(b x + a\right)}^{n}\right) + B^{3} \log\left(e\right) + A B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 3 \, {\left(B^{3} \log\left(e\right)^{2} + 2 \, A B^{2} \log\left(e\right) + A^{2} B\right)} \log\left({\left(b x + a\right)}^{n}\right) - 3 \, {\left(B^{3} \log\left({\left(b x + a\right)}^{n}\right)^{2} + B^{3} \log\left(e\right)^{2} + 2 \, A B^{2} \log\left(e\right) + A^{2} B + 2 \, {\left(B^{3} \log\left(e\right) + A B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b g h x^{2} + a f h + {\left(b f h + a g h\right)} x}\,{d x}"," ",0,"A^3*(log(b*x + a)/((b*f - a*g)*h) - log(g*x + f)/((b*f - a*g)*h)) - integrate(-(B^3*log((b*x + a)^n)^3 - B^3*log((d*x + c)^n)^3 + B^3*log(e)^3 + 3*A*B^2*log(e)^2 + 3*A^2*B*log(e) + 3*(B^3*log(e) + A*B^2)*log((b*x + a)^n)^2 + 3*(B^3*log((b*x + a)^n) + B^3*log(e) + A*B^2)*log((d*x + c)^n)^2 + 3*(B^3*log(e)^2 + 2*A*B^2*log(e) + A^2*B)*log((b*x + a)^n) - 3*(B^3*log((b*x + a)^n)^2 + B^3*log(e)^2 + 2*A*B^2*log(e) + A^2*B + 2*(B^3*log(e) + A*B^2)*log((b*x + a)^n))*log((d*x + c)^n))/(b*g*h*x^2 + a*f*h + (b*f*h + a*g*h)*x), x)","F",0
260,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x)),x, algorithm=""maxima"")","A^{2} {\left(\frac{\log\left(b x + a\right)}{{\left(b f - a g\right)} h} - \frac{\log\left(g x + f\right)}{{\left(b f - a g\right)} h}\right)} + \int \frac{B^{2} \log\left({\left(b x + a\right)}^{n}\right)^{2} + B^{2} \log\left({\left(d x + c\right)}^{n}\right)^{2} + B^{2} \log\left(e\right)^{2} + 2 \, A B \log\left(e\right) + 2 \, {\left(B^{2} \log\left(e\right) + A B\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B^{2} \log\left({\left(b x + a\right)}^{n}\right) + B^{2} \log\left(e\right) + A B\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b g h x^{2} + a f h + {\left(b f h + a g h\right)} x}\,{d x}"," ",0,"A^2*(log(b*x + a)/((b*f - a*g)*h) - log(g*x + f)/((b*f - a*g)*h)) + integrate((B^2*log((b*x + a)^n)^2 + B^2*log((d*x + c)^n)^2 + B^2*log(e)^2 + 2*A*B*log(e) + 2*(B^2*log(e) + A*B)*log((b*x + a)^n) - 2*(B^2*log((b*x + a)^n) + B^2*log(e) + A*B)*log((d*x + c)^n))/(b*g*h*x^2 + a*f*h + (b*f*h + a*g*h)*x), x)","F",0
261,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x)),x, algorithm=""maxima"")","A {\left(\frac{\log\left(b x + a\right)}{{\left(b f - a g\right)} h} - \frac{\log\left(g x + f\right)}{{\left(b f - a g\right)} h}\right)} - B \int -\frac{\log\left({\left(b x + a\right)}^{n}\right) - \log\left({\left(d x + c\right)}^{n}\right) + \log\left(e\right)}{b g h x^{2} + a f h + {\left(b f h + a g h\right)} x}\,{d x}"," ",0,"A*(log(b*x + a)/((b*f - a*g)*h) - log(g*x + f)/((b*f - a*g)*h)) - B*integrate(-(log((b*x + a)^n) - log((d*x + c)^n) + log(e))/(b*g*h*x^2 + a*f*h + (b*f*h + a*g*h)*x), x)","F",0
262,0,0,0,0.000000," ","integrate(1/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x))/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g h x^{2} + a f h + {\left(b f x + a g x\right)} h\right)} {\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*h*x^2 + a*f*h + (b*f*x + a*g*x)*h)*(B*log((b*x + a)^n*e/(d*x + c)^n) + A)), x)","F",0
263,0,0,0,0.000000," ","integrate(1/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x))/(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","{\left(d f - c g\right)} \int \frac{1}{{\left(b c f^{2} h n - a d f^{2} h n\right)} A B + {\left(b c f^{2} h n \log\left(e\right) - a d f^{2} h n \log\left(e\right)\right)} B^{2} + {\left({\left(b c g^{2} h n - a d g^{2} h n\right)} A B + {\left(b c g^{2} h n \log\left(e\right) - a d g^{2} h n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c f g h n - a d f g h n\right)} A B + {\left(b c f g h n \log\left(e\right) - a d f g h n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{2} h n - a d g^{2} h n\right)} B^{2} x^{2} + 2 \, {\left(b c f g h n - a d f g h n\right)} B^{2} x + {\left(b c f^{2} h n - a d f^{2} h n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g^{2} h n - a d g^{2} h n\right)} B^{2} x^{2} + 2 \, {\left(b c f g h n - a d f g h n\right)} B^{2} x + {\left(b c f^{2} h n - a d f^{2} h n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x} - \frac{d x + c}{{\left(b c f h n - a d f h n\right)} A B + {\left(b c f h n \log\left(e\right) - a d f h n \log\left(e\right)\right)} B^{2} + {\left({\left(b c g h n - a d g h n\right)} A B + {\left(b c g h n \log\left(e\right) - a d g h n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g h n - a d g h n\right)} B^{2} x + {\left(b c f h n - a d f h n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g h n - a d g h n\right)} B^{2} x + {\left(b c f h n - a d f h n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}"," ",0,"(d*f - c*g)*integrate(1/((b*c*f^2*h*n - a*d*f^2*h*n)*A*B + (b*c*f^2*h*n*log(e) - a*d*f^2*h*n*log(e))*B^2 + ((b*c*g^2*h*n - a*d*g^2*h*n)*A*B + (b*c*g^2*h*n*log(e) - a*d*g^2*h*n*log(e))*B^2)*x^2 + 2*((b*c*f*g*h*n - a*d*f*g*h*n)*A*B + (b*c*f*g*h*n*log(e) - a*d*f*g*h*n*log(e))*B^2)*x + ((b*c*g^2*h*n - a*d*g^2*h*n)*B^2*x^2 + 2*(b*c*f*g*h*n - a*d*f*g*h*n)*B^2*x + (b*c*f^2*h*n - a*d*f^2*h*n)*B^2)*log((b*x + a)^n) - ((b*c*g^2*h*n - a*d*g^2*h*n)*B^2*x^2 + 2*(b*c*f*g*h*n - a*d*f*g*h*n)*B^2*x + (b*c*f^2*h*n - a*d*f^2*h*n)*B^2)*log((d*x + c)^n)), x) - (d*x + c)/((b*c*f*h*n - a*d*f*h*n)*A*B + (b*c*f*h*n*log(e) - a*d*f*h*n*log(e))*B^2 + ((b*c*g*h*n - a*d*g*h*n)*A*B + (b*c*g*h*n*log(e) - a*d*g*h*n*log(e))*B^2)*x + ((b*c*g*h*n - a*d*g*h*n)*B^2*x + (b*c*f*h*n - a*d*f*h*n)*B^2)*log((b*x + a)^n) - ((b*c*g*h*n - a*d*g*h*n)*B^2*x + (b*c*f*h*n - a*d*f*h*n)*B^2)*log((d*x + c)^n))","F",0
