1,1,676,0,1.473254," ","integrate((b*g*x+a*g)^4*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{5} \, B b^{4} g^{4} 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^{4} g^{4} x^{5} + B a b^{3} g^{4} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a b^{3} g^{4} x^{4} + 2 \, B a^{2} b^{2} g^{4} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A a^{2} b^{2} g^{4} x^{3} + 2 \, B a^{3} b g^{4} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A a^{3} b g^{4} x^{2} + \frac{1}{60} \, B b^{4} g^{4} 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} \, B a b^{3} g^{4} 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)} + B a^{2} b^{2} g^{4} 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 \, B a^{3} b g^{4} 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^{4} g^{4} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a^{4} g^{4} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{4} g^{4} x"," ",0,"1/5*B*b^4*g^4*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A*b^4*g^4*x^5 + B*a*b^3*g^4*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b^3*g^4*x^4 + 2*B*a^2*b^2*g^4*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*a^2*b^2*g^4*x^3 + 2*B*a^3*b*g^4*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*a^3*b*g^4*x^2 + 1/60*B*b^4*g^4*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*B*a*b^3*g^4*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)) + B*a^2*b^2*g^4*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*B*a^3*b*g^4*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^4*g^4*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^4*g^4*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^4*g^4*x","B",0
2,1,479,0,1.407626," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, B b^{3} g^{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} g^{3} x^{4} + B a b^{2} g^{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} g^{3} x^{3} + \frac{3}{2} \, B a^{2} b g^{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 g^{3} x^{2} - \frac{1}{24} \, B b^{3} g^{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} g^{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 g^{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} g^{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} g^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{3} g^{3} x"," ",0,"1/4*B*b^3*g^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*b^3*g^3*x^4 + B*a*b^2*g^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b^2*g^3*x^3 + 3/2*B*a^2*b*g^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*a^2*b*g^3*x^2 - 1/24*B*b^3*g^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*g^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*g^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*g^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^3*g^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^3*g^3*x","B",0
3,1,309,0,1.385632," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, B b^{2} g^{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} g^{2} x^{3} + B a b g^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a b g^{2} x^{2} + \frac{1}{6} \, B b^{2} g^{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 g^{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} g^{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} g^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a^{2} g^{2} x"," ",0,"1/3*B*b^2*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A*b^2*g^2*x^3 + B*a*b*g^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*b*g^2*x^2 + 1/6*B*b^2*g^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*g^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*g^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a^2*g^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a^2*g^2*x","B",0
4,1,156,0,1.347193," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{2} \, B b g 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 g x^{2} - \frac{1}{2} \, B b g 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 g n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B a g x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A a g x"," ",0,"1/2*B*b*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*b*g*x^2 - 1/2*B*b*g*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*g*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*a*g*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*a*g*x","A",0
5,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g),x, algorithm=""maxima"")","B {\left(\frac{\log\left(b x + a\right) \log\left({\left(b x + a\right)}^{n}\right) - \log\left(b x + a\right) \log\left({\left(d x + c\right)}^{n}\right)}{b g} + \int \frac{b d x \log\left(e\right) + b c \log\left(e\right) - {\left(b c n - a d n\right)} \log\left(b x + a\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}\right)} + \frac{A \log\left(b g x + a g\right)}{b g}"," ",0,"B*((log(b*x + a)*log((b*x + a)^n) - log(b*x + a)*log((d*x + c)^n))/(b*g) + integrate((b*d*x*log(e) + b*c*log(e) - (b*c*n - a*d*n)*log(b*x + a))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)) + A*log(b*g*x + a*g)/(b*g)","F",0
6,1,137,0,1.191075," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B 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)} - \frac{B \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}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-B*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*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*g^2*x + a*b*g^2) - A/(b^2*g^2*x + a*b*g^2)","B",0
7,1,259,0,1.362823," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","\frac{1}{4} \, B 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{B \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}{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*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*B*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/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","A",0
8,1,432,0,1.347528," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{18} \, B 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{B \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}{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*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)) - 1/3*B*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/(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
9,1,651,0,1.600298," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\frac{1}{48} \, B 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{B \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}{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*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)) - 1/4*B*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/(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
10,1,2945,0,8.285379," ","integrate((b*g*x+a*g)^4*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{5} \, A B b^{4} g^{4} 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^{4} g^{4} x^{5} + 2 \, A B a b^{3} g^{4} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a b^{3} g^{4} x^{4} + 4 \, A B a^{2} b^{2} g^{4} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A^{2} a^{2} b^{2} g^{4} x^{3} + 4 \, A B a^{3} b g^{4} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A^{2} a^{3} b g^{4} x^{2} + \frac{1}{30} \, A B b^{4} g^{4} 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}{3} \, A B a b^{3} g^{4} 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)} + 2 \, A B a^{2} b^{2} g^{4} 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)} - 4 \, A B a^{3} b g^{4} 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^{4} g^{4} 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^{4} g^{4} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{4} g^{4} x - \frac{{\left({\left(25 \, g^{4} n^{2} + 12 \, g^{4} n \log\left(e\right)\right)} b^{4} c^{5} - {\left(113 \, g^{4} n^{2} + 60 \, g^{4} n \log\left(e\right)\right)} a b^{3} c^{4} d + 4 \, {\left(49 \, g^{4} n^{2} + 30 \, g^{4} n \log\left(e\right)\right)} a^{2} b^{2} c^{3} d^{2} - 12 \, {\left(13 \, g^{4} n^{2} + 10 \, g^{4} n \log\left(e\right)\right)} a^{3} b c^{2} d^{3} + 12 \, {\left(4 \, g^{4} n^{2} + 5 \, g^{4} n \log\left(e\right)\right)} a^{4} c d^{4}\right)} B^{2} \log\left(d x + c\right)}{30 \, d^{5}} - \frac{2 \, {\left(b^{5} c^{5} g^{4} n^{2} - 5 \, a b^{4} c^{4} d g^{4} n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n^{2} + 5 \, a^{4} b c d^{4} g^{4} n^{2} - a^{5} d^{5} g^{4} 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}}{5 \, b d^{5}} + \frac{12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right)^{2} - 12 \, B^{2} a^{5} d^{5} g^{4} n^{2} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{5} c d^{4} g^{4} n \log\left(e\right) - {\left(g^{4} n \log\left(e\right) + 10 \, g^{4} \log\left(e\right)^{2}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left({\left(g^{4} n^{2} + 4 \, g^{4} n \log\left(e\right)\right)} b^{5} c^{2} d^{3} - 2 \, {\left(g^{4} n^{2} + 10 \, g^{4} n \log\left(e\right)\right)} a b^{4} c d^{4} + {\left(g^{4} n^{2} + 16 \, g^{4} n \log\left(e\right) + 60 \, g^{4} \log\left(e\right)^{2}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left({\left(7 \, g^{4} n^{2} + 12 \, g^{4} n \log\left(e\right)\right)} b^{5} c^{3} d^{2} - 3 \, {\left(9 \, g^{4} n^{2} + 20 \, g^{4} n \log\left(e\right)\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(11 \, g^{4} n^{2} + 40 \, g^{4} n \log\left(e\right)\right)} a^{2} b^{3} c d^{4} - {\left(13 \, g^{4} n^{2} + 72 \, g^{4} n \log\left(e\right) + 120 \, g^{4} \log\left(e\right)^{2}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 24 \, {\left(b^{5} c^{5} g^{4} n^{2} - 5 \, a b^{4} c^{4} d g^{4} n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n^{2} + 5 \, a^{4} b c d^{4} g^{4} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) - 12 \, {\left(b^{5} c^{5} g^{4} n^{2} - 5 \, a b^{4} c^{4} d g^{4} n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n^{2} + 5 \, a^{4} b c d^{4} g^{4} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + 2 \, {\left({\left(13 \, g^{4} n^{2} + 12 \, g^{4} n \log\left(e\right)\right)} b^{5} c^{4} d - {\left(59 \, g^{4} n^{2} + 60 \, g^{4} n \log\left(e\right)\right)} a b^{4} c^{3} d^{2} + 6 \, {\left(17 \, g^{4} n^{2} + 20 \, g^{4} n \log\left(e\right)\right)} a^{2} b^{3} c^{2} d^{3} - {\left(79 \, g^{4} n^{2} + 120 \, g^{4} n \log\left(e\right)\right)} a^{3} b^{2} c d^{4} + {\left(23 \, g^{4} n^{2} + 48 \, g^{4} n \log\left(e\right) + 30 \, g^{4} \log\left(e\right)^{2}\right)} a^{4} b d^{5}\right)} B^{2} x + 2 \, {\left(12 \, a b^{4} c^{4} d g^{4} n^{2} - 54 \, a^{2} b^{3} c^{3} d^{2} g^{4} n^{2} + 94 \, a^{3} b^{2} c^{2} d^{3} g^{4} n^{2} - 77 \, a^{4} b c d^{4} g^{4} n^{2} + {\left(25 \, g^{4} n^{2} + 12 \, g^{4} n \log\left(e\right)\right)} a^{5} d^{5}\right)} B^{2} \log\left(b x + a\right) + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) + 12 \, B^{2} a^{5} d^{5} g^{4} n \log\left(b x + a\right) - 3 \, {\left(b^{5} c d^{4} g^{4} n - {\left(g^{4} n + 20 \, g^{4} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 4 \, {\left(b^{5} c^{2} d^{3} g^{4} n - 5 \, a b^{4} c d^{4} g^{4} n + 2 \, {\left(2 \, g^{4} n + 15 \, g^{4} \log\left(e\right)\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - 6 \, {\left(b^{5} c^{3} d^{2} g^{4} n - 5 \, a b^{4} c^{2} d^{3} g^{4} n + 10 \, a^{2} b^{3} c d^{4} g^{4} n - 2 \, {\left(3 \, g^{4} n + 10 \, g^{4} \log\left(e\right)\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 12 \, {\left(b^{5} c^{4} d g^{4} n - 5 \, a b^{4} c^{3} d^{2} g^{4} n + 10 \, a^{2} b^{3} c^{2} d^{3} g^{4} n - 10 \, a^{3} b^{2} c d^{4} g^{4} n + {\left(4 \, g^{4} n + 5 \, g^{4} \log\left(e\right)\right)} a^{4} b d^{5}\right)} B^{2} x - 12 \, {\left(b^{5} c^{5} g^{4} n - 5 \, a b^{4} c^{4} d g^{4} n + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n + 5 \, a^{4} b c d^{4} g^{4} 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^{4} x^{5} \log\left(e\right) + 12 \, B^{2} a^{5} d^{5} g^{4} n \log\left(b x + a\right) - 3 \, {\left(b^{5} c d^{4} g^{4} n - {\left(g^{4} n + 20 \, g^{4} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 4 \, {\left(b^{5} c^{2} d^{3} g^{4} n - 5 \, a b^{4} c d^{4} g^{4} n + 2 \, {\left(2 \, g^{4} n + 15 \, g^{4} \log\left(e\right)\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - 6 \, {\left(b^{5} c^{3} d^{2} g^{4} n - 5 \, a b^{4} c^{2} d^{3} g^{4} n + 10 \, a^{2} b^{3} c d^{4} g^{4} n - 2 \, {\left(3 \, g^{4} n + 10 \, g^{4} \log\left(e\right)\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 12 \, {\left(b^{5} c^{4} d g^{4} n - 5 \, a b^{4} c^{3} d^{2} g^{4} n + 10 \, a^{2} b^{3} c^{2} d^{3} g^{4} n - 10 \, a^{3} b^{2} c d^{4} g^{4} n + {\left(4 \, g^{4} n + 5 \, g^{4} \log\left(e\right)\right)} a^{4} b d^{5}\right)} B^{2} x - 12 \, {\left(b^{5} c^{5} g^{4} n - 5 \, a b^{4} c^{4} d g^{4} n + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n + 5 \, a^{4} b c d^{4} g^{4} n\right)} B^{2} \log\left(d x + c\right) + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{60 \, b d^{5}}"," ",0,"2/5*A*B*b^4*g^4*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A^2*b^4*g^4*x^5 + 2*A*B*a*b^3*g^4*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b^3*g^4*x^4 + 4*A*B*a^2*b^2*g^4*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A^2*a^2*b^2*g^4*x^3 + 4*A*B*a^3*b*g^4*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A^2*a^3*b*g^4*x^2 + 1/30*A*B*b^4*g^4*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)) - 1/3*A*B*a*b^3*g^4*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*A*B*a^2*b^2*g^4*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*A*B*a^3*b*g^4*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^4*g^4*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^4*g^4*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^4*g^4*x - 1/30*((25*g^4*n^2 + 12*g^4*n*log(e))*b^4*c^5 - (113*g^4*n^2 + 60*g^4*n*log(e))*a*b^3*c^4*d + 4*(49*g^4*n^2 + 30*g^4*n*log(e))*a^2*b^2*c^3*d^2 - 12*(13*g^4*n^2 + 10*g^4*n*log(e))*a^3*b*c^2*d^3 + 12*(4*g^4*n^2 + 5*g^4*n*log(e))*a^4*c*d^4)*B^2*log(d*x + c)/d^5 - 2/5*(b^5*c^5*g^4*n^2 - 5*a*b^4*c^4*d*g^4*n^2 + 10*a^2*b^3*c^3*d^2*g^4*n^2 - 10*a^3*b^2*c^2*d^3*g^4*n^2 + 5*a^4*b*c*d^4*g^4*n^2 - a^5*d^5*g^4*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*d^5) + 1/60*(12*B^2*b^5*d^5*g^4*x^5*log(e)^2 - 12*B^2*a^5*d^5*g^4*n^2*log(b*x + a)^2 - 6*(b^5*c*d^4*g^4*n*log(e) - (g^4*n*log(e) + 10*g^4*log(e)^2)*a*b^4*d^5)*B^2*x^4 + 2*((g^4*n^2 + 4*g^4*n*log(e))*b^5*c^2*d^3 - 2*(g^4*n^2 + 10*g^4*n*log(e))*a*b^4*c*d^4 + (g^4*n^2 + 16*g^4*n*log(e) + 60*g^4*log(e)^2)*a^2*b^3*d^5)*B^2*x^3 - ((7*g^4*n^2 + 12*g^4*n*log(e))*b^5*c^3*d^2 - 3*(9*g^4*n^2 + 20*g^4*n*log(e))*a*b^4*c^2*d^3 + 3*(11*g^4*n^2 + 40*g^4*n*log(e))*a^2*b^3*c*d^4 - (13*g^4*n^2 + 72*g^4*n*log(e) + 120*g^4*log(e)^2)*a^3*b^2*d^5)*B^2*x^2 + 24*(b^5*c^5*g^4*n^2 - 5*a*b^4*c^4*d*g^4*n^2 + 10*a^2*b^3*c^3*d^2*g^4*n^2 - 10*a^3*b^2*c^2*d^3*g^4*n^2 + 5*a^4*b*c*d^4*g^4*n^2)*B^2*log(b*x + a)*log(d*x + c) - 12*(b^5*c^5*g^4*n^2 - 5*a*b^4*c^4*d*g^4*n^2 + 10*a^2*b^3*c^3*d^2*g^4*n^2 - 10*a^3*b^2*c^2*d^3*g^4*n^2 + 5*a^4*b*c*d^4*g^4*n^2)*B^2*log(d*x + c)^2 + 2*((13*g^4*n^2 + 12*g^4*n*log(e))*b^5*c^4*d - (59*g^4*n^2 + 60*g^4*n*log(e))*a*b^4*c^3*d^2 + 6*(17*g^4*n^2 + 20*g^4*n*log(e))*a^2*b^3*c^2*d^3 - (79*g^4*n^2 + 120*g^4*n*log(e))*a^3*b^2*c*d^4 + (23*g^4*n^2 + 48*g^4*n*log(e) + 30*g^4*log(e)^2)*a^4*b*d^5)*B^2*x + 2*(12*a*b^4*c^4*d*g^4*n^2 - 54*a^2*b^3*c^3*d^2*g^4*n^2 + 94*a^3*b^2*c^2*d^3*g^4*n^2 - 77*a^4*b*c*d^4*g^4*n^2 + (25*g^4*n^2 + 12*g^4*n*log(e))*a^5*d^5)*B^2*log(b*x + a) + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x)*log((b*x + a)^n)^2 + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x)*log((d*x + c)^n)^2 + 2*(12*B^2*b^5*d^5*g^4*x^5*log(e) + 12*B^2*a^5*d^5*g^4*n*log(b*x + a) - 3*(b^5*c*d^4*g^4*n - (g^4*n + 20*g^4*log(e))*a*b^4*d^5)*B^2*x^4 + 4*(b^5*c^2*d^3*g^4*n - 5*a*b^4*c*d^4*g^4*n + 2*(2*g^4*n + 15*g^4*log(e))*a^2*b^3*d^5)*B^2*x^3 - 6*(b^5*c^3*d^2*g^4*n - 5*a*b^4*c^2*d^3*g^4*n + 10*a^2*b^3*c*d^4*g^4*n - 2*(3*g^4*n + 10*g^4*log(e))*a^3*b^2*d^5)*B^2*x^2 + 12*(b^5*c^4*d*g^4*n - 5*a*b^4*c^3*d^2*g^4*n + 10*a^2*b^3*c^2*d^3*g^4*n - 10*a^3*b^2*c*d^4*g^4*n + (4*g^4*n + 5*g^4*log(e))*a^4*b*d^5)*B^2*x - 12*(b^5*c^5*g^4*n - 5*a*b^4*c^4*d*g^4*n + 10*a^2*b^3*c^3*d^2*g^4*n - 10*a^3*b^2*c^2*d^3*g^4*n + 5*a^4*b*c*d^4*g^4*n)*B^2*log(d*x + c))*log((b*x + a)^n) - 2*(12*B^2*b^5*d^5*g^4*x^5*log(e) + 12*B^2*a^5*d^5*g^4*n*log(b*x + a) - 3*(b^5*c*d^4*g^4*n - (g^4*n + 20*g^4*log(e))*a*b^4*d^5)*B^2*x^4 + 4*(b^5*c^2*d^3*g^4*n - 5*a*b^4*c*d^4*g^4*n + 2*(2*g^4*n + 15*g^4*log(e))*a^2*b^3*d^5)*B^2*x^3 - 6*(b^5*c^3*d^2*g^4*n - 5*a*b^4*c^2*d^3*g^4*n + 10*a^2*b^3*c*d^4*g^4*n - 2*(3*g^4*n + 10*g^4*log(e))*a^3*b^2*d^5)*B^2*x^2 + 12*(b^5*c^4*d*g^4*n - 5*a*b^4*c^3*d^2*g^4*n + 10*a^2*b^3*c^2*d^3*g^4*n - 10*a^3*b^2*c*d^4*g^4*n + (4*g^4*n + 5*g^4*log(e))*a^4*b*d^5)*B^2*x - 12*(b^5*c^5*g^4*n - 5*a*b^4*c^4*d*g^4*n + 10*a^2*b^3*c^3*d^2*g^4*n - 10*a^3*b^2*c^2*d^3*g^4*n + 5*a^4*b*c*d^4*g^4*n)*B^2*log(d*x + c) + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^5)","B",0
11,1,2175,0,8.015283," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A B b^{3} g^{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} g^{3} x^{4} + 2 \, A B a b^{2} g^{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} g^{3} x^{3} + 3 \, A B a^{2} b g^{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 g^{3} x^{2} - \frac{1}{12} \, A B b^{3} g^{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} g^{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 g^{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} g^{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} g^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{3} g^{3} x + \frac{{\left({\left(11 \, g^{3} n^{2} + 6 \, g^{3} n \log\left(e\right)\right)} b^{3} c^{4} - 2 \, {\left(19 \, g^{3} n^{2} + 12 \, g^{3} n \log\left(e\right)\right)} a b^{2} c^{3} d + 9 \, {\left(5 \, g^{3} n^{2} + 4 \, g^{3} n \log\left(e\right)\right)} a^{2} b c^{2} d^{2} - 6 \, {\left(3 \, g^{3} n^{2} + 4 \, g^{3} n \log\left(e\right)\right)} a^{3} c d^{3}\right)} B^{2} \log\left(d x + c\right)}{12 \, d^{4}} + \frac{{\left(b^{4} c^{4} g^{3} n^{2} - 4 \, a b^{3} c^{3} d g^{3} n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n^{2} - 4 \, a^{3} b c d^{3} g^{3} n^{2} + a^{4} d^{4} g^{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 d^{4}} + \frac{3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right)^{2} - 3 \, B^{2} a^{4} d^{4} g^{3} n^{2} \log\left(b x + a\right)^{2} - 2 \, {\left(b^{4} c d^{3} g^{3} n \log\left(e\right) - {\left(g^{3} n \log\left(e\right) + 6 \, g^{3} \log\left(e\right)^{2}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left({\left(g^{3} n^{2} + 3 \, g^{3} n \log\left(e\right)\right)} b^{4} c^{2} d^{2} - 2 \, {\left(g^{3} n^{2} + 6 \, g^{3} n \log\left(e\right)\right)} a b^{3} c d^{3} + {\left(g^{3} n^{2} + 9 \, g^{3} n \log\left(e\right) + 18 \, g^{3} \log\left(e\right)^{2}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 6 \, {\left(b^{4} c^{4} g^{3} n^{2} - 4 \, a b^{3} c^{3} d g^{3} n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n^{2} - 4 \, a^{3} b c d^{3} g^{3} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) + 3 \, {\left(b^{4} c^{4} g^{3} n^{2} - 4 \, a b^{3} c^{3} d g^{3} n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n^{2} - 4 \, a^{3} b c d^{3} g^{3} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} - {\left({\left(5 \, g^{3} n^{2} + 6 \, g^{3} n \log\left(e\right)\right)} b^{4} c^{3} d - {\left(17 \, g^{3} n^{2} + 24 \, g^{3} n \log\left(e\right)\right)} a b^{3} c^{2} d^{2} + {\left(19 \, g^{3} n^{2} + 36 \, g^{3} n \log\left(e\right)\right)} a^{2} b^{2} c d^{3} - {\left(7 \, g^{3} n^{2} + 18 \, g^{3} n \log\left(e\right) + 12 \, g^{3} \log\left(e\right)^{2}\right)} a^{3} b d^{4}\right)} B^{2} x - {\left(6 \, a b^{3} c^{3} d g^{3} n^{2} - 21 \, a^{2} b^{2} c^{2} d^{2} g^{3} n^{2} + 26 \, a^{3} b c d^{3} g^{3} n^{2} - {\left(11 \, g^{3} n^{2} + 6 \, g^{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} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 6 \, B^{2} a^{4} d^{4} g^{3} n \log\left(b x + a\right) - 2 \, {\left(b^{4} c d^{3} g^{3} n - {\left(g^{3} n + 12 \, g^{3} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + 3 \, {\left(b^{4} c^{2} d^{2} g^{3} n - 4 \, a b^{3} c d^{3} g^{3} n + 3 \, {\left(g^{3} n + 4 \, g^{3} \log\left(e\right)\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 6 \, {\left(b^{4} c^{3} d g^{3} n - 4 \, a b^{3} c^{2} d^{2} g^{3} n + 6 \, a^{2} b^{2} c d^{3} g^{3} n - {\left(3 \, g^{3} n + 4 \, g^{3} \log\left(e\right)\right)} a^{3} b d^{4}\right)} B^{2} x + 6 \, {\left(b^{4} c^{4} g^{3} n - 4 \, a b^{3} c^{3} d g^{3} n + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n - 4 \, a^{3} b c d^{3} g^{3} 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^{3} x^{4} \log\left(e\right) + 6 \, B^{2} a^{4} d^{4} g^{3} n \log\left(b x + a\right) - 2 \, {\left(b^{4} c d^{3} g^{3} n - {\left(g^{3} n + 12 \, g^{3} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + 3 \, {\left(b^{4} c^{2} d^{2} g^{3} n - 4 \, a b^{3} c d^{3} g^{3} n + 3 \, {\left(g^{3} n + 4 \, g^{3} \log\left(e\right)\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 6 \, {\left(b^{4} c^{3} d g^{3} n - 4 \, a b^{3} c^{2} d^{2} g^{3} n + 6 \, a^{2} b^{2} c d^{3} g^{3} n - {\left(3 \, g^{3} n + 4 \, g^{3} \log\left(e\right)\right)} a^{3} b d^{4}\right)} B^{2} x + 6 \, {\left(b^{4} c^{4} g^{3} n - 4 \, a b^{3} c^{3} d g^{3} n + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n - 4 \, a^{3} b c d^{3} g^{3} n\right)} B^{2} \log\left(d x + c\right) + 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{12 \, b d^{4}}"," ",0,"1/2*A*B*b^3*g^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*b^3*g^3*x^4 + 2*A*B*a*b^2*g^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b^2*g^3*x^3 + 3*A*B*a^2*b*g^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A^2*a^2*b*g^3*x^2 - 1/12*A*B*b^3*g^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*g^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*g^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*g^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^3*g^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^3*g^3*x + 1/12*((11*g^3*n^2 + 6*g^3*n*log(e))*b^3*c^4 - 2*(19*g^3*n^2 + 12*g^3*n*log(e))*a*b^2*c^3*d + 9*(5*g^3*n^2 + 4*g^3*n*log(e))*a^2*b*c^2*d^2 - 6*(3*g^3*n^2 + 4*g^3*n*log(e))*a^3*c*d^3)*B^2*log(d*x + c)/d^4 + 1/2*(b^4*c^4*g^3*n^2 - 4*a*b^3*c^3*d*g^3*n^2 + 6*a^2*b^2*c^2*d^2*g^3*n^2 - 4*a^3*b*c*d^3*g^3*n^2 + a^4*d^4*g^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*d^4) + 1/12*(3*B^2*b^4*d^4*g^3*x^4*log(e)^2 - 3*B^2*a^4*d^4*g^3*n^2*log(b*x + a)^2 - 2*(b^4*c*d^3*g^3*n*log(e) - (g^3*n*log(e) + 6*g^3*log(e)^2)*a*b^3*d^4)*B^2*x^3 + ((g^3*n^2 + 3*g^3*n*log(e))*b^4*c^2*d^2 - 2*(g^3*n^2 + 6*g^3*n*log(e))*a*b^3*c*d^3 + (g^3*n^2 + 9*g^3*n*log(e) + 18*g^3*log(e)^2)*a^2*b^2*d^4)*B^2*x^2 - 6*(b^4*c^4*g^3*n^2 - 4*a*b^3*c^3*d*g^3*n^2 + 6*a^2*b^2*c^2*d^2*g^3*n^2 - 4*a^3*b*c*d^3*g^3*n^2)*B^2*log(b*x + a)*log(d*x + c) + 3*(b^4*c^4*g^3*n^2 - 4*a*b^3*c^3*d*g^3*n^2 + 6*a^2*b^2*c^2*d^2*g^3*n^2 - 4*a^3*b*c*d^3*g^3*n^2)*B^2*log(d*x + c)^2 - ((5*g^3*n^2 + 6*g^3*n*log(e))*b^4*c^3*d - (17*g^3*n^2 + 24*g^3*n*log(e))*a*b^3*c^2*d^2 + (19*g^3*n^2 + 36*g^3*n*log(e))*a^2*b^2*c*d^3 - (7*g^3*n^2 + 18*g^3*n*log(e) + 12*g^3*log(e)^2)*a^3*b*d^4)*B^2*x - (6*a*b^3*c^3*d*g^3*n^2 - 21*a^2*b^2*c^2*d^2*g^3*n^2 + 26*a^3*b*c*d^3*g^3*n^2 - (11*g^3*n^2 + 6*g^3*n*log(e))*a^4*d^4)*B^2*log(b*x + a) + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x)*log((b*x + a)^n)^2 + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x)*log((d*x + c)^n)^2 + (6*B^2*b^4*d^4*g^3*x^4*log(e) + 6*B^2*a^4*d^4*g^3*n*log(b*x + a) - 2*(b^4*c*d^3*g^3*n - (g^3*n + 12*g^3*log(e))*a*b^3*d^4)*B^2*x^3 + 3*(b^4*c^2*d^2*g^3*n - 4*a*b^3*c*d^3*g^3*n + 3*(g^3*n + 4*g^3*log(e))*a^2*b^2*d^4)*B^2*x^2 - 6*(b^4*c^3*d*g^3*n - 4*a*b^3*c^2*d^2*g^3*n + 6*a^2*b^2*c*d^3*g^3*n - (3*g^3*n + 4*g^3*log(e))*a^3*b*d^4)*B^2*x + 6*(b^4*c^4*g^3*n - 4*a*b^3*c^3*d*g^3*n + 6*a^2*b^2*c^2*d^2*g^3*n - 4*a^3*b*c*d^3*g^3*n)*B^2*log(d*x + c))*log((b*x + a)^n) - (6*B^2*b^4*d^4*g^3*x^4*log(e) + 6*B^2*a^4*d^4*g^3*n*log(b*x + a) - 2*(b^4*c*d^3*g^3*n - (g^3*n + 12*g^3*log(e))*a*b^3*d^4)*B^2*x^3 + 3*(b^4*c^2*d^2*g^3*n - 4*a*b^3*c*d^3*g^3*n + 3*(g^3*n + 4*g^3*log(e))*a^2*b^2*d^4)*B^2*x^2 - 6*(b^4*c^3*d*g^3*n - 4*a*b^3*c^2*d^2*g^3*n + 6*a^2*b^2*c*d^3*g^3*n - (3*g^3*n + 4*g^3*log(e))*a^3*b*d^4)*B^2*x + 6*(b^4*c^4*g^3*n - 4*a*b^3*c^3*d*g^3*n + 6*a^2*b^2*c^2*d^2*g^3*n - 4*a^3*b*c*d^3*g^3*n)*B^2*log(d*x + c) + 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^4)","B",0
12,1,1501,0,11.465976," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{3} \, A B b^{2} g^{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} g^{2} x^{3} + 2 \, A B a b g^{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 g^{2} x^{2} + \frac{1}{3} \, A B b^{2} g^{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 g^{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} g^{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} g^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a^{2} g^{2} x - \frac{{\left({\left(3 \, g^{2} n^{2} + 2 \, g^{2} n \log\left(e\right)\right)} b^{2} c^{3} - {\left(7 \, g^{2} n^{2} + 6 \, g^{2} n \log\left(e\right)\right)} a b c^{2} d + 2 \, {\left(2 \, g^{2} n^{2} + 3 \, g^{2} n \log\left(e\right)\right)} a^{2} c d^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, d^{3}} - \frac{2 \, {\left(b^{3} c^{3} g^{2} n^{2} - 3 \, a b^{2} c^{2} d g^{2} n^{2} + 3 \, a^{2} b c d^{2} g^{2} n^{2} - a^{3} d^{3} g^{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 d^{3}} + \frac{B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right)^{2} - B^{2} a^{3} d^{3} g^{2} n^{2} \log\left(b x + a\right)^{2} - {\left(b^{3} c d^{2} g^{2} n \log\left(e\right) - {\left(g^{2} n \log\left(e\right) + 3 \, g^{2} \log\left(e\right)^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{3} g^{2} n^{2} - 3 \, a b^{2} c^{2} d g^{2} n^{2} + 3 \, a^{2} b c d^{2} g^{2} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{3} c^{3} g^{2} n^{2} - 3 \, a b^{2} c^{2} d g^{2} n^{2} + 3 \, a^{2} b c d^{2} g^{2} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + {\left({\left(g^{2} n^{2} + 2 \, g^{2} n \log\left(e\right)\right)} b^{3} c^{2} d - 2 \, {\left(g^{2} n^{2} + 3 \, g^{2} n \log\left(e\right)\right)} a b^{2} c d^{2} + {\left(g^{2} n^{2} + 4 \, g^{2} n \log\left(e\right) + 3 \, g^{2} \log\left(e\right)^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + {\left(2 \, a b^{2} c^{2} d g^{2} n^{2} - 5 \, a^{2} b c d^{2} g^{2} n^{2} + {\left(3 \, g^{2} n^{2} + 2 \, g^{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} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + 2 \, B^{2} a^{3} d^{3} g^{2} n \log\left(b x + a\right) - {\left(b^{3} c d^{2} g^{2} n - {\left(g^{2} n + 6 \, g^{2} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{2} d g^{2} n - 3 \, a b^{2} c d^{2} g^{2} n + {\left(2 \, g^{2} n + 3 \, g^{2} \log\left(e\right)\right)} a^{2} b d^{3}\right)} B^{2} x - 2 \, {\left(b^{3} c^{3} g^{2} n - 3 \, a b^{2} c^{2} d g^{2} n + 3 \, a^{2} b c d^{2} g^{2} n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + 2 \, B^{2} a^{3} d^{3} g^{2} n \log\left(b x + a\right) - {\left(b^{3} c d^{2} g^{2} n - {\left(g^{2} n + 6 \, g^{2} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{2} d g^{2} n - 3 \, a b^{2} c d^{2} g^{2} n + {\left(2 \, g^{2} n + 3 \, g^{2} \log\left(e\right)\right)} a^{2} b d^{3}\right)} B^{2} x - 2 \, {\left(b^{3} c^{3} g^{2} n - 3 \, a b^{2} c^{2} d g^{2} n + 3 \, a^{2} b c d^{2} g^{2} n\right)} B^{2} \log\left(d x + c\right) + 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{3 \, b d^{3}}"," ",0,"2/3*A*B*b^2*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A^2*b^2*g^2*x^3 + 2*A*B*a*b*g^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*b*g^2*x^2 + 1/3*A*B*b^2*g^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*g^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*g^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a^2*g^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a^2*g^2*x - 1/3*((3*g^2*n^2 + 2*g^2*n*log(e))*b^2*c^3 - (7*g^2*n^2 + 6*g^2*n*log(e))*a*b*c^2*d + 2*(2*g^2*n^2 + 3*g^2*n*log(e))*a^2*c*d^2)*B^2*log(d*x + c)/d^3 - 2/3*(b^3*c^3*g^2*n^2 - 3*a*b^2*c^2*d*g^2*n^2 + 3*a^2*b*c*d^2*g^2*n^2 - a^3*d^3*g^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*d^3) + 1/3*(B^2*b^3*d^3*g^2*x^3*log(e)^2 - B^2*a^3*d^3*g^2*n^2*log(b*x + a)^2 - (b^3*c*d^2*g^2*n*log(e) - (g^2*n*log(e) + 3*g^2*log(e)^2)*a*b^2*d^3)*B^2*x^2 + 2*(b^3*c^3*g^2*n^2 - 3*a*b^2*c^2*d*g^2*n^2 + 3*a^2*b*c*d^2*g^2*n^2)*B^2*log(b*x + a)*log(d*x + c) - (b^3*c^3*g^2*n^2 - 3*a*b^2*c^2*d*g^2*n^2 + 3*a^2*b*c*d^2*g^2*n^2)*B^2*log(d*x + c)^2 + ((g^2*n^2 + 2*g^2*n*log(e))*b^3*c^2*d - 2*(g^2*n^2 + 3*g^2*n*log(e))*a*b^2*c*d^2 + (g^2*n^2 + 4*g^2*n*log(e) + 3*g^2*log(e)^2)*a^2*b*d^3)*B^2*x + (2*a*b^2*c^2*d*g^2*n^2 - 5*a^2*b*c*d^2*g^2*n^2 + (3*g^2*n^2 + 2*g^2*n*log(e))*a^3*d^3)*B^2*log(b*x + a) + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x)*log((b*x + a)^n)^2 + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x)*log((d*x + c)^n)^2 + (2*B^2*b^3*d^3*g^2*x^3*log(e) + 2*B^2*a^3*d^3*g^2*n*log(b*x + a) - (b^3*c*d^2*g^2*n - (g^2*n + 6*g^2*log(e))*a*b^2*d^3)*B^2*x^2 + 2*(b^3*c^2*d*g^2*n - 3*a*b^2*c*d^2*g^2*n + (2*g^2*n + 3*g^2*log(e))*a^2*b*d^3)*B^2*x - 2*(b^3*c^3*g^2*n - 3*a*b^2*c^2*d*g^2*n + 3*a^2*b*c*d^2*g^2*n)*B^2*log(d*x + c))*log((b*x + a)^n) - (2*B^2*b^3*d^3*g^2*x^3*log(e) + 2*B^2*a^3*d^3*g^2*n*log(b*x + a) - (b^3*c*d^2*g^2*n - (g^2*n + 6*g^2*log(e))*a*b^2*d^3)*B^2*x^2 + 2*(b^3*c^2*d*g^2*n - 3*a*b^2*c*d^2*g^2*n + (2*g^2*n + 3*g^2*log(e))*a^2*b*d^3)*B^2*x - 2*(b^3*c^3*g^2*n - 3*a*b^2*c^2*d*g^2*n + 3*a^2*b*c*d^2*g^2*n)*B^2*log(d*x + c) + 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^3)","B",0
13,1,828,0,7.481025," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","A B b g 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 g x^{2} - A B b g 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 g 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 g x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} a g x + \frac{{\left({\left(g n^{2} + g n \log\left(e\right)\right)} b c^{2} - {\left(g n^{2} + 2 \, g n \log\left(e\right)\right)} a c d\right)} B^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b^{2} c^{2} g n^{2} - 2 \, a b c d g n^{2} + a^{2} d^{2} g 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 d^{2}} - \frac{B^{2} a^{2} d^{2} g n^{2} \log\left(b x + a\right)^{2} - B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} + 2 \, {\left(b^{2} c^{2} g n^{2} - 2 \, a b c d g n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{2} c^{2} g n^{2} - 2 \, a b c d g n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + 2 \, {\left(b^{2} c d g n \log\left(e\right) - {\left(g n \log\left(e\right) + g \log\left(e\right)^{2}\right)} a b d^{2}\right)} B^{2} x + 2 \, {\left(a b c d g n^{2} - {\left(g n^{2} + g 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} g x^{2} + 2 \, B^{2} a b d^{2} g x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} - {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} - 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + B^{2} a^{2} d^{2} g n \log\left(b x + a\right) - {\left(b^{2} c d g n - {\left(g n + 2 \, g \log\left(e\right)\right)} a b d^{2}\right)} B^{2} x + {\left(b^{2} c^{2} g n - 2 \, a b c d g n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + B^{2} a^{2} d^{2} g n \log\left(b x + a\right) - {\left(b^{2} c d g n - {\left(g n + 2 \, g \log\left(e\right)\right)} a b d^{2}\right)} B^{2} x + {\left(b^{2} c^{2} g n - 2 \, a b c d g n\right)} B^{2} \log\left(d x + c\right) + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, b d^{2}}"," ",0,"A*B*b*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*b*g*x^2 - A*B*b*g*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*g*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*a*g*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*a*g*x + ((g*n^2 + g*n*log(e))*b*c^2 - (g*n^2 + 2*g*n*log(e))*a*c*d)*B^2*log(d*x + c)/d^2 + (b^2*c^2*g*n^2 - 2*a*b*c*d*g*n^2 + a^2*d^2*g*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*d^2) - 1/2*(B^2*a^2*d^2*g*n^2*log(b*x + a)^2 - B^2*b^2*d^2*g*x^2*log(e)^2 + 2*(b^2*c^2*g*n^2 - 2*a*b*c*d*g*n^2)*B^2*log(b*x + a)*log(d*x + c) - (b^2*c^2*g*n^2 - 2*a*b*c*d*g*n^2)*B^2*log(d*x + c)^2 + 2*(b^2*c*d*g*n*log(e) - (g*n*log(e) + g*log(e)^2)*a*b*d^2)*B^2*x + 2*(a*b*c*d*g*n^2 - (g*n^2 + g*n*log(e))*a^2*d^2)*B^2*log(b*x + a) - (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x)*log((b*x + a)^n)^2 - (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x)*log((d*x + c)^n)^2 - 2*(B^2*b^2*d^2*g*x^2*log(e) + B^2*a^2*d^2*g*n*log(b*x + a) - (b^2*c*d*g*n - (g*n + 2*g*log(e))*a*b*d^2)*B^2*x + (b^2*c^2*g*n - 2*a*b*c*d*g*n)*B^2*log(d*x + c))*log((b*x + a)^n) + 2*(B^2*b^2*d^2*g*x^2*log(e) + B^2*a^2*d^2*g*n*log(b*x + a) - (b^2*c*d*g*n - (g*n + 2*g*log(e))*a*b*d^2)*B^2*x + (b^2*c^2*g*n - 2*a*b*c*d*g*n)*B^2*log(d*x + c) + (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^2)","B",0
14,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g),x, algorithm=""maxima"")","\frac{B^{2} \log\left(b x + a\right) \log\left({\left(d x + c\right)}^{n}\right)^{2}}{b g} + \frac{A^{2} \log\left(b g x + a g\right)}{b g} - \int -\frac{B^{2} b c \log\left(e\right)^{2} + 2 \, A B b c \log\left(e\right) + {\left(B^{2} b d x + B^{2} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b d \log\left(e\right)^{2} + 2 \, A B b d \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x + {\left(B^{2} b d n x + B^{2} a d n\right)} \log\left(b x + a\right) + {\left(B^{2} b d x + B^{2} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}"," ",0,"B^2*log(b*x + a)*log((d*x + c)^n)^2/(b*g) + A^2*log(b*g*x + a*g)/(b*g) - integrate(-(B^2*b*c*log(e)^2 + 2*A*B*b*c*log(e) + (B^2*b*d*x + B^2*b*c)*log((b*x + a)^n)^2 + (B^2*b*d*log(e)^2 + 2*A*B*b*d*log(e))*x + 2*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x)*log((b*x + a)^n) - 2*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x + (B^2*b*d*n*x + B^2*a*d*n)*log(b*x + a) + (B^2*b*d*x + B^2*b*c)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)","F",0
15,1,430,0,1.473073," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-2 \, A B 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)} - {\left(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)} \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)} n^{2}}{a b^{2} c g^{2} - a^{2} b d g^{2} + {\left(b^{3} c g^{2} - a b^{2} d g^{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}}{b^{2} g^{2} x + a b g^{2}} - \frac{2 \, A B \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}}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-2*A*B*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)) - (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))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - ((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^2/(a*b^2*c*g^2 - a^2*b*d*g^2 + (b^3*c*g^2 - a*b^2*d*g^2)*x))*B^2 - B^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(b^2*g^2*x + a*b*g^2) - 2*A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(b^2*g^2*x + a*b*g^2) - A^2/(b^2*g^2*x + a*b*g^2)","B",0
16,1,861,0,1.739991," ","integrate((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 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}{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} - \frac{B^{2} \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{A B \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}}{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*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)) + 1/4*(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 - 1/2*B^2*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) - A*B*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/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
17,1,1432,0,2.343849," ","integrate((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 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}{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} - \frac{B^{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{2 \, A B \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}}{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*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)) - 1/54*(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 - 1/3*B^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) - 2/3*A*B*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/(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
18,1,2136,0,2.977576," ","integrate((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 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}{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} - \frac{B^{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{A B \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}}{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*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)) + 1/288*(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 - 1/4*B^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) - 1/2*A*B*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/(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
19,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{{\left(b g x + a g\right)}^{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)^2/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
20,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{b g x + a g}{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)/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{2} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^2*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{3} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^3*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
24,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b^{3} d g^{2} x^{4} + a^{3} c g^{2} + {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{3} + 3 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x^{2} + {\left(3 \, a^{2} b c g^{2} + a^{3} d g^{2}\right)} x}{{\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}} + \int \frac{4 \, b^{3} d g^{2} x^{3} + 3 \, a^{2} b c g^{2} + a^{3} d g^{2} + 3 \, {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{2} + 6 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x}{{\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}}\,{d x}"," ",0,"-(b^3*d*g^2*x^4 + a^3*c*g^2 + (b^3*c*g^2 + 3*a*b^2*d*g^2)*x^3 + 3*(a*b^2*c*g^2 + a^2*b*d*g^2)*x^2 + (3*a^2*b*c*g^2 + a^3*d*g^2)*x)/((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) + integrate((4*b^3*d*g^2*x^3 + 3*a^2*b*c*g^2 + a^3*d*g^2 + 3*(b^3*c*g^2 + 3*a*b^2*d*g^2)*x^2 + 6*(a*b^2*c*g^2 + a^2*b*d*g^2)*x)/((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), x)","F",0
25,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b^{2} d g x^{3} + a^{2} c g + {\left(b^{2} c g + 2 \, a b d g\right)} x^{2} + {\left(2 \, a b c g + a^{2} d g\right)} x}{{\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}} + \int \frac{3 \, b^{2} d g x^{2} + 2 \, a b c g + a^{2} d g + 2 \, {\left(b^{2} c g + 2 \, a b d g\right)} x}{{\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}}\,{d x}"," ",0,"-(b^2*d*g*x^3 + a^2*c*g + (b^2*c*g + 2*a*b*d*g)*x^2 + (2*a*b*c*g + a^2*d*g)*x)/((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) + integrate((3*b^2*d*g*x^2 + 2*a*b*c*g + a^2*d*g + 2*(b^2*c*g + 2*a*b*d*g)*x)/((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), x)","F",0
26,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","d \int \frac{1}{{\left(b c g n - a d g n\right)} B^{2} \log\left({\left(b x + a\right)}^{n}\right) - {\left(b c g n - a d g n\right)} B^{2} \log\left({\left(d x + c\right)}^{n}\right) + {\left(b c g n - a d g n\right)} A B + {\left(b c g n \log\left(e\right) - a d g n \log\left(e\right)\right)} B^{2}}\,{d x} - \frac{d x + c}{{\left(b c g n - a d g n\right)} B^{2} \log\left({\left(b x + a\right)}^{n}\right) - {\left(b c g n - a d g n\right)} B^{2} \log\left({\left(d x + c\right)}^{n}\right) + {\left(b c g n - a d g n\right)} A B + {\left(b c g n \log\left(e\right) - a d g n \log\left(e\right)\right)} B^{2}}"," ",0,"d*integrate(1/((b*c*g*n - a*d*g*n)*B^2*log((b*x + a)^n) - (b*c*g*n - a*d*g*n)*B^2*log((d*x + c)^n) + (b*c*g*n - a*d*g*n)*A*B + (b*c*g*n*log(e) - a*d*g*n*log(e))*B^2), x) - (d*x + c)/((b*c*g*n - a*d*g*n)*B^2*log((b*x + a)^n) - (b*c*g*n - a*d*g*n)*B^2*log((d*x + c)^n) + (b*c*g*n - a*d*g*n)*A*B + (b*c*g*n*log(e) - a*d*g*n*log(e))*B^2)","F",0
27,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{d x + c}{{\left(a b c g^{2} n - a^{2} d g^{2} n\right)} A B + {\left(a b c g^{2} n \log\left(e\right) - a^{2} d g^{2} n \log\left(e\right)\right)} B^{2} + {\left({\left(b^{2} c g^{2} n - a b d g^{2} n\right)} A B + {\left(b^{2} c g^{2} n \log\left(e\right) - a b d g^{2} n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b^{2} c g^{2} n - a b d g^{2} n\right)} B^{2} x + {\left(a b c g^{2} n - a^{2} d g^{2} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b^{2} c g^{2} n - a b d g^{2} n\right)} B^{2} x + {\left(a b c g^{2} n - a^{2} d g^{2} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)} + \int -\frac{1}{B^{2} a^{2} g^{2} n \log\left(e\right) + A B a^{2} g^{2} n + {\left(B^{2} b^{2} g^{2} n \log\left(e\right) + A B b^{2} g^{2} n\right)} x^{2} + 2 \, {\left(B^{2} a b g^{2} n \log\left(e\right) + A B a b g^{2} n\right)} x + {\left(B^{2} b^{2} g^{2} n x^{2} + 2 \, B^{2} a b g^{2} n x + B^{2} a^{2} g^{2} n\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B^{2} b^{2} g^{2} n x^{2} + 2 \, B^{2} a b g^{2} n x + B^{2} a^{2} g^{2} n\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x}"," ",0,"-(d*x + c)/((a*b*c*g^2*n - a^2*d*g^2*n)*A*B + (a*b*c*g^2*n*log(e) - a^2*d*g^2*n*log(e))*B^2 + ((b^2*c*g^2*n - a*b*d*g^2*n)*A*B + (b^2*c*g^2*n*log(e) - a*b*d*g^2*n*log(e))*B^2)*x + ((b^2*c*g^2*n - a*b*d*g^2*n)*B^2*x + (a*b*c*g^2*n - a^2*d*g^2*n)*B^2)*log((b*x + a)^n) - ((b^2*c*g^2*n - a*b*d*g^2*n)*B^2*x + (a*b*c*g^2*n - a^2*d*g^2*n)*B^2)*log((d*x + c)^n)) + integrate(-1/(B^2*a^2*g^2*n*log(e) + A*B*a^2*g^2*n + (B^2*b^2*g^2*n*log(e) + A*B*b^2*g^2*n)*x^2 + 2*(B^2*a*b*g^2*n*log(e) + A*B*a*b*g^2*n)*x + (B^2*b^2*g^2*n*x^2 + 2*B^2*a*b*g^2*n*x + B^2*a^2*g^2*n)*log((b*x + a)^n) - (B^2*b^2*g^2*n*x^2 + 2*B^2*a*b*g^2*n*x + B^2*a^2*g^2*n)*log((d*x + c)^n)), x)","F",0
28,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{d x + c}{{\left(a^{2} b c g^{3} n - a^{3} d g^{3} n\right)} A B + {\left(a^{2} b c g^{3} n \log\left(e\right) - a^{3} d g^{3} n \log\left(e\right)\right)} B^{2} + {\left({\left(b^{3} c g^{3} n - a b^{2} d g^{3} n\right)} A B + {\left(b^{3} c g^{3} n \log\left(e\right) - a b^{2} d g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(a b^{2} c g^{3} n - a^{2} b d g^{3} n\right)} A B + {\left(a b^{2} c g^{3} n \log\left(e\right) - a^{2} b d g^{3} n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b^{3} c g^{3} n - a b^{2} d g^{3} n\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} n - a^{2} b d g^{3} n\right)} B^{2} x + {\left(a^{2} b c g^{3} n - a^{3} d g^{3} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b^{3} c g^{3} n - a b^{2} d g^{3} n\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} n - a^{2} b d g^{3} n\right)} B^{2} x + {\left(a^{2} b c g^{3} n - a^{3} d g^{3} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)} - \int \frac{b d x + 2 \, b c - a d}{{\left({\left(b^{4} c g^{3} n - a b^{3} d g^{3} n\right)} A B + {\left(b^{4} c g^{3} n \log\left(e\right) - a b^{3} d g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(a^{3} b c g^{3} n - a^{4} d g^{3} n\right)} A B + {\left(a^{3} b c g^{3} n \log\left(e\right) - a^{4} d g^{3} n \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(a b^{3} c g^{3} n - a^{2} b^{2} d g^{3} n\right)} A B + {\left(a b^{3} c g^{3} n \log\left(e\right) - a^{2} b^{2} d g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(a^{2} b^{2} c g^{3} n - a^{3} b d g^{3} n\right)} A B + {\left(a^{2} b^{2} c g^{3} n \log\left(e\right) - a^{3} b d g^{3} n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b^{4} c g^{3} n - a b^{3} d g^{3} n\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} n - a^{2} b^{2} d g^{3} n\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} n - a^{3} b d g^{3} n\right)} B^{2} x + {\left(a^{3} b c g^{3} n - a^{4} d g^{3} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b^{4} c g^{3} n - a b^{3} d g^{3} n\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} n - a^{2} b^{2} d g^{3} n\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} n - a^{3} b d g^{3} n\right)} B^{2} x + {\left(a^{3} b c g^{3} n - a^{4} d g^{3} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x}"," ",0,"-(d*x + c)/((a^2*b*c*g^3*n - a^3*d*g^3*n)*A*B + (a^2*b*c*g^3*n*log(e) - a^3*d*g^3*n*log(e))*B^2 + ((b^3*c*g^3*n - a*b^2*d*g^3*n)*A*B + (b^3*c*g^3*n*log(e) - a*b^2*d*g^3*n*log(e))*B^2)*x^2 + 2*((a*b^2*c*g^3*n - a^2*b*d*g^3*n)*A*B + (a*b^2*c*g^3*n*log(e) - a^2*b*d*g^3*n*log(e))*B^2)*x + ((b^3*c*g^3*n - a*b^2*d*g^3*n)*B^2*x^2 + 2*(a*b^2*c*g^3*n - a^2*b*d*g^3*n)*B^2*x + (a^2*b*c*g^3*n - a^3*d*g^3*n)*B^2)*log((b*x + a)^n) - ((b^3*c*g^3*n - a*b^2*d*g^3*n)*B^2*x^2 + 2*(a*b^2*c*g^3*n - a^2*b*d*g^3*n)*B^2*x + (a^2*b*c*g^3*n - a^3*d*g^3*n)*B^2)*log((d*x + c)^n)) - integrate((b*d*x + 2*b*c - a*d)/(((b^4*c*g^3*n - a*b^3*d*g^3*n)*A*B + (b^4*c*g^3*n*log(e) - a*b^3*d*g^3*n*log(e))*B^2)*x^3 + (a^3*b*c*g^3*n - a^4*d*g^3*n)*A*B + (a^3*b*c*g^3*n*log(e) - a^4*d*g^3*n*log(e))*B^2 + 3*((a*b^3*c*g^3*n - a^2*b^2*d*g^3*n)*A*B + (a*b^3*c*g^3*n*log(e) - a^2*b^2*d*g^3*n*log(e))*B^2)*x^2 + 3*((a^2*b^2*c*g^3*n - a^3*b*d*g^3*n)*A*B + (a^2*b^2*c*g^3*n*log(e) - a^3*b*d*g^3*n*log(e))*B^2)*x + ((b^4*c*g^3*n - a*b^3*d*g^3*n)*B^2*x^3 + 3*(a*b^3*c*g^3*n - a^2*b^2*d*g^3*n)*B^2*x^2 + 3*(a^2*b^2*c*g^3*n - a^3*b*d*g^3*n)*B^2*x + (a^3*b*c*g^3*n - a^4*d*g^3*n)*B^2)*log((b*x + a)^n) - ((b^4*c*g^3*n - a*b^3*d*g^3*n)*B^2*x^3 + 3*(a*b^3*c*g^3*n - a^2*b^2*d*g^3*n)*B^2*x^2 + 3*(a^2*b^2*c*g^3*n - a^3*b*d*g^3*n)*B^2*x + (a^3*b*c*g^3*n - a^4*d*g^3*n)*B^2)*log((d*x + c)^n)), x)","F",0
29,1,676,0,1.377861," ","integrate((d*g*x+c*g)^4*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{5} \, B d^{4} g^{4} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{5} \, A d^{4} g^{4} x^{5} + B c d^{3} g^{4} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c d^{3} g^{4} x^{4} + 2 \, B c^{2} d^{2} g^{4} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A c^{2} d^{2} g^{4} x^{3} + 2 \, B c^{3} d g^{4} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A c^{3} d g^{4} x^{2} + \frac{1}{60} \, B d^{4} g^{4} 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} \, B c d^{3} g^{4} 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)} + B c^{2} d^{2} g^{4} 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 \, B c^{3} d g^{4} 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^{4} g^{4} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B c^{4} g^{4} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c^{4} g^{4} x"," ",0,"1/5*B*d^4*g^4*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A*d^4*g^4*x^5 + B*c*d^3*g^4*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c*d^3*g^4*x^4 + 2*B*c^2*d^2*g^4*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*c^2*d^2*g^4*x^3 + 2*B*c^3*d*g^4*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*c^3*d*g^4*x^2 + 1/60*B*d^4*g^4*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*B*c*d^3*g^4*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)) + B*c^2*d^2*g^4*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*B*c^3*d*g^4*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^4*g^4*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*c^4*g^4*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c^4*g^4*x","B",0
30,1,479,0,1.368047," ","integrate((d*g*x+c*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, B d^{3} g^{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} g^{3} x^{4} + B c d^{2} g^{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} g^{3} x^{3} + \frac{3}{2} \, B c^{2} d g^{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 g^{3} x^{2} - \frac{1}{24} \, B d^{3} g^{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} g^{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 g^{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} g^{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} g^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c^{3} g^{3} x"," ",0,"1/4*B*d^3*g^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*d^3*g^3*x^4 + B*c*d^2*g^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c*d^2*g^3*x^3 + 3/2*B*c^2*d*g^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*c^2*d*g^3*x^2 - 1/24*B*d^3*g^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*g^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*g^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*g^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*c^3*g^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c^3*g^3*x","B",0
31,1,309,0,1.287529," ","integrate((d*g*x+c*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, B d^{2} g^{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} g^{2} x^{3} + B c d g^{2} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c d g^{2} x^{2} + \frac{1}{6} \, B d^{2} g^{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 g^{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} g^{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} g^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c^{2} g^{2} x"," ",0,"1/3*B*d^2*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A*d^2*g^2*x^3 + B*c*d*g^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c*d*g^2*x^2 + 1/6*B*d^2*g^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*g^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*g^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*c^2*g^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c^2*g^2*x","B",0
32,1,156,0,1.136474," ","integrate((d*g*x+c*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{2} \, B d g 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 g x^{2} - \frac{1}{2} \, B d g 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 g n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B c g x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A c g x"," ",0,"1/2*B*d*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*d*g*x^2 - 1/2*B*d*g*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*g*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*c*g*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*c*g*x","A",0
33,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*g*x+c*g),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 g} - 2 \, \int \frac{n \log\left(b x + a\right) + \log\left(e\right)}{d g x + c g}\,{d x}\right)} + \frac{A \log\left(d g x + c g\right)}{d g}"," ",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*g) - 2*integrate((n*log(b*x + a) + log(e))/(d*g*x + c*g), x)) + A*log(d*g*x + c*g)/(d*g)","F",0
34,1,136,0,1.132638," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*g*x+c*g)^2,x, algorithm=""maxima"")","B n {\left(\frac{1}{d^{2} g^{2} x + c d g^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} g^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} g^{2}}\right)} - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{d^{2} g^{2} x + c d g^{2}} - \frac{A}{d^{2} g^{2} x + c d g^{2}}"," ",0,"B*n*(1/(d^2*g^2*x + c*d*g^2) + b*log(b*x + a)/((b*c*d - a*d^2)*g^2) - b*log(d*x + c)/((b*c*d - a*d^2)*g^2)) - B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*g^2*x + c*d*g^2) - A/(d^2*g^2*x + c*d*g^2)","A",0
35,1,259,0,1.355113," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*g*x+c*g)^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)} g^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} g^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} g^{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)} g^{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)} g^{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} g^{3} x^{2} + 2 \, c d^{2} g^{3} x + c^{2} d g^{3}\right)}} - \frac{A}{2 \, {\left(d^{3} g^{3} x^{2} + 2 \, c d^{2} g^{3} x + c^{2} d g^{3}\right)}}"," ",0,"1/4*B*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*g^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*g^3*x + (b*c^3*d - a*c^2*d^2)*g^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g^3)) - 1/2*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*g^3*x^2 + 2*c*d^2*g^3*x + c^2*d*g^3) - 1/2*A/(d^3*g^3*x^2 + 2*c*d^2*g^3*x + c^2*d*g^3)","A",0
36,1,433,0,1.365353," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*g*x+c*g)^4,x, algorithm=""maxima"")","\frac{1}{18} \, B n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 11 \, b^{2} c^{2} - 7 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(5 \, b^{2} c d - a b d^{2}\right)} x}{{\left(b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} g^{4} x^{3} + 3 \, {\left(b^{2} c^{3} d^{3} - 2 \, a b c^{2} d^{4} + a^{2} c d^{5}\right)} g^{4} x^{2} + 3 \, {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} g^{4} x + {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} g^{4}} + \frac{6 \, b^{3} \log\left(b x + a\right)}{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} g^{4}} - \frac{6 \, b^{3} \log\left(d x + c\right)}{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} g^{4}}\right)} - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(d^{4} g^{4} x^{3} + 3 \, c d^{3} g^{4} x^{2} + 3 \, c^{2} d^{2} g^{4} x + c^{3} d g^{4}\right)}} - \frac{A}{3 \, {\left(d^{4} g^{4} x^{3} + 3 \, c d^{3} g^{4} x^{2} + 3 \, c^{2} d^{2} g^{4} x + c^{3} d g^{4}\right)}}"," ",0,"1/18*B*n*((6*b^2*d^2*x^2 + 11*b^2*c^2 - 7*a*b*c*d + 2*a^2*d^2 + 3*(5*b^2*c*d - a*b*d^2)*x)/((b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*g^4*x^3 + 3*(b^2*c^3*d^3 - 2*a*b*c^2*d^4 + a^2*c*d^5)*g^4*x^2 + 3*(b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*g^4*x + (b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*g^4) + 6*b^3*log(b*x + a)/((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*g^4) - 6*b^3*log(d*x + c)/((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*g^4)) - 1/3*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^4*g^4*x^3 + 3*c*d^3*g^4*x^2 + 3*c^2*d^2*g^4*x + c^3*d*g^4) - 1/3*A/(d^4*g^4*x^3 + 3*c*d^3*g^4*x^2 + 3*c^2*d^2*g^4*x + c^3*d*g^4)","B",0
37,1,652,0,1.057765," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*g*x+c*g)^5,x, algorithm=""maxima"")","\frac{1}{48} \, B n {\left(\frac{12 \, b^{3} d^{3} x^{3} + 25 \, b^{3} c^{3} - 23 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} - 3 \, a^{3} d^{3} + 6 \, {\left(7 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(13 \, b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{3} c^{3} d^{5} - 3 \, a b^{2} c^{2} d^{6} + 3 \, a^{2} b c d^{7} - a^{3} d^{8}\right)} g^{5} x^{4} + 4 \, {\left(b^{3} c^{4} d^{4} - 3 \, a b^{2} c^{3} d^{5} + 3 \, a^{2} b c^{2} d^{6} - a^{3} c d^{7}\right)} g^{5} x^{3} + 6 \, {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} g^{5} x^{2} + 4 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} g^{5} x + {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4}\right)} g^{5}} + \frac{12 \, b^{4} \log\left(b x + a\right)}{{\left(b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} g^{5}} - \frac{12 \, b^{4} \log\left(d x + c\right)}{{\left(b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} g^{5}}\right)} - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{4 \, {\left(d^{5} g^{5} x^{4} + 4 \, c d^{4} g^{5} x^{3} + 6 \, c^{2} d^{3} g^{5} x^{2} + 4 \, c^{3} d^{2} g^{5} x + c^{4} d g^{5}\right)}} - \frac{A}{4 \, {\left(d^{5} g^{5} x^{4} + 4 \, c d^{4} g^{5} x^{3} + 6 \, c^{2} d^{3} g^{5} x^{2} + 4 \, c^{3} d^{2} g^{5} x + c^{4} d g^{5}\right)}}"," ",0,"1/48*B*n*((12*b^3*d^3*x^3 + 25*b^3*c^3 - 23*a*b^2*c^2*d + 13*a^2*b*c*d^2 - 3*a^3*d^3 + 6*(7*b^3*c*d^2 - a*b^2*d^3)*x^2 + 4*(13*b^3*c^2*d - 5*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^3*c^3*d^5 - 3*a*b^2*c^2*d^6 + 3*a^2*b*c*d^7 - a^3*d^8)*g^5*x^4 + 4*(b^3*c^4*d^4 - 3*a*b^2*c^3*d^5 + 3*a^2*b*c^2*d^6 - a^3*c*d^7)*g^5*x^3 + 6*(b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*g^5*x^2 + 4*(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*g^5*x + (b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4)*g^5) + 12*b^4*log(b*x + a)/((b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*g^5) - 12*b^4*log(d*x + c)/((b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*g^5)) - 1/4*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^5*g^5*x^4 + 4*c*d^4*g^5*x^3 + 6*c^2*d^3*g^5*x^2 + 4*c^3*d^2*g^5*x + c^4*d*g^5) - 1/4*A/(d^5*g^5*x^4 + 4*c*d^4*g^5*x^3 + 6*c^2*d^3*g^5*x^2 + 4*c^3*d^2*g^5*x + c^4*d*g^5)","B",0
38,1,2880,0,4.783243," ","integrate((d*g*x+c*g)^4*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{5} \, A B d^{4} g^{4} 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} d^{4} g^{4} x^{5} + 2 \, A B c d^{3} g^{4} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c d^{3} g^{4} x^{4} + 4 \, A B c^{2} d^{2} g^{4} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A^{2} c^{2} d^{2} g^{4} x^{3} + 4 \, A B c^{3} d g^{4} x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A^{2} c^{3} d g^{4} x^{2} + \frac{1}{30} \, A B d^{4} g^{4} 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}{3} \, A B c d^{3} g^{4} 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)} + 2 \, A B c^{2} d^{2} g^{4} 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)} - 4 \, A B c^{3} d g^{4} 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^{4} g^{4} 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^{4} g^{4} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c^{4} g^{4} x - \frac{{\left(77 \, a b^{3} c^{4} d g^{4} n^{2} - 94 \, a^{2} b^{2} c^{3} d^{2} g^{4} n^{2} + 54 \, a^{3} b c^{2} d^{3} g^{4} n^{2} - 12 \, a^{4} c d^{4} g^{4} n^{2} - {\left(25 \, g^{4} n^{2} - 12 \, g^{4} n \log\left(e\right)\right)} b^{4} c^{5}\right)} B^{2} \log\left(d x + c\right)}{30 \, b^{4} d} - \frac{2 \, {\left(b^{5} c^{5} g^{4} n^{2} - 5 \, a b^{4} c^{4} d g^{4} n^{2} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n^{2} + 5 \, a^{4} b c d^{4} g^{4} n^{2} - a^{5} d^{5} g^{4} 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}}{5 \, b^{5} d} + \frac{12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right)^{2} + 24 \, B^{2} b^{5} c^{5} g^{4} n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - 12 \, B^{2} b^{5} c^{5} g^{4} n^{2} \log\left(d x + c\right)^{2} + 6 \, {\left(a b^{4} d^{5} g^{4} n \log\left(e\right) - {\left(g^{4} n \log\left(e\right) - 10 \, g^{4} \log\left(e\right)^{2}\right)} b^{5} c d^{4}\right)} B^{2} x^{4} + 2 \, {\left({\left(g^{4} n^{2} - 16 \, g^{4} n \log\left(e\right) + 60 \, g^{4} \log\left(e\right)^{2}\right)} b^{5} c^{2} d^{3} - 2 \, {\left(g^{4} n^{2} - 10 \, g^{4} n \log\left(e\right)\right)} a b^{4} c d^{4} + {\left(g^{4} n^{2} - 4 \, g^{4} n \log\left(e\right)\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + {\left({\left(13 \, g^{4} n^{2} - 72 \, g^{4} n \log\left(e\right) + 120 \, g^{4} \log\left(e\right)^{2}\right)} b^{5} c^{3} d^{2} - 3 \, {\left(11 \, g^{4} n^{2} - 40 \, g^{4} n \log\left(e\right)\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(9 \, g^{4} n^{2} - 20 \, g^{4} n \log\left(e\right)\right)} a^{2} b^{3} c d^{4} - {\left(7 \, g^{4} n^{2} - 12 \, g^{4} n \log\left(e\right)\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 12 \, {\left(5 \, a b^{4} c^{4} d g^{4} n^{2} - 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n^{2} + 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n^{2} - 5 \, a^{4} b c d^{4} g^{4} n^{2} + a^{5} d^{5} g^{4} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + 2 \, {\left({\left(23 \, g^{4} n^{2} - 48 \, g^{4} n \log\left(e\right) + 30 \, g^{4} \log\left(e\right)^{2}\right)} b^{5} c^{4} d - {\left(79 \, g^{4} n^{2} - 120 \, g^{4} n \log\left(e\right)\right)} a b^{4} c^{3} d^{2} + 6 \, {\left(17 \, g^{4} n^{2} - 20 \, g^{4} n \log\left(e\right)\right)} a^{2} b^{3} c^{2} d^{3} - {\left(59 \, g^{4} n^{2} - 60 \, g^{4} n \log\left(e\right)\right)} a^{3} b^{2} c d^{4} + {\left(13 \, g^{4} n^{2} - 12 \, g^{4} n \log\left(e\right)\right)} a^{4} b d^{5}\right)} B^{2} x - 2 \, {\left(12 \, {\left(4 \, g^{4} n^{2} - 5 \, g^{4} n \log\left(e\right)\right)} a b^{4} c^{4} d - 12 \, {\left(13 \, g^{4} n^{2} - 10 \, g^{4} n \log\left(e\right)\right)} a^{2} b^{3} c^{3} d^{2} + 4 \, {\left(49 \, g^{4} n^{2} - 30 \, g^{4} n \log\left(e\right)\right)} a^{3} b^{2} c^{2} d^{3} - {\left(113 \, g^{4} n^{2} - 60 \, g^{4} n \log\left(e\right)\right)} a^{4} b c d^{4} + {\left(25 \, g^{4} n^{2} - 12 \, g^{4} n \log\left(e\right)\right)} a^{5} d^{5}\right)} B^{2} \log\left(b x + a\right) + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} b^{5} c d^{4} g^{4} x^{4} + 10 \, B^{2} b^{5} c^{2} d^{3} g^{4} x^{3} + 10 \, B^{2} b^{5} c^{3} d^{2} g^{4} x^{2} + 5 \, B^{2} b^{5} c^{4} d g^{4} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} b^{5} c d^{4} g^{4} x^{4} + 10 \, B^{2} b^{5} c^{2} d^{3} g^{4} x^{3} + 10 \, B^{2} b^{5} c^{3} d^{2} g^{4} x^{2} + 5 \, B^{2} b^{5} c^{4} d g^{4} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) - 12 \, B^{2} b^{5} c^{5} g^{4} n \log\left(d x + c\right) + 3 \, {\left(a b^{4} d^{5} g^{4} n - {\left(g^{4} n - 20 \, g^{4} \log\left(e\right)\right)} b^{5} c d^{4}\right)} B^{2} x^{4} + 4 \, {\left(5 \, a b^{4} c d^{4} g^{4} n - a^{2} b^{3} d^{5} g^{4} n - 2 \, {\left(2 \, g^{4} n - 15 \, g^{4} \log\left(e\right)\right)} b^{5} c^{2} d^{3}\right)} B^{2} x^{3} + 6 \, {\left(10 \, a b^{4} c^{2} d^{3} g^{4} n - 5 \, a^{2} b^{3} c d^{4} g^{4} n + a^{3} b^{2} d^{5} g^{4} n - 2 \, {\left(3 \, g^{4} n - 10 \, g^{4} \log\left(e\right)\right)} b^{5} c^{3} d^{2}\right)} B^{2} x^{2} + 12 \, {\left(10 \, a b^{4} c^{3} d^{2} g^{4} n - 10 \, a^{2} b^{3} c^{2} d^{3} g^{4} n + 5 \, a^{3} b^{2} c d^{4} g^{4} n - a^{4} b d^{5} g^{4} n - {\left(4 \, g^{4} n - 5 \, g^{4} \log\left(e\right)\right)} b^{5} c^{4} d\right)} B^{2} x + 12 \, {\left(5 \, a b^{4} c^{4} d g^{4} n - 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n + 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n - 5 \, a^{4} b c d^{4} g^{4} n + a^{5} d^{5} g^{4} n\right)} B^{2} \log\left(b x + a\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) - 12 \, B^{2} b^{5} c^{5} g^{4} n \log\left(d x + c\right) + 3 \, {\left(a b^{4} d^{5} g^{4} n - {\left(g^{4} n - 20 \, g^{4} \log\left(e\right)\right)} b^{5} c d^{4}\right)} B^{2} x^{4} + 4 \, {\left(5 \, a b^{4} c d^{4} g^{4} n - a^{2} b^{3} d^{5} g^{4} n - 2 \, {\left(2 \, g^{4} n - 15 \, g^{4} \log\left(e\right)\right)} b^{5} c^{2} d^{3}\right)} B^{2} x^{3} + 6 \, {\left(10 \, a b^{4} c^{2} d^{3} g^{4} n - 5 \, a^{2} b^{3} c d^{4} g^{4} n + a^{3} b^{2} d^{5} g^{4} n - 2 \, {\left(3 \, g^{4} n - 10 \, g^{4} \log\left(e\right)\right)} b^{5} c^{3} d^{2}\right)} B^{2} x^{2} + 12 \, {\left(10 \, a b^{4} c^{3} d^{2} g^{4} n - 10 \, a^{2} b^{3} c^{2} d^{3} g^{4} n + 5 \, a^{3} b^{2} c d^{4} g^{4} n - a^{4} b d^{5} g^{4} n - {\left(4 \, g^{4} n - 5 \, g^{4} \log\left(e\right)\right)} b^{5} c^{4} d\right)} B^{2} x + 12 \, {\left(5 \, a b^{4} c^{4} d g^{4} n - 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} n + 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} n - 5 \, a^{4} b c d^{4} g^{4} n + a^{5} d^{5} g^{4} n\right)} B^{2} \log\left(b x + a\right) + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} b^{5} c d^{4} g^{4} x^{4} + 10 \, B^{2} b^{5} c^{2} d^{3} g^{4} x^{3} + 10 \, B^{2} b^{5} c^{3} d^{2} g^{4} x^{2} + 5 \, B^{2} b^{5} c^{4} d g^{4} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{60 \, b^{5} d}"," ",0,"2/5*A*B*d^4*g^4*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A^2*d^4*g^4*x^5 + 2*A*B*c*d^3*g^4*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c*d^3*g^4*x^4 + 4*A*B*c^2*d^2*g^4*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A^2*c^2*d^2*g^4*x^3 + 4*A*B*c^3*d*g^4*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A^2*c^3*d*g^4*x^2 + 1/30*A*B*d^4*g^4*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)) - 1/3*A*B*c*d^3*g^4*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*A*B*c^2*d^2*g^4*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*A*B*c^3*d*g^4*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^4*g^4*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*c^4*g^4*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c^4*g^4*x - 1/30*(77*a*b^3*c^4*d*g^4*n^2 - 94*a^2*b^2*c^3*d^2*g^4*n^2 + 54*a^3*b*c^2*d^3*g^4*n^2 - 12*a^4*c*d^4*g^4*n^2 - (25*g^4*n^2 - 12*g^4*n*log(e))*b^4*c^5)*B^2*log(d*x + c)/(b^4*d) - 2/5*(b^5*c^5*g^4*n^2 - 5*a*b^4*c^4*d*g^4*n^2 + 10*a^2*b^3*c^3*d^2*g^4*n^2 - 10*a^3*b^2*c^2*d^3*g^4*n^2 + 5*a^4*b*c*d^4*g^4*n^2 - a^5*d^5*g^4*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^5*d) + 1/60*(12*B^2*b^5*d^5*g^4*x^5*log(e)^2 + 24*B^2*b^5*c^5*g^4*n^2*log(b*x + a)*log(d*x + c) - 12*B^2*b^5*c^5*g^4*n^2*log(d*x + c)^2 + 6*(a*b^4*d^5*g^4*n*log(e) - (g^4*n*log(e) - 10*g^4*log(e)^2)*b^5*c*d^4)*B^2*x^4 + 2*((g^4*n^2 - 16*g^4*n*log(e) + 60*g^4*log(e)^2)*b^5*c^2*d^3 - 2*(g^4*n^2 - 10*g^4*n*log(e))*a*b^4*c*d^4 + (g^4*n^2 - 4*g^4*n*log(e))*a^2*b^3*d^5)*B^2*x^3 + ((13*g^4*n^2 - 72*g^4*n*log(e) + 120*g^4*log(e)^2)*b^5*c^3*d^2 - 3*(11*g^4*n^2 - 40*g^4*n*log(e))*a*b^4*c^2*d^3 + 3*(9*g^4*n^2 - 20*g^4*n*log(e))*a^2*b^3*c*d^4 - (7*g^4*n^2 - 12*g^4*n*log(e))*a^3*b^2*d^5)*B^2*x^2 - 12*(5*a*b^4*c^4*d*g^4*n^2 - 10*a^2*b^3*c^3*d^2*g^4*n^2 + 10*a^3*b^2*c^2*d^3*g^4*n^2 - 5*a^4*b*c*d^4*g^4*n^2 + a^5*d^5*g^4*n^2)*B^2*log(b*x + a)^2 + 2*((23*g^4*n^2 - 48*g^4*n*log(e) + 30*g^4*log(e)^2)*b^5*c^4*d - (79*g^4*n^2 - 120*g^4*n*log(e))*a*b^4*c^3*d^2 + 6*(17*g^4*n^2 - 20*g^4*n*log(e))*a^2*b^3*c^2*d^3 - (59*g^4*n^2 - 60*g^4*n*log(e))*a^3*b^2*c*d^4 + (13*g^4*n^2 - 12*g^4*n*log(e))*a^4*b*d^5)*B^2*x - 2*(12*(4*g^4*n^2 - 5*g^4*n*log(e))*a*b^4*c^4*d - 12*(13*g^4*n^2 - 10*g^4*n*log(e))*a^2*b^3*c^3*d^2 + 4*(49*g^4*n^2 - 30*g^4*n*log(e))*a^3*b^2*c^2*d^3 - (113*g^4*n^2 - 60*g^4*n*log(e))*a^4*b*c*d^4 + (25*g^4*n^2 - 12*g^4*n*log(e))*a^5*d^5)*B^2*log(b*x + a) + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*b^5*c*d^4*g^4*x^4 + 10*B^2*b^5*c^2*d^3*g^4*x^3 + 10*B^2*b^5*c^3*d^2*g^4*x^2 + 5*B^2*b^5*c^4*d*g^4*x)*log((b*x + a)^n)^2 + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*b^5*c*d^4*g^4*x^4 + 10*B^2*b^5*c^2*d^3*g^4*x^3 + 10*B^2*b^5*c^3*d^2*g^4*x^2 + 5*B^2*b^5*c^4*d*g^4*x)*log((d*x + c)^n)^2 + 2*(12*B^2*b^5*d^5*g^4*x^5*log(e) - 12*B^2*b^5*c^5*g^4*n*log(d*x + c) + 3*(a*b^4*d^5*g^4*n - (g^4*n - 20*g^4*log(e))*b^5*c*d^4)*B^2*x^4 + 4*(5*a*b^4*c*d^4*g^4*n - a^2*b^3*d^5*g^4*n - 2*(2*g^4*n - 15*g^4*log(e))*b^5*c^2*d^3)*B^2*x^3 + 6*(10*a*b^4*c^2*d^3*g^4*n - 5*a^2*b^3*c*d^4*g^4*n + a^3*b^2*d^5*g^4*n - 2*(3*g^4*n - 10*g^4*log(e))*b^5*c^3*d^2)*B^2*x^2 + 12*(10*a*b^4*c^3*d^2*g^4*n - 10*a^2*b^3*c^2*d^3*g^4*n + 5*a^3*b^2*c*d^4*g^4*n - a^4*b*d^5*g^4*n - (4*g^4*n - 5*g^4*log(e))*b^5*c^4*d)*B^2*x + 12*(5*a*b^4*c^4*d*g^4*n - 10*a^2*b^3*c^3*d^2*g^4*n + 10*a^3*b^2*c^2*d^3*g^4*n - 5*a^4*b*c*d^4*g^4*n + a^5*d^5*g^4*n)*B^2*log(b*x + a))*log((b*x + a)^n) - 2*(12*B^2*b^5*d^5*g^4*x^5*log(e) - 12*B^2*b^5*c^5*g^4*n*log(d*x + c) + 3*(a*b^4*d^5*g^4*n - (g^4*n - 20*g^4*log(e))*b^5*c*d^4)*B^2*x^4 + 4*(5*a*b^4*c*d^4*g^4*n - a^2*b^3*d^5*g^4*n - 2*(2*g^4*n - 15*g^4*log(e))*b^5*c^2*d^3)*B^2*x^3 + 6*(10*a*b^4*c^2*d^3*g^4*n - 5*a^2*b^3*c*d^4*g^4*n + a^3*b^2*d^5*g^4*n - 2*(3*g^4*n - 10*g^4*log(e))*b^5*c^3*d^2)*B^2*x^2 + 12*(10*a*b^4*c^3*d^2*g^4*n - 10*a^2*b^3*c^2*d^3*g^4*n + 5*a^3*b^2*c*d^4*g^4*n - a^4*b*d^5*g^4*n - (4*g^4*n - 5*g^4*log(e))*b^5*c^4*d)*B^2*x + 12*(5*a*b^4*c^4*d*g^4*n - 10*a^2*b^3*c^3*d^2*g^4*n + 10*a^3*b^2*c^2*d^3*g^4*n - 5*a^4*b*c*d^4*g^4*n + a^5*d^5*g^4*n)*B^2*log(b*x + a) + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*b^5*c*d^4*g^4*x^4 + 10*B^2*b^5*c^2*d^3*g^4*x^3 + 10*B^2*b^5*c^3*d^2*g^4*x^2 + 5*B^2*b^5*c^4*d*g^4*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^5*d)","B",0
39,1,2129,0,4.846261," ","integrate((d*g*x+c*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A B d^{3} g^{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} g^{3} x^{4} + 2 \, A B c d^{2} g^{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} g^{3} x^{3} + 3 \, A B c^{2} d g^{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 g^{3} x^{2} - \frac{1}{12} \, A B d^{3} g^{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} g^{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 g^{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} g^{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} g^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c^{3} g^{3} x - \frac{{\left(26 \, a b^{2} c^{3} d g^{3} n^{2} - 21 \, a^{2} b c^{2} d^{2} g^{3} n^{2} + 6 \, a^{3} c d^{3} g^{3} n^{2} - {\left(11 \, g^{3} n^{2} - 6 \, g^{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} g^{3} n^{2} - 4 \, a b^{3} c^{3} d g^{3} n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n^{2} - 4 \, a^{3} b c d^{3} g^{3} n^{2} + a^{4} d^{4} g^{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} g^{3} x^{4} \log\left(e\right)^{2} + 6 \, B^{2} b^{4} c^{4} g^{3} n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - 3 \, B^{2} b^{4} c^{4} g^{3} n^{2} \log\left(d x + c\right)^{2} + 2 \, {\left(a b^{3} d^{4} g^{3} n \log\left(e\right) - {\left(g^{3} n \log\left(e\right) - 6 \, g^{3} \log\left(e\right)^{2}\right)} b^{4} c d^{3}\right)} B^{2} x^{3} + {\left({\left(g^{3} n^{2} - 9 \, g^{3} n \log\left(e\right) + 18 \, g^{3} \log\left(e\right)^{2}\right)} b^{4} c^{2} d^{2} - 2 \, {\left(g^{3} n^{2} - 6 \, g^{3} n \log\left(e\right)\right)} a b^{3} c d^{3} + {\left(g^{3} n^{2} - 3 \, g^{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 g^{3} n^{2} - 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n^{2} + 4 \, a^{3} b c d^{3} g^{3} n^{2} - a^{4} d^{4} g^{3} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + {\left({\left(7 \, g^{3} n^{2} - 18 \, g^{3} n \log\left(e\right) + 12 \, g^{3} \log\left(e\right)^{2}\right)} b^{4} c^{3} d - {\left(19 \, g^{3} n^{2} - 36 \, g^{3} n \log\left(e\right)\right)} a b^{3} c^{2} d^{2} + {\left(17 \, g^{3} n^{2} - 24 \, g^{3} n \log\left(e\right)\right)} a^{2} b^{2} c d^{3} - {\left(5 \, g^{3} n^{2} - 6 \, g^{3} n \log\left(e\right)\right)} a^{3} b d^{4}\right)} B^{2} x - {\left(6 \, {\left(3 \, g^{3} n^{2} - 4 \, g^{3} n \log\left(e\right)\right)} a b^{3} c^{3} d - 9 \, {\left(5 \, g^{3} n^{2} - 4 \, g^{3} n \log\left(e\right)\right)} a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(19 \, g^{3} n^{2} - 12 \, g^{3} n \log\left(e\right)\right)} a^{3} b c d^{3} - {\left(11 \, g^{3} n^{2} - 6 \, g^{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} g^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} g^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} g^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d g^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} g^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} g^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d g^{3} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) - 6 \, B^{2} b^{4} c^{4} g^{3} n \log\left(d x + c\right) + 2 \, {\left(a b^{3} d^{4} g^{3} n - {\left(g^{3} n - 12 \, g^{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} g^{3} n - a^{2} b^{2} d^{4} g^{3} n - 3 \, {\left(g^{3} n - 4 \, g^{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} g^{3} n - 4 \, a^{2} b^{2} c d^{3} g^{3} n + a^{3} b d^{4} g^{3} n - {\left(3 \, g^{3} n - 4 \, g^{3} \log\left(e\right)\right)} b^{4} c^{3} d\right)} B^{2} x + 6 \, {\left(4 \, a b^{3} c^{3} d g^{3} n - 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n + 4 \, a^{3} b c d^{3} g^{3} n - a^{4} d^{4} g^{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} g^{3} x^{4} \log\left(e\right) - 6 \, B^{2} b^{4} c^{4} g^{3} n \log\left(d x + c\right) + 2 \, {\left(a b^{3} d^{4} g^{3} n - {\left(g^{3} n - 12 \, g^{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} g^{3} n - a^{2} b^{2} d^{4} g^{3} n - 3 \, {\left(g^{3} n - 4 \, g^{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} g^{3} n - 4 \, a^{2} b^{2} c d^{3} g^{3} n + a^{3} b d^{4} g^{3} n - {\left(3 \, g^{3} n - 4 \, g^{3} \log\left(e\right)\right)} b^{4} c^{3} d\right)} B^{2} x + 6 \, {\left(4 \, a b^{3} c^{3} d g^{3} n - 6 \, a^{2} b^{2} c^{2} d^{2} g^{3} n + 4 \, a^{3} b c d^{3} g^{3} n - a^{4} d^{4} g^{3} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} g^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} g^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d g^{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*g^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*d^3*g^3*x^4 + 2*A*B*c*d^2*g^3*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c*d^2*g^3*x^3 + 3*A*B*c^2*d*g^3*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A^2*c^2*d*g^3*x^2 - 1/12*A*B*d^3*g^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*g^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*g^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*g^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*c^3*g^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c^3*g^3*x - 1/12*(26*a*b^2*c^3*d*g^3*n^2 - 21*a^2*b*c^2*d^2*g^3*n^2 + 6*a^3*c*d^3*g^3*n^2 - (11*g^3*n^2 - 6*g^3*n*log(e))*b^3*c^4)*B^2*log(d*x + c)/(b^3*d) - 1/2*(b^4*c^4*g^3*n^2 - 4*a*b^3*c^3*d*g^3*n^2 + 6*a^2*b^2*c^2*d^2*g^3*n^2 - 4*a^3*b*c*d^3*g^3*n^2 + a^4*d^4*g^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*g^3*x^4*log(e)^2 + 6*B^2*b^4*c^4*g^3*n^2*log(b*x + a)*log(d*x + c) - 3*B^2*b^4*c^4*g^3*n^2*log(d*x + c)^2 + 2*(a*b^3*d^4*g^3*n*log(e) - (g^3*n*log(e) - 6*g^3*log(e)^2)*b^4*c*d^3)*B^2*x^3 + ((g^3*n^2 - 9*g^3*n*log(e) + 18*g^3*log(e)^2)*b^4*c^2*d^2 - 2*(g^3*n^2 - 6*g^3*n*log(e))*a*b^3*c*d^3 + (g^3*n^2 - 3*g^3*n*log(e))*a^2*b^2*d^4)*B^2*x^2 - 3*(4*a*b^3*c^3*d*g^3*n^2 - 6*a^2*b^2*c^2*d^2*g^3*n^2 + 4*a^3*b*c*d^3*g^3*n^2 - a^4*d^4*g^3*n^2)*B^2*log(b*x + a)^2 + ((7*g^3*n^2 - 18*g^3*n*log(e) + 12*g^3*log(e)^2)*b^4*c^3*d - (19*g^3*n^2 - 36*g^3*n*log(e))*a*b^3*c^2*d^2 + (17*g^3*n^2 - 24*g^3*n*log(e))*a^2*b^2*c*d^3 - (5*g^3*n^2 - 6*g^3*n*log(e))*a^3*b*d^4)*B^2*x - (6*(3*g^3*n^2 - 4*g^3*n*log(e))*a*b^3*c^3*d - 9*(5*g^3*n^2 - 4*g^3*n*log(e))*a^2*b^2*c^2*d^2 + 2*(19*g^3*n^2 - 12*g^3*n*log(e))*a^3*b*c*d^3 - (11*g^3*n^2 - 6*g^3*n*log(e))*a^4*d^4)*B^2*log(b*x + a) + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*c*d^3*g^3*x^3 + 6*B^2*b^4*c^2*d^2*g^3*x^2 + 4*B^2*b^4*c^3*d*g^3*x)*log((b*x + a)^n)^2 + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*c*d^3*g^3*x^3 + 6*B^2*b^4*c^2*d^2*g^3*x^2 + 4*B^2*b^4*c^3*d*g^3*x)*log((d*x + c)^n)^2 + (6*B^2*b^4*d^4*g^3*x^4*log(e) - 6*B^2*b^4*c^4*g^3*n*log(d*x + c) + 2*(a*b^3*d^4*g^3*n - (g^3*n - 12*g^3*log(e))*b^4*c*d^3)*B^2*x^3 + 3*(4*a*b^3*c*d^3*g^3*n - a^2*b^2*d^4*g^3*n - 3*(g^3*n - 4*g^3*log(e))*b^4*c^2*d^2)*B^2*x^2 + 6*(6*a*b^3*c^2*d^2*g^3*n - 4*a^2*b^2*c*d^3*g^3*n + a^3*b*d^4*g^3*n - (3*g^3*n - 4*g^3*log(e))*b^4*c^3*d)*B^2*x + 6*(4*a*b^3*c^3*d*g^3*n - 6*a^2*b^2*c^2*d^2*g^3*n + 4*a^3*b*c*d^3*g^3*n - a^4*d^4*g^3*n)*B^2*log(b*x + a))*log((b*x + a)^n) - (6*B^2*b^4*d^4*g^3*x^4*log(e) - 6*B^2*b^4*c^4*g^3*n*log(d*x + c) + 2*(a*b^3*d^4*g^3*n - (g^3*n - 12*g^3*log(e))*b^4*c*d^3)*B^2*x^3 + 3*(4*a*b^3*c*d^3*g^3*n - a^2*b^2*d^4*g^3*n - 3*(g^3*n - 4*g^3*log(e))*b^4*c^2*d^2)*B^2*x^2 + 6*(6*a*b^3*c^2*d^2*g^3*n - 4*a^2*b^2*c*d^3*g^3*n + a^3*b*d^4*g^3*n - (3*g^3*n - 4*g^3*log(e))*b^4*c^3*d)*B^2*x + 6*(4*a*b^3*c^3*d*g^3*n - 6*a^2*b^2*c^2*d^2*g^3*n + 4*a^3*b*c*d^3*g^3*n - a^4*d^4*g^3*n)*B^2*log(b*x + a) + 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*c*d^3*g^3*x^3 + 6*B^2*b^4*c^2*d^2*g^3*x^2 + 4*B^2*b^4*c^3*d*g^3*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^4*d)","B",0
40,1,1473,0,5.751287," ","integrate((d*g*x+c*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{3} \, A B d^{2} g^{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} g^{2} x^{3} + 2 \, A B c d g^{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 g^{2} x^{2} + \frac{1}{3} \, A B d^{2} g^{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 g^{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} g^{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} g^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c^{2} g^{2} x - \frac{{\left(5 \, a b c^{2} d g^{2} n^{2} - 2 \, a^{2} c d^{2} g^{2} n^{2} - {\left(3 \, g^{2} n^{2} - 2 \, g^{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} g^{2} n^{2} - 3 \, a b^{2} c^{2} d g^{2} n^{2} + 3 \, a^{2} b c d^{2} g^{2} n^{2} - a^{3} d^{3} g^{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} g^{2} x^{3} \log\left(e\right)^{2} + 2 \, B^{2} b^{3} c^{3} g^{2} n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - B^{2} b^{3} c^{3} g^{2} n^{2} \log\left(d x + c\right)^{2} + {\left(a b^{2} d^{3} g^{2} n \log\left(e\right) - {\left(g^{2} n \log\left(e\right) - 3 \, g^{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 g^{2} n^{2} - 3 \, a^{2} b c d^{2} g^{2} n^{2} + a^{3} d^{3} g^{2} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + {\left({\left(g^{2} n^{2} - 4 \, g^{2} n \log\left(e\right) + 3 \, g^{2} \log\left(e\right)^{2}\right)} b^{3} c^{2} d - 2 \, {\left(g^{2} n^{2} - 3 \, g^{2} n \log\left(e\right)\right)} a b^{2} c d^{2} + {\left(g^{2} n^{2} - 2 \, g^{2} n \log\left(e\right)\right)} a^{2} b d^{3}\right)} B^{2} x - {\left(2 \, {\left(2 \, g^{2} n^{2} - 3 \, g^{2} n \log\left(e\right)\right)} a b^{2} c^{2} d - {\left(7 \, g^{2} n^{2} - 6 \, g^{2} n \log\left(e\right)\right)} a^{2} b c d^{2} + {\left(3 \, g^{2} n^{2} - 2 \, g^{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} g^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} g^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d g^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} g^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d g^{2} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) - 2 \, B^{2} b^{3} c^{3} g^{2} n \log\left(d x + c\right) + {\left(a b^{2} d^{3} g^{2} n - {\left(g^{2} n - 6 \, g^{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} g^{2} n - a^{2} b d^{3} g^{2} n - {\left(2 \, g^{2} n - 3 \, g^{2} \log\left(e\right)\right)} b^{3} c^{2} d\right)} B^{2} x + 2 \, {\left(3 \, a b^{2} c^{2} d g^{2} n - 3 \, a^{2} b c d^{2} g^{2} n + a^{3} d^{3} g^{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} g^{2} x^{3} \log\left(e\right) - 2 \, B^{2} b^{3} c^{3} g^{2} n \log\left(d x + c\right) + {\left(a b^{2} d^{3} g^{2} n - {\left(g^{2} n - 6 \, g^{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} g^{2} n - a^{2} b d^{3} g^{2} n - {\left(2 \, g^{2} n - 3 \, g^{2} \log\left(e\right)\right)} b^{3} c^{2} d\right)} B^{2} x + 2 \, {\left(3 \, a b^{2} c^{2} d g^{2} n - 3 \, a^{2} b c d^{2} g^{2} n + a^{3} d^{3} g^{2} n\right)} B^{2} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} g^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d g^{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*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A^2*d^2*g^2*x^3 + 2*A*B*c*d*g^2*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c*d*g^2*x^2 + 1/3*A*B*d^2*g^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*g^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*g^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*c^2*g^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c^2*g^2*x - 1/3*(5*a*b*c^2*d*g^2*n^2 - 2*a^2*c*d^2*g^2*n^2 - (3*g^2*n^2 - 2*g^2*n*log(e))*b^2*c^3)*B^2*log(d*x + c)/(b^2*d) - 2/3*(b^3*c^3*g^2*n^2 - 3*a*b^2*c^2*d*g^2*n^2 + 3*a^2*b*c*d^2*g^2*n^2 - a^3*d^3*g^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*g^2*x^3*log(e)^2 + 2*B^2*b^3*c^3*g^2*n^2*log(b*x + a)*log(d*x + c) - B^2*b^3*c^3*g^2*n^2*log(d*x + c)^2 + (a*b^2*d^3*g^2*n*log(e) - (g^2*n*log(e) - 3*g^2*log(e)^2)*b^3*c*d^2)*B^2*x^2 - (3*a*b^2*c^2*d*g^2*n^2 - 3*a^2*b*c*d^2*g^2*n^2 + a^3*d^3*g^2*n^2)*B^2*log(b*x + a)^2 + ((g^2*n^2 - 4*g^2*n*log(e) + 3*g^2*log(e)^2)*b^3*c^2*d - 2*(g^2*n^2 - 3*g^2*n*log(e))*a*b^2*c*d^2 + (g^2*n^2 - 2*g^2*n*log(e))*a^2*b*d^3)*B^2*x - (2*(2*g^2*n^2 - 3*g^2*n*log(e))*a*b^2*c^2*d - (7*g^2*n^2 - 6*g^2*n*log(e))*a^2*b*c*d^2 + (3*g^2*n^2 - 2*g^2*n*log(e))*a^3*d^3)*B^2*log(b*x + a) + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*c*d^2*g^2*x^2 + 3*B^2*b^3*c^2*d*g^2*x)*log((b*x + a)^n)^2 + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*c*d^2*g^2*x^2 + 3*B^2*b^3*c^2*d*g^2*x)*log((d*x + c)^n)^2 + (2*B^2*b^3*d^3*g^2*x^3*log(e) - 2*B^2*b^3*c^3*g^2*n*log(d*x + c) + (a*b^2*d^3*g^2*n - (g^2*n - 6*g^2*log(e))*b^3*c*d^2)*B^2*x^2 + 2*(3*a*b^2*c*d^2*g^2*n - a^2*b*d^3*g^2*n - (2*g^2*n - 3*g^2*log(e))*b^3*c^2*d)*B^2*x + 2*(3*a*b^2*c^2*d*g^2*n - 3*a^2*b*c*d^2*g^2*n + a^3*d^3*g^2*n)*B^2*log(b*x + a))*log((b*x + a)^n) - (2*B^2*b^3*d^3*g^2*x^3*log(e) - 2*B^2*b^3*c^3*g^2*n*log(d*x + c) + (a*b^2*d^3*g^2*n - (g^2*n - 6*g^2*log(e))*b^3*c*d^2)*B^2*x^2 + 2*(3*a*b^2*c*d^2*g^2*n - a^2*b*d^3*g^2*n - (2*g^2*n - 3*g^2*log(e))*b^3*c^2*d)*B^2*x + 2*(3*a*b^2*c^2*d*g^2*n - 3*a^2*b*c*d^2*g^2*n + a^3*d^3*g^2*n)*B^2*log(b*x + a) + 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*c*d^2*g^2*x^2 + 3*B^2*b^3*c^2*d*g^2*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d)","B",0
41,1,825,0,4.366750," ","integrate((d*g*x+c*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","A B d g 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 g x^{2} - A B d g 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 g 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 g x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} c g x - \frac{{\left(a c d g n^{2} - {\left(g n^{2} - g 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} g n^{2} - 2 \, a b c d g n^{2} + a^{2} d^{2} g 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} g n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - B^{2} b^{2} c^{2} g n^{2} \log\left(d x + c\right)^{2} + B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} - {\left(2 \, a b c d g n^{2} - a^{2} d^{2} g n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + 2 \, {\left(a b d^{2} g n \log\left(e\right) - {\left(g n \log\left(e\right) - g \log\left(e\right)^{2}\right)} b^{2} c d\right)} B^{2} x - 2 \, {\left({\left(g n^{2} - 2 \, g n \log\left(e\right)\right)} a b c d - {\left(g n^{2} - g 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} g x^{2} + 2 \, B^{2} b^{2} c d g x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} c d g x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) - B^{2} b^{2} c^{2} g n \log\left(d x + c\right) + {\left(a b d^{2} g n - {\left(g n - 2 \, g \log\left(e\right)\right)} b^{2} c d\right)} B^{2} x + {\left(2 \, a b c d g n - a^{2} d^{2} g 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} g x^{2} \log\left(e\right) - B^{2} b^{2} c^{2} g n \log\left(d x + c\right) + {\left(a b d^{2} g n - {\left(g n - 2 \, g \log\left(e\right)\right)} b^{2} c d\right)} B^{2} x + {\left(2 \, a b c d g n - a^{2} d^{2} g n\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} c d g 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*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*d*g*x^2 - A*B*d*g*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*g*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*c*g*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*c*g*x - (a*c*d*g*n^2 - (g*n^2 - g*n*log(e))*b*c^2)*B^2*log(d*x + c)/(b*d) - (b^2*c^2*g*n^2 - 2*a*b*c*d*g*n^2 + a^2*d^2*g*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*g*n^2*log(b*x + a)*log(d*x + c) - B^2*b^2*c^2*g*n^2*log(d*x + c)^2 + B^2*b^2*d^2*g*x^2*log(e)^2 - (2*a*b*c*d*g*n^2 - a^2*d^2*g*n^2)*B^2*log(b*x + a)^2 + 2*(a*b*d^2*g*n*log(e) - (g*n*log(e) - g*log(e)^2)*b^2*c*d)*B^2*x - 2*((g*n^2 - 2*g*n*log(e))*a*b*c*d - (g*n^2 - g*n*log(e))*a^2*d^2)*B^2*log(b*x + a) + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*c*d*g*x)*log((b*x + a)^n)^2 + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*c*d*g*x)*log((d*x + c)^n)^2 + 2*(B^2*b^2*d^2*g*x^2*log(e) - B^2*b^2*c^2*g*n*log(d*x + c) + (a*b*d^2*g*n - (g*n - 2*g*log(e))*b^2*c*d)*B^2*x + (2*a*b*c*d*g*n - a^2*d^2*g*n)*B^2*log(b*x + a))*log((b*x + a)^n) - 2*(B^2*b^2*d^2*g*x^2*log(e) - B^2*b^2*c^2*g*n*log(d*x + c) + (a*b*d^2*g*n - (g*n - 2*g*log(e))*b^2*c*d)*B^2*x + (2*a*b*c*d*g*n - a^2*d^2*g*n)*B^2*log(b*x + a) + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*c*d*g*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d)","B",0
42,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*g*x+c*g),x, algorithm=""maxima"")","\frac{B^{2} \log\left(d x + c\right) \log\left({\left(d x + c\right)}^{n}\right)^{2}}{d g} + \frac{A^{2} \log\left(d g x + c g\right)}{d g} - \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 g x + c g}\,{d x}"," ",0,"B^2*log(d*x + c)*log((d*x + c)^n)^2/(d*g) + A^2*log(d*g*x + c*g)/(d*g) - 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*g*x + c*g), x)","F",0
43,1,428,0,0.861377," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*g*x+c*g)^2,x, algorithm=""maxima"")","2 \, A B n {\left(\frac{1}{d^{2} g^{2} x + c d g^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} g^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} g^{2}}\right)} + {\left(2 \, n {\left(\frac{1}{d^{2} g^{2} x + c d g^{2}} + \frac{b \log\left(b x + a\right)}{{\left(b c d - a d^{2}\right)} g^{2}} - \frac{b \log\left(d x + c\right)}{{\left(b c d - a d^{2}\right)} g^{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 g^{2} - a c d^{2} g^{2} + {\left(b c d^{2} g^{2} - a d^{3} g^{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} g^{2} x + c d g^{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} g^{2} x + c d g^{2}} - \frac{A^{2}}{d^{2} g^{2} x + c d g^{2}}"," ",0,"2*A*B*n*(1/(d^2*g^2*x + c*d*g^2) + b*log(b*x + a)/((b*c*d - a*d^2)*g^2) - b*log(d*x + c)/((b*c*d - a*d^2)*g^2)) + (2*n*(1/(d^2*g^2*x + c*d*g^2) + b*log(b*x + a)/((b*c*d - a*d^2)*g^2) - b*log(d*x + c)/((b*c*d - a*d^2)*g^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*g^2 - a*c*d^2*g^2 + (b*c*d^2*g^2 - a*d^3*g^2)*x))*B^2 - B^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(d^2*g^2*x + c*d*g^2) - 2*A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^2*g^2*x + c*d*g^2) - A^2/(d^2*g^2*x + c*d*g^2)","B",0
44,1,861,0,1.226425," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*g*x+c*g)^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)} g^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} g^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} g^{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)} g^{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)} g^{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)} g^{3} x^{2} + 2 \, {\left(b c^{2} d^{2} - a c d^{3}\right)} g^{3} x + {\left(b c^{3} d - a c^{2} d^{2}\right)} g^{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)} g^{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)} g^{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 g^{3} - 2 \, a b c^{3} d^{2} g^{3} + a^{2} c^{2} d^{3} g^{3} + {\left(b^{2} c^{2} d^{3} g^{3} - 2 \, a b c d^{4} g^{3} + a^{2} d^{5} g^{3}\right)} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} g^{3} - 2 \, a b c^{2} d^{3} g^{3} + a^{2} c d^{4} g^{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} g^{3} x^{2} + 2 \, c d^{2} g^{3} x + c^{2} d g^{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} g^{3} x^{2} + 2 \, c d^{2} g^{3} x + c^{2} d g^{3}} - \frac{A^{2}}{2 \, {\left(d^{3} g^{3} x^{2} + 2 \, c d^{2} g^{3} x + c^{2} d g^{3}\right)}}"," ",0,"1/2*A*B*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*g^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*g^3*x + (b*c^3*d - a*c^2*d^2)*g^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g^3)) + 1/4*(2*n*((2*b*d*x + 3*b*c - a*d)/((b*c*d^3 - a*d^4)*g^3*x^2 + 2*(b*c^2*d^2 - a*c*d^3)*g^3*x + (b*c^3*d - a*c^2*d^2)*g^3) + 2*b^2*log(b*x + a)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g^3) - 2*b^2*log(d*x + c)/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g^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*g^3 - 2*a*b*c^3*d^2*g^3 + a^2*c^2*d^3*g^3 + (b^2*c^2*d^3*g^3 - 2*a*b*c*d^4*g^3 + a^2*d^5*g^3)*x^2 + 2*(b^2*c^3*d^2*g^3 - 2*a*b*c^2*d^3*g^3 + a^2*c*d^4*g^3)*x))*B^2 - 1/2*B^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(d^3*g^3*x^2 + 2*c*d^2*g^3*x + c^2*d*g^3) - A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^3*g^3*x^2 + 2*c*d^2*g^3*x + c^2*d*g^3) - 1/2*A^2/(d^3*g^3*x^2 + 2*c*d^2*g^3*x + c^2*d*g^3)","B",0
45,1,1435,0,1.293064," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*g*x+c*g)^4,x, algorithm=""maxima"")","\frac{1}{9} \, A B n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 11 \, b^{2} c^{2} - 7 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(5 \, b^{2} c d - a b d^{2}\right)} x}{{\left(b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} g^{4} x^{3} + 3 \, {\left(b^{2} c^{3} d^{3} - 2 \, a b c^{2} d^{4} + a^{2} c d^{5}\right)} g^{4} x^{2} + 3 \, {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} g^{4} x + {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} g^{4}} + \frac{6 \, b^{3} \log\left(b x + a\right)}{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} g^{4}} - \frac{6 \, b^{3} \log\left(d x + c\right)}{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} g^{4}}\right)} + \frac{1}{54} \, {\left(6 \, n {\left(\frac{6 \, b^{2} d^{2} x^{2} + 11 \, b^{2} c^{2} - 7 \, a b c d + 2 \, a^{2} d^{2} + 3 \, {\left(5 \, b^{2} c d - a b d^{2}\right)} x}{{\left(b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} g^{4} x^{3} + 3 \, {\left(b^{2} c^{3} d^{3} - 2 \, a b c^{2} d^{4} + a^{2} c d^{5}\right)} g^{4} x^{2} + 3 \, {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} g^{4} x + {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} g^{4}} + \frac{6 \, b^{3} \log\left(b x + a\right)}{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} g^{4}} - \frac{6 \, b^{3} \log\left(d x + c\right)}{{\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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 \, b^{3} c^{3} - 108 \, a b^{2} c^{2} d + 27 \, a^{2} b c d^{2} - 4 \, 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 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(b x + a\right)^{2} + 18 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(49 \, b^{3} c^{2} d - 54 \, a b^{2} c d^{2} + 5 \, a^{2} b d^{3}\right)} x + 66 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} x^{3} + 33 \, b^{3} c d^{2} x^{2} + 33 \, b^{3} c^{2} d x + 11 \, b^{3} c^{3} + 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{b^{3} c^{6} d g^{4} - 3 \, a b^{2} c^{5} d^{2} g^{4} + 3 \, a^{2} b c^{4} d^{3} g^{4} - a^{3} c^{3} d^{4} g^{4} + {\left(b^{3} c^{3} d^{4} g^{4} - 3 \, a b^{2} c^{2} d^{5} g^{4} + 3 \, a^{2} b c d^{6} g^{4} - a^{3} d^{7} g^{4}\right)} x^{3} + 3 \, {\left(b^{3} c^{4} d^{3} g^{4} - 3 \, a b^{2} c^{3} d^{4} g^{4} + 3 \, a^{2} b c^{2} d^{5} g^{4} - a^{3} c d^{6} g^{4}\right)} x^{2} + 3 \, {\left(b^{3} c^{5} d^{2} g^{4} - 3 \, a b^{2} c^{4} d^{3} g^{4} + 3 \, a^{2} b c^{3} d^{4} g^{4} - a^{3} c^{2} d^{5} g^{4}\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}}{3 \, {\left(d^{4} g^{4} x^{3} + 3 \, c d^{3} g^{4} x^{2} + 3 \, c^{2} d^{2} g^{4} x + c^{3} d g^{4}\right)}} - \frac{2 \, A B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(d^{4} g^{4} x^{3} + 3 \, c d^{3} g^{4} x^{2} + 3 \, c^{2} d^{2} g^{4} x + c^{3} d g^{4}\right)}} - \frac{A^{2}}{3 \, {\left(d^{4} g^{4} x^{3} + 3 \, c d^{3} g^{4} x^{2} + 3 \, c^{2} d^{2} g^{4} x + c^{3} d g^{4}\right)}}"," ",0,"1/9*A*B*n*((6*b^2*d^2*x^2 + 11*b^2*c^2 - 7*a*b*c*d + 2*a^2*d^2 + 3*(5*b^2*c*d - a*b*d^2)*x)/((b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*g^4*x^3 + 3*(b^2*c^3*d^3 - 2*a*b*c^2*d^4 + a^2*c*d^5)*g^4*x^2 + 3*(b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*g^4*x + (b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*g^4) + 6*b^3*log(b*x + a)/((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*g^4) - 6*b^3*log(d*x + c)/((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*g^4)) + 1/54*(6*n*((6*b^2*d^2*x^2 + 11*b^2*c^2 - 7*a*b*c*d + 2*a^2*d^2 + 3*(5*b^2*c*d - a*b*d^2)*x)/((b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*g^4*x^3 + 3*(b^2*c^3*d^3 - 2*a*b*c^2*d^4 + a^2*c*d^5)*g^4*x^2 + 3*(b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*g^4*x + (b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*g^4) + 6*b^3*log(b*x + a)/((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*g^4) - 6*b^3*log(d*x + c)/((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*g^4))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (85*b^3*c^3 - 108*a*b^2*c^2*d + 27*a^2*b*c*d^2 - 4*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*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(b*x + a)^2 + 18*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(d*x + c)^2 + 3*(49*b^3*c^2*d - 54*a*b^2*c*d^2 + 5*a^2*b*d^3)*x + 66*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(b*x + a) - 6*(11*b^3*d^3*x^3 + 33*b^3*c*d^2*x^2 + 33*b^3*c^2*d*x + 11*b^3*c^3 + 6*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(b*x + a))*log(d*x + c))*n^2/(b^3*c^6*d*g^4 - 3*a*b^2*c^5*d^2*g^4 + 3*a^2*b*c^4*d^3*g^4 - a^3*c^3*d^4*g^4 + (b^3*c^3*d^4*g^4 - 3*a*b^2*c^2*d^5*g^4 + 3*a^2*b*c*d^6*g^4 - a^3*d^7*g^4)*x^3 + 3*(b^3*c^4*d^3*g^4 - 3*a*b^2*c^3*d^4*g^4 + 3*a^2*b*c^2*d^5*g^4 - a^3*c*d^6*g^4)*x^2 + 3*(b^3*c^5*d^2*g^4 - 3*a*b^2*c^4*d^3*g^4 + 3*a^2*b*c^3*d^4*g^4 - a^3*c^2*d^5*g^4)*x))*B^2 - 1/3*B^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(d^4*g^4*x^3 + 3*c*d^3*g^4*x^2 + 3*c^2*d^2*g^4*x + c^3*d*g^4) - 2/3*A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^4*g^4*x^3 + 3*c*d^3*g^4*x^2 + 3*c^2*d^2*g^4*x + c^3*d*g^4) - 1/3*A^2/(d^4*g^4*x^3 + 3*c*d^3*g^4*x^2 + 3*c^2*d^2*g^4*x + c^3*d*g^4)","B",0
46,1,2138,0,2.109119," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*g*x+c*g)^5,x, algorithm=""maxima"")","\frac{1}{24} \, A B n {\left(\frac{12 \, b^{3} d^{3} x^{3} + 25 \, b^{3} c^{3} - 23 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} - 3 \, a^{3} d^{3} + 6 \, {\left(7 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(13 \, b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{3} c^{3} d^{5} - 3 \, a b^{2} c^{2} d^{6} + 3 \, a^{2} b c d^{7} - a^{3} d^{8}\right)} g^{5} x^{4} + 4 \, {\left(b^{3} c^{4} d^{4} - 3 \, a b^{2} c^{3} d^{5} + 3 \, a^{2} b c^{2} d^{6} - a^{3} c d^{7}\right)} g^{5} x^{3} + 6 \, {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} g^{5} x^{2} + 4 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} g^{5} x + {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4}\right)} g^{5}} + \frac{12 \, b^{4} \log\left(b x + a\right)}{{\left(b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} g^{5}} - \frac{12 \, b^{4} \log\left(d x + c\right)}{{\left(b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} g^{5}}\right)} + \frac{1}{288} \, {\left(12 \, n {\left(\frac{12 \, b^{3} d^{3} x^{3} + 25 \, b^{3} c^{3} - 23 \, a b^{2} c^{2} d + 13 \, a^{2} b c d^{2} - 3 \, a^{3} d^{3} + 6 \, {\left(7 \, b^{3} c d^{2} - a b^{2} d^{3}\right)} x^{2} + 4 \, {\left(13 \, b^{3} c^{2} d - 5 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} x}{{\left(b^{3} c^{3} d^{5} - 3 \, a b^{2} c^{2} d^{6} + 3 \, a^{2} b c d^{7} - a^{3} d^{8}\right)} g^{5} x^{4} + 4 \, {\left(b^{3} c^{4} d^{4} - 3 \, a b^{2} c^{3} d^{5} + 3 \, a^{2} b c^{2} d^{6} - a^{3} c d^{7}\right)} g^{5} x^{3} + 6 \, {\left(b^{3} c^{5} d^{3} - 3 \, a b^{2} c^{4} d^{4} + 3 \, a^{2} b c^{3} d^{5} - a^{3} c^{2} d^{6}\right)} g^{5} x^{2} + 4 \, {\left(b^{3} c^{6} d^{2} - 3 \, a b^{2} c^{5} d^{3} + 3 \, a^{2} b c^{4} d^{4} - a^{3} c^{3} d^{5}\right)} g^{5} x + {\left(b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} - a^{3} c^{4} d^{4}\right)} g^{5}} + \frac{12 \, b^{4} \log\left(b x + a\right)}{{\left(b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} g^{5}} - \frac{12 \, b^{4} \log\left(d x + c\right)}{{\left(b^{4} c^{4} d - 4 \, a b^{3} c^{3} d^{2} + 6 \, a^{2} b^{2} c^{2} d^{3} - 4 \, a^{3} b c d^{4} + a^{4} d^{5}\right)} g^{5}}\right)} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) - \frac{{\left(415 \, b^{4} c^{4} - 576 \, a b^{3} c^{3} d + 216 \, a^{2} b^{2} c^{2} d^{2} - 64 \, a^{3} b c d^{3} + 9 \, a^{4} d^{4} + 300 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(163 \, b^{4} c^{2} d^{2} - 176 \, a b^{3} c d^{3} + 13 \, a^{2} b^{2} d^{4}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(271 \, b^{4} c^{3} d - 324 \, a b^{3} c^{2} d^{2} + 60 \, a^{2} b^{2} c d^{3} - 7 \, a^{3} b d^{4}\right)} x + 300 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(b x + a\right) - 12 \, {\left(25 \, b^{4} d^{4} x^{4} + 100 \, b^{4} c d^{3} x^{3} + 150 \, b^{4} c^{2} d^{2} x^{2} + 100 \, b^{4} c^{3} d x + 25 \, b^{4} c^{4} + 12 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} n^{2}}{b^{4} c^{8} d g^{5} - 4 \, a b^{3} c^{7} d^{2} g^{5} + 6 \, a^{2} b^{2} c^{6} d^{3} g^{5} - 4 \, a^{3} b c^{5} d^{4} g^{5} + a^{4} c^{4} d^{5} g^{5} + {\left(b^{4} c^{4} d^{5} g^{5} - 4 \, a b^{3} c^{3} d^{6} g^{5} + 6 \, a^{2} b^{2} c^{2} d^{7} g^{5} - 4 \, a^{3} b c d^{8} g^{5} + a^{4} d^{9} g^{5}\right)} x^{4} + 4 \, {\left(b^{4} c^{5} d^{4} g^{5} - 4 \, a b^{3} c^{4} d^{5} g^{5} + 6 \, a^{2} b^{2} c^{3} d^{6} g^{5} - 4 \, a^{3} b c^{2} d^{7} g^{5} + a^{4} c d^{8} g^{5}\right)} x^{3} + 6 \, {\left(b^{4} c^{6} d^{3} g^{5} - 4 \, a b^{3} c^{5} d^{4} g^{5} + 6 \, a^{2} b^{2} c^{4} d^{5} g^{5} - 4 \, a^{3} b c^{3} d^{6} g^{5} + a^{4} c^{2} d^{7} g^{5}\right)} x^{2} + 4 \, {\left(b^{4} c^{7} d^{2} g^{5} - 4 \, a b^{3} c^{6} d^{3} g^{5} + 6 \, a^{2} b^{2} c^{5} d^{4} g^{5} - 4 \, a^{3} b c^{4} d^{5} g^{5} + a^{4} c^{3} d^{6} g^{5}\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}}{4 \, {\left(d^{5} g^{5} x^{4} + 4 \, c d^{4} g^{5} x^{3} + 6 \, c^{2} d^{3} g^{5} x^{2} + 4 \, c^{3} d^{2} g^{5} x + c^{4} d g^{5}\right)}} - \frac{A B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(d^{5} g^{5} x^{4} + 4 \, c d^{4} g^{5} x^{3} + 6 \, c^{2} d^{3} g^{5} x^{2} + 4 \, c^{3} d^{2} g^{5} x + c^{4} d g^{5}\right)}} - \frac{A^{2}}{4 \, {\left(d^{5} g^{5} x^{4} + 4 \, c d^{4} g^{5} x^{3} + 6 \, c^{2} d^{3} g^{5} x^{2} + 4 \, c^{3} d^{2} g^{5} x + c^{4} d g^{5}\right)}}"," ",0,"1/24*A*B*n*((12*b^3*d^3*x^3 + 25*b^3*c^3 - 23*a*b^2*c^2*d + 13*a^2*b*c*d^2 - 3*a^3*d^3 + 6*(7*b^3*c*d^2 - a*b^2*d^3)*x^2 + 4*(13*b^3*c^2*d - 5*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^3*c^3*d^5 - 3*a*b^2*c^2*d^6 + 3*a^2*b*c*d^7 - a^3*d^8)*g^5*x^4 + 4*(b^3*c^4*d^4 - 3*a*b^2*c^3*d^5 + 3*a^2*b*c^2*d^6 - a^3*c*d^7)*g^5*x^3 + 6*(b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*g^5*x^2 + 4*(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*g^5*x + (b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4)*g^5) + 12*b^4*log(b*x + a)/((b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*g^5) - 12*b^4*log(d*x + c)/((b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*g^5)) + 1/288*(12*n*((12*b^3*d^3*x^3 + 25*b^3*c^3 - 23*a*b^2*c^2*d + 13*a^2*b*c*d^2 - 3*a^3*d^3 + 6*(7*b^3*c*d^2 - a*b^2*d^3)*x^2 + 4*(13*b^3*c^2*d - 5*a*b^2*c*d^2 + a^2*b*d^3)*x)/((b^3*c^3*d^5 - 3*a*b^2*c^2*d^6 + 3*a^2*b*c*d^7 - a^3*d^8)*g^5*x^4 + 4*(b^3*c^4*d^4 - 3*a*b^2*c^3*d^5 + 3*a^2*b*c^2*d^6 - a^3*c*d^7)*g^5*x^3 + 6*(b^3*c^5*d^3 - 3*a*b^2*c^4*d^4 + 3*a^2*b*c^3*d^5 - a^3*c^2*d^6)*g^5*x^2 + 4*(b^3*c^6*d^2 - 3*a*b^2*c^5*d^3 + 3*a^2*b*c^4*d^4 - a^3*c^3*d^5)*g^5*x + (b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 - a^3*c^4*d^4)*g^5) + 12*b^4*log(b*x + a)/((b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*g^5) - 12*b^4*log(d*x + c)/((b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4 + a^4*d^5)*g^5))*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) - (415*b^4*c^4 - 576*a*b^3*c^3*d + 216*a^2*b^2*c^2*d^2 - 64*a^3*b*c*d^3 + 9*a^4*d^4 + 300*(b^4*c*d^3 - a*b^3*d^4)*x^3 + 6*(163*b^4*c^2*d^2 - 176*a*b^3*c*d^3 + 13*a^2*b^2*d^4)*x^2 + 72*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(b*x + a)^2 + 72*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(d*x + c)^2 + 4*(271*b^4*c^3*d - 324*a*b^3*c^2*d^2 + 60*a^2*b^2*c*d^3 - 7*a^3*b*d^4)*x + 300*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(b*x + a) - 12*(25*b^4*d^4*x^4 + 100*b^4*c*d^3*x^3 + 150*b^4*c^2*d^2*x^2 + 100*b^4*c^3*d*x + 25*b^4*c^4 + 12*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(b*x + a))*log(d*x + c))*n^2/(b^4*c^8*d*g^5 - 4*a*b^3*c^7*d^2*g^5 + 6*a^2*b^2*c^6*d^3*g^5 - 4*a^3*b*c^5*d^4*g^5 + a^4*c^4*d^5*g^5 + (b^4*c^4*d^5*g^5 - 4*a*b^3*c^3*d^6*g^5 + 6*a^2*b^2*c^2*d^7*g^5 - 4*a^3*b*c*d^8*g^5 + a^4*d^9*g^5)*x^4 + 4*(b^4*c^5*d^4*g^5 - 4*a*b^3*c^4*d^5*g^5 + 6*a^2*b^2*c^3*d^6*g^5 - 4*a^3*b*c^2*d^7*g^5 + a^4*c*d^8*g^5)*x^3 + 6*(b^4*c^6*d^3*g^5 - 4*a*b^3*c^5*d^4*g^5 + 6*a^2*b^2*c^4*d^5*g^5 - 4*a^3*b*c^3*d^6*g^5 + a^4*c^2*d^7*g^5)*x^2 + 4*(b^4*c^7*d^2*g^5 - 4*a*b^3*c^6*d^3*g^5 + 6*a^2*b^2*c^5*d^4*g^5 - 4*a^3*b*c^4*d^5*g^5 + a^4*c^3*d^6*g^5)*x))*B^2 - 1/4*B^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)^2/(d^5*g^5*x^4 + 4*c*d^4*g^5*x^3 + 6*c^2*d^3*g^5*x^2 + 4*c^3*d^2*g^5*x + c^4*d*g^5) - 1/2*A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(d^5*g^5*x^4 + 4*c*d^4*g^5*x^3 + 6*c^2*d^3*g^5*x^2 + 4*c^3*d^2*g^5*x + c^4*d*g^5) - 1/4*A^2/(d^5*g^5*x^4 + 4*c*d^4*g^5*x^3 + 6*c^2*d^3*g^5*x^2 + 4*c^3*d^2*g^5*x + c^4*d*g^5)","B",0
47,0,0,0,0.000000," ","integrate((d*g*x+c*g)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{{\left(d g x + c g\right)}^{2}}{B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A}\,{d x}"," ",0,"integrate((d*g*x + c*g)^2/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
48,0,0,0,0.000000," ","integrate((d*g*x+c*g)/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{d g x + c g}{B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A}\,{d x}"," ",0,"integrate((d*g*x + c*g)/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
49,0,0,0,0.000000," ","integrate(1/(d*g*x+c*g)/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(d g x + c g\right)} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((d*g*x + c*g)*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
50,0,0,0,0.000000," ","integrate(1/(d*g*x+c*g)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(d g x + c g\right)}^{2} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((d*g*x + c*g)^2*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
51,0,0,0,0.000000," ","integrate(1/(d*g*x+c*g)^3/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(d g x + c g\right)}^{3} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((d*g*x + c*g)^3*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
52,0,0,0,0.000000," ","integrate((d*g*x+c*g)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b d^{3} g^{2} x^{4} + a c^{3} g^{2} + {\left(3 \, b c d^{2} g^{2} + a d^{3} g^{2}\right)} x^{3} + 3 \, {\left(b c^{2} d g^{2} + a c d^{2} g^{2}\right)} x^{2} + {\left(b c^{3} g^{2} + 3 \, a c^{2} d g^{2}\right)} x}{{\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}} + \int \frac{4 \, b d^{3} g^{2} x^{3} + b c^{3} g^{2} + 3 \, a c^{2} d g^{2} + 3 \, {\left(3 \, b c d^{2} g^{2} + a d^{3} g^{2}\right)} x^{2} + 6 \, {\left(b c^{2} d g^{2} + a c d^{2} g^{2}\right)} x}{{\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}}\,{d x}"," ",0,"-(b*d^3*g^2*x^4 + a*c^3*g^2 + (3*b*c*d^2*g^2 + a*d^3*g^2)*x^3 + 3*(b*c^2*d*g^2 + a*c*d^2*g^2)*x^2 + (b*c^3*g^2 + 3*a*c^2*d*g^2)*x)/((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) + integrate((4*b*d^3*g^2*x^3 + b*c^3*g^2 + 3*a*c^2*d*g^2 + 3*(3*b*c*d^2*g^2 + a*d^3*g^2)*x^2 + 6*(b*c^2*d*g^2 + a*c*d^2*g^2)*x)/((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), x)","F",0
53,0,0,0,0.000000," ","integrate((d*g*x+c*g)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b d^{2} g x^{3} + a c^{2} g + {\left(2 \, b c d g + a d^{2} g\right)} x^{2} + {\left(b c^{2} g + 2 \, a c d g\right)} x}{{\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}} + \int \frac{3 \, b d^{2} g x^{2} + b c^{2} g + 2 \, a c d g + 2 \, {\left(2 \, b c d g + a d^{2} g\right)} x}{{\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}}\,{d x}"," ",0,"-(b*d^2*g*x^3 + a*c^2*g + (2*b*c*d*g + a*d^2*g)*x^2 + (b*c^2*g + 2*a*c*d*g)*x)/((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) + integrate((3*b*d^2*g*x^2 + b*c^2*g + 2*a*c*d*g + 2*(2*b*c*d*g + a*d^2*g)*x)/((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), x)","F",0
54,0,0,0,0.000000," ","integrate(1/(d*g*x+c*g)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","b \int \frac{1}{{\left(b c g n - a d g n\right)} B^{2} \log\left({\left(b x + a\right)}^{n}\right) - {\left(b c g n - a d g n\right)} B^{2} \log\left({\left(d x + c\right)}^{n}\right) + {\left(b c g n - a d g n\right)} A B + {\left(b c g n \log\left(e\right) - a d g n \log\left(e\right)\right)} B^{2}}\,{d x} - \frac{b x + a}{{\left(b c g n - a d g n\right)} B^{2} \log\left({\left(b x + a\right)}^{n}\right) - {\left(b c g n - a d g n\right)} B^{2} \log\left({\left(d x + c\right)}^{n}\right) + {\left(b c g n - a d g n\right)} A B + {\left(b c g n \log\left(e\right) - a d g n \log\left(e\right)\right)} B^{2}}"," ",0,"b*integrate(1/((b*c*g*n - a*d*g*n)*B^2*log((b*x + a)^n) - (b*c*g*n - a*d*g*n)*B^2*log((d*x + c)^n) + (b*c*g*n - a*d*g*n)*A*B + (b*c*g*n*log(e) - a*d*g*n*log(e))*B^2), x) - (b*x + a)/((b*c*g*n - a*d*g*n)*B^2*log((b*x + a)^n) - (b*c*g*n - a*d*g*n)*B^2*log((d*x + c)^n) + (b*c*g*n - a*d*g*n)*A*B + (b*c*g*n*log(e) - a*d*g*n*log(e))*B^2)","F",0
55,0,0,0,0.000000," ","integrate(1/(d*g*x+c*g)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b x + a}{{\left(b c^{2} g^{2} n - a c d g^{2} n\right)} A B + {\left(b c^{2} g^{2} n \log\left(e\right) - a c d g^{2} n \log\left(e\right)\right)} B^{2} + {\left({\left(b c d g^{2} n - a d^{2} g^{2} n\right)} A B + {\left(b c d g^{2} n \log\left(e\right) - a d^{2} g^{2} n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c d g^{2} n - a d^{2} g^{2} n\right)} B^{2} x + {\left(b c^{2} g^{2} n - a c d g^{2} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c d g^{2} n - a d^{2} g^{2} n\right)} B^{2} x + {\left(b c^{2} g^{2} n - a c d g^{2} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)} - \int -\frac{1}{B^{2} c^{2} g^{2} n \log\left(e\right) + A B c^{2} g^{2} n + {\left(B^{2} d^{2} g^{2} n \log\left(e\right) + A B d^{2} g^{2} n\right)} x^{2} + 2 \, {\left(B^{2} c d g^{2} n \log\left(e\right) + A B c d g^{2} n\right)} x + {\left(B^{2} d^{2} g^{2} n x^{2} + 2 \, B^{2} c d g^{2} n x + B^{2} c^{2} g^{2} n\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(B^{2} d^{2} g^{2} n x^{2} + 2 \, B^{2} c d g^{2} n x + B^{2} c^{2} g^{2} n\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x}"," ",0,"-(b*x + a)/((b*c^2*g^2*n - a*c*d*g^2*n)*A*B + (b*c^2*g^2*n*log(e) - a*c*d*g^2*n*log(e))*B^2 + ((b*c*d*g^2*n - a*d^2*g^2*n)*A*B + (b*c*d*g^2*n*log(e) - a*d^2*g^2*n*log(e))*B^2)*x + ((b*c*d*g^2*n - a*d^2*g^2*n)*B^2*x + (b*c^2*g^2*n - a*c*d*g^2*n)*B^2)*log((b*x + a)^n) - ((b*c*d*g^2*n - a*d^2*g^2*n)*B^2*x + (b*c^2*g^2*n - a*c*d*g^2*n)*B^2)*log((d*x + c)^n)) - integrate(-1/(B^2*c^2*g^2*n*log(e) + A*B*c^2*g^2*n + (B^2*d^2*g^2*n*log(e) + A*B*d^2*g^2*n)*x^2 + 2*(B^2*c*d*g^2*n*log(e) + A*B*c*d*g^2*n)*x + (B^2*d^2*g^2*n*x^2 + 2*B^2*c*d*g^2*n*x + B^2*c^2*g^2*n)*log((b*x + a)^n) - (B^2*d^2*g^2*n*x^2 + 2*B^2*c*d*g^2*n*x + B^2*c^2*g^2*n)*log((d*x + c)^n)), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(d*g*x+c*g)^3/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b x + a}{{\left(b c^{3} g^{3} n - a c^{2} d g^{3} n\right)} A B + {\left(b c^{3} g^{3} n \log\left(e\right) - a c^{2} d g^{3} n \log\left(e\right)\right)} B^{2} + {\left({\left(b c d^{2} g^{3} n - a d^{3} g^{3} n\right)} A B + {\left(b c d^{2} g^{3} n \log\left(e\right) - a d^{3} g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c^{2} d g^{3} n - a c d^{2} g^{3} n\right)} A B + {\left(b c^{2} d g^{3} n \log\left(e\right) - a c d^{2} g^{3} n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c d^{2} g^{3} n - a d^{3} g^{3} n\right)} B^{2} x^{2} + 2 \, {\left(b c^{2} d g^{3} n - a c d^{2} g^{3} n\right)} B^{2} x + {\left(b c^{3} g^{3} n - a c^{2} d g^{3} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c d^{2} g^{3} n - a d^{3} g^{3} n\right)} B^{2} x^{2} + 2 \, {\left(b c^{2} d g^{3} n - a c d^{2} g^{3} n\right)} B^{2} x + {\left(b c^{3} g^{3} n - a c^{2} d g^{3} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)} - \int \frac{b d x - b c + 2 \, a d}{{\left({\left(b c d^{3} g^{3} n - a d^{4} g^{3} n\right)} A B + {\left(b c d^{3} g^{3} n \log\left(e\right) - a d^{4} g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c^{4} g^{3} n - a c^{3} d g^{3} n\right)} A B + {\left(b c^{4} g^{3} n \log\left(e\right) - a c^{3} d g^{3} n \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(b c^{2} d^{2} g^{3} n - a c d^{3} g^{3} n\right)} A B + {\left(b c^{2} d^{2} g^{3} n \log\left(e\right) - a c d^{3} g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(b c^{3} d g^{3} n - a c^{2} d^{2} g^{3} n\right)} A B + {\left(b c^{3} d g^{3} n \log\left(e\right) - a c^{2} d^{2} g^{3} n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c d^{3} g^{3} n - a d^{4} g^{3} n\right)} B^{2} x^{3} + 3 \, {\left(b c^{2} d^{2} g^{3} n - a c d^{3} g^{3} n\right)} B^{2} x^{2} + 3 \, {\left(b c^{3} d g^{3} n - a c^{2} d^{2} g^{3} n\right)} B^{2} x + {\left(b c^{4} g^{3} n - a c^{3} d g^{3} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c d^{3} g^{3} n - a d^{4} g^{3} n\right)} B^{2} x^{3} + 3 \, {\left(b c^{2} d^{2} g^{3} n - a c d^{3} g^{3} n\right)} B^{2} x^{2} + 3 \, {\left(b c^{3} d g^{3} n - a c^{2} d^{2} g^{3} n\right)} B^{2} x + {\left(b c^{4} g^{3} n - a c^{3} d g^{3} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x}"," ",0,"-(b*x + a)/((b*c^3*g^3*n - a*c^2*d*g^3*n)*A*B + (b*c^3*g^3*n*log(e) - a*c^2*d*g^3*n*log(e))*B^2 + ((b*c*d^2*g^3*n - a*d^3*g^3*n)*A*B + (b*c*d^2*g^3*n*log(e) - a*d^3*g^3*n*log(e))*B^2)*x^2 + 2*((b*c^2*d*g^3*n - a*c*d^2*g^3*n)*A*B + (b*c^2*d*g^3*n*log(e) - a*c*d^2*g^3*n*log(e))*B^2)*x + ((b*c*d^2*g^3*n - a*d^3*g^3*n)*B^2*x^2 + 2*(b*c^2*d*g^3*n - a*c*d^2*g^3*n)*B^2*x + (b*c^3*g^3*n - a*c^2*d*g^3*n)*B^2)*log((b*x + a)^n) - ((b*c*d^2*g^3*n - a*d^3*g^3*n)*B^2*x^2 + 2*(b*c^2*d*g^3*n - a*c*d^2*g^3*n)*B^2*x + (b*c^3*g^3*n - a*c^2*d*g^3*n)*B^2)*log((d*x + c)^n)) - integrate((b*d*x - b*c + 2*a*d)/(((b*c*d^3*g^3*n - a*d^4*g^3*n)*A*B + (b*c*d^3*g^3*n*log(e) - a*d^4*g^3*n*log(e))*B^2)*x^3 + (b*c^4*g^3*n - a*c^3*d*g^3*n)*A*B + (b*c^4*g^3*n*log(e) - a*c^3*d*g^3*n*log(e))*B^2 + 3*((b*c^2*d^2*g^3*n - a*c*d^3*g^3*n)*A*B + (b*c^2*d^2*g^3*n*log(e) - a*c*d^3*g^3*n*log(e))*B^2)*x^2 + 3*((b*c^3*d*g^3*n - a*c^2*d^2*g^3*n)*A*B + (b*c^3*d*g^3*n*log(e) - a*c^2*d^2*g^3*n*log(e))*B^2)*x + ((b*c*d^3*g^3*n - a*d^4*g^3*n)*B^2*x^3 + 3*(b*c^2*d^2*g^3*n - a*c*d^3*g^3*n)*B^2*x^2 + 3*(b*c^3*d*g^3*n - a*c^2*d^2*g^3*n)*B^2*x + (b*c^4*g^3*n - a*c^3*d*g^3*n)*B^2)*log((b*x + a)^n) - ((b*c*d^3*g^3*n - a*d^4*g^3*n)*B^2*x^3 + 3*(b*c^2*d^2*g^3*n - a*c*d^3*g^3*n)*B^2*x^2 + 3*(b*c^3*d*g^3*n - a*c^2*d^2*g^3*n)*B^2*x + (b*c^4*g^3*n - a*c^3*d*g^3*n)*B^2)*log((d*x + c)^n)), x)","F",0
57,1,631,0,0.907862," ","integrate((g*x+f)^4*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{5} \, B g^{4} x^{5} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{5} \, A g^{4} x^{5} + B f g^{3} x^{4} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A f g^{3} x^{4} + 2 \, B f^{2} g^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A f^{2} g^{2} x^{3} + 2 \, B f^{3} g x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + 2 \, A f^{3} g x^{2} + \frac{1}{60} \, B g^{4} 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} \, B f g^{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)} + B f^{2} g^{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 \, B f^{3} g 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 f^{4} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B f^{4} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A f^{4} x"," ",0,"1/5*B*g^4*x^5*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/5*A*g^4*x^5 + B*f*g^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*f*g^3*x^4 + 2*B*f^2*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*f^2*g^2*x^3 + 2*B*f^3*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 2*A*f^3*g*x^2 + 1/60*B*g^4*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*B*f*g^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)) + B*f^2*g^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*B*f^3*g*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*f^4*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*f^4*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*f^4*x","A",0
58,1,443,0,0.926905," ","integrate((g*x+f)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{4} \, B g^{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 g^{3} x^{4} + B f g^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A f g^{2} x^{3} + \frac{3}{2} \, B f^{2} g x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{3}{2} \, A f^{2} g x^{2} - \frac{1}{24} \, B g^{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 f g^{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 f^{2} g 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 f^{3} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B f^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A f^{3} x"," ",0,"1/4*B*g^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A*g^3*x^4 + B*f*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*f*g^2*x^3 + 3/2*B*f^2*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A*f^2*g*x^2 - 1/24*B*g^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*f*g^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*f^2*g*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*f^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*f^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*f^3*x","A",0
59,1,282,0,0.887797," ","integrate((g*x+f)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{3} \, B g^{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 g^{2} x^{3} + B f g x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A f g x^{2} + \frac{1}{6} \, B g^{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 f g 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 f^{2} n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B f^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A f^{2} x"," ",0,"1/3*B*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A*g^2*x^3 + B*f*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*f*g*x^2 + 1/6*B*g^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*f*g*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*f^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*f^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*f^2*x","A",0
60,1,150,0,0.759511," ","integrate((g*x+f)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\frac{1}{2} \, B g x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + \frac{1}{2} \, A g x^{2} - \frac{1}{2} \, B g 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 f n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B f x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A f x"," ",0,"1/2*B*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A*g*x^2 - 1/2*B*g*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*f*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*f*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A*f*x","A",0
61,1,52,0,0.625752," ","integrate(A+B*log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""maxima"")","B n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + B x \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A x"," ",0,"B*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + B*x*log(e*((b*x + a)/(d*x + c))^n) + A*x","A",0
62,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(g*x+f),x, algorithm=""maxima"")","-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)}{g x + f}\,{d x} + \frac{A \log\left(g x + f\right)}{g}"," ",0,"-B*integrate(-(log((b*x + a)^n) - log((d*x + c)^n) + log(e))/(g*x + f), x) + A*log(g*x + f)/g","F",0
63,1,142,0,0.813729," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(g*x+f)^2,x, algorithm=""maxima"")","B n {\left(\frac{b \log\left(b x + a\right)}{b f g - a g^{2}} - \frac{d \log\left(d x + c\right)}{d f g - c g^{2}} + \frac{{\left(b c - a d\right)} \log\left(g x + f\right)}{b d f^{2} + a c g^{2} - {\left(b c + a d\right)} f g}\right)} - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{g^{2} x + f g} - \frac{A}{g^{2} x + f g}"," ",0,"B*n*(b*log(b*x + a)/(b*f*g - a*g^2) - d*log(d*x + c)/(d*f*g - c*g^2) + (b*c - a*d)*log(g*x + f)/(b*d*f^2 + a*c*g^2 - (b*c + a*d)*f*g)) - B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(g^2*x + f*g) - A/(g^2*x + f*g)","A",0
64,1,355,0,0.997101," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(g*x+f)^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{b^{2} \log\left(b x + a\right)}{b^{2} f^{2} g - 2 \, a b f g^{2} + a^{2} g^{3}} - \frac{d^{2} \log\left(d x + c\right)}{d^{2} f^{2} g - 2 \, c d f g^{2} + c^{2} g^{3}} + \frac{{\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g\right)} \log\left(g x + f\right)}{b^{2} d^{2} f^{4} + a^{2} c^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{3}} - \frac{b c - a d}{b d f^{3} + a c f g^{2} - {\left(b c + a d\right)} f^{2} g + {\left(b d f^{2} g + a c g^{3} - {\left(b c + a d\right)} f g^{2}\right)} x}\right)} B n - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g\right)}} - \frac{A}{2 \, {\left(g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g\right)}}"," ",0,"1/2*(b^2*log(b*x + a)/(b^2*f^2*g - 2*a*b*f*g^2 + a^2*g^3) - d^2*log(d*x + c)/(d^2*f^2*g - 2*c*d*f*g^2 + c^2*g^3) + (2*(b^2*c*d - a*b*d^2)*f - (b^2*c^2 - a^2*d^2)*g)*log(g*x + f)/(b^2*d^2*f^4 + a^2*c^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^3*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^2 - 2*(a*b*c^2 + a^2*c*d)*f*g^3) - (b*c - a*d)/(b*d*f^3 + a*c*f*g^2 - (b*c + a*d)*f^2*g + (b*d*f^2*g + a*c*g^3 - (b*c + a*d)*f*g^2)*x))*B*n - 1/2*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(g^3*x^2 + 2*f*g^2*x + f^2*g) - 1/2*A/(g^3*x^2 + 2*f*g^2*x + f^2*g)","A",0
65,1,852,0,1.408863," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(g*x+f)^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{2 \, b^{3} \log\left(b x + a\right)}{b^{3} f^{3} g - 3 \, a b^{2} f^{2} g^{2} + 3 \, a^{2} b f g^{3} - a^{3} g^{4}} - \frac{2 \, d^{3} \log\left(d x + c\right)}{d^{3} f^{3} g - 3 \, c d^{2} f^{2} g^{2} + 3 \, c^{2} d f g^{3} - c^{3} g^{4}} + \frac{2 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{2}\right)} \log\left(g x + f\right)}{b^{3} d^{3} f^{6} + a^{3} c^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{5}} - \frac{5 \, {\left(b^{2} c d - a b d^{2}\right)} f^{2} - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} f g + {\left(a b c^{2} - a^{2} c d\right)} g^{2} + 2 \, {\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f g - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g^{2}\right)} x}{b^{2} d^{2} f^{6} + a^{2} c^{2} f^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{5} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{4} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{3} g^{3} + {\left(b^{2} d^{2} f^{4} g^{2} + a^{2} c^{2} g^{6} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g^{3} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{4} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} f^{5} g + a^{2} c^{2} f g^{5} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{4} g^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{3} g^{3} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2} g^{4}\right)} x}\right)} B n - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g\right)}} - \frac{A}{3 \, {\left(g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g\right)}}"," ",0,"1/6*(2*b^3*log(b*x + a)/(b^3*f^3*g - 3*a*b^2*f^2*g^2 + 3*a^2*b*f*g^3 - a^3*g^4) - 2*d^3*log(d*x + c)/(d^3*f^3*g - 3*c*d^2*f^2*g^2 + 3*c^2*d*f*g^3 - c^3*g^4) + 2*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g + (b^3*c^3 - a^3*d^3)*g^2)*log(g*x + f)/(b^3*d^3*f^6 + a^3*c^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^5) - (5*(b^2*c*d - a*b*d^2)*f^2 - 3*(b^2*c^2 - a^2*d^2)*f*g + (a*b*c^2 - a^2*c*d)*g^2 + 2*(2*(b^2*c*d - a*b*d^2)*f*g - (b^2*c^2 - a^2*d^2)*g^2)*x)/(b^2*d^2*f^6 + a^2*c^2*f^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^5*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^4*g^2 - 2*(a*b*c^2 + a^2*c*d)*f^3*g^3 + (b^2*d^2*f^4*g^2 + a^2*c^2*g^6 - 2*(b^2*c*d + a*b*d^2)*f^3*g^3 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^4 - 2*(a*b*c^2 + a^2*c*d)*f*g^5)*x^2 + 2*(b^2*d^2*f^5*g + a^2*c^2*f*g^5 - 2*(b^2*c*d + a*b*d^2)*f^4*g^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^3*g^3 - 2*(a*b*c^2 + a^2*c*d)*f^2*g^4)*x))*B*n - 1/3*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g) - 1/3*A/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g)","B",0
66,1,1761,0,1.798446," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(g*x+f)^5,x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{6 \, b^{4} \log\left(b x + a\right)}{b^{4} f^{4} g - 4 \, a b^{3} f^{3} g^{2} + 6 \, a^{2} b^{2} f^{2} g^{3} - 4 \, a^{3} b f g^{4} + a^{4} g^{5}} - \frac{6 \, d^{4} \log\left(d x + c\right)}{d^{4} f^{4} g - 4 \, c d^{3} f^{3} g^{2} + 6 \, c^{2} d^{2} f^{2} g^{3} - 4 \, c^{3} d f g^{4} + c^{4} g^{5}} + \frac{6 \, {\left(4 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f^{3} - 6 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} f^{2} g + 4 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} f g^{2} - {\left(b^{4} c^{4} - a^{4} d^{4}\right)} g^{3}\right)} \log\left(g x + f\right)}{b^{4} d^{4} f^{8} + a^{4} c^{4} g^{8} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} f^{7} g + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} f^{6} g^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} f^{5} g^{3} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} f^{4} g^{4} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} f^{3} g^{5} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f^{2} g^{6} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} f g^{7}} - \frac{26 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{4} - 31 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{3} g + {\left(11 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 15 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3}\right)} f^{2} g^{2} - 7 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} f g^{3} + 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} g^{4} + 6 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} g^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g^{3} + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{4}\right)} x^{2} + 3 \, {\left(14 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{3} g - 15 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{2} g^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f g^{3} - {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} g^{4}\right)} x}{b^{3} d^{3} f^{9} + a^{3} c^{3} f^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{8} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{7} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{5} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{4} g^{5} + {\left(b^{3} d^{3} f^{6} g^{3} + a^{3} c^{3} g^{9} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{5} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{6} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{7} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{8}\right)} x^{3} + 3 \, {\left(b^{3} d^{3} f^{7} g^{2} + a^{3} c^{3} f g^{8} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{5} g^{4} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{4} g^{5} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{3} g^{6} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{2} g^{7}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} f^{8} g + a^{3} c^{3} f^{2} g^{7} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{7} g^{2} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{6} g^{3} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{4} g^{5} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{3} g^{6}\right)} x}\right)} B n - \frac{B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{4 \, {\left(g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g\right)}} - \frac{A}{4 \, {\left(g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g\right)}}"," ",0,"1/24*(6*b^4*log(b*x + a)/(b^4*f^4*g - 4*a*b^3*f^3*g^2 + 6*a^2*b^2*f^2*g^3 - 4*a^3*b*f*g^4 + a^4*g^5) - 6*d^4*log(d*x + c)/(d^4*f^4*g - 4*c*d^3*f^3*g^2 + 6*c^2*d^2*f^2*g^3 - 4*c^3*d*f*g^4 + c^4*g^5) + 6*(4*(b^4*c*d^3 - a*b^3*d^4)*f^3 - 6*(b^4*c^2*d^2 - a^2*b^2*d^4)*f^2*g + 4*(b^4*c^3*d - a^3*b*d^4)*f*g^2 - (b^4*c^4 - a^4*d^4)*g^3)*log(g*x + f)/(b^4*d^4*f^8 + a^4*c^4*g^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*f^7*g + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*f^6*g^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*f^5*g^3 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*f^4*g^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*f^3*g^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f^2*g^6 - 4*(a^3*b*c^4 + a^4*c^3*d)*f*g^7) - (26*(b^3*c*d^2 - a*b^2*d^3)*f^4 - 31*(b^3*c^2*d - a^2*b*d^3)*f^3*g + (11*b^3*c^3 + 15*a*b^2*c^2*d - 15*a^2*b*c*d^2 - 11*a^3*d^3)*f^2*g^2 - 7*(a*b^2*c^3 - a^3*c*d^2)*f*g^3 + 2*(a^2*b*c^3 - a^3*c^2*d)*g^4 + 6*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2*g^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g^3 + (b^3*c^3 - a^3*d^3)*g^4)*x^2 + 3*(14*(b^3*c*d^2 - a*b^2*d^3)*f^3*g - 15*(b^3*c^2*d - a^2*b*d^3)*f^2*g^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f*g^3 - (a*b^2*c^3 - a^3*c*d^2)*g^4)*x)/(b^3*d^3*f^9 + a^3*c^3*f^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^8*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^7*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^6*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^5*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^4*g^5 + (b^3*d^3*f^6*g^3 + a^3*c^3*g^9 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g^4 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^5 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^6 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^7 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^8)*x^3 + 3*(b^3*d^3*f^7*g^2 + a^3*c^3*f*g^8 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^6*g^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^5*g^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^4*g^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3*g^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^2*g^7)*x^2 + 3*(b^3*d^3*f^8*g + a^3*c^3*f^2*g^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^7*g^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^6*g^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^5*g^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^4*g^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^3*g^6)*x))*B*n - 1/4*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g) - 1/4*A/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g)","B",0
67,1,2651,0,5.352526," ","integrate((g*x+f)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A B g^{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} g^{3} x^{4} + 2 \, A B f g^{2} x^{3} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} f g^{2} x^{3} + 3 \, A B f^{2} g 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} f^{2} g x^{2} - \frac{1}{12} \, A B g^{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 f g^{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 f^{2} g 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 f^{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 f^{3} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} f^{3} x - \frac{{\left(6 \, a^{3} c d^{3} g^{3} n^{2} - 3 \, {\left(8 \, c d^{3} f g^{2} n^{2} - c^{2} d^{2} g^{3} n^{2}\right)} a^{2} b + 2 \, {\left(18 \, c d^{3} f^{2} g n^{2} - 6 \, c^{2} d^{2} f g^{2} n^{2} + c^{3} d g^{3} n^{2}\right)} a b^{2} + {\left(24 \, c d^{3} f^{3} n \log\left(e\right) - {\left(11 \, g^{3} n^{2} + 6 \, g^{3} n \log\left(e\right)\right)} c^{4} + 12 \, {\left(3 \, f g^{2} n^{2} + 2 \, f g^{2} n \log\left(e\right)\right)} c^{3} d - 36 \, {\left(f^{2} g n^{2} + f^{2} g n \log\left(e\right)\right)} c^{2} d^{2}\right)} b^{3}\right)} B^{2} \log\left(d x + c\right)}{12 \, b^{3} d^{4}} + \frac{{\left(4 \, a b^{3} d^{4} f^{3} n^{2} - 6 \, a^{2} b^{2} d^{4} f^{2} g n^{2} + 4 \, a^{3} b d^{4} f g^{2} n^{2} - a^{4} d^{4} g^{3} n^{2} - {\left(4 \, c d^{3} f^{3} n^{2} - 6 \, c^{2} d^{2} f^{2} g n^{2} + 4 \, c^{3} d f g^{2} n^{2} - c^{4} g^{3} n^{2}\right)} b^{4}\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^{4}} + \frac{3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right)^{2} + 6 \, {\left(4 \, c d^{3} f^{3} n^{2} - 6 \, c^{2} d^{2} f^{2} g n^{2} + 4 \, c^{3} d f g^{2} n^{2} - c^{4} g^{3} n^{2}\right)} B^{2} b^{4} \log\left(b x + a\right) \log\left(d x + c\right) - 3 \, {\left(4 \, c d^{3} f^{3} n^{2} - 6 \, c^{2} d^{2} f^{2} g n^{2} + 4 \, c^{3} d f g^{2} n^{2} - c^{4} g^{3} n^{2}\right)} B^{2} b^{4} \log\left(d x + c\right)^{2} + 2 \, {\left(a b^{3} d^{4} g^{3} n \log\left(e\right) - {\left(c d^{3} g^{3} n \log\left(e\right) - 6 \, d^{4} f g^{2} \log\left(e\right)^{2}\right)} b^{4}\right)} B^{2} x^{3} + {\left({\left(g^{3} n^{2} - 3 \, g^{3} n \log\left(e\right)\right)} a^{2} b^{2} d^{4} - 2 \, {\left(c d^{3} g^{3} n^{2} - 6 \, d^{4} f g^{2} n \log\left(e\right)\right)} a b^{3} - {\left(12 \, c d^{3} f g^{2} n \log\left(e\right) - 18 \, d^{4} f^{2} g \log\left(e\right)^{2} - {\left(g^{3} n^{2} + 3 \, g^{3} n \log\left(e\right)\right)} c^{2} d^{2}\right)} b^{4}\right)} B^{2} x^{2} - 3 \, {\left(4 \, a b^{3} d^{4} f^{3} n^{2} - 6 \, a^{2} b^{2} d^{4} f^{2} g n^{2} + 4 \, a^{3} b d^{4} f g^{2} n^{2} - a^{4} d^{4} g^{3} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} - {\left({\left(5 \, g^{3} n^{2} - 6 \, g^{3} n \log\left(e\right)\right)} a^{3} b d^{4} - {\left(5 \, c d^{3} g^{3} n^{2} + 12 \, {\left(f g^{2} n^{2} - 2 \, f g^{2} n \log\left(e\right)\right)} d^{4}\right)} a^{2} b^{2} + {\left(24 \, c d^{3} f g^{2} n^{2} - 5 \, c^{2} d^{2} g^{3} n^{2} - 36 \, d^{4} f^{2} g n \log\left(e\right)\right)} a b^{3} + {\left(36 \, c d^{3} f^{2} g n \log\left(e\right) - 12 \, d^{4} f^{3} \log\left(e\right)^{2} + {\left(5 \, g^{3} n^{2} + 6 \, g^{3} n \log\left(e\right)\right)} c^{3} d - 12 \, {\left(f g^{2} n^{2} + 2 \, f g^{2} n \log\left(e\right)\right)} c^{2} d^{2}\right)} b^{4}\right)} B^{2} x + {\left({\left(11 \, g^{3} n^{2} - 6 \, g^{3} n \log\left(e\right)\right)} a^{4} d^{4} - 2 \, {\left(c d^{3} g^{3} n^{2} + 6 \, {\left(3 \, f g^{2} n^{2} - 2 \, f g^{2} n \log\left(e\right)\right)} d^{4}\right)} a^{3} b + 3 \, {\left(4 \, c d^{3} f g^{2} n^{2} - c^{2} d^{2} g^{3} n^{2} + 12 \, {\left(f^{2} g n^{2} - f^{2} g n \log\left(e\right)\right)} d^{4}\right)} a^{2} b^{2} - 6 \, {\left(6 \, c d^{3} f^{2} g n^{2} - 4 \, c^{2} d^{2} f g^{2} n^{2} + c^{3} d g^{3} n^{2} - 4 \, d^{4} f^{3} n \log\left(e\right)\right)} a b^{3}\right)} B^{2} \log\left(b x + a\right) + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{3} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) - 6 \, {\left(4 \, c d^{3} f^{3} n - 6 \, c^{2} d^{2} f^{2} g n + 4 \, c^{3} d f g^{2} n - c^{4} g^{3} n\right)} B^{2} b^{4} \log\left(d x + c\right) + 2 \, {\left(a b^{3} d^{4} g^{3} n - {\left(c d^{3} g^{3} n - 12 \, d^{4} f g^{2} \log\left(e\right)\right)} b^{4}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} d^{4} f g^{2} n - a^{2} b^{2} d^{4} g^{3} n - {\left(4 \, c d^{3} f g^{2} n - c^{2} d^{2} g^{3} n - 12 \, d^{4} f^{2} g \log\left(e\right)\right)} b^{4}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} d^{4} f^{2} g n - 4 \, a^{2} b^{2} d^{4} f g^{2} n + a^{3} b d^{4} g^{3} n - {\left(6 \, c d^{3} f^{2} g n - 4 \, c^{2} d^{2} f g^{2} n + c^{3} d g^{3} n - 4 \, d^{4} f^{3} \log\left(e\right)\right)} b^{4}\right)} B^{2} x + 6 \, {\left(4 \, a b^{3} d^{4} f^{3} n - 6 \, a^{2} b^{2} d^{4} f^{2} g n + 4 \, a^{3} b d^{4} f g^{2} n - a^{4} d^{4} g^{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} g^{3} x^{4} \log\left(e\right) - 6 \, {\left(4 \, c d^{3} f^{3} n - 6 \, c^{2} d^{2} f^{2} g n + 4 \, c^{3} d f g^{2} n - c^{4} g^{3} n\right)} B^{2} b^{4} \log\left(d x + c\right) + 2 \, {\left(a b^{3} d^{4} g^{3} n - {\left(c d^{3} g^{3} n - 12 \, d^{4} f g^{2} \log\left(e\right)\right)} b^{4}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} d^{4} f g^{2} n - a^{2} b^{2} d^{4} g^{3} n - {\left(4 \, c d^{3} f g^{2} n - c^{2} d^{2} g^{3} n - 12 \, d^{4} f^{2} g \log\left(e\right)\right)} b^{4}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} d^{4} f^{2} g n - 4 \, a^{2} b^{2} d^{4} f g^{2} n + a^{3} b d^{4} g^{3} n - {\left(6 \, c d^{3} f^{2} g n - 4 \, c^{2} d^{2} f g^{2} n + c^{3} d g^{3} n - 4 \, d^{4} f^{3} \log\left(e\right)\right)} b^{4}\right)} B^{2} x + 6 \, {\left(4 \, a b^{3} d^{4} f^{3} n - 6 \, a^{2} b^{2} d^{4} f^{2} g n + 4 \, a^{3} b d^{4} f g^{2} n - a^{4} d^{4} g^{3} n\right)} B^{2} \log\left(b x + a\right) + 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{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^{4}}"," ",0,"1/2*A*B*g^3*x^4*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/4*A^2*g^3*x^4 + 2*A*B*f*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*f*g^2*x^3 + 3*A*B*f^2*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 3/2*A^2*f^2*g*x^2 - 1/12*A*B*g^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*f*g^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*f^2*g*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*f^3*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*f^3*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*f^3*x - 1/12*(6*a^3*c*d^3*g^3*n^2 - 3*(8*c*d^3*f*g^2*n^2 - c^2*d^2*g^3*n^2)*a^2*b + 2*(18*c*d^3*f^2*g*n^2 - 6*c^2*d^2*f*g^2*n^2 + c^3*d*g^3*n^2)*a*b^2 + (24*c*d^3*f^3*n*log(e) - (11*g^3*n^2 + 6*g^3*n*log(e))*c^4 + 12*(3*f*g^2*n^2 + 2*f*g^2*n*log(e))*c^3*d - 36*(f^2*g*n^2 + f^2*g*n*log(e))*c^2*d^2)*b^3)*B^2*log(d*x + c)/(b^3*d^4) + 1/2*(4*a*b^3*d^4*f^3*n^2 - 6*a^2*b^2*d^4*f^2*g*n^2 + 4*a^3*b*d^4*f*g^2*n^2 - a^4*d^4*g^3*n^2 - (4*c*d^3*f^3*n^2 - 6*c^2*d^2*f^2*g*n^2 + 4*c^3*d*f*g^2*n^2 - c^4*g^3*n^2)*b^4)*(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) + 1/12*(3*B^2*b^4*d^4*g^3*x^4*log(e)^2 + 6*(4*c*d^3*f^3*n^2 - 6*c^2*d^2*f^2*g*n^2 + 4*c^3*d*f*g^2*n^2 - c^4*g^3*n^2)*B^2*b^4*log(b*x + a)*log(d*x + c) - 3*(4*c*d^3*f^3*n^2 - 6*c^2*d^2*f^2*g*n^2 + 4*c^3*d*f*g^2*n^2 - c^4*g^3*n^2)*B^2*b^4*log(d*x + c)^2 + 2*(a*b^3*d^4*g^3*n*log(e) - (c*d^3*g^3*n*log(e) - 6*d^4*f*g^2*log(e)^2)*b^4)*B^2*x^3 + ((g^3*n^2 - 3*g^3*n*log(e))*a^2*b^2*d^4 - 2*(c*d^3*g^3*n^2 - 6*d^4*f*g^2*n*log(e))*a*b^3 - (12*c*d^3*f*g^2*n*log(e) - 18*d^4*f^2*g*log(e)^2 - (g^3*n^2 + 3*g^3*n*log(e))*c^2*d^2)*b^4)*B^2*x^2 - 3*(4*a*b^3*d^4*f^3*n^2 - 6*a^2*b^2*d^4*f^2*g*n^2 + 4*a^3*b*d^4*f*g^2*n^2 - a^4*d^4*g^3*n^2)*B^2*log(b*x + a)^2 - ((5*g^3*n^2 - 6*g^3*n*log(e))*a^3*b*d^4 - (5*c*d^3*g^3*n^2 + 12*(f*g^2*n^2 - 2*f*g^2*n*log(e))*d^4)*a^2*b^2 + (24*c*d^3*f*g^2*n^2 - 5*c^2*d^2*g^3*n^2 - 36*d^4*f^2*g*n*log(e))*a*b^3 + (36*c*d^3*f^2*g*n*log(e) - 12*d^4*f^3*log(e)^2 + (5*g^3*n^2 + 6*g^3*n*log(e))*c^3*d - 12*(f*g^2*n^2 + 2*f*g^2*n*log(e))*c^2*d^2)*b^4)*B^2*x + ((11*g^3*n^2 - 6*g^3*n*log(e))*a^4*d^4 - 2*(c*d^3*g^3*n^2 + 6*(3*f*g^2*n^2 - 2*f*g^2*n*log(e))*d^4)*a^3*b + 3*(4*c*d^3*f*g^2*n^2 - c^2*d^2*g^3*n^2 + 12*(f^2*g*n^2 - f^2*g*n*log(e))*d^4)*a^2*b^2 - 6*(6*c*d^3*f^2*g*n^2 - 4*c^2*d^2*f*g^2*n^2 + c^3*d*g^3*n^2 - 4*d^4*f^3*n*log(e))*a*b^3)*B^2*log(b*x + a) + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x)*log((b*x + a)^n)^2 + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x)*log((d*x + c)^n)^2 + (6*B^2*b^4*d^4*g^3*x^4*log(e) - 6*(4*c*d^3*f^3*n - 6*c^2*d^2*f^2*g*n + 4*c^3*d*f*g^2*n - c^4*g^3*n)*B^2*b^4*log(d*x + c) + 2*(a*b^3*d^4*g^3*n - (c*d^3*g^3*n - 12*d^4*f*g^2*log(e))*b^4)*B^2*x^3 + 3*(4*a*b^3*d^4*f*g^2*n - a^2*b^2*d^4*g^3*n - (4*c*d^3*f*g^2*n - c^2*d^2*g^3*n - 12*d^4*f^2*g*log(e))*b^4)*B^2*x^2 + 6*(6*a*b^3*d^4*f^2*g*n - 4*a^2*b^2*d^4*f*g^2*n + a^3*b*d^4*g^3*n - (6*c*d^3*f^2*g*n - 4*c^2*d^2*f*g^2*n + c^3*d*g^3*n - 4*d^4*f^3*log(e))*b^4)*B^2*x + 6*(4*a*b^3*d^4*f^3*n - 6*a^2*b^2*d^4*f^2*g*n + 4*a^3*b*d^4*f*g^2*n - a^4*d^4*g^3*n)*B^2*log(b*x + a))*log((b*x + a)^n) - (6*B^2*b^4*d^4*g^3*x^4*log(e) - 6*(4*c*d^3*f^3*n - 6*c^2*d^2*f^2*g*n + 4*c^3*d*f*g^2*n - c^4*g^3*n)*B^2*b^4*log(d*x + c) + 2*(a*b^3*d^4*g^3*n - (c*d^3*g^3*n - 12*d^4*f*g^2*log(e))*b^4)*B^2*x^3 + 3*(4*a*b^3*d^4*f*g^2*n - a^2*b^2*d^4*g^3*n - (4*c*d^3*f*g^2*n - c^2*d^2*g^3*n - 12*d^4*f^2*g*log(e))*b^4)*B^2*x^2 + 6*(6*a*b^3*d^4*f^2*g*n - 4*a^2*b^2*d^4*f*g^2*n + a^3*b*d^4*g^3*n - (6*c*d^3*f^2*g*n - 4*c^2*d^2*f*g^2*n + c^3*d*g^3*n - 4*d^4*f^3*log(e))*b^4)*B^2*x + 6*(4*a*b^3*d^4*f^3*n - 6*a^2*b^2*d^4*f^2*g*n + 4*a^3*b*d^4*f*g^2*n - a^4*d^4*g^3*n)*B^2*log(b*x + a) + 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^4*d^4)","B",0
68,1,1659,0,4.829727," ","integrate((g*x+f)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","\frac{2}{3} \, A B g^{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} g^{2} x^{3} + 2 \, A B f g x^{2} \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} f g x^{2} + \frac{1}{3} \, A B g^{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 f g 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 f^{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 f^{2} x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} f^{2} x + \frac{{\left(2 \, a^{2} c d^{2} g^{2} n^{2} - {\left(6 \, c d^{2} f g n^{2} - c^{2} d g^{2} n^{2}\right)} a b - {\left(6 \, c d^{2} f^{2} n \log\left(e\right) + {\left(3 \, g^{2} n^{2} + 2 \, g^{2} n \log\left(e\right)\right)} c^{3} - 6 \, {\left(f g n^{2} + f g n \log\left(e\right)\right)} c^{2} d\right)} b^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, b^{2} d^{3}} + \frac{2 \, {\left(3 \, a b^{2} d^{3} f^{2} n^{2} - 3 \, a^{2} b d^{3} f g n^{2} + a^{3} d^{3} g^{2} n^{2} - {\left(3 \, c d^{2} f^{2} n^{2} - 3 \, c^{2} d f g n^{2} + c^{3} g^{2} n^{2}\right)} b^{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}}{3 \, b^{3} d^{3}} + \frac{B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right)^{2} + 2 \, {\left(3 \, c d^{2} f^{2} n^{2} - 3 \, c^{2} d f g n^{2} + c^{3} g^{2} n^{2}\right)} B^{2} b^{3} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(3 \, c d^{2} f^{2} n^{2} - 3 \, c^{2} d f g n^{2} + c^{3} g^{2} n^{2}\right)} B^{2} b^{3} \log\left(d x + c\right)^{2} + {\left(a b^{2} d^{3} g^{2} n \log\left(e\right) - {\left(c d^{2} g^{2} n \log\left(e\right) - 3 \, d^{3} f g \log\left(e\right)^{2}\right)} b^{3}\right)} B^{2} x^{2} - {\left(3 \, a b^{2} d^{3} f^{2} n^{2} - 3 \, a^{2} b d^{3} f g n^{2} + a^{3} d^{3} g^{2} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + {\left({\left(g^{2} n^{2} - 2 \, g^{2} n \log\left(e\right)\right)} a^{2} b d^{3} - 2 \, {\left(c d^{2} g^{2} n^{2} - 3 \, d^{3} f g n \log\left(e\right)\right)} a b^{2} - {\left(6 \, c d^{2} f g n \log\left(e\right) - 3 \, d^{3} f^{2} \log\left(e\right)^{2} - {\left(g^{2} n^{2} + 2 \, g^{2} n \log\left(e\right)\right)} c^{2} d\right)} b^{3}\right)} B^{2} x - {\left({\left(3 \, g^{2} n^{2} - 2 \, g^{2} n \log\left(e\right)\right)} a^{3} d^{3} - {\left(c d^{2} g^{2} n^{2} + 6 \, {\left(f g n^{2} - f g n \log\left(e\right)\right)} d^{3}\right)} a^{2} b + 2 \, {\left(3 \, c d^{2} f g n^{2} - c^{2} d g^{2} n^{2} - 3 \, d^{3} f^{2} n \log\left(e\right)\right)} a b^{2}\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{2} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) - 2 \, {\left(3 \, c d^{2} f^{2} n - 3 \, c^{2} d f g n + c^{3} g^{2} n\right)} B^{2} b^{3} \log\left(d x + c\right) + {\left(a b^{2} d^{3} g^{2} n - {\left(c d^{2} g^{2} n - 6 \, d^{3} f g \log\left(e\right)\right)} b^{3}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f g n - a^{2} b d^{3} g^{2} n - {\left(3 \, c d^{2} f g n - c^{2} d g^{2} n - 3 \, d^{3} f^{2} \log\left(e\right)\right)} b^{3}\right)} B^{2} x + 2 \, {\left(3 \, a b^{2} d^{3} f^{2} n - 3 \, a^{2} b d^{3} f g n + a^{3} d^{3} g^{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} g^{2} x^{3} \log\left(e\right) - 2 \, {\left(3 \, c d^{2} f^{2} n - 3 \, c^{2} d f g n + c^{3} g^{2} n\right)} B^{2} b^{3} \log\left(d x + c\right) + {\left(a b^{2} d^{3} g^{2} n - {\left(c d^{2} g^{2} n - 6 \, d^{3} f g \log\left(e\right)\right)} b^{3}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f g n - a^{2} b d^{3} g^{2} n - {\left(3 \, c d^{2} f g n - c^{2} d g^{2} n - 3 \, d^{3} f^{2} \log\left(e\right)\right)} b^{3}\right)} B^{2} x + 2 \, {\left(3 \, a b^{2} d^{3} f^{2} n - 3 \, a^{2} b d^{3} f g n + a^{3} d^{3} g^{2} n\right)} B^{2} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{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^{3}}"," ",0,"2/3*A*B*g^2*x^3*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/3*A^2*g^2*x^3 + 2*A*B*f*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*f*g*x^2 + 1/3*A*B*g^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*f*g*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*f^2*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*f^2*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*f^2*x + 1/3*(2*a^2*c*d^2*g^2*n^2 - (6*c*d^2*f*g*n^2 - c^2*d*g^2*n^2)*a*b - (6*c*d^2*f^2*n*log(e) + (3*g^2*n^2 + 2*g^2*n*log(e))*c^3 - 6*(f*g*n^2 + f*g*n*log(e))*c^2*d)*b^2)*B^2*log(d*x + c)/(b^2*d^3) + 2/3*(3*a*b^2*d^3*f^2*n^2 - 3*a^2*b*d^3*f*g*n^2 + a^3*d^3*g^2*n^2 - (3*c*d^2*f^2*n^2 - 3*c^2*d*f*g*n^2 + c^3*g^2*n^2)*b^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^3*d^3) + 1/3*(B^2*b^3*d^3*g^2*x^3*log(e)^2 + 2*(3*c*d^2*f^2*n^2 - 3*c^2*d*f*g*n^2 + c^3*g^2*n^2)*B^2*b^3*log(b*x + a)*log(d*x + c) - (3*c*d^2*f^2*n^2 - 3*c^2*d*f*g*n^2 + c^3*g^2*n^2)*B^2*b^3*log(d*x + c)^2 + (a*b^2*d^3*g^2*n*log(e) - (c*d^2*g^2*n*log(e) - 3*d^3*f*g*log(e)^2)*b^3)*B^2*x^2 - (3*a*b^2*d^3*f^2*n^2 - 3*a^2*b*d^3*f*g*n^2 + a^3*d^3*g^2*n^2)*B^2*log(b*x + a)^2 + ((g^2*n^2 - 2*g^2*n*log(e))*a^2*b*d^3 - 2*(c*d^2*g^2*n^2 - 3*d^3*f*g*n*log(e))*a*b^2 - (6*c*d^2*f*g*n*log(e) - 3*d^3*f^2*log(e)^2 - (g^2*n^2 + 2*g^2*n*log(e))*c^2*d)*b^3)*B^2*x - ((3*g^2*n^2 - 2*g^2*n*log(e))*a^3*d^3 - (c*d^2*g^2*n^2 + 6*(f*g*n^2 - f*g*n*log(e))*d^3)*a^2*b + 2*(3*c*d^2*f*g*n^2 - c^2*d*g^2*n^2 - 3*d^3*f^2*n*log(e))*a*b^2)*B^2*log(b*x + a) + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x)*log((b*x + a)^n)^2 + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x)*log((d*x + c)^n)^2 + (2*B^2*b^3*d^3*g^2*x^3*log(e) - 2*(3*c*d^2*f^2*n - 3*c^2*d*f*g*n + c^3*g^2*n)*B^2*b^3*log(d*x + c) + (a*b^2*d^3*g^2*n - (c*d^2*g^2*n - 6*d^3*f*g*log(e))*b^3)*B^2*x^2 + 2*(3*a*b^2*d^3*f*g*n - a^2*b*d^3*g^2*n - (3*c*d^2*f*g*n - c^2*d*g^2*n - 3*d^3*f^2*log(e))*b^3)*B^2*x + 2*(3*a*b^2*d^3*f^2*n - 3*a^2*b*d^3*f*g*n + a^3*d^3*g^2*n)*B^2*log(b*x + a))*log((b*x + a)^n) - (2*B^2*b^3*d^3*g^2*x^3*log(e) - 2*(3*c*d^2*f^2*n - 3*c^2*d*f*g*n + c^3*g^2*n)*B^2*b^3*log(d*x + c) + (a*b^2*d^3*g^2*n - (c*d^2*g^2*n - 6*d^3*f*g*log(e))*b^3)*B^2*x^2 + 2*(3*a*b^2*d^3*f*g*n - a^2*b*d^3*g^2*n - (3*c*d^2*f*g*n - c^2*d*g^2*n - 3*d^3*f^2*log(e))*b^3)*B^2*x + 2*(3*a*b^2*d^3*f^2*n - 3*a^2*b*d^3*f*g*n + a^3*d^3*g^2*n)*B^2*log(b*x + a) + 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d^3)","B",0
69,1,899,0,5.190686," ","integrate((g*x+f)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","A B g 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} g x^{2} - A B g 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 f n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B f x \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right) + A^{2} f x - \frac{{\left(a c d g n^{2} + {\left(2 \, c d f n \log\left(e\right) - {\left(g n^{2} + g n \log\left(e\right)\right)} c^{2}\right)} b\right)} B^{2} \log\left(d x + c\right)}{b d^{2}} + \frac{{\left(2 \, a b d^{2} f n^{2} - a^{2} d^{2} g n^{2} - {\left(2 \, c d f n^{2} - c^{2} g n^{2}\right)} b^{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^{2}} + \frac{B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} + 2 \, {\left(2 \, c d f n^{2} - c^{2} g n^{2}\right)} B^{2} b^{2} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(2 \, c d f n^{2} - c^{2} g n^{2}\right)} B^{2} b^{2} \log\left(d x + c\right)^{2} - {\left(2 \, a b d^{2} f n^{2} - a^{2} d^{2} g n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + 2 \, {\left(a b d^{2} g n \log\left(e\right) - {\left(c d g n \log\left(e\right) - d^{2} f \log\left(e\right)^{2}\right)} b^{2}\right)} B^{2} x + 2 \, {\left({\left(g n^{2} - g n \log\left(e\right)\right)} a^{2} d^{2} - {\left(c d g n^{2} - 2 \, d^{2} f n \log\left(e\right)\right)} a b\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) - {\left(2 \, c d f n - c^{2} g n\right)} B^{2} b^{2} \log\left(d x + c\right) + {\left(a b d^{2} g n - {\left(c d g n - 2 \, d^{2} f \log\left(e\right)\right)} b^{2}\right)} B^{2} x + {\left(2 \, a b d^{2} f n - a^{2} d^{2} g 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} g x^{2} \log\left(e\right) - {\left(2 \, c d f n - c^{2} g n\right)} B^{2} b^{2} \log\left(d x + c\right) + {\left(a b d^{2} g n - {\left(c d g n - 2 \, d^{2} f \log\left(e\right)\right)} b^{2}\right)} B^{2} x + {\left(2 \, a b d^{2} f n - a^{2} d^{2} g n\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f 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^{2}}"," ",0,"A*B*g*x^2*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + 1/2*A^2*g*x^2 - A*B*g*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*f*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*f*x*log(e*(b*x/(d*x + c) + a/(d*x + c))^n) + A^2*f*x - (a*c*d*g*n^2 + (2*c*d*f*n*log(e) - (g*n^2 + g*n*log(e))*c^2)*b)*B^2*log(d*x + c)/(b*d^2) + (2*a*b*d^2*f*n^2 - a^2*d^2*g*n^2 - (2*c*d*f*n^2 - c^2*g*n^2)*b^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) + 1/2*(B^2*b^2*d^2*g*x^2*log(e)^2 + 2*(2*c*d*f*n^2 - c^2*g*n^2)*B^2*b^2*log(b*x + a)*log(d*x + c) - (2*c*d*f*n^2 - c^2*g*n^2)*B^2*b^2*log(d*x + c)^2 - (2*a*b*d^2*f*n^2 - a^2*d^2*g*n^2)*B^2*log(b*x + a)^2 + 2*(a*b*d^2*g*n*log(e) - (c*d*g*n*log(e) - d^2*f*log(e)^2)*b^2)*B^2*x + 2*((g*n^2 - g*n*log(e))*a^2*d^2 - (c*d*g*n^2 - 2*d^2*f*n*log(e))*a*b)*B^2*log(b*x + a) + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x)*log((b*x + a)^n)^2 + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x)*log((d*x + c)^n)^2 + 2*(B^2*b^2*d^2*g*x^2*log(e) - (2*c*d*f*n - c^2*g*n)*B^2*b^2*log(d*x + c) + (a*b*d^2*g*n - (c*d*g*n - 2*d^2*f*log(e))*b^2)*B^2*x + (2*a*b*d^2*f*n - a^2*d^2*g*n)*B^2*log(b*x + a))*log((b*x + a)^n) - 2*(B^2*b^2*d^2*g*x^2*log(e) - (2*c*d*f*n - c^2*g*n)*B^2*b^2*log(d*x + c) + (a*b*d^2*g*n - (c*d*g*n - 2*d^2*f*log(e))*b^2)*B^2*x + (2*a*b*d^2*f*n - a^2*d^2*g*n)*B^2*log(b*x + a) + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d^2)","B",0
70,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","2 \, A B n {\left(\frac{a \log\left(b x + a\right)}{b} - \frac{c \log\left(d x + c\right)}{d}\right)} + 2 \, A B x \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A^{2} x + B^{2} {\left(\frac{2 \, b c n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - b c n^{2} \log\left(d x + c\right)^{2} + b d x \log\left({\left(b x + a\right)}^{n}\right)^{2} + b d x \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(a d n \log\left(b x + a\right) - b c n \log\left(d x + c\right) + b d x \log\left(e\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(a d n \log\left(b x + a\right) - b c n \log\left(d x + c\right) + b d x \log\left({\left(b x + a\right)}^{n}\right) + b d x \log\left(e\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b d} - \int -\frac{b^{2} d x^{2} \log\left(e\right)^{2} + a b c \log\left(e\right)^{2} - {\left({\left(2 \, n \log\left(e\right) - \log\left(e\right)^{2}\right)} b^{2} c - {\left(2 \, n \log\left(e\right) + \log\left(e\right)^{2}\right)} a b d\right)} x - 2 \, {\left(b^{2} c n^{2} x + 2 \, a b c n^{2} - a^{2} d n^{2}\right)} \log\left(b x + a\right)}{b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x}\,{d x}\right)}"," ",0,"2*A*B*n*(a*log(b*x + a)/b - c*log(d*x + c)/d) + 2*A*B*x*log(e*((b*x + a)/(d*x + c))^n) + A^2*x + B^2*((2*b*c*n^2*log(b*x + a)*log(d*x + c) - b*c*n^2*log(d*x + c)^2 + b*d*x*log((b*x + a)^n)^2 + b*d*x*log((d*x + c)^n)^2 + 2*(a*d*n*log(b*x + a) - b*c*n*log(d*x + c) + b*d*x*log(e))*log((b*x + a)^n) - 2*(a*d*n*log(b*x + a) - b*c*n*log(d*x + c) + b*d*x*log((b*x + a)^n) + b*d*x*log(e))*log((d*x + c)^n))/(b*d) - integrate(-(b^2*d*x^2*log(e)^2 + a*b*c*log(e)^2 - ((2*n*log(e) - log(e)^2)*b^2*c - (2*n*log(e) + log(e)^2)*a*b*d)*x - 2*(b^2*c*n^2*x + 2*a*b*c*n^2 - a^2*d*n^2)*log(b*x + a))/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x), x))","F",0
71,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(g*x+f),x, algorithm=""maxima"")","\frac{A^{2} \log\left(g x + f\right)}{g} + \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)}{g x + f}\,{d x}"," ",0,"A^2*log(g*x + f)/g + 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))/(g*x + f), x)","F",0
72,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(g*x+f)^2,x, algorithm=""maxima"")","2 \, A B n {\left(\frac{b \log\left(b x + a\right)}{b f g - a g^{2}} - \frac{d \log\left(d x + c\right)}{d f g - c g^{2}} + \frac{{\left(b c - a d\right)} \log\left(g x + f\right)}{b d f^{2} + a c g^{2} - {\left(b c + a d\right)} f g}\right)} - B^{2} {\left(\frac{\log\left({\left(d x + c\right)}^{n}\right)^{2}}{g^{2} x + f g} + \int -\frac{d g x \log\left(e\right)^{2} + c g \log\left(e\right)^{2} + {\left(d g x + c g\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + 2 \, {\left(d f n + {\left(g n - g \log\left(e\right)\right)} d x - c g \log\left(e\right) - {\left(d g x + c g\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d g^{3} x^{3} + c f^{2} g + {\left(2 \, d f g^{2} + c g^{3}\right)} x^{2} + {\left(d f^{2} g + 2 \, c f g^{2}\right)} x}\,{d x}\right)} - \frac{2 \, A B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{g^{2} x + f g} - \frac{A^{2}}{g^{2} x + f g}"," ",0,"2*A*B*n*(b*log(b*x + a)/(b*f*g - a*g^2) - d*log(d*x + c)/(d*f*g - c*g^2) + (b*c - a*d)*log(g*x + f)/(b*d*f^2 + a*c*g^2 - (b*c + a*d)*f*g)) - B^2*(log((d*x + c)^n)^2/(g^2*x + f*g) + integrate(-(d*g*x*log(e)^2 + c*g*log(e)^2 + (d*g*x + c*g)*log((b*x + a)^n)^2 + 2*(d*g*x*log(e) + c*g*log(e))*log((b*x + a)^n) + 2*(d*f*n + (g*n - g*log(e))*d*x - c*g*log(e) - (d*g*x + c*g)*log((b*x + a)^n))*log((d*x + c)^n))/(d*g^3*x^3 + c*f^2*g + (2*d*f*g^2 + c*g^3)*x^2 + (d*f^2*g + 2*c*f*g^2)*x), x)) - 2*A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(g^2*x + f*g) - A^2/(g^2*x + f*g)","F",0
73,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(g*x+f)^3,x, algorithm=""maxima"")","{\left(\frac{b^{2} \log\left(b x + a\right)}{b^{2} f^{2} g - 2 \, a b f g^{2} + a^{2} g^{3}} - \frac{d^{2} \log\left(d x + c\right)}{d^{2} f^{2} g - 2 \, c d f g^{2} + c^{2} g^{3}} + \frac{{\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g\right)} \log\left(g x + f\right)}{b^{2} d^{2} f^{4} + a^{2} c^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{3}} - \frac{b c - a d}{b d f^{3} + a c f g^{2} - {\left(b c + a d\right)} f^{2} g + {\left(b d f^{2} g + a c g^{3} - {\left(b c + a d\right)} f g^{2}\right)} x}\right)} A B n - \frac{1}{2} \, B^{2} {\left(\frac{\log\left({\left(d x + c\right)}^{n}\right)^{2}}{g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g} + 2 \, \int -\frac{d g x \log\left(e\right)^{2} + c g \log\left(e\right)^{2} + {\left(d g x + c g\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + {\left(d f n + {\left(g n - 2 \, g \log\left(e\right)\right)} d x - 2 \, c g \log\left(e\right) - 2 \, {\left(d g x + c g\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d g^{4} x^{4} + c f^{3} g + {\left(3 \, d f g^{3} + c g^{4}\right)} x^{3} + 3 \, {\left(d f^{2} g^{2} + c f g^{3}\right)} x^{2} + {\left(d f^{3} g + 3 \, c f^{2} g^{2}\right)} x}\,{d x}\right)} - \frac{A B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g} - \frac{A^{2}}{2 \, {\left(g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g\right)}}"," ",0,"(b^2*log(b*x + a)/(b^2*f^2*g - 2*a*b*f*g^2 + a^2*g^3) - d^2*log(d*x + c)/(d^2*f^2*g - 2*c*d*f*g^2 + c^2*g^3) + (2*(b^2*c*d - a*b*d^2)*f - (b^2*c^2 - a^2*d^2)*g)*log(g*x + f)/(b^2*d^2*f^4 + a^2*c^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^3*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^2 - 2*(a*b*c^2 + a^2*c*d)*f*g^3) - (b*c - a*d)/(b*d*f^3 + a*c*f*g^2 - (b*c + a*d)*f^2*g + (b*d*f^2*g + a*c*g^3 - (b*c + a*d)*f*g^2)*x))*A*B*n - 1/2*B^2*(log((d*x + c)^n)^2/(g^3*x^2 + 2*f*g^2*x + f^2*g) + 2*integrate(-(d*g*x*log(e)^2 + c*g*log(e)^2 + (d*g*x + c*g)*log((b*x + a)^n)^2 + 2*(d*g*x*log(e) + c*g*log(e))*log((b*x + a)^n) + (d*f*n + (g*n - 2*g*log(e))*d*x - 2*c*g*log(e) - 2*(d*g*x + c*g)*log((b*x + a)^n))*log((d*x + c)^n))/(d*g^4*x^4 + c*f^3*g + (3*d*f*g^3 + c*g^4)*x^3 + 3*(d*f^2*g^2 + c*f*g^3)*x^2 + (d*f^3*g + 3*c*f^2*g^2)*x), x)) - A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(g^3*x^2 + 2*f*g^2*x + f^2*g) - 1/2*A^2/(g^3*x^2 + 2*f*g^2*x + f^2*g)","F",0
74,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(g*x+f)^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, b^{3} \log\left(b x + a\right)}{b^{3} f^{3} g - 3 \, a b^{2} f^{2} g^{2} + 3 \, a^{2} b f g^{3} - a^{3} g^{4}} - \frac{2 \, d^{3} \log\left(d x + c\right)}{d^{3} f^{3} g - 3 \, c d^{2} f^{2} g^{2} + 3 \, c^{2} d f g^{3} - c^{3} g^{4}} + \frac{2 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{2}\right)} \log\left(g x + f\right)}{b^{3} d^{3} f^{6} + a^{3} c^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{5}} - \frac{5 \, {\left(b^{2} c d - a b d^{2}\right)} f^{2} - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} f g + {\left(a b c^{2} - a^{2} c d\right)} g^{2} + 2 \, {\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f g - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g^{2}\right)} x}{b^{2} d^{2} f^{6} + a^{2} c^{2} f^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{5} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{4} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{3} g^{3} + {\left(b^{2} d^{2} f^{4} g^{2} + a^{2} c^{2} g^{6} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g^{3} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{4} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} f^{5} g + a^{2} c^{2} f g^{5} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{4} g^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{3} g^{3} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2} g^{4}\right)} x}\right)} A B n - \frac{1}{3} \, B^{2} {\left(\frac{\log\left({\left(d x + c\right)}^{n}\right)^{2}}{g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g} + 3 \, \int -\frac{3 \, d g x \log\left(e\right)^{2} + 3 \, c g \log\left(e\right)^{2} + 3 \, {\left(d g x + c g\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 6 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + 2 \, {\left(d f n + {\left(g n - 3 \, g \log\left(e\right)\right)} d x - 3 \, c g \log\left(e\right) - 3 \, {\left(d g x + c g\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{3 \, {\left(d g^{5} x^{5} + c f^{4} g + {\left(4 \, d f g^{4} + c g^{5}\right)} x^{4} + 2 \, {\left(3 \, d f^{2} g^{3} + 2 \, c f g^{4}\right)} x^{3} + 2 \, {\left(2 \, d f^{3} g^{2} + 3 \, c f^{2} g^{3}\right)} x^{2} + {\left(d f^{4} g + 4 \, c f^{3} g^{2}\right)} x\right)}}\,{d x}\right)} - \frac{2 \, A B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{3 \, {\left(g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g\right)}} - \frac{A^{2}}{3 \, {\left(g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g\right)}}"," ",0,"1/3*(2*b^3*log(b*x + a)/(b^3*f^3*g - 3*a*b^2*f^2*g^2 + 3*a^2*b*f*g^3 - a^3*g^4) - 2*d^3*log(d*x + c)/(d^3*f^3*g - 3*c*d^2*f^2*g^2 + 3*c^2*d*f*g^3 - c^3*g^4) + 2*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g + (b^3*c^3 - a^3*d^3)*g^2)*log(g*x + f)/(b^3*d^3*f^6 + a^3*c^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^5) - (5*(b^2*c*d - a*b*d^2)*f^2 - 3*(b^2*c^2 - a^2*d^2)*f*g + (a*b*c^2 - a^2*c*d)*g^2 + 2*(2*(b^2*c*d - a*b*d^2)*f*g - (b^2*c^2 - a^2*d^2)*g^2)*x)/(b^2*d^2*f^6 + a^2*c^2*f^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^5*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^4*g^2 - 2*(a*b*c^2 + a^2*c*d)*f^3*g^3 + (b^2*d^2*f^4*g^2 + a^2*c^2*g^6 - 2*(b^2*c*d + a*b*d^2)*f^3*g^3 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^4 - 2*(a*b*c^2 + a^2*c*d)*f*g^5)*x^2 + 2*(b^2*d^2*f^5*g + a^2*c^2*f*g^5 - 2*(b^2*c*d + a*b*d^2)*f^4*g^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^3*g^3 - 2*(a*b*c^2 + a^2*c*d)*f^2*g^4)*x))*A*B*n - 1/3*B^2*(log((d*x + c)^n)^2/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g) + 3*integrate(-1/3*(3*d*g*x*log(e)^2 + 3*c*g*log(e)^2 + 3*(d*g*x + c*g)*log((b*x + a)^n)^2 + 6*(d*g*x*log(e) + c*g*log(e))*log((b*x + a)^n) + 2*(d*f*n + (g*n - 3*g*log(e))*d*x - 3*c*g*log(e) - 3*(d*g*x + c*g)*log((b*x + a)^n))*log((d*x + c)^n))/(d*g^5*x^5 + c*f^4*g + (4*d*f*g^4 + c*g^5)*x^4 + 2*(3*d*f^2*g^3 + 2*c*f*g^4)*x^3 + 2*(2*d*f^3*g^2 + 3*c*f^2*g^3)*x^2 + (d*f^4*g + 4*c*f^3*g^2)*x), x)) - 2/3*A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g) - 1/3*A^2/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g)","F",0
75,0,0,0,0.000000," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(g*x+f)^5,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(\frac{6 \, b^{4} \log\left(b x + a\right)}{b^{4} f^{4} g - 4 \, a b^{3} f^{3} g^{2} + 6 \, a^{2} b^{2} f^{2} g^{3} - 4 \, a^{3} b f g^{4} + a^{4} g^{5}} - \frac{6 \, d^{4} \log\left(d x + c\right)}{d^{4} f^{4} g - 4 \, c d^{3} f^{3} g^{2} + 6 \, c^{2} d^{2} f^{2} g^{3} - 4 \, c^{3} d f g^{4} + c^{4} g^{5}} + \frac{6 \, {\left(4 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f^{3} - 6 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} f^{2} g + 4 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} f g^{2} - {\left(b^{4} c^{4} - a^{4} d^{4}\right)} g^{3}\right)} \log\left(g x + f\right)}{b^{4} d^{4} f^{8} + a^{4} c^{4} g^{8} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} f^{7} g + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} f^{6} g^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} f^{5} g^{3} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} f^{4} g^{4} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} f^{3} g^{5} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f^{2} g^{6} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} f g^{7}} - \frac{26 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{4} - 31 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{3} g + {\left(11 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 15 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3}\right)} f^{2} g^{2} - 7 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} f g^{3} + 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} g^{4} + 6 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} g^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g^{3} + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{4}\right)} x^{2} + 3 \, {\left(14 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{3} g - 15 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{2} g^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f g^{3} - {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} g^{4}\right)} x}{b^{3} d^{3} f^{9} + a^{3} c^{3} f^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{8} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{7} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{5} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{4} g^{5} + {\left(b^{3} d^{3} f^{6} g^{3} + a^{3} c^{3} g^{9} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{5} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{6} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{7} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{8}\right)} x^{3} + 3 \, {\left(b^{3} d^{3} f^{7} g^{2} + a^{3} c^{3} f g^{8} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{5} g^{4} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{4} g^{5} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{3} g^{6} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{2} g^{7}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} f^{8} g + a^{3} c^{3} f^{2} g^{7} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{7} g^{2} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{6} g^{3} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{4} g^{5} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{3} g^{6}\right)} x}\right)} A B n - \frac{1}{4} \, B^{2} {\left(\frac{\log\left({\left(d x + c\right)}^{n}\right)^{2}}{g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g} + 4 \, \int -\frac{2 \, d g x \log\left(e\right)^{2} + 2 \, c g \log\left(e\right)^{2} + 2 \, {\left(d g x + c g\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 4 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + {\left(d f n + {\left(g n - 4 \, g \log\left(e\right)\right)} d x - 4 \, c g \log\left(e\right) - 4 \, {\left(d g x + c g\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, {\left(d g^{6} x^{6} + c f^{5} g + {\left(5 \, d f g^{5} + c g^{6}\right)} x^{5} + 5 \, {\left(2 \, d f^{2} g^{4} + c f g^{5}\right)} x^{4} + 10 \, {\left(d f^{3} g^{3} + c f^{2} g^{4}\right)} x^{3} + 5 \, {\left(d f^{4} g^{2} + 2 \, c f^{3} g^{3}\right)} x^{2} + {\left(d f^{5} g + 5 \, c f^{4} g^{2}\right)} x\right)}}\,{d x}\right)} - \frac{A B \log\left(e {\left(\frac{b x}{d x + c} + \frac{a}{d x + c}\right)}^{n}\right)}{2 \, {\left(g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g\right)}} - \frac{A^{2}}{4 \, {\left(g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g\right)}}"," ",0,"1/12*(6*b^4*log(b*x + a)/(b^4*f^4*g - 4*a*b^3*f^3*g^2 + 6*a^2*b^2*f^2*g^3 - 4*a^3*b*f*g^4 + a^4*g^5) - 6*d^4*log(d*x + c)/(d^4*f^4*g - 4*c*d^3*f^3*g^2 + 6*c^2*d^2*f^2*g^3 - 4*c^3*d*f*g^4 + c^4*g^5) + 6*(4*(b^4*c*d^3 - a*b^3*d^4)*f^3 - 6*(b^4*c^2*d^2 - a^2*b^2*d^4)*f^2*g + 4*(b^4*c^3*d - a^3*b*d^4)*f*g^2 - (b^4*c^4 - a^4*d^4)*g^3)*log(g*x + f)/(b^4*d^4*f^8 + a^4*c^4*g^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*f^7*g + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*f^6*g^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*f^5*g^3 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*f^4*g^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*f^3*g^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f^2*g^6 - 4*(a^3*b*c^4 + a^4*c^3*d)*f*g^7) - (26*(b^3*c*d^2 - a*b^2*d^3)*f^4 - 31*(b^3*c^2*d - a^2*b*d^3)*f^3*g + (11*b^3*c^3 + 15*a*b^2*c^2*d - 15*a^2*b*c*d^2 - 11*a^3*d^3)*f^2*g^2 - 7*(a*b^2*c^3 - a^3*c*d^2)*f*g^3 + 2*(a^2*b*c^3 - a^3*c^2*d)*g^4 + 6*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2*g^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g^3 + (b^3*c^3 - a^3*d^3)*g^4)*x^2 + 3*(14*(b^3*c*d^2 - a*b^2*d^3)*f^3*g - 15*(b^3*c^2*d - a^2*b*d^3)*f^2*g^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f*g^3 - (a*b^2*c^3 - a^3*c*d^2)*g^4)*x)/(b^3*d^3*f^9 + a^3*c^3*f^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^8*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^7*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^6*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^5*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^4*g^5 + (b^3*d^3*f^6*g^3 + a^3*c^3*g^9 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g^4 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^5 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^6 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^7 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^8)*x^3 + 3*(b^3*d^3*f^7*g^2 + a^3*c^3*f*g^8 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^6*g^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^5*g^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^4*g^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3*g^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^2*g^7)*x^2 + 3*(b^3*d^3*f^8*g + a^3*c^3*f^2*g^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^7*g^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^6*g^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^5*g^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^4*g^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^3*g^6)*x))*A*B*n - 1/4*B^2*(log((d*x + c)^n)^2/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g) + 4*integrate(-1/2*(2*d*g*x*log(e)^2 + 2*c*g*log(e)^2 + 2*(d*g*x + c*g)*log((b*x + a)^n)^2 + 4*(d*g*x*log(e) + c*g*log(e))*log((b*x + a)^n) + (d*f*n + (g*n - 4*g*log(e))*d*x - 4*c*g*log(e) - 4*(d*g*x + c*g)*log((b*x + a)^n))*log((d*x + c)^n))/(d*g^6*x^6 + c*f^5*g + (5*d*f*g^5 + c*g^6)*x^5 + 5*(2*d*f^2*g^4 + c*f*g^5)*x^4 + 10*(d*f^3*g^3 + c*f^2*g^4)*x^3 + 5*(d*f^4*g^2 + 2*c*f^3*g^3)*x^2 + (d*f^5*g + 5*c*f^4*g^2)*x), x)) - 1/2*A*B*log(e*(b*x/(d*x + c) + a/(d*x + c))^n)/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g) - 1/4*A^2/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g)","F",0
76,0,0,0,0.000000," ","integrate((g*x+f)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{{\left(g x + f\right)}^{2}}{B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A}\,{d x}"," ",0,"integrate((g*x + f)^2/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
77,0,0,0,0.000000," ","integrate((g*x+f)/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{g x + f}{B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A}\,{d x}"," ",0,"integrate((g*x + f)/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
78,0,0,0,0.000000," ","integrate(1/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A}\,{d x}"," ",0,"integrate(1/(B*log(e*((b*x + a)/(d*x + c))^n) + A), x)","F",0
79,0,0,0,0.000000," ","integrate(1/(g*x+f)/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
80,0,0,0,0.000000," ","integrate(1/(g*x+f)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)}^{2} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)^2*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
81,0,0,0,0.000000," ","integrate(1/(g*x+f)^3/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)}^{3} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)^3*(B*log(e*((b*x + a)/(d*x + c))^n) + A)), x)","F",0
82,0,0,0,0.000000," ","integrate((g*x+f)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b d g^{2} x^{4} + a c f^{2} + {\left(a d g^{2} + {\left(2 \, d f g + c g^{2}\right)} b\right)} x^{3} + {\left({\left(2 \, d f g + c g^{2}\right)} a + {\left(d f^{2} + 2 \, c f g\right)} b\right)} x^{2} + {\left(b c f^{2} + {\left(d f^{2} + 2 \, c f g\right)} a\right)} x}{{\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}} + \int \frac{4 \, b d g^{2} x^{3} + b c f^{2} + 3 \, {\left(a d g^{2} + {\left(2 \, d f g + c g^{2}\right)} b\right)} x^{2} + {\left(d f^{2} + 2 \, c f g\right)} a + 2 \, {\left({\left(2 \, d f g + c g^{2}\right)} a + {\left(d f^{2} + 2 \, c f g\right)} b\right)} x}{{\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}}\,{d x}"," ",0,"-(b*d*g^2*x^4 + a*c*f^2 + (a*d*g^2 + (2*d*f*g + c*g^2)*b)*x^3 + ((2*d*f*g + c*g^2)*a + (d*f^2 + 2*c*f*g)*b)*x^2 + (b*c*f^2 + (d*f^2 + 2*c*f*g)*a)*x)/((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) + integrate((4*b*d*g^2*x^3 + b*c*f^2 + 3*(a*d*g^2 + (2*d*f*g + c*g^2)*b)*x^2 + (d*f^2 + 2*c*f*g)*a + 2*((2*d*f*g + c*g^2)*a + (d*f^2 + 2*c*f*g)*b)*x)/((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), x)","F",0
83,0,0,0,0.000000," ","integrate((g*x+f)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b d g x^{3} + a c f + {\left(a d g + {\left(d f + c g\right)} b\right)} x^{2} + {\left(b c f + {\left(d f + c g\right)} a\right)} x}{{\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}} + \int \frac{3 \, b d g x^{2} + b c f + {\left(d f + c g\right)} a + 2 \, {\left(a d g + {\left(d f + c g\right)} b\right)} x}{{\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}}\,{d x}"," ",0,"-(b*d*g*x^3 + a*c*f + (a*d*g + (d*f + c*g)*b)*x^2 + (b*c*f + (d*f + c*g)*a)*x)/((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) + integrate((3*b*d*g*x^2 + b*c*f + (d*f + c*g)*a + 2*(a*d*g + (d*f + c*g)*b)*x)/((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), x)","F",0
84,0,0,0,0.000000," ","integrate(1/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{{\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}} + \int \frac{2 \, b d x + b c + a d}{{\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}}\,{d x}"," ",0,"-(b*d*x^2 + a*c + (b*c + a*d)*x)/((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) + integrate((2*b*d*x + b*c + a*d)/((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), x)","F",0
85,0,0,0,0.000000," ","integrate(1/(g*x+f)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{{\left(b c f n - a d f n\right)} A B + {\left(b c f n \log\left(e\right) - a d f n \log\left(e\right)\right)} B^{2} + {\left({\left(b c g n - a d g n\right)} A B + {\left(b c g n \log\left(e\right) - a d g n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g n - a d g n\right)} B^{2} x + {\left(b c f n - a d f n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g n - a d g n\right)} B^{2} x + {\left(b c f n - a d f n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)} + \int \frac{b d g x^{2} + 2 \, b d f x + b c f + {\left(d f - c g\right)} a}{{\left(b c f^{2} n - a d f^{2} n\right)} A B + {\left(b c f^{2} n \log\left(e\right) - a d f^{2} n \log\left(e\right)\right)} B^{2} + {\left({\left(b c g^{2} n - a d g^{2} n\right)} A B + {\left(b c g^{2} n \log\left(e\right) - a d g^{2} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c f g n - a d f g n\right)} A B + {\left(b c f g n \log\left(e\right) - a d f g n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{2} n - a d g^{2} n\right)} B^{2} x^{2} + 2 \, {\left(b c f g n - a d f g n\right)} B^{2} x + {\left(b c f^{2} n - a d f^{2} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g^{2} n - a d g^{2} n\right)} B^{2} x^{2} + 2 \, {\left(b c f g n - a d f g n\right)} B^{2} x + {\left(b c f^{2} n - a d f^{2} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x}"," ",0,"-(b*d*x^2 + a*c + (b*c + a*d)*x)/((b*c*f*n - a*d*f*n)*A*B + (b*c*f*n*log(e) - a*d*f*n*log(e))*B^2 + ((b*c*g*n - a*d*g*n)*A*B + (b*c*g*n*log(e) - a*d*g*n*log(e))*B^2)*x + ((b*c*g*n - a*d*g*n)*B^2*x + (b*c*f*n - a*d*f*n)*B^2)*log((b*x + a)^n) - ((b*c*g*n - a*d*g*n)*B^2*x + (b*c*f*n - a*d*f*n)*B^2)*log((d*x + c)^n)) + integrate((b*d*g*x^2 + 2*b*d*f*x + b*c*f + (d*f - c*g)*a)/((b*c*f^2*n - a*d*f^2*n)*A*B + (b*c*f^2*n*log(e) - a*d*f^2*n*log(e))*B^2 + ((b*c*g^2*n - a*d*g^2*n)*A*B + (b*c*g^2*n*log(e) - a*d*g^2*n*log(e))*B^2)*x^2 + 2*((b*c*f*g*n - a*d*f*g*n)*A*B + (b*c*f*g*n*log(e) - a*d*f*g*n*log(e))*B^2)*x + ((b*c*g^2*n - a*d*g^2*n)*B^2*x^2 + 2*(b*c*f*g*n - a*d*f*g*n)*B^2*x + (b*c*f^2*n - a*d*f^2*n)*B^2)*log((b*x + a)^n) - ((b*c*g^2*n - a*d*g^2*n)*B^2*x^2 + 2*(b*c*f*g*n - a*d*f*g*n)*B^2*x + (b*c*f^2*n - a*d*f^2*n)*B^2)*log((d*x + c)^n)), x)","F",0
86,0,0,0,0.000000," ","integrate(1/(g*x+f)^2/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{{\left(b c f^{2} n - a d f^{2} n\right)} A B + {\left(b c f^{2} n \log\left(e\right) - a d f^{2} n \log\left(e\right)\right)} B^{2} + {\left({\left(b c g^{2} n - a d g^{2} n\right)} A B + {\left(b c g^{2} n \log\left(e\right) - a d g^{2} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c f g n - a d f g n\right)} A B + {\left(b c f g n \log\left(e\right) - a d f g n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{2} n - a d g^{2} n\right)} B^{2} x^{2} + 2 \, {\left(b c f g n - a d f g n\right)} B^{2} x + {\left(b c f^{2} n - a d f^{2} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g^{2} n - a d g^{2} n\right)} B^{2} x^{2} + 2 \, {\left(b c f g n - a d f g n\right)} B^{2} x + {\left(b c f^{2} n - a d f^{2} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)} - \int -\frac{b c f + {\left(d f - 2 \, c g\right)} a - {\left(a d g - {\left(2 \, d f - c g\right)} b\right)} x}{{\left({\left(b c g^{3} n - a d g^{3} n\right)} A B + {\left(b c g^{3} n \log\left(e\right) - a d g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{3} n - a d f^{3} n\right)} A B + {\left(b c f^{3} n \log\left(e\right) - a d f^{3} n \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(b c f g^{2} n - a d f g^{2} n\right)} A B + {\left(b c f g^{2} n \log\left(e\right) - a d f g^{2} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(b c f^{2} g n - a d f^{2} g n\right)} A B + {\left(b c f^{2} g n \log\left(e\right) - a d f^{2} g n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{3} n - a d g^{3} n\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} n - a d f g^{2} n\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g n - a d f^{2} g n\right)} B^{2} x + {\left(b c f^{3} n - a d f^{3} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g^{3} n - a d g^{3} n\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} n - a d f g^{2} n\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g n - a d f^{2} g n\right)} B^{2} x + {\left(b c f^{3} n - a d f^{3} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x}"," ",0,"-(b*d*x^2 + a*c + (b*c + a*d)*x)/((b*c*f^2*n - a*d*f^2*n)*A*B + (b*c*f^2*n*log(e) - a*d*f^2*n*log(e))*B^2 + ((b*c*g^2*n - a*d*g^2*n)*A*B + (b*c*g^2*n*log(e) - a*d*g^2*n*log(e))*B^2)*x^2 + 2*((b*c*f*g*n - a*d*f*g*n)*A*B + (b*c*f*g*n*log(e) - a*d*f*g*n*log(e))*B^2)*x + ((b*c*g^2*n - a*d*g^2*n)*B^2*x^2 + 2*(b*c*f*g*n - a*d*f*g*n)*B^2*x + (b*c*f^2*n - a*d*f^2*n)*B^2)*log((b*x + a)^n) - ((b*c*g^2*n - a*d*g^2*n)*B^2*x^2 + 2*(b*c*f*g*n - a*d*f*g*n)*B^2*x + (b*c*f^2*n - a*d*f^2*n)*B^2)*log((d*x + c)^n)) - integrate(-(b*c*f + (d*f - 2*c*g)*a - (a*d*g - (2*d*f - c*g)*b)*x)/(((b*c*g^3*n - a*d*g^3*n)*A*B + (b*c*g^3*n*log(e) - a*d*g^3*n*log(e))*B^2)*x^3 + (b*c*f^3*n - a*d*f^3*n)*A*B + (b*c*f^3*n*log(e) - a*d*f^3*n*log(e))*B^2 + 3*((b*c*f*g^2*n - a*d*f*g^2*n)*A*B + (b*c*f*g^2*n*log(e) - a*d*f*g^2*n*log(e))*B^2)*x^2 + 3*((b*c*f^2*g*n - a*d*f^2*g*n)*A*B + (b*c*f^2*g*n*log(e) - a*d*f^2*g*n*log(e))*B^2)*x + ((b*c*g^3*n - a*d*g^3*n)*B^2*x^3 + 3*(b*c*f*g^2*n - a*d*f*g^2*n)*B^2*x^2 + 3*(b*c*f^2*g*n - a*d*f^2*g*n)*B^2*x + (b*c*f^3*n - a*d*f^3*n)*B^2)*log((b*x + a)^n) - ((b*c*g^3*n - a*d*g^3*n)*B^2*x^3 + 3*(b*c*f*g^2*n - a*d*f*g^2*n)*B^2*x^2 + 3*(b*c*f^2*g*n - a*d*f^2*g*n)*B^2*x + (b*c*f^3*n - a*d*f^3*n)*B^2)*log((d*x + c)^n)), x)","F",0
87,0,0,0,0.000000," ","integrate(1/(g*x+f)^3/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{{\left({\left(b c g^{3} n - a d g^{3} n\right)} A B + {\left(b c g^{3} n \log\left(e\right) - a d g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{3} n - a d f^{3} n\right)} A B + {\left(b c f^{3} n \log\left(e\right) - a d f^{3} n \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(b c f g^{2} n - a d f g^{2} n\right)} A B + {\left(b c f g^{2} n \log\left(e\right) - a d f g^{2} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(b c f^{2} g n - a d f^{2} g n\right)} A B + {\left(b c f^{2} g n \log\left(e\right) - a d f^{2} g n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{3} n - a d g^{3} n\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} n - a d f g^{2} n\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g n - a d f^{2} g n\right)} B^{2} x + {\left(b c f^{3} n - a d f^{3} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g^{3} n - a d g^{3} n\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} n - a d f g^{2} n\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g n - a d f^{2} g n\right)} B^{2} x + {\left(b c f^{3} n - a d f^{3} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)} - \int \frac{b d g x^{2} - b c f - {\left(d f - 3 \, c g\right)} a + 2 \, {\left(a d g - {\left(d f - c g\right)} b\right)} x}{{\left({\left(b c g^{4} n - a d g^{4} n\right)} A B + {\left(b c g^{4} n \log\left(e\right) - a d g^{4} n \log\left(e\right)\right)} B^{2}\right)} x^{4} + 4 \, {\left({\left(b c f g^{3} n - a d f g^{3} n\right)} A B + {\left(b c f g^{3} n \log\left(e\right) - a d f g^{3} n \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{4} n - a d f^{4} n\right)} A B + {\left(b c f^{4} n \log\left(e\right) - a d f^{4} n \log\left(e\right)\right)} B^{2} + 6 \, {\left({\left(b c f^{2} g^{2} n - a d f^{2} g^{2} n\right)} A B + {\left(b c f^{2} g^{2} n \log\left(e\right) - a d f^{2} g^{2} n \log\left(e\right)\right)} B^{2}\right)} x^{2} + 4 \, {\left({\left(b c f^{3} g n - a d f^{3} g n\right)} A B + {\left(b c f^{3} g n \log\left(e\right) - a d f^{3} g n \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{4} n - a d g^{4} n\right)} B^{2} x^{4} + 4 \, {\left(b c f g^{3} n - a d f g^{3} n\right)} B^{2} x^{3} + 6 \, {\left(b c f^{2} g^{2} n - a d f^{2} g^{2} n\right)} B^{2} x^{2} + 4 \, {\left(b c f^{3} g n - a d f^{3} g n\right)} B^{2} x + {\left(b c f^{4} n - a d f^{4} n\right)} B^{2}\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left({\left(b c g^{4} n - a d g^{4} n\right)} B^{2} x^{4} + 4 \, {\left(b c f g^{3} n - a d f g^{3} n\right)} B^{2} x^{3} + 6 \, {\left(b c f^{2} g^{2} n - a d f^{2} g^{2} n\right)} B^{2} x^{2} + 4 \, {\left(b c f^{3} g n - a d f^{3} g n\right)} B^{2} x + {\left(b c f^{4} n - a d f^{4} n\right)} B^{2}\right)} \log\left({\left(d x + c\right)}^{n}\right)}\,{d x}"," ",0,"-(b*d*x^2 + a*c + (b*c + a*d)*x)/(((b*c*g^3*n - a*d*g^3*n)*A*B + (b*c*g^3*n*log(e) - a*d*g^3*n*log(e))*B^2)*x^3 + (b*c*f^3*n - a*d*f^3*n)*A*B + (b*c*f^3*n*log(e) - a*d*f^3*n*log(e))*B^2 + 3*((b*c*f*g^2*n - a*d*f*g^2*n)*A*B + (b*c*f*g^2*n*log(e) - a*d*f*g^2*n*log(e))*B^2)*x^2 + 3*((b*c*f^2*g*n - a*d*f^2*g*n)*A*B + (b*c*f^2*g*n*log(e) - a*d*f^2*g*n*log(e))*B^2)*x + ((b*c*g^3*n - a*d*g^3*n)*B^2*x^3 + 3*(b*c*f*g^2*n - a*d*f*g^2*n)*B^2*x^2 + 3*(b*c*f^2*g*n - a*d*f^2*g*n)*B^2*x + (b*c*f^3*n - a*d*f^3*n)*B^2)*log((b*x + a)^n) - ((b*c*g^3*n - a*d*g^3*n)*B^2*x^3 + 3*(b*c*f*g^2*n - a*d*f*g^2*n)*B^2*x^2 + 3*(b*c*f^2*g*n - a*d*f^2*g*n)*B^2*x + (b*c*f^3*n - a*d*f^3*n)*B^2)*log((d*x + c)^n)) - integrate((b*d*g*x^2 - b*c*f - (d*f - 3*c*g)*a + 2*(a*d*g - (d*f - c*g)*b)*x)/(((b*c*g^4*n - a*d*g^4*n)*A*B + (b*c*g^4*n*log(e) - a*d*g^4*n*log(e))*B^2)*x^4 + 4*((b*c*f*g^3*n - a*d*f*g^3*n)*A*B + (b*c*f*g^3*n*log(e) - a*d*f*g^3*n*log(e))*B^2)*x^3 + (b*c*f^4*n - a*d*f^4*n)*A*B + (b*c*f^4*n*log(e) - a*d*f^4*n*log(e))*B^2 + 6*((b*c*f^2*g^2*n - a*d*f^2*g^2*n)*A*B + (b*c*f^2*g^2*n*log(e) - a*d*f^2*g^2*n*log(e))*B^2)*x^2 + 4*((b*c*f^3*g*n - a*d*f^3*g*n)*A*B + (b*c*f^3*g*n*log(e) - a*d*f^3*g*n*log(e))*B^2)*x + ((b*c*g^4*n - a*d*g^4*n)*B^2*x^4 + 4*(b*c*f*g^3*n - a*d*f*g^3*n)*B^2*x^3 + 6*(b*c*f^2*g^2*n - a*d*f^2*g^2*n)*B^2*x^2 + 4*(b*c*f^3*g*n - a*d*f^3*g*n)*B^2*x + (b*c*f^4*n - a*d*f^4*n)*B^2)*log((b*x + a)^n) - ((b*c*g^4*n - a*d*g^4*n)*B^2*x^4 + 4*(b*c*f*g^3*n - a*d*f*g^3*n)*B^2*x^3 + 6*(b*c*f^2*g^2*n - a*d*f^2*g^2*n)*B^2*x^2 + 4*(b*c*f^3*g*n - a*d*f^3*g*n)*B^2*x + (b*c*f^4*n - a*d*f^4*n)*B^2)*log((d*x + c)^n)), x)","F",0
88,1,623,0,1.317394," ","integrate((b*g*x+a*g)^4*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{5} \, A b^{4} g^{4} x^{5} + A a b^{3} g^{4} x^{4} + 2 \, A a^{2} b^{2} g^{4} x^{3} + 2 \, A a^{3} b g^{4} 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^{4} g^{4} + 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} b g^{4} + {\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^{2} g^{4} + \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)} B a b^{3} g^{4} + \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^{4} g^{4} + A a^{4} g^{4} x"," ",0,"1/5*A*b^4*g^4*x^5 + A*a*b^3*g^4*x^4 + 2*A*a^2*b^2*g^4*x^3 + 2*A*a^3*b*g^4*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^4*g^4 + 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*b*g^4 + (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^2*g^4 + 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))*B*a*b^3*g^4 + 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^4*g^4 + A*a^4*g^4*x","B",0
89,1,439,0,1.330223," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{4} \, A b^{3} g^{3} x^{4} + A a b^{2} g^{3} x^{3} + \frac{3}{2} \, A a^{2} b g^{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} g^{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 g^{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} g^{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} g^{3} + A a^{3} g^{3} x"," ",0,"1/4*A*b^3*g^3*x^4 + A*a*b^2*g^3*x^3 + 3/2*A*a^2*b*g^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*g^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*g^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*g^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*g^3 + A*a^3*g^3*x","B",0
90,1,280,0,1.238094," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{3} \, A b^{2} g^{2} x^{3} + A a b g^{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} g^{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 g^{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} g^{2} + A a^{2} g^{2} x"," ",0,"1/3*A*b^2*g^2*x^3 + A*a*b*g^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*g^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*g^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*g^2 + A*a^2*g^2*x","B",0
91,1,144,0,1.458924," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{2} \, A b g 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 g + \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 g + A a g x"," ",0,"1/2*A*b*g*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*g + 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*g + A*a*g*x","A",0
92,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g),x, algorithm=""maxima"")","-B {\left(\frac{\log\left(b x + a\right) \log\left(d x + c\right)}{b g} - \int \frac{b d x \log\left(e\right) + b c \log\left(e\right) + {\left(2 \, b d x + b c + a d\right)} \log\left(b x + a\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}\right)} + \frac{A \log\left(b g x + a g\right)}{b g}"," ",0,"-B*(log(b*x + a)*log(d*x + c)/(b*g) - integrate((b*d*x*log(e) + b*c*log(e) + (2*b*d*x + b*c + a*d)*log(b*x + a))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)) + A*log(b*g*x + a*g)/(b*g)","F",0
93,1,132,0,1.088671," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B {\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}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-B*(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/(b^2*g^2*x + a*b*g^2)","B",0
94,1,255,0,1.255847," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","\frac{1}{4} \, B {\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{A}{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*((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*A/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","A",0
95,1,428,0,1.360346," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{18} \, 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^{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{A}{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*((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*A/(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
96,1,647,0,1.540159," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\frac{1}{48} \, B {\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{A}{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*((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*A/(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
97,1,2389,0,2.376284," ","integrate((b*g*x+a*g)^4*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{5} \, A^{2} b^{4} g^{4} x^{5} + A^{2} a b^{3} g^{4} x^{4} + 2 \, A^{2} a^{2} b^{2} g^{4} x^{3} + 2 \, A^{2} a^{3} b g^{4} 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^{4} g^{4} + 4 \, {\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} b g^{4} + 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^{2} g^{4} + \frac{1}{3} \, {\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^{3} g^{4} + \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^{4} g^{4} + A^{2} a^{4} g^{4} x - \frac{{\left({\left(12 \, g^{4} \log\left(e\right) + 25 \, g^{4}\right)} b^{4} c^{5} - {\left(60 \, g^{4} \log\left(e\right) + 113 \, g^{4}\right)} a b^{3} c^{4} d + 4 \, {\left(30 \, g^{4} \log\left(e\right) + 49 \, g^{4}\right)} a^{2} b^{2} c^{3} d^{2} - 12 \, {\left(10 \, g^{4} \log\left(e\right) + 13 \, g^{4}\right)} a^{3} b c^{2} d^{3} + 12 \, {\left(5 \, g^{4} \log\left(e\right) + 4 \, g^{4}\right)} a^{4} c d^{4}\right)} B^{2} \log\left(d x + c\right)}{30 \, d^{5}} - \frac{2 \, {\left(b^{5} c^{5} g^{4} - 5 \, a b^{4} c^{4} d g^{4} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} + 5 \, a^{4} b c d^{4} g^{4} - a^{5} d^{5} g^{4}\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}}{5 \, b d^{5}} + \frac{12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right)^{2} - 6 \, {\left(b^{5} c d^{4} g^{4} \log\left(e\right) - {\left(10 \, g^{4} \log\left(e\right)^{2} + g^{4} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left({\left(4 \, g^{4} \log\left(e\right) + g^{4}\right)} b^{5} c^{2} d^{3} - 2 \, {\left(10 \, g^{4} \log\left(e\right) + g^{4}\right)} a b^{4} c d^{4} + {\left(60 \, g^{4} \log\left(e\right)^{2} + 16 \, g^{4} \log\left(e\right) + g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left({\left(12 \, g^{4} \log\left(e\right) + 7 \, g^{4}\right)} b^{5} c^{3} d^{2} - 3 \, {\left(20 \, g^{4} \log\left(e\right) + 9 \, g^{4}\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(40 \, g^{4} \log\left(e\right) + 11 \, g^{4}\right)} a^{2} b^{3} c d^{4} - {\left(120 \, g^{4} \log\left(e\right)^{2} + 72 \, g^{4} \log\left(e\right) + 13 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 2 \, {\left({\left(12 \, g^{4} \log\left(e\right) + 13 \, g^{4}\right)} b^{5} c^{4} d - {\left(60 \, g^{4} \log\left(e\right) + 59 \, g^{4}\right)} a b^{4} c^{3} d^{2} + 6 \, {\left(20 \, g^{4} \log\left(e\right) + 17 \, g^{4}\right)} a^{2} b^{3} c^{2} d^{3} - {\left(120 \, g^{4} \log\left(e\right) + 79 \, g^{4}\right)} a^{3} b^{2} c d^{4} + {\left(30 \, g^{4} \log\left(e\right)^{2} + 48 \, g^{4} \log\left(e\right) + 23 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + B^{2} a^{5} d^{5} g^{4}\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + {\left(b^{5} c^{5} g^{4} - 5 \, a b^{4} c^{4} d g^{4} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} + 5 \, a^{4} b c d^{4} g^{4}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) - 3 \, {\left(b^{5} c d^{4} g^{4} - {\left(20 \, g^{4} \log\left(e\right) + g^{4}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 4 \, {\left(b^{5} c^{2} d^{3} g^{4} - 5 \, a b^{4} c d^{4} g^{4} + 2 \, {\left(15 \, g^{4} \log\left(e\right) + 2 \, g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - 6 \, {\left(b^{5} c^{3} d^{2} g^{4} - 5 \, a b^{4} c^{2} d^{3} g^{4} + 10 \, a^{2} b^{3} c d^{4} g^{4} - 2 \, {\left(10 \, g^{4} \log\left(e\right) + 3 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 12 \, {\left(b^{5} c^{4} d g^{4} - 5 \, a b^{4} c^{3} d^{2} g^{4} + 10 \, a^{2} b^{3} c^{2} d^{3} g^{4} - 10 \, a^{3} b^{2} c d^{4} g^{4} + {\left(5 \, g^{4} \log\left(e\right) + 4 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x + {\left(12 \, a b^{4} c^{4} d g^{4} - 54 \, a^{2} b^{3} c^{3} d^{2} g^{4} + 94 \, a^{3} b^{2} c^{2} d^{3} g^{4} - 77 \, a^{4} b c d^{4} g^{4} + {\left(12 \, g^{4} \log\left(e\right) + 25 \, g^{4}\right)} a^{5} d^{5}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) - 3 \, {\left(b^{5} c d^{4} g^{4} - {\left(20 \, g^{4} \log\left(e\right) + g^{4}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 4 \, {\left(b^{5} c^{2} d^{3} g^{4} - 5 \, a b^{4} c d^{4} g^{4} + 2 \, {\left(15 \, g^{4} \log\left(e\right) + 2 \, g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - 6 \, {\left(b^{5} c^{3} d^{2} g^{4} - 5 \, a b^{4} c^{2} d^{3} g^{4} + 10 \, a^{2} b^{3} c d^{4} g^{4} - 2 \, {\left(10 \, g^{4} \log\left(e\right) + 3 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 12 \, {\left(b^{5} c^{4} d g^{4} - 5 \, a b^{4} c^{3} d^{2} g^{4} + 10 \, a^{2} b^{3} c^{2} d^{3} g^{4} - 10 \, a^{3} b^{2} c d^{4} g^{4} + {\left(5 \, g^{4} \log\left(e\right) + 4 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + B^{2} a^{5} d^{5} g^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{60 \, b d^{5}}"," ",0,"1/5*A^2*b^4*g^4*x^5 + A^2*a*b^3*g^4*x^4 + 2*A^2*a^2*b^2*g^4*x^3 + 2*A^2*a^3*b*g^4*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^4*g^4 + 4*(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*b*g^4 + 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^2*g^4 + 1/3*(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^3*g^4 + 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^4*g^4 + A^2*a^4*g^4*x - 1/30*((12*g^4*log(e) + 25*g^4)*b^4*c^5 - (60*g^4*log(e) + 113*g^4)*a*b^3*c^4*d + 4*(30*g^4*log(e) + 49*g^4)*a^2*b^2*c^3*d^2 - 12*(10*g^4*log(e) + 13*g^4)*a^3*b*c^2*d^3 + 12*(5*g^4*log(e) + 4*g^4)*a^4*c*d^4)*B^2*log(d*x + c)/d^5 - 2/5*(b^5*c^5*g^4 - 5*a*b^4*c^4*d*g^4 + 10*a^2*b^3*c^3*d^2*g^4 - 10*a^3*b^2*c^2*d^3*g^4 + 5*a^4*b*c*d^4*g^4 - a^5*d^5*g^4)*(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*d^5) + 1/60*(12*B^2*b^5*d^5*g^4*x^5*log(e)^2 - 6*(b^5*c*d^4*g^4*log(e) - (10*g^4*log(e)^2 + g^4*log(e))*a*b^4*d^5)*B^2*x^4 + 2*((4*g^4*log(e) + g^4)*b^5*c^2*d^3 - 2*(10*g^4*log(e) + g^4)*a*b^4*c*d^4 + (60*g^4*log(e)^2 + 16*g^4*log(e) + g^4)*a^2*b^3*d^5)*B^2*x^3 - ((12*g^4*log(e) + 7*g^4)*b^5*c^3*d^2 - 3*(20*g^4*log(e) + 9*g^4)*a*b^4*c^2*d^3 + 3*(40*g^4*log(e) + 11*g^4)*a^2*b^3*c*d^4 - (120*g^4*log(e)^2 + 72*g^4*log(e) + 13*g^4)*a^3*b^2*d^5)*B^2*x^2 + 2*((12*g^4*log(e) + 13*g^4)*b^5*c^4*d - (60*g^4*log(e) + 59*g^4)*a*b^4*c^3*d^2 + 6*(20*g^4*log(e) + 17*g^4)*a^2*b^3*c^2*d^3 - (120*g^4*log(e) + 79*g^4)*a^3*b^2*c*d^4 + (30*g^4*log(e)^2 + 48*g^4*log(e) + 23*g^4)*a^4*b*d^5)*B^2*x + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + B^2*a^5*d^5*g^4)*log(b*x + a)^2 + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + (b^5*c^5*g^4 - 5*a*b^4*c^4*d*g^4 + 10*a^2*b^3*c^3*d^2*g^4 - 10*a^3*b^2*c^2*d^3*g^4 + 5*a^4*b*c*d^4*g^4)*B^2)*log(d*x + c)^2 + 2*(12*B^2*b^5*d^5*g^4*x^5*log(e) - 3*(b^5*c*d^4*g^4 - (20*g^4*log(e) + g^4)*a*b^4*d^5)*B^2*x^4 + 4*(b^5*c^2*d^3*g^4 - 5*a*b^4*c*d^4*g^4 + 2*(15*g^4*log(e) + 2*g^4)*a^2*b^3*d^5)*B^2*x^3 - 6*(b^5*c^3*d^2*g^4 - 5*a*b^4*c^2*d^3*g^4 + 10*a^2*b^3*c*d^4*g^4 - 2*(10*g^4*log(e) + 3*g^4)*a^3*b^2*d^5)*B^2*x^2 + 12*(b^5*c^4*d*g^4 - 5*a*b^4*c^3*d^2*g^4 + 10*a^2*b^3*c^2*d^3*g^4 - 10*a^3*b^2*c*d^4*g^4 + (5*g^4*log(e) + 4*g^4)*a^4*b*d^5)*B^2*x + (12*a*b^4*c^4*d*g^4 - 54*a^2*b^3*c^3*d^2*g^4 + 94*a^3*b^2*c^2*d^3*g^4 - 77*a^4*b*c*d^4*g^4 + (12*g^4*log(e) + 25*g^4)*a^5*d^5)*B^2)*log(b*x + a) - 2*(12*B^2*b^5*d^5*g^4*x^5*log(e) - 3*(b^5*c*d^4*g^4 - (20*g^4*log(e) + g^4)*a*b^4*d^5)*B^2*x^4 + 4*(b^5*c^2*d^3*g^4 - 5*a*b^4*c*d^4*g^4 + 2*(15*g^4*log(e) + 2*g^4)*a^2*b^3*d^5)*B^2*x^3 - 6*(b^5*c^3*d^2*g^4 - 5*a*b^4*c^2*d^3*g^4 + 10*a^2*b^3*c*d^4*g^4 - 2*(10*g^4*log(e) + 3*g^4)*a^3*b^2*d^5)*B^2*x^2 + 12*(b^5*c^4*d*g^4 - 5*a*b^4*c^3*d^2*g^4 + 10*a^2*b^3*c^2*d^3*g^4 - 10*a^3*b^2*c*d^4*g^4 + (5*g^4*log(e) + 4*g^4)*a^4*b*d^5)*B^2*x + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + B^2*a^5*d^5*g^4)*log(b*x + a))*log(d*x + c))/(b*d^5)","B",0
98,1,1732,0,2.369337," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} b^{3} g^{3} x^{4} + A^{2} a b^{2} g^{3} x^{3} + \frac{3}{2} \, A^{2} a^{2} b g^{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} g^{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 g^{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} g^{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} g^{3} + A^{2} a^{3} g^{3} x + \frac{{\left({\left(6 \, g^{3} \log\left(e\right) + 11 \, g^{3}\right)} b^{3} c^{4} - 2 \, {\left(12 \, g^{3} \log\left(e\right) + 19 \, g^{3}\right)} a b^{2} c^{3} d + 9 \, {\left(4 \, g^{3} \log\left(e\right) + 5 \, g^{3}\right)} a^{2} b c^{2} d^{2} - 6 \, {\left(4 \, g^{3} \log\left(e\right) + 3 \, g^{3}\right)} a^{3} c d^{3}\right)} B^{2} \log\left(d x + c\right)}{12 \, d^{4}} + \frac{{\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} - 4 \, a^{3} b c d^{3} g^{3} + a^{4} d^{4} 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^{2}}{2 \, b d^{4}} + \frac{3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right)^{2} - 2 \, {\left(b^{4} c d^{3} g^{3} \log\left(e\right) - {\left(6 \, g^{3} \log\left(e\right)^{2} + g^{3} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left({\left(3 \, g^{3} \log\left(e\right) + g^{3}\right)} b^{4} c^{2} d^{2} - 2 \, {\left(6 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{3} c d^{3} + {\left(18 \, g^{3} \log\left(e\right)^{2} + 9 \, g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - {\left({\left(6 \, g^{3} \log\left(e\right) + 5 \, g^{3}\right)} b^{4} c^{3} d - {\left(24 \, g^{3} \log\left(e\right) + 17 \, g^{3}\right)} a b^{3} c^{2} d^{2} + {\left(36 \, g^{3} \log\left(e\right) + 19 \, g^{3}\right)} a^{2} b^{2} c d^{3} - {\left(12 \, g^{3} \log\left(e\right)^{2} + 18 \, g^{3} \log\left(e\right) + 7 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x + B^{2} a^{4} d^{4} g^{3}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x - {\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} - 4 \, a^{3} b c d^{3} g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) - 2 \, {\left(b^{4} c d^{3} g^{3} - {\left(12 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 4 \, a b^{3} c d^{3} g^{3} + 3 \, {\left(4 \, g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 6 \, {\left(b^{4} c^{3} d g^{3} - 4 \, a b^{3} c^{2} d^{2} g^{3} + 6 \, a^{2} b^{2} c d^{3} g^{3} - {\left(4 \, g^{3} \log\left(e\right) + 3 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x - {\left(6 \, a b^{3} c^{3} d g^{3} - 21 \, a^{2} b^{2} c^{2} d^{2} g^{3} + 26 \, a^{3} b c d^{3} g^{3} - {\left(6 \, g^{3} \log\left(e\right) + 11 \, g^{3}\right)} a^{4} d^{4}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) - 2 \, {\left(b^{4} c d^{3} g^{3} - {\left(12 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 4 \, a b^{3} c d^{3} g^{3} + 3 \, {\left(4 \, g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 6 \, {\left(b^{4} c^{3} d g^{3} - 4 \, a b^{3} c^{2} d^{2} g^{3} + 6 \, a^{2} b^{2} c d^{3} g^{3} - {\left(4 \, g^{3} \log\left(e\right) + 3 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x + B^{2} a^{4} d^{4} g^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b d^{4}}"," ",0,"1/4*A^2*b^3*g^3*x^4 + A^2*a*b^2*g^3*x^3 + 3/2*A^2*a^2*b*g^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*g^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*g^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*g^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*g^3 + A^2*a^3*g^3*x + 1/12*((6*g^3*log(e) + 11*g^3)*b^3*c^4 - 2*(12*g^3*log(e) + 19*g^3)*a*b^2*c^3*d + 9*(4*g^3*log(e) + 5*g^3)*a^2*b*c^2*d^2 - 6*(4*g^3*log(e) + 3*g^3)*a^3*c*d^3)*B^2*log(d*x + c)/d^4 + 1/2*(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 - 4*a^3*b*c*d^3*g^3 + a^4*d^4*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^2/(b*d^4) + 1/12*(3*B^2*b^4*d^4*g^3*x^4*log(e)^2 - 2*(b^4*c*d^3*g^3*log(e) - (6*g^3*log(e)^2 + g^3*log(e))*a*b^3*d^4)*B^2*x^3 + ((3*g^3*log(e) + g^3)*b^4*c^2*d^2 - 2*(6*g^3*log(e) + g^3)*a*b^3*c*d^3 + (18*g^3*log(e)^2 + 9*g^3*log(e) + g^3)*a^2*b^2*d^4)*B^2*x^2 - ((6*g^3*log(e) + 5*g^3)*b^4*c^3*d - (24*g^3*log(e) + 17*g^3)*a*b^3*c^2*d^2 + (36*g^3*log(e) + 19*g^3)*a^2*b^2*c*d^3 - (12*g^3*log(e)^2 + 18*g^3*log(e) + 7*g^3)*a^3*b*d^4)*B^2*x + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x + B^2*a^4*d^4*g^3)*log(b*x + a)^2 + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x - (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 - 4*a^3*b*c*d^3*g^3)*B^2)*log(d*x + c)^2 + (6*B^2*b^4*d^4*g^3*x^4*log(e) - 2*(b^4*c*d^3*g^3 - (12*g^3*log(e) + g^3)*a*b^3*d^4)*B^2*x^3 + 3*(b^4*c^2*d^2*g^3 - 4*a*b^3*c*d^3*g^3 + 3*(4*g^3*log(e) + g^3)*a^2*b^2*d^4)*B^2*x^2 - 6*(b^4*c^3*d*g^3 - 4*a*b^3*c^2*d^2*g^3 + 6*a^2*b^2*c*d^3*g^3 - (4*g^3*log(e) + 3*g^3)*a^3*b*d^4)*B^2*x - (6*a*b^3*c^3*d*g^3 - 21*a^2*b^2*c^2*d^2*g^3 + 26*a^3*b*c*d^3*g^3 - (6*g^3*log(e) + 11*g^3)*a^4*d^4)*B^2)*log(b*x + a) - (6*B^2*b^4*d^4*g^3*x^4*log(e) - 2*(b^4*c*d^3*g^3 - (12*g^3*log(e) + g^3)*a*b^3*d^4)*B^2*x^3 + 3*(b^4*c^2*d^2*g^3 - 4*a*b^3*c*d^3*g^3 + 3*(4*g^3*log(e) + g^3)*a^2*b^2*d^4)*B^2*x^2 - 6*(b^4*c^3*d*g^3 - 4*a*b^3*c^2*d^2*g^3 + 6*a^2*b^2*c*d^3*g^3 - (4*g^3*log(e) + 3*g^3)*a^3*b*d^4)*B^2*x + 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x + B^2*a^4*d^4*g^3)*log(b*x + a))*log(d*x + c))/(b*d^4)","B",0
99,1,1165,0,2.332635," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A^{2} b^{2} g^{2} x^{3} + A^{2} a b g^{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} g^{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 g^{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} g^{2} + A^{2} a^{2} g^{2} x - \frac{{\left({\left(2 \, g^{2} \log\left(e\right) + 3 \, g^{2}\right)} b^{2} c^{3} - {\left(6 \, g^{2} \log\left(e\right) + 7 \, g^{2}\right)} a b c^{2} d + 2 \, {\left(3 \, g^{2} \log\left(e\right) + 2 \, g^{2}\right)} a^{2} c d^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, d^{3}} - \frac{2 \, {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 3 \, a^{2} b c d^{2} g^{2} - a^{3} d^{3} 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^{2}}{3 \, b d^{3}} + \frac{B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right)^{2} - {\left(b^{3} c d^{2} g^{2} \log\left(e\right) - {\left(3 \, g^{2} \log\left(e\right)^{2} + g^{2} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + {\left({\left(2 \, g^{2} \log\left(e\right) + g^{2}\right)} b^{3} c^{2} d - 2 \, {\left(3 \, g^{2} \log\left(e\right) + g^{2}\right)} a b^{2} c d^{2} + {\left(3 \, g^{2} \log\left(e\right)^{2} + 4 \, g^{2} \log\left(e\right) + g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + B^{2} a^{3} d^{3} g^{2}\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 3 \, a^{2} b c d^{2} g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) - {\left(b^{3} c d^{2} g^{2} - {\left(6 \, g^{2} \log\left(e\right) + g^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{2} d g^{2} - 3 \, a b^{2} c d^{2} g^{2} + {\left(3 \, g^{2} \log\left(e\right) + 2 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + {\left(2 \, a b^{2} c^{2} d g^{2} - 5 \, a^{2} b c d^{2} g^{2} + {\left(2 \, g^{2} \log\left(e\right) + 3 \, g^{2}\right)} a^{3} d^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) - {\left(b^{3} c d^{2} g^{2} - {\left(6 \, g^{2} \log\left(e\right) + g^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{2} d g^{2} - 3 \, a b^{2} c d^{2} g^{2} + {\left(3 \, g^{2} \log\left(e\right) + 2 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + B^{2} a^{3} d^{3} g^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, b d^{3}}"," ",0,"1/3*A^2*b^2*g^2*x^3 + A^2*a*b*g^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*g^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*g^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*g^2 + A^2*a^2*g^2*x - 1/3*((2*g^2*log(e) + 3*g^2)*b^2*c^3 - (6*g^2*log(e) + 7*g^2)*a*b*c^2*d + 2*(3*g^2*log(e) + 2*g^2)*a^2*c*d^2)*B^2*log(d*x + c)/d^3 - 2/3*(b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 3*a^2*b*c*d^2*g^2 - a^3*d^3*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^2/(b*d^3) + 1/3*(B^2*b^3*d^3*g^2*x^3*log(e)^2 - (b^3*c*d^2*g^2*log(e) - (3*g^2*log(e)^2 + g^2*log(e))*a*b^2*d^3)*B^2*x^2 + ((2*g^2*log(e) + g^2)*b^3*c^2*d - 2*(3*g^2*log(e) + g^2)*a*b^2*c*d^2 + (3*g^2*log(e)^2 + 4*g^2*log(e) + g^2)*a^2*b*d^3)*B^2*x + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + B^2*a^3*d^3*g^2)*log(b*x + a)^2 + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + (b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 3*a^2*b*c*d^2*g^2)*B^2)*log(d*x + c)^2 + (2*B^2*b^3*d^3*g^2*x^3*log(e) - (b^3*c*d^2*g^2 - (6*g^2*log(e) + g^2)*a*b^2*d^3)*B^2*x^2 + 2*(b^3*c^2*d*g^2 - 3*a*b^2*c*d^2*g^2 + (3*g^2*log(e) + 2*g^2)*a^2*b*d^3)*B^2*x + (2*a*b^2*c^2*d*g^2 - 5*a^2*b*c*d^2*g^2 + (2*g^2*log(e) + 3*g^2)*a^3*d^3)*B^2)*log(b*x + a) - (2*B^2*b^3*d^3*g^2*x^3*log(e) - (b^3*c*d^2*g^2 - (6*g^2*log(e) + g^2)*a*b^2*d^3)*B^2*x^2 + 2*(b^3*c^2*d*g^2 - 3*a*b^2*c*d^2*g^2 + (3*g^2*log(e) + 2*g^2)*a^2*b*d^3)*B^2*x + 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + B^2*a^3*d^3*g^2)*log(b*x + a))*log(d*x + c))/(b*d^3)","B",0
100,1,611,0,2.210245," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A^{2} b g 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 g + {\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 g + A^{2} a g x + \frac{{\left({\left(g \log\left(e\right) + g\right)} b c^{2} - {\left(2 \, g \log\left(e\right) + g\right)} a c d\right)} B^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b^{2} c^{2} g - 2 \, a b c d g + a^{2} d^{2} 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^{2}}{b d^{2}} + \frac{B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} - 2 \, {\left(b^{2} c d g \log\left(e\right) - {\left(g \log\left(e\right)^{2} + g \log\left(e\right)\right)} a b d^{2}\right)} B^{2} x + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x + B^{2} a^{2} d^{2} g\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x - {\left(b^{2} c^{2} g - 2 \, a b c d g\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + {\left({\left(2 \, g \log\left(e\right) + g\right)} a b d^{2} - b^{2} c d g\right)} B^{2} x + {\left({\left(g \log\left(e\right) + g\right)} a^{2} d^{2} - a b c d g\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + {\left({\left(2 \, g \log\left(e\right) + g\right)} a b d^{2} - b^{2} c d g\right)} B^{2} x + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x + B^{2} a^{2} d^{2} g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b d^{2}}"," ",0,"1/2*A^2*b*g*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*g + (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*g + A^2*a*g*x + ((g*log(e) + g)*b*c^2 - (2*g*log(e) + g)*a*c*d)*B^2*log(d*x + c)/d^2 + (b^2*c^2*g - 2*a*b*c*d*g + a^2*d^2*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^2/(b*d^2) + 1/2*(B^2*b^2*d^2*g*x^2*log(e)^2 - 2*(b^2*c*d*g*log(e) - (g*log(e)^2 + g*log(e))*a*b*d^2)*B^2*x + (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x + B^2*a^2*d^2*g)*log(b*x + a)^2 + (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x - (b^2*c^2*g - 2*a*b*c*d*g)*B^2)*log(d*x + c)^2 + 2*(B^2*b^2*d^2*g*x^2*log(e) + ((2*g*log(e) + g)*a*b*d^2 - b^2*c*d*g)*B^2*x + ((g*log(e) + g)*a^2*d^2 - a*b*c*d*g)*B^2)*log(b*x + a) - 2*(B^2*b^2*d^2*g*x^2*log(e) + ((2*g*log(e) + g)*a*b*d^2 - b^2*c*d*g)*B^2*x + (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x + B^2*a^2*d^2*g)*log(b*x + a))*log(d*x + c))/(b*d^2)","B",0
101,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g),x, algorithm=""maxima"")","\frac{B^{2} \log\left(b x + a\right) \log\left(d x + c\right)^{2}}{b g} + \frac{A^{2} \log\left(b g x + a g\right)}{b g} - \int -\frac{B^{2} b c \log\left(e\right)^{2} + 2 \, A B b c \log\left(e\right) + {\left(B^{2} b d x + B^{2} b c\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b d \log\left(e\right)^{2} + 2 \, A B b d \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x + {\left(2 \, B^{2} b d x + {\left(b c + a d\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}"," ",0,"B^2*log(b*x + a)*log(d*x + c)^2/(b*g) + A^2*log(b*g*x + a*g)/(b*g) - integrate(-(B^2*b*c*log(e)^2 + 2*A*B*b*c*log(e) + (B^2*b*d*x + B^2*b*c)*log(b*x + a)^2 + (B^2*b*d*log(e)^2 + 2*A*B*b*d*log(e))*x + 2*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x)*log(b*x + a) - 2*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x + (2*B^2*b*d*x + (b*c + a*d)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)","F",0
102,1,416,0,1.404832," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-{\left(2 \, {\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)} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right) - \frac{{\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)}{a b^{2} c g^{2} - a^{2} b d g^{2} + {\left(b^{3} c g^{2} - a b^{2} d g^{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)}{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{B^{2} \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)^{2}}{b^{2} g^{2} x + a b g^{2}} - \frac{A^{2}}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-(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))*log(b*e*x/(d*x + c) + a*e/(d*x + c)) - ((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^2*c*g^2 - a^2*b*d*g^2 + (b^3*c*g^2 - a*b^2*d*g^2)*x))*B^2 - 2*A*B*(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)) - B^2*log(b*e*x/(d*x + c) + a*e/(d*x + c))^2/(b^2*g^2*x + a*b*g^2) - A^2/(b^2*g^2*x + a*b*g^2)","B",0
103,1,848,0,1.814635," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","\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} + \frac{1}{2} \, A B {\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} \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{A^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"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 + 1/2*A*B*((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*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*A^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
104,1,1419,0,2.452253," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\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} - \frac{1}{9} \, 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^{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} \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{A^{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,"-1/54*(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 - 1/9*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^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*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*A^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
105,1,2123,0,3.409827," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\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} + \frac{1}{24} \, A B {\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} \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{A^{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,"1/288*(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 + 1/24*A*B*((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*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*A^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
106,1,158,0,1.170617," ","integrate(log(d*(b*x+a)/b/(d*x+c))/(d*f*x+c*f),x, algorithm=""maxima"")","-\frac{b {\left(\frac{\log\left(d x + c\right)^{2}}{b f} - \frac{2 \, {\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 f}\right)}}{2 \, d} - \frac{b {\left(\frac{d \log\left(b x + a\right)}{b} - \frac{d \log\left(d x + c\right)}{b}\right)} \log\left(d f x + c f\right)}{d^{2} f} + \frac{\log\left(d f x + c f\right) \log\left(\frac{{\left(b x + a\right)} d}{{\left(d x + c\right)} b}\right)}{d f}"," ",0,"-1/2*b*(log(d*x + c)^2/(b*f) - 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*f))/d - b*(d*log(b*x + a)/b - d*log(d*x + c)/b)*log(d*f*x + c*f)/(d^2*f) + log(d*f*x + c*f)*log((b*x + a)*d/((d*x + c)*b))/(d*f)","B",0
107,1,61,0,1.210746," ","integrate(log(1+1/(b*x+a))/(b*x+a),x, algorithm=""maxima"")","\frac{2 \, \log\left(b x + a + 1\right) \log\left(b x + a\right) - \log\left(b x + a\right)^{2}}{2 \, b} - \frac{\log\left(b x + a + 1\right) \log\left(b x + a\right) + {\rm Li}_2\left(-b x - a\right)}{b}"," ",0,"1/2*(2*log(b*x + a + 1)*log(b*x + a) - log(b*x + a)^2)/b - (log(b*x + a + 1)*log(b*x + a) + dilog(-b*x - a))/b","B",0
108,1,59,0,1.303696," ","integrate(log(1-1/(b*x+a))/(b*x+a),x, algorithm=""maxima"")","-\frac{\log\left(b x + a\right)^{2} - 2 \, \log\left(b x + a\right) \log\left(b x + a - 1\right)}{2 \, b} - \frac{\log\left(b x + a\right) \log\left(-b x - a + 1\right) + {\rm Li}_2\left(b x + a\right)}{b}"," ",0,"-1/2*(log(b*x + a)^2 - 2*log(b*x + a)*log(b*x + a - 1))/b - (log(b*x + a)*log(-b*x - a + 1) + dilog(b*x + a))/b","B",0
109,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{{\left(b g x + a g\right)}^{2}}{B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)^2/(B*log((b*x + a)*e/(d*x + c)) + A), x)","F",0
110,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{b g x + a g}{B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)/(B*log((b*x + a)*e/(d*x + c)) + A), x)","F",0
111,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)} {\left(B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)*(B*log((b*x + a)*e/(d*x + c)) + A)), x)","F",0
112,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{2} {\left(B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^2*(B*log((b*x + a)*e/(d*x + c)) + A)), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{3} {\left(B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^3*(B*log((b*x + a)*e/(d*x + c)) + A)), x)","F",0
114,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{b^{3} d g^{2} x^{4} + a^{3} c g^{2} + {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{3} + 3 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x^{2} + {\left(3 \, a^{2} b c g^{2} + a^{3} d g^{2}\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}} + \int \frac{4 \, b^{3} d g^{2} x^{3} + 3 \, a^{2} b c g^{2} + a^{3} d g^{2} + 3 \, {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{2} + 6 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}}\,{d x}"," ",0,"-(b^3*d*g^2*x^4 + a^3*c*g^2 + (b^3*c*g^2 + 3*a*b^2*d*g^2)*x^3 + 3*(a*b^2*c*g^2 + a^2*b*d*g^2)*x^2 + (3*a^2*b*c*g^2 + a^3*d*g^2)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate((4*b^3*d*g^2*x^3 + 3*a^2*b*c*g^2 + a^3*d*g^2 + 3*(b^3*c*g^2 + 3*a*b^2*d*g^2)*x^2 + 6*(a*b^2*c*g^2 + a^2*b*d*g^2)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
115,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{b^{2} d g x^{3} + a^{2} c g + {\left(b^{2} c g + 2 \, a b d g\right)} x^{2} + {\left(2 \, a b c g + a^{2} d g\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}} + \int \frac{3 \, b^{2} d g x^{2} + 2 \, a b c g + a^{2} d g + 2 \, {\left(b^{2} c g + 2 \, a b d g\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}}\,{d x}"," ",0,"-(b^2*d*g*x^3 + a^2*c*g + (b^2*c*g + 2*a*b*d*g)*x^2 + (2*a*b*c*g + a^2*d*g)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate((3*b^2*d*g*x^2 + 2*a*b*c*g + a^2*d*g + 2*(b^2*c*g + 2*a*b*d*g)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
116,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","d \int \frac{1}{{\left(b c g - a d g\right)} B^{2} \log\left(b x + a\right) - {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right) + {\left(b c g - a d g\right)} A B + {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}}\,{d x} - \frac{d x + c}{{\left(b c g - a d g\right)} B^{2} \log\left(b x + a\right) - {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right) + {\left(b c g - a d g\right)} A B + {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}}"," ",0,"d*integrate(1/((b*c*g - a*d*g)*B^2*log(b*x + a) - (b*c*g - a*d*g)*B^2*log(d*x + c) + (b*c*g - a*d*g)*A*B + (b*c*g*log(e) - a*d*g*log(e))*B^2), x) - (d*x + c)/((b*c*g - a*d*g)*B^2*log(b*x + a) - (b*c*g - a*d*g)*B^2*log(d*x + c) + (b*c*g - a*d*g)*A*B + (b*c*g*log(e) - a*d*g*log(e))*B^2)","F",0
117,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{d x + c}{{\left(a b c g^{2} - a^{2} d g^{2}\right)} A B + {\left(a b c g^{2} \log\left(e\right) - a^{2} d g^{2} \log\left(e\right)\right)} B^{2} + {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} A B + {\left(b^{2} c g^{2} \log\left(e\right) - a b d g^{2} \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} B^{2} x + {\left(a b c g^{2} - a^{2} d g^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} B^{2} x + {\left(a b c g^{2} - a^{2} d g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)} + \int -\frac{1}{B^{2} a^{2} g^{2} \log\left(e\right) + A B a^{2} g^{2} + {\left(B^{2} b^{2} g^{2} \log\left(e\right) + A B b^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} a b g^{2} \log\left(e\right) + A B a b g^{2}\right)} x + {\left(B^{2} b^{2} g^{2} x^{2} + 2 \, B^{2} a b g^{2} x + B^{2} a^{2} g^{2}\right)} \log\left(b x + a\right) - {\left(B^{2} b^{2} g^{2} x^{2} + 2 \, B^{2} a b g^{2} x + B^{2} a^{2} g^{2}\right)} \log\left(d x + c\right)}\,{d x}"," ",0,"-(d*x + c)/((a*b*c*g^2 - a^2*d*g^2)*A*B + (a*b*c*g^2*log(e) - a^2*d*g^2*log(e))*B^2 + ((b^2*c*g^2 - a*b*d*g^2)*A*B + (b^2*c*g^2*log(e) - a*b*d*g^2*log(e))*B^2)*x + ((b^2*c*g^2 - a*b*d*g^2)*B^2*x + (a*b*c*g^2 - a^2*d*g^2)*B^2)*log(b*x + a) - ((b^2*c*g^2 - a*b*d*g^2)*B^2*x + (a*b*c*g^2 - a^2*d*g^2)*B^2)*log(d*x + c)) + integrate(-1/(B^2*a^2*g^2*log(e) + A*B*a^2*g^2 + (B^2*b^2*g^2*log(e) + A*B*b^2*g^2)*x^2 + 2*(B^2*a*b*g^2*log(e) + A*B*a*b*g^2)*x + (B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(b*x + a) - (B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(d*x + c)), x)","F",0
118,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{d x + c}{{\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} A B + {\left(a^{2} b c g^{3} \log\left(e\right) - a^{3} d g^{3} \log\left(e\right)\right)} B^{2} + {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} A B + {\left(b^{3} c g^{3} \log\left(e\right) - a b^{2} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} A B + {\left(a b^{2} c g^{3} \log\left(e\right) - a^{2} b d g^{3} \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} B^{2} x + {\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} B^{2} x + {\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)} - \int \frac{b d x + 2 \, b c - a d}{{\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} A B + {\left(b^{4} c g^{3} \log\left(e\right) - a b^{3} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} A B + {\left(a^{3} b c g^{3} \log\left(e\right) - a^{4} d g^{3} \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} A B + {\left(a b^{3} c g^{3} \log\left(e\right) - a^{2} b^{2} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} A B + {\left(a^{2} b^{2} c g^{3} \log\left(e\right) - a^{3} b d g^{3} \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} B^{2} x + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} B^{2} x + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)}\,{d x}"," ",0,"-(d*x + c)/((a^2*b*c*g^3 - a^3*d*g^3)*A*B + (a^2*b*c*g^3*log(e) - a^3*d*g^3*log(e))*B^2 + ((b^3*c*g^3 - a*b^2*d*g^3)*A*B + (b^3*c*g^3*log(e) - a*b^2*d*g^3*log(e))*B^2)*x^2 + 2*((a*b^2*c*g^3 - a^2*b*d*g^3)*A*B + (a*b^2*c*g^3*log(e) - a^2*b*d*g^3*log(e))*B^2)*x + ((b^3*c*g^3 - a*b^2*d*g^3)*B^2*x^2 + 2*(a*b^2*c*g^3 - a^2*b*d*g^3)*B^2*x + (a^2*b*c*g^3 - a^3*d*g^3)*B^2)*log(b*x + a) - ((b^3*c*g^3 - a*b^2*d*g^3)*B^2*x^2 + 2*(a*b^2*c*g^3 - a^2*b*d*g^3)*B^2*x + (a^2*b*c*g^3 - a^3*d*g^3)*B^2)*log(d*x + c)) - integrate((b*d*x + 2*b*c - a*d)/(((b^4*c*g^3 - a*b^3*d*g^3)*A*B + (b^4*c*g^3*log(e) - a*b^3*d*g^3*log(e))*B^2)*x^3 + (a^3*b*c*g^3 - a^4*d*g^3)*A*B + (a^3*b*c*g^3*log(e) - a^4*d*g^3*log(e))*B^2 + 3*((a*b^3*c*g^3 - a^2*b^2*d*g^3)*A*B + (a*b^3*c*g^3*log(e) - a^2*b^2*d*g^3*log(e))*B^2)*x^2 + 3*((a^2*b^2*c*g^3 - a^3*b*d*g^3)*A*B + (a^2*b^2*c*g^3*log(e) - a^3*b*d*g^3*log(e))*B^2)*x + ((b^4*c*g^3 - a*b^3*d*g^3)*B^2*x^3 + 3*(a*b^3*c*g^3 - a^2*b^2*d*g^3)*B^2*x^2 + 3*(a^2*b^2*c*g^3 - a^3*b*d*g^3)*B^2*x + (a^3*b*c*g^3 - a^4*d*g^3)*B^2)*log(b*x + a) - ((b^4*c*g^3 - a*b^3*d*g^3)*B^2*x^3 + 3*(a*b^3*c*g^3 - a^2*b^2*d*g^3)*B^2*x^2 + 3*(a^2*b^2*c*g^3 - a^3*b*d*g^3)*B^2*x + (a^3*b*c*g^3 - a^4*d*g^3)*B^2)*log(d*x + c)), x)","F",0
119,1,885,0,1.444647," ","integrate((b*g*x+a*g)^4*(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\frac{1}{5} \, A b^{4} g^{4} x^{5} + A a b^{3} g^{4} x^{4} + 2 \, A a^{2} b^{2} g^{4} x^{3} + 2 \, A a^{3} b g^{4} x^{2} + {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B a^{4} g^{4} + 2 \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B a^{3} b g^{4} + 2 \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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^{2} g^{4} + \frac{1}{3} \, {\left(3 \, x^{4} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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^{3} g^{4} + \frac{1}{30} \, {\left(6 \, x^{5} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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^{4} g^{4} + A a^{4} g^{4} x"," ",0,"1/5*A*b^4*g^4*x^5 + A*a*b^3*g^4*x^4 + 2*A*a^2*b^2*g^4*x^3 + 2*A*a^3*b*g^4*x^2 + (x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*B*a^4*g^4 + 2*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*B*a^3*b*g^4 + 2*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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^2*g^4 + 1/3*(3*x^4*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 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^3*g^4 + 1/30*(6*x^5*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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^4*g^4 + A*a^4*g^4*x","B",0
120,1,647,0,1.601748," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\frac{1}{4} \, A b^{3} g^{3} x^{4} + A a b^{2} g^{3} x^{3} + \frac{3}{2} \, A a^{2} b g^{3} x^{2} + {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B a^{3} g^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B a^{2} b g^{3} + {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} g^{3} + \frac{1}{12} \, {\left(3 \, x^{4} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} g^{3} + A a^{3} g^{3} x"," ",0,"1/4*A*b^3*g^3*x^4 + A*a*b^2*g^3*x^3 + 3/2*A*a^2*b*g^3*x^2 + (x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*B*a^3*g^3 + 3/2*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*B*a^2*b*g^3 + (x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*g^3 + 1/12*(3*x^4*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 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*g^3 + A*a^3*g^3*x","B",0
121,1,437,0,1.414269," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\frac{1}{3} \, A b^{2} g^{2} x^{3} + A a b g^{2} x^{2} + {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B a^{2} g^{2} + {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B a b g^{2} + \frac{1}{3} \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} g^{2} + A a^{2} g^{2} x"," ",0,"1/3*A*b^2*g^2*x^3 + A*a*b*g^2*x^2 + (x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*B*a^2*g^2 + (x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*B*a*b*g^2 + 1/3*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*g^2 + A*a^2*g^2*x","B",0
122,1,250,0,1.323904," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\frac{1}{2} \, A b g x^{2} + {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B a g + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B b g + A a g x"," ",0,"1/2*A*b*g*x^2 + (x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*B*a*g + 1/2*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*B*b*g + A*a*g*x","B",0
123,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(b*g*x+a*g),x, algorithm=""maxima"")","-B {\left(\frac{2 \, \log\left(b x + a\right) \log\left(d x + c\right)}{b g} - \int \frac{b d x \log\left(e\right) + b c \log\left(e\right) + 2 \, {\left(2 \, b d x + b c + a d\right)} \log\left(b x + a\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}\right)} + \frac{A \log\left(b g x + a g\right)}{b g}"," ",0,"-B*(2*log(b*x + a)*log(d*x + c)/(b*g) - integrate((b*d*x*log(e) + b*c*log(e) + 2*(2*b*d*x + b*c + a*d)*log(b*x + a))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)) + A*log(b*g*x + a*g)/(b*g)","F",0
124,1,187,0,1.222343," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B {\left(\frac{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{b^{2} g^{2} x + a b g^{2}} + \frac{2}{b^{2} g^{2} x + a b g^{2}} + \frac{2 \, d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{2 \, d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{A}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-B*(log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(b^2*g^2*x + a*b*g^2) + 2/(b^2*g^2*x + a*b*g^2) + 2*d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - 2*d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A/(b^2*g^2*x + a*b*g^2)","B",0
125,1,307,0,1.236890," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","\frac{1}{2} \, B {\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{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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{A}{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*((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) - log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(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*A/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
126,1,480,0,1.387405," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{1}{9} \, 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^{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{3 \, \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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{A}{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*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^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) + 3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*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) + 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*A/(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
127,1,699,0,1.618433," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\frac{1}{24} \, B {\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{6 \, \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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{A}{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*B*((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) - 6*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*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) + 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*A/(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
128,1,2650,0,3.088304," ","integrate((b*g*x+a*g)^4*(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","\frac{1}{5} \, A^{2} b^{4} g^{4} x^{5} + A^{2} a b^{3} g^{4} x^{4} + 2 \, A^{2} a^{2} b^{2} g^{4} x^{3} + 2 \, A^{2} a^{3} b g^{4} x^{2} + 2 \, {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B a^{4} g^{4} + 4 \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B a^{3} b g^{4} + 4 \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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^{2} g^{4} + \frac{2}{3} \, {\left(3 \, x^{4} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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^{3} g^{4} + \frac{1}{15} \, {\left(6 \, x^{5} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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^{4} g^{4} + A^{2} a^{4} g^{4} x - \frac{2 \, {\left({\left(6 \, g^{4} \log\left(e\right) + 25 \, g^{4}\right)} b^{4} c^{5} - {\left(30 \, g^{4} \log\left(e\right) + 113 \, g^{4}\right)} a b^{3} c^{4} d + 4 \, {\left(15 \, g^{4} \log\left(e\right) + 49 \, g^{4}\right)} a^{2} b^{2} c^{3} d^{2} - 12 \, {\left(5 \, g^{4} \log\left(e\right) + 13 \, g^{4}\right)} a^{3} b c^{2} d^{3} + 6 \, {\left(5 \, g^{4} \log\left(e\right) + 8 \, g^{4}\right)} a^{4} c d^{4}\right)} B^{2} \log\left(d x + c\right)}{15 \, d^{5}} - \frac{8 \, {\left(b^{5} c^{5} g^{4} - 5 \, a b^{4} c^{4} d g^{4} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} + 5 \, a^{4} b c d^{4} g^{4} - a^{5} d^{5} g^{4}\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}}{5 \, b d^{5}} + \frac{3 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right)^{2} - 3 \, {\left(b^{5} c d^{4} g^{4} \log\left(e\right) - {\left(5 \, g^{4} \log\left(e\right)^{2} + g^{4} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 2 \, {\left({\left(2 \, g^{4} \log\left(e\right) + g^{4}\right)} b^{5} c^{2} d^{3} - 2 \, {\left(5 \, g^{4} \log\left(e\right) + g^{4}\right)} a b^{4} c d^{4} + {\left(15 \, g^{4} \log\left(e\right)^{2} + 8 \, g^{4} \log\left(e\right) + g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - {\left({\left(6 \, g^{4} \log\left(e\right) + 7 \, g^{4}\right)} b^{5} c^{3} d^{2} - 3 \, {\left(10 \, g^{4} \log\left(e\right) + 9 \, g^{4}\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(20 \, g^{4} \log\left(e\right) + 11 \, g^{4}\right)} a^{2} b^{3} c d^{4} - {\left(30 \, g^{4} \log\left(e\right)^{2} + 36 \, g^{4} \log\left(e\right) + 13 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + {\left(2 \, {\left(6 \, g^{4} \log\left(e\right) + 13 \, g^{4}\right)} b^{5} c^{4} d - 2 \, {\left(30 \, g^{4} \log\left(e\right) + 59 \, g^{4}\right)} a b^{4} c^{3} d^{2} + 12 \, {\left(10 \, g^{4} \log\left(e\right) + 17 \, g^{4}\right)} a^{2} b^{3} c^{2} d^{3} - 2 \, {\left(60 \, g^{4} \log\left(e\right) + 79 \, g^{4}\right)} a^{3} b^{2} c d^{4} + {\left(15 \, g^{4} \log\left(e\right)^{2} + 48 \, g^{4} \log\left(e\right) + 46 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + B^{2} a^{5} d^{5} g^{4}\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + {\left(b^{5} c^{5} g^{4} - 5 \, a b^{4} c^{4} d g^{4} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} + 5 \, a^{4} b c d^{4} g^{4}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) - 3 \, {\left(b^{5} c d^{4} g^{4} - {\left(10 \, g^{4} \log\left(e\right) + g^{4}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 4 \, {\left(b^{5} c^{2} d^{3} g^{4} - 5 \, a b^{4} c d^{4} g^{4} + {\left(15 \, g^{4} \log\left(e\right) + 4 \, g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - 6 \, {\left(b^{5} c^{3} d^{2} g^{4} - 5 \, a b^{4} c^{2} d^{3} g^{4} + 10 \, a^{2} b^{3} c d^{4} g^{4} - 2 \, {\left(5 \, g^{4} \log\left(e\right) + 3 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 6 \, {\left(2 \, b^{5} c^{4} d g^{4} - 10 \, a b^{4} c^{3} d^{2} g^{4} + 20 \, a^{2} b^{3} c^{2} d^{3} g^{4} - 20 \, a^{3} b^{2} c d^{4} g^{4} + {\left(5 \, g^{4} \log\left(e\right) + 8 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x + {\left(12 \, a b^{4} c^{4} d g^{4} - 54 \, a^{2} b^{3} c^{3} d^{2} g^{4} + 94 \, a^{3} b^{2} c^{2} d^{3} g^{4} - 77 \, a^{4} b c d^{4} g^{4} + {\left(6 \, g^{4} \log\left(e\right) + 25 \, g^{4}\right)} a^{5} d^{5}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) - 3 \, {\left(b^{5} c d^{4} g^{4} - {\left(10 \, g^{4} \log\left(e\right) + g^{4}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} + 4 \, {\left(b^{5} c^{2} d^{3} g^{4} - 5 \, a b^{4} c d^{4} g^{4} + {\left(15 \, g^{4} \log\left(e\right) + 4 \, g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} - 6 \, {\left(b^{5} c^{3} d^{2} g^{4} - 5 \, a b^{4} c^{2} d^{3} g^{4} + 10 \, a^{2} b^{3} c d^{4} g^{4} - 2 \, {\left(5 \, g^{4} \log\left(e\right) + 3 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} + 6 \, {\left(2 \, b^{5} c^{4} d g^{4} - 10 \, a b^{4} c^{3} d^{2} g^{4} + 20 \, a^{2} b^{3} c^{2} d^{3} g^{4} - 20 \, a^{3} b^{2} c d^{4} g^{4} + {\left(5 \, g^{4} \log\left(e\right) + 8 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + B^{2} a^{5} d^{5} g^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{15 \, b d^{5}}"," ",0,"1/5*A^2*b^4*g^4*x^5 + A^2*a*b^3*g^4*x^4 + 2*A^2*a^2*b^2*g^4*x^3 + 2*A^2*a^3*b*g^4*x^2 + 2*(x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*A*B*a^4*g^4 + 4*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*A*B*a^3*b*g^4 + 4*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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^2*g^4 + 2/3*(3*x^4*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 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^3*g^4 + 1/15*(6*x^5*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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^4*g^4 + A^2*a^4*g^4*x - 2/15*((6*g^4*log(e) + 25*g^4)*b^4*c^5 - (30*g^4*log(e) + 113*g^4)*a*b^3*c^4*d + 4*(15*g^4*log(e) + 49*g^4)*a^2*b^2*c^3*d^2 - 12*(5*g^4*log(e) + 13*g^4)*a^3*b*c^2*d^3 + 6*(5*g^4*log(e) + 8*g^4)*a^4*c*d^4)*B^2*log(d*x + c)/d^5 - 8/5*(b^5*c^5*g^4 - 5*a*b^4*c^4*d*g^4 + 10*a^2*b^3*c^3*d^2*g^4 - 10*a^3*b^2*c^2*d^3*g^4 + 5*a^4*b*c*d^4*g^4 - a^5*d^5*g^4)*(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*d^5) + 1/15*(3*B^2*b^5*d^5*g^4*x^5*log(e)^2 - 3*(b^5*c*d^4*g^4*log(e) - (5*g^4*log(e)^2 + g^4*log(e))*a*b^4*d^5)*B^2*x^4 + 2*((2*g^4*log(e) + g^4)*b^5*c^2*d^3 - 2*(5*g^4*log(e) + g^4)*a*b^4*c*d^4 + (15*g^4*log(e)^2 + 8*g^4*log(e) + g^4)*a^2*b^3*d^5)*B^2*x^3 - ((6*g^4*log(e) + 7*g^4)*b^5*c^3*d^2 - 3*(10*g^4*log(e) + 9*g^4)*a*b^4*c^2*d^3 + 3*(20*g^4*log(e) + 11*g^4)*a^2*b^3*c*d^4 - (30*g^4*log(e)^2 + 36*g^4*log(e) + 13*g^4)*a^3*b^2*d^5)*B^2*x^2 + (2*(6*g^4*log(e) + 13*g^4)*b^5*c^4*d - 2*(30*g^4*log(e) + 59*g^4)*a*b^4*c^3*d^2 + 12*(10*g^4*log(e) + 17*g^4)*a^2*b^3*c^2*d^3 - 2*(60*g^4*log(e) + 79*g^4)*a^3*b^2*c*d^4 + (15*g^4*log(e)^2 + 48*g^4*log(e) + 46*g^4)*a^4*b*d^5)*B^2*x + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + B^2*a^5*d^5*g^4)*log(b*x + a)^2 + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + (b^5*c^5*g^4 - 5*a*b^4*c^4*d*g^4 + 10*a^2*b^3*c^3*d^2*g^4 - 10*a^3*b^2*c^2*d^3*g^4 + 5*a^4*b*c*d^4*g^4)*B^2)*log(d*x + c)^2 + 2*(6*B^2*b^5*d^5*g^4*x^5*log(e) - 3*(b^5*c*d^4*g^4 - (10*g^4*log(e) + g^4)*a*b^4*d^5)*B^2*x^4 + 4*(b^5*c^2*d^3*g^4 - 5*a*b^4*c*d^4*g^4 + (15*g^4*log(e) + 4*g^4)*a^2*b^3*d^5)*B^2*x^3 - 6*(b^5*c^3*d^2*g^4 - 5*a*b^4*c^2*d^3*g^4 + 10*a^2*b^3*c*d^4*g^4 - 2*(5*g^4*log(e) + 3*g^4)*a^3*b^2*d^5)*B^2*x^2 + 6*(2*b^5*c^4*d*g^4 - 10*a*b^4*c^3*d^2*g^4 + 20*a^2*b^3*c^2*d^3*g^4 - 20*a^3*b^2*c*d^4*g^4 + (5*g^4*log(e) + 8*g^4)*a^4*b*d^5)*B^2*x + (12*a*b^4*c^4*d*g^4 - 54*a^2*b^3*c^3*d^2*g^4 + 94*a^3*b^2*c^2*d^3*g^4 - 77*a^4*b*c*d^4*g^4 + (6*g^4*log(e) + 25*g^4)*a^5*d^5)*B^2)*log(b*x + a) - 2*(6*B^2*b^5*d^5*g^4*x^5*log(e) - 3*(b^5*c*d^4*g^4 - (10*g^4*log(e) + g^4)*a*b^4*d^5)*B^2*x^4 + 4*(b^5*c^2*d^3*g^4 - 5*a*b^4*c*d^4*g^4 + (15*g^4*log(e) + 4*g^4)*a^2*b^3*d^5)*B^2*x^3 - 6*(b^5*c^3*d^2*g^4 - 5*a*b^4*c^2*d^3*g^4 + 10*a^2*b^3*c*d^4*g^4 - 2*(5*g^4*log(e) + 3*g^4)*a^3*b^2*d^5)*B^2*x^2 + 6*(2*b^5*c^4*d*g^4 - 10*a*b^4*c^3*d^2*g^4 + 20*a^2*b^3*c^2*d^3*g^4 - 20*a^3*b^2*c*d^4*g^4 + (5*g^4*log(e) + 8*g^4)*a^4*b*d^5)*B^2*x + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + B^2*a^5*d^5*g^4)*log(b*x + a))*log(d*x + c))/(b*d^5)","B",0
129,1,1948,0,2.984422," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} b^{3} g^{3} x^{4} + A^{2} a b^{2} g^{3} x^{3} + \frac{3}{2} \, A^{2} a^{2} b g^{3} x^{2} + 2 \, {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B a^{3} g^{3} + 3 \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B a^{2} b g^{3} + 2 \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} g^{3} + \frac{1}{6} \, {\left(3 \, x^{4} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} g^{3} + A^{2} a^{3} g^{3} x + \frac{{\left({\left(3 \, g^{3} \log\left(e\right) + 11 \, g^{3}\right)} b^{3} c^{4} - 2 \, {\left(6 \, g^{3} \log\left(e\right) + 19 \, g^{3}\right)} a b^{2} c^{3} d + 9 \, {\left(2 \, g^{3} \log\left(e\right) + 5 \, g^{3}\right)} a^{2} b c^{2} d^{2} - 6 \, {\left(2 \, g^{3} \log\left(e\right) + 3 \, g^{3}\right)} a^{3} c d^{3}\right)} B^{2} \log\left(d x + c\right)}{3 \, d^{4}} + \frac{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} - 4 \, a^{3} b c d^{3} g^{3} + a^{4} d^{4} 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^{2}}{b d^{4}} + \frac{3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right)^{2} - 4 \, {\left(b^{4} c d^{3} g^{3} \log\left(e\right) - {\left(3 \, g^{3} \log\left(e\right)^{2} + g^{3} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + 2 \, {\left({\left(3 \, g^{3} \log\left(e\right) + 2 \, g^{3}\right)} b^{4} c^{2} d^{2} - 4 \, {\left(3 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{3} c d^{3} + {\left(9 \, g^{3} \log\left(e\right)^{2} + 9 \, g^{3} \log\left(e\right) + 2 \, g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 4 \, {\left({\left(3 \, g^{3} \log\left(e\right) + 5 \, g^{3}\right)} b^{4} c^{3} d - {\left(12 \, g^{3} \log\left(e\right) + 17 \, g^{3}\right)} a b^{3} c^{2} d^{2} + {\left(18 \, g^{3} \log\left(e\right) + 19 \, g^{3}\right)} a^{2} b^{2} c d^{3} - {\left(3 \, g^{3} \log\left(e\right)^{2} + 9 \, g^{3} \log\left(e\right) + 7 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + 12 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x + B^{2} a^{4} d^{4} g^{3}\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x - {\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} - 4 \, a^{3} b c d^{3} g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) - 2 \, {\left(b^{4} c d^{3} g^{3} - {\left(6 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 4 \, a b^{3} c d^{3} g^{3} + 3 \, {\left(2 \, g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 6 \, {\left(b^{4} c^{3} d g^{3} - 4 \, a b^{3} c^{2} d^{2} g^{3} + 6 \, a^{2} b^{2} c d^{3} g^{3} - {\left(2 \, g^{3} \log\left(e\right) + 3 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x - {\left(6 \, a b^{3} c^{3} d g^{3} - 21 \, a^{2} b^{2} c^{2} d^{2} g^{3} + 26 \, a^{3} b c d^{3} g^{3} - {\left(3 \, g^{3} \log\left(e\right) + 11 \, g^{3}\right)} a^{4} d^{4}\right)} B^{2}\right)} \log\left(b x + a\right) - 4 \, {\left(3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) - 2 \, {\left(b^{4} c d^{3} g^{3} - {\left(6 \, g^{3} \log\left(e\right) + g^{3}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 4 \, a b^{3} c d^{3} g^{3} + 3 \, {\left(2 \, g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 6 \, {\left(b^{4} c^{3} d g^{3} - 4 \, a b^{3} c^{2} d^{2} g^{3} + 6 \, a^{2} b^{2} c d^{3} g^{3} - {\left(2 \, g^{3} \log\left(e\right) + 3 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x + B^{2} a^{4} d^{4} g^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b d^{4}}"," ",0,"1/4*A^2*b^3*g^3*x^4 + A^2*a*b^2*g^3*x^3 + 3/2*A^2*a^2*b*g^3*x^2 + 2*(x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*A*B*a^3*g^3 + 3*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*A*B*a^2*b*g^3 + 2*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*g^3 + 1/6*(3*x^4*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 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*g^3 + A^2*a^3*g^3*x + 1/3*((3*g^3*log(e) + 11*g^3)*b^3*c^4 - 2*(6*g^3*log(e) + 19*g^3)*a*b^2*c^3*d + 9*(2*g^3*log(e) + 5*g^3)*a^2*b*c^2*d^2 - 6*(2*g^3*log(e) + 3*g^3)*a^3*c*d^3)*B^2*log(d*x + c)/d^4 + 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 - 4*a^3*b*c*d^3*g^3 + a^4*d^4*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^2/(b*d^4) + 1/12*(3*B^2*b^4*d^4*g^3*x^4*log(e)^2 - 4*(b^4*c*d^3*g^3*log(e) - (3*g^3*log(e)^2 + g^3*log(e))*a*b^3*d^4)*B^2*x^3 + 2*((3*g^3*log(e) + 2*g^3)*b^4*c^2*d^2 - 4*(3*g^3*log(e) + g^3)*a*b^3*c*d^3 + (9*g^3*log(e)^2 + 9*g^3*log(e) + 2*g^3)*a^2*b^2*d^4)*B^2*x^2 - 4*((3*g^3*log(e) + 5*g^3)*b^4*c^3*d - (12*g^3*log(e) + 17*g^3)*a*b^3*c^2*d^2 + (18*g^3*log(e) + 19*g^3)*a^2*b^2*c*d^3 - (3*g^3*log(e)^2 + 9*g^3*log(e) + 7*g^3)*a^3*b*d^4)*B^2*x + 12*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x + B^2*a^4*d^4*g^3)*log(b*x + a)^2 + 12*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x - (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 - 4*a^3*b*c*d^3*g^3)*B^2)*log(d*x + c)^2 + 4*(3*B^2*b^4*d^4*g^3*x^4*log(e) - 2*(b^4*c*d^3*g^3 - (6*g^3*log(e) + g^3)*a*b^3*d^4)*B^2*x^3 + 3*(b^4*c^2*d^2*g^3 - 4*a*b^3*c*d^3*g^3 + 3*(2*g^3*log(e) + g^3)*a^2*b^2*d^4)*B^2*x^2 - 6*(b^4*c^3*d*g^3 - 4*a*b^3*c^2*d^2*g^3 + 6*a^2*b^2*c*d^3*g^3 - (2*g^3*log(e) + 3*g^3)*a^3*b*d^4)*B^2*x - (6*a*b^3*c^3*d*g^3 - 21*a^2*b^2*c^2*d^2*g^3 + 26*a^3*b*c*d^3*g^3 - (3*g^3*log(e) + 11*g^3)*a^4*d^4)*B^2)*log(b*x + a) - 4*(3*B^2*b^4*d^4*g^3*x^4*log(e) - 2*(b^4*c*d^3*g^3 - (6*g^3*log(e) + g^3)*a*b^3*d^4)*B^2*x^3 + 3*(b^4*c^2*d^2*g^3 - 4*a*b^3*c*d^3*g^3 + 3*(2*g^3*log(e) + g^3)*a^2*b^2*d^4)*B^2*x^2 - 6*(b^4*c^3*d*g^3 - 4*a*b^3*c^2*d^2*g^3 + 6*a^2*b^2*c*d^3*g^3 - (2*g^3*log(e) + 3*g^3)*a^3*b*d^4)*B^2*x + 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x + B^2*a^4*d^4*g^3)*log(b*x + a))*log(d*x + c))/(b*d^4)","B",0
130,1,1326,0,2.633638," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A^{2} b^{2} g^{2} x^{3} + A^{2} a b g^{2} x^{2} + 2 \, {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B a^{2} g^{2} + 2 \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B a b g^{2} + \frac{2}{3} \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} g^{2} + A^{2} a^{2} g^{2} x - \frac{4 \, {\left({\left(g^{2} \log\left(e\right) + 3 \, g^{2}\right)} b^{2} c^{3} - {\left(3 \, g^{2} \log\left(e\right) + 7 \, g^{2}\right)} a b c^{2} d + {\left(3 \, g^{2} \log\left(e\right) + 4 \, g^{2}\right)} a^{2} c d^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, d^{3}} - \frac{8 \, {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 3 \, a^{2} b c d^{2} g^{2} - a^{3} d^{3} 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^{2}}{3 \, b d^{3}} + \frac{B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right)^{2} - {\left(2 \, b^{3} c d^{2} g^{2} \log\left(e\right) - {\left(3 \, g^{2} \log\left(e\right)^{2} + 2 \, g^{2} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + {\left(4 \, {\left(g^{2} \log\left(e\right) + g^{2}\right)} b^{3} c^{2} d - 4 \, {\left(3 \, g^{2} \log\left(e\right) + 2 \, g^{2}\right)} a b^{2} c d^{2} + {\left(3 \, g^{2} \log\left(e\right)^{2} + 8 \, g^{2} \log\left(e\right) + 4 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + B^{2} a^{3} d^{3} g^{2}\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 3 \, a^{2} b c d^{2} g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) - {\left(b^{3} c d^{2} g^{2} - {\left(3 \, g^{2} \log\left(e\right) + g^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + {\left(2 \, b^{3} c^{2} d g^{2} - 6 \, a b^{2} c d^{2} g^{2} + {\left(3 \, g^{2} \log\left(e\right) + 4 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + {\left(2 \, a b^{2} c^{2} d g^{2} - 5 \, a^{2} b c d^{2} g^{2} + {\left(g^{2} \log\left(e\right) + 3 \, g^{2}\right)} a^{3} d^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) - {\left(b^{3} c d^{2} g^{2} - {\left(3 \, g^{2} \log\left(e\right) + g^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + {\left(2 \, b^{3} c^{2} d g^{2} - 6 \, a b^{2} c d^{2} g^{2} + {\left(3 \, g^{2} \log\left(e\right) + 4 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + B^{2} a^{3} d^{3} g^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, b d^{3}}"," ",0,"1/3*A^2*b^2*g^2*x^3 + A^2*a*b*g^2*x^2 + 2*(x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*A*B*a^2*g^2 + 2*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*A*B*a*b*g^2 + 2/3*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*g^2 + A^2*a^2*g^2*x - 4/3*((g^2*log(e) + 3*g^2)*b^2*c^3 - (3*g^2*log(e) + 7*g^2)*a*b*c^2*d + (3*g^2*log(e) + 4*g^2)*a^2*c*d^2)*B^2*log(d*x + c)/d^3 - 8/3*(b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 3*a^2*b*c*d^2*g^2 - a^3*d^3*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^2/(b*d^3) + 1/3*(B^2*b^3*d^3*g^2*x^3*log(e)^2 - (2*b^3*c*d^2*g^2*log(e) - (3*g^2*log(e)^2 + 2*g^2*log(e))*a*b^2*d^3)*B^2*x^2 + (4*(g^2*log(e) + g^2)*b^3*c^2*d - 4*(3*g^2*log(e) + 2*g^2)*a*b^2*c*d^2 + (3*g^2*log(e)^2 + 8*g^2*log(e) + 4*g^2)*a^2*b*d^3)*B^2*x + 4*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + B^2*a^3*d^3*g^2)*log(b*x + a)^2 + 4*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + (b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 3*a^2*b*c*d^2*g^2)*B^2)*log(d*x + c)^2 + 4*(B^2*b^3*d^3*g^2*x^3*log(e) - (b^3*c*d^2*g^2 - (3*g^2*log(e) + g^2)*a*b^2*d^3)*B^2*x^2 + (2*b^3*c^2*d*g^2 - 6*a*b^2*c*d^2*g^2 + (3*g^2*log(e) + 4*g^2)*a^2*b*d^3)*B^2*x + (2*a*b^2*c^2*d*g^2 - 5*a^2*b*c*d^2*g^2 + (g^2*log(e) + 3*g^2)*a^3*d^3)*B^2)*log(b*x + a) - 4*(B^2*b^3*d^3*g^2*x^3*log(e) - (b^3*c*d^2*g^2 - (3*g^2*log(e) + g^2)*a*b^2*d^3)*B^2*x^2 + (2*b^3*c^2*d*g^2 - 6*a*b^2*c*d^2*g^2 + (3*g^2*log(e) + 4*g^2)*a^2*b*d^3)*B^2*x + 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + B^2*a^3*d^3*g^2)*log(b*x + a))*log(d*x + c))/(b*d^3)","B",0
131,1,727,0,2.419954," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A^{2} b g x^{2} + 2 \, {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B a g + {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B b g + A^{2} a g x + \frac{2 \, {\left({\left(g \log\left(e\right) + 2 \, g\right)} b c^{2} - 2 \, {\left(g \log\left(e\right) + g\right)} a c d\right)} B^{2} \log\left(d x + c\right)}{d^{2}} + \frac{4 \, {\left(b^{2} c^{2} g - 2 \, a b c d g + a^{2} d^{2} 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^{2}}{b d^{2}} + \frac{B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} - 2 \, {\left(2 \, b^{2} c d g \log\left(e\right) - {\left(g \log\left(e\right)^{2} + 2 \, g \log\left(e\right)\right)} a b d^{2}\right)} B^{2} x + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x + B^{2} a^{2} d^{2} g\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x - {\left(b^{2} c^{2} g - 2 \, a b c d g\right)} B^{2}\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + 2 \, {\left({\left(g \log\left(e\right) + g\right)} a b d^{2} - b^{2} c d g\right)} B^{2} x + {\left({\left(g \log\left(e\right) + 2 \, g\right)} a^{2} d^{2} - 2 \, a b c d g\right)} B^{2}\right)} \log\left(b x + a\right) - 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + 2 \, {\left({\left(g \log\left(e\right) + g\right)} a b d^{2} - b^{2} c d g\right)} B^{2} x + 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x + B^{2} a^{2} d^{2} g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b d^{2}}"," ",0,"1/2*A^2*b*g*x^2 + 2*(x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*A*B*a*g + (x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*A*B*b*g + A^2*a*g*x + 2*((g*log(e) + 2*g)*b*c^2 - 2*(g*log(e) + g)*a*c*d)*B^2*log(d*x + c)/d^2 + 4*(b^2*c^2*g - 2*a*b*c*d*g + a^2*d^2*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^2/(b*d^2) + 1/2*(B^2*b^2*d^2*g*x^2*log(e)^2 - 2*(2*b^2*c*d*g*log(e) - (g*log(e)^2 + 2*g*log(e))*a*b*d^2)*B^2*x + 4*(B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x + B^2*a^2*d^2*g)*log(b*x + a)^2 + 4*(B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x - (b^2*c^2*g - 2*a*b*c*d*g)*B^2)*log(d*x + c)^2 + 4*(B^2*b^2*d^2*g*x^2*log(e) + 2*((g*log(e) + g)*a*b*d^2 - b^2*c*d*g)*B^2*x + ((g*log(e) + 2*g)*a^2*d^2 - 2*a*b*c*d*g)*B^2)*log(b*x + a) - 4*(B^2*b^2*d^2*g*x^2*log(e) + 2*((g*log(e) + g)*a*b*d^2 - b^2*c*d*g)*B^2*x + 2*(B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x + B^2*a^2*d^2*g)*log(b*x + a))*log(d*x + c))/(b*d^2)","B",0
132,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(b*g*x+a*g),x, algorithm=""maxima"")","\frac{4 \, B^{2} \log\left(b x + a\right) \log\left(d x + c\right)^{2}}{b g} + \frac{A^{2} \log\left(b g x + a g\right)}{b g} - \int -\frac{B^{2} b c \log\left(e\right)^{2} + 2 \, A B b c \log\left(e\right) + 4 \, {\left(B^{2} b d x + B^{2} b c\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b d \log\left(e\right)^{2} + 2 \, A B b d \log\left(e\right)\right)} x + 4 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x\right)} \log\left(b x + a\right) - 4 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x + 2 \, {\left(2 \, B^{2} b d x + {\left(b c + a d\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}"," ",0,"4*B^2*log(b*x + a)*log(d*x + c)^2/(b*g) + A^2*log(b*g*x + a*g)/(b*g) - integrate(-(B^2*b*c*log(e)^2 + 2*A*B*b*c*log(e) + 4*(B^2*b*d*x + B^2*b*c)*log(b*x + a)^2 + (B^2*b*d*log(e)^2 + 2*A*B*b*d*log(e))*x + 4*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x)*log(b*x + a) - 4*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x + 2*(2*B^2*b*d*x + (b*c + a*d)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)","F",0
133,1,574,0,1.594731," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-4 \, {\left({\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)} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{{\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)}{a b^{2} c g^{2} - a^{2} b d g^{2} + {\left(b^{3} c g^{2} - a b^{2} d g^{2}\right)} x}\right)} B^{2} - 2 \, A B {\left(\frac{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{b^{2} g^{2} x + a b g^{2}} + \frac{2}{b^{2} g^{2} x + a b g^{2}} + \frac{2 \, d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} - \frac{2 \, d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{B^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}}{b^{2} g^{2} x + a b g^{2}} - \frac{A^{2}}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-4*((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))*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^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^2*c*g^2 - a^2*b*d*g^2 + (b^3*c*g^2 - a*b^2*d*g^2)*x))*B^2 - 2*A*B*(log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(b^2*g^2*x + a*b*g^2) + 2/(b^2*g^2*x + a*b*g^2) + 2*d*log(b*x + a)/((b^2*c - a*b*d)*g^2) - 2*d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - B^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))^2/(b^2*g^2*x + a*b*g^2) - A^2/(b^2*g^2*x + a*b*g^2)","B",0
134,1,1001,0,1.937302," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","{\left({\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^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} + A B {\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{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{A^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"(((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^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^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^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 + A*B*((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) - log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(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*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
135,1,1575,0,2.667584," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","-\frac{2}{27} \, {\left(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 \, 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^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} - \frac{2}{9} \, 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^{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{3 \, \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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{A^{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,"-2/27*(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*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^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + (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 - 2/9*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^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) + 3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*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) + 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*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))^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*A^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
136,1,2279,0,3.443412," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","\frac{1}{72} \, {\left(6 \, {\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^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} + \frac{1}{12} \, A B {\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{6 \, \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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{A^{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,"1/72*(6*((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^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - (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 + 1/12*A*B*((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) - 6*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*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) + 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*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))^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*A^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
137,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{{\left(b g x + a g\right)}^{2}}{B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)^2/(B*log((b*x + a)^2*e/(d*x + c)^2) + A), x)","F",0
138,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{b g x + a g}{B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)/(B*log((b*x + a)^2*e/(d*x + c)^2) + A), x)","F",0
139,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)} {\left(B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)*(B*log((b*x + a)^2*e/(d*x + c)^2) + A)), x)","F",0
140,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{2} {\left(B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^2*(B*log((b*x + a)^2*e/(d*x + c)^2) + A)), x)","F",0
141,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{3} {\left(B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^3*(B*log((b*x + a)^2*e/(d*x + c)^2) + A)), x)","F",0
142,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{b^{3} d g^{2} x^{4} + a^{3} c g^{2} + {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{3} + 3 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x^{2} + {\left(3 \, a^{2} b c g^{2} + a^{3} d g^{2}\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}} + \int \frac{4 \, b^{3} d g^{2} x^{3} + 3 \, a^{2} b c g^{2} + a^{3} d g^{2} + 3 \, {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{2} + 6 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}}\,{d x}"," ",0,"-1/2*(b^3*d*g^2*x^4 + a^3*c*g^2 + (b^3*c*g^2 + 3*a*b^2*d*g^2)*x^3 + 3*(a*b^2*c*g^2 + a^2*b*d*g^2)*x^2 + (3*a^2*b*c*g^2 + a^3*d*g^2)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate(1/2*(4*b^3*d*g^2*x^3 + 3*a^2*b*c*g^2 + a^3*d*g^2 + 3*(b^3*c*g^2 + 3*a*b^2*d*g^2)*x^2 + 6*(a*b^2*c*g^2 + a^2*b*d*g^2)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
143,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{b^{2} d g x^{3} + a^{2} c g + {\left(b^{2} c g + 2 \, a b d g\right)} x^{2} + {\left(2 \, a b c g + a^{2} d g\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}} + \int \frac{3 \, b^{2} d g x^{2} + 2 \, a b c g + a^{2} d g + 2 \, {\left(b^{2} c g + 2 \, a b d g\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}}\,{d x}"," ",0,"-1/2*(b^2*d*g*x^3 + a^2*c*g + (b^2*c*g + 2*a*b*d*g)*x^2 + (2*a*b*c*g + a^2*d*g)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate(1/2*(3*b^2*d*g*x^2 + 2*a*b*c*g + a^2*d*g + 2*(b^2*c*g + 2*a*b*d*g)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
144,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","d \int \frac{1}{2 \, {\left(2 \, {\left(b c g - a d g\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right) + {\left(b c g - a d g\right)} A B + {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}\right)}}\,{d x} - \frac{d x + c}{2 \, {\left(2 \, {\left(b c g - a d g\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right) + {\left(b c g - a d g\right)} A B + {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}\right)}}"," ",0,"d*integrate(1/2/(2*(b*c*g - a*d*g)*B^2*log(b*x + a) - 2*(b*c*g - a*d*g)*B^2*log(d*x + c) + (b*c*g - a*d*g)*A*B + (b*c*g*log(e) - a*d*g*log(e))*B^2), x) - 1/2*(d*x + c)/(2*(b*c*g - a*d*g)*B^2*log(b*x + a) - 2*(b*c*g - a*d*g)*B^2*log(d*x + c) + (b*c*g - a*d*g)*A*B + (b*c*g*log(e) - a*d*g*log(e))*B^2)","F",0
145,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{d x + c}{2 \, {\left({\left(a b c g^{2} - a^{2} d g^{2}\right)} A B + {\left(a b c g^{2} \log\left(e\right) - a^{2} d g^{2} \log\left(e\right)\right)} B^{2} + {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} A B + {\left(b^{2} c g^{2} \log\left(e\right) - a b d g^{2} \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} B^{2} x + {\left(a b c g^{2} - a^{2} d g^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} B^{2} x + {\left(a b c g^{2} - a^{2} d g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}} + \int -\frac{1}{2 \, {\left(B^{2} a^{2} g^{2} \log\left(e\right) + A B a^{2} g^{2} + {\left(B^{2} b^{2} g^{2} \log\left(e\right) + A B b^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} a b g^{2} \log\left(e\right) + A B a b g^{2}\right)} x + 2 \, {\left(B^{2} b^{2} g^{2} x^{2} + 2 \, B^{2} a b g^{2} x + B^{2} a^{2} g^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} b^{2} g^{2} x^{2} + 2 \, B^{2} a b g^{2} x + B^{2} a^{2} g^{2}\right)} \log\left(d x + c\right)\right)}}\,{d x}"," ",0,"-1/2*(d*x + c)/((a*b*c*g^2 - a^2*d*g^2)*A*B + (a*b*c*g^2*log(e) - a^2*d*g^2*log(e))*B^2 + ((b^2*c*g^2 - a*b*d*g^2)*A*B + (b^2*c*g^2*log(e) - a*b*d*g^2*log(e))*B^2)*x + 2*((b^2*c*g^2 - a*b*d*g^2)*B^2*x + (a*b*c*g^2 - a^2*d*g^2)*B^2)*log(b*x + a) - 2*((b^2*c*g^2 - a*b*d*g^2)*B^2*x + (a*b*c*g^2 - a^2*d*g^2)*B^2)*log(d*x + c)) + integrate(-1/2/(B^2*a^2*g^2*log(e) + A*B*a^2*g^2 + (B^2*b^2*g^2*log(e) + A*B*b^2*g^2)*x^2 + 2*(B^2*a*b*g^2*log(e) + A*B*a*b*g^2)*x + 2*(B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(b*x + a) - 2*(B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(d*x + c)), x)","F",0
146,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{d x + c}{2 \, {\left({\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} A B + {\left(a^{2} b c g^{3} \log\left(e\right) - a^{3} d g^{3} \log\left(e\right)\right)} B^{2} + {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} A B + {\left(b^{3} c g^{3} \log\left(e\right) - a b^{2} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} A B + {\left(a b^{2} c g^{3} \log\left(e\right) - a^{2} b d g^{3} \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} B^{2} x + {\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} B^{2} x + {\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}} - \int \frac{b d x + 2 \, b c - a d}{2 \, {\left({\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} A B + {\left(b^{4} c g^{3} \log\left(e\right) - a b^{3} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} A B + {\left(a^{3} b c g^{3} \log\left(e\right) - a^{4} d g^{3} \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} A B + {\left(a b^{3} c g^{3} \log\left(e\right) - a^{2} b^{2} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} A B + {\left(a^{2} b^{2} c g^{3} \log\left(e\right) - a^{3} b d g^{3} \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} B^{2} x + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} B^{2} x + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}}\,{d x}"," ",0,"-1/2*(d*x + c)/((a^2*b*c*g^3 - a^3*d*g^3)*A*B + (a^2*b*c*g^3*log(e) - a^3*d*g^3*log(e))*B^2 + ((b^3*c*g^3 - a*b^2*d*g^3)*A*B + (b^3*c*g^3*log(e) - a*b^2*d*g^3*log(e))*B^2)*x^2 + 2*((a*b^2*c*g^3 - a^2*b*d*g^3)*A*B + (a*b^2*c*g^3*log(e) - a^2*b*d*g^3*log(e))*B^2)*x + 2*((b^3*c*g^3 - a*b^2*d*g^3)*B^2*x^2 + 2*(a*b^2*c*g^3 - a^2*b*d*g^3)*B^2*x + (a^2*b*c*g^3 - a^3*d*g^3)*B^2)*log(b*x + a) - 2*((b^3*c*g^3 - a*b^2*d*g^3)*B^2*x^2 + 2*(a*b^2*c*g^3 - a^2*b*d*g^3)*B^2*x + (a^2*b*c*g^3 - a^3*d*g^3)*B^2)*log(d*x + c)) - integrate(1/2*(b*d*x + 2*b*c - a*d)/(((b^4*c*g^3 - a*b^3*d*g^3)*A*B + (b^4*c*g^3*log(e) - a*b^3*d*g^3*log(e))*B^2)*x^3 + (a^3*b*c*g^3 - a^4*d*g^3)*A*B + (a^3*b*c*g^3*log(e) - a^4*d*g^3*log(e))*B^2 + 3*((a*b^3*c*g^3 - a^2*b^2*d*g^3)*A*B + (a*b^3*c*g^3*log(e) - a^2*b^2*d*g^3*log(e))*B^2)*x^2 + 3*((a^2*b^2*c*g^3 - a^3*b*d*g^3)*A*B + (a^2*b^2*c*g^3*log(e) - a^3*b*d*g^3*log(e))*B^2)*x + 2*((b^4*c*g^3 - a*b^3*d*g^3)*B^2*x^3 + 3*(a*b^3*c*g^3 - a^2*b^2*d*g^3)*B^2*x^2 + 3*(a^2*b^2*c*g^3 - a^3*b*d*g^3)*B^2*x + (a^3*b*c*g^3 - a^4*d*g^3)*B^2)*log(b*x + a) - 2*((b^4*c*g^3 - a*b^3*d*g^3)*B^2*x^3 + 3*(a*b^3*c*g^3 - a^2*b^2*d*g^3)*B^2*x^2 + 3*(a^2*b^2*c*g^3 - a^3*b*d*g^3)*B^2*x + (a^3*b*c*g^3 - a^4*d*g^3)*B^2)*log(d*x + c)), x)","F",0
147,1,671,0,1.468257," ","integrate((b*x+a)^4*(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{1}{5} \, B b^{4} x^{5} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{5} \, A b^{4} x^{5} + B a b^{3} x^{4} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A a b^{3} x^{4} + 2 \, B a^{2} b^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + 2 \, A a^{2} b^{2} x^{3} + 2 \, B a^{3} b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + 2 \, A a^{3} b x^{2} + B a^{4} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A a^{4} x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B a^{4}}{e} - \frac{2 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} B a^{3} b}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} B a^{2} b^{2}}{e} - \frac{{\left(\frac{6 \, a^{4} e n \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} e n \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} e n - a b^{2} d^{3} e n\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d e n - a^{2} b d^{3} e n\right)} x^{2} + 6 \, {\left(b^{3} c^{3} e n - a^{3} d^{3} e n\right)} x}{b^{3} d^{3}}\right)} B a b^{3}}{6 \, e} + \frac{{\left(\frac{12 \, a^{5} e n \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} e n \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} e n - a b^{3} d^{4} e n\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} e n - a^{2} b^{2} d^{4} e n\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d e n - a^{3} b d^{4} e n\right)} x^{2} - 12 \, {\left(b^{4} c^{4} e n - a^{4} d^{4} e n\right)} x}{b^{4} d^{4}}\right)} B b^{4}}{60 \, e}"," ",0,"1/5*B*b^4*x^5*log((b*x + a)^n*e/(d*x + c)^n) + 1/5*A*b^4*x^5 + B*a*b^3*x^4*log((b*x + a)^n*e/(d*x + c)^n) + A*a*b^3*x^4 + 2*B*a^2*b^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + 2*A*a^2*b^2*x^3 + 2*B*a^3*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 2*A*a^3*b*x^2 + B*a^4*x*log((b*x + a)^n*e/(d*x + c)^n) + A*a^4*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B*a^4/e - 2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*B*a^3*b/e + (2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*B*a^2*b^2/e - 1/6*(6*a^4*e*n*log(b*x + a)/b^4 - 6*c^4*e*n*log(d*x + c)/d^4 + (2*(b^3*c*d^2*e*n - a*b^2*d^3*e*n)*x^3 - 3*(b^3*c^2*d*e*n - a^2*b*d^3*e*n)*x^2 + 6*(b^3*c^3*e*n - a^3*d^3*e*n)*x)/(b^3*d^3))*B*a*b^3/e + 1/60*(12*a^5*e*n*log(b*x + a)/b^5 - 12*c^5*e*n*log(d*x + c)/d^5 - (3*(b^4*c*d^3*e*n - a*b^3*d^4*e*n)*x^4 - 4*(b^4*c^2*d^2*e*n - a^2*b^2*d^4*e*n)*x^3 + 6*(b^4*c^3*d*e*n - a^3*b*d^4*e*n)*x^2 - 12*(b^4*c^4*e*n - a^4*d^4*e*n)*x)/(b^4*d^4))*B*b^4/e","B",0
148,1,467,0,1.402198," ","integrate((b*x+a)^3*(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{1}{4} \, B b^{3} x^{4} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{4} \, A b^{3} x^{4} + B a b^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A a b^{2} x^{3} + \frac{3}{2} \, B a^{2} b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{3}{2} \, A a^{2} b x^{2} + B a^{3} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A a^{3} x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B a^{3}}{e} - \frac{3 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} B a^{2} b}{2 \, e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} B a b^{2}}{2 \, e} - \frac{{\left(\frac{6 \, a^{4} e n \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} e n \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} e n - a b^{2} d^{3} e n\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d e n - a^{2} b d^{3} e n\right)} x^{2} + 6 \, {\left(b^{3} c^{3} e n - a^{3} d^{3} e n\right)} x}{b^{3} d^{3}}\right)} B b^{3}}{24 \, e}"," ",0,"1/4*B*b^3*x^4*log((b*x + a)^n*e/(d*x + c)^n) + 1/4*A*b^3*x^4 + B*a*b^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + A*a*b^2*x^3 + 3/2*B*a^2*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 3/2*A*a^2*b*x^2 + B*a^3*x*log((b*x + a)^n*e/(d*x + c)^n) + A*a^3*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B*a^3/e - 3/2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*B*a^2*b/e + 1/2*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*B*a*b^2/e - 1/24*(6*a^4*e*n*log(b*x + a)/b^4 - 6*c^4*e*n*log(d*x + c)/d^4 + (2*(b^3*c*d^2*e*n - a*b^2*d^3*e*n)*x^3 - 3*(b^3*c^2*d*e*n - a^2*b*d^3*e*n)*x^2 + 6*(b^3*c^3*e*n - a^3*d^3*e*n)*x)/(b^3*d^3))*B*b^3/e","B",0
149,1,294,0,1.268242," ","integrate((b*x+a)^2*(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{1}{3} \, B b^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{3} \, A b^{2} x^{3} + B a b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A a b x^{2} + B a^{2} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A a^{2} x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B a^{2}}{e} - \frac{{\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} B a b}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} B b^{2}}{6 \, e}"," ",0,"1/3*B*b^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + 1/3*A*b^2*x^3 + B*a*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + A*a*b*x^2 + B*a^2*x*log((b*x + a)^n*e/(d*x + c)^n) + A*a^2*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B*a^2/e - (a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*B*a*b/e + 1/6*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*B*b^2/e","B",0
150,1,154,0,1.232729," ","integrate((b*x+a)*(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{1}{2} \, B b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{2} \, A b x^{2} + B a x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A a x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B a}{e} - \frac{{\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} B b}{2 \, e}"," ",0,"1/2*B*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 1/2*A*b*x^2 + B*a*x*log((b*x + a)^n*e/(d*x + c)^n) + A*a*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B*a/e - 1/2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*B*b/e","A",0
151,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(b*x+a),x, algorithm=""maxima"")","B {\left(\frac{\log\left(b x + a\right) \log\left({\left(b x + a\right)}^{n}\right) - \log\left(b x + a\right) \log\left({\left(d x + c\right)}^{n}\right)}{b} + \int \frac{b d x \log\left(e\right) + b c \log\left(e\right) - {\left(b c n - a d n\right)} \log\left(b x + a\right)}{b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x}\,{d x}\right)} + \frac{A \log\left(b x + a\right)}{b}"," ",0,"B*((log(b*x + a)*log((b*x + a)^n) - log(b*x + a)*log((d*x + c)^n))/b + integrate((b*d*x*log(e) + b*c*log(e) - (b*c*n - a*d*n)*log(b*x + a))/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x), x)) + A*log(b*x + a)/b","F",0
152,1,116,0,1.195071," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{d e n \log\left(b x + a\right)}{b^{2} c - a b d} - \frac{d e n \log\left(d x + c\right)}{b^{2} c - a b d} + \frac{e n}{b^{2} x + a b}\right)} B}{e} - \frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{b^{2} x + a b} - \frac{A}{b^{2} x + a b}"," ",0,"-(d*e*n*log(b*x + a)/(b^2*c - a*b*d) - d*e*n*log(d*x + c)/(b^2*c - a*b*d) + e*n/(b^2*x + a*b))*B/e - B*log((b*x + a)^n*e/(d*x + c)^n)/(b^2*x + a*b) - A/(b^2*x + a*b)","A",0
153,1,230,0,1.375918," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, d^{2} e n \log\left(b x + a\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} - \frac{2 \, d^{2} e n \log\left(d x + c\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} + \frac{2 \, b d e n x - b c e n + 3 \, a d e n}{a^{2} b^{2} c - a^{3} b d + {\left(b^{4} c - a b^{3} d\right)} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x}\right)} B}{4 \, e} - \frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}} - \frac{A}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"1/4*(2*d^2*e*n*log(b*x + a)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - 2*d^2*e*n*log(d*x + c)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) + (2*b*d*e*n*x - b*c*e*n + 3*a*d*e*n)/(a^2*b^2*c - a^3*b*d + (b^4*c - a*b^3*d)*x^2 + 2*(a*b^3*c - a^2*b^2*d)*x))*B/e - 1/2*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^3*x^2 + 2*a*b^2*x + a^2*b) - 1/2*A/(b^3*x^2 + 2*a*b^2*x + a^2*b)","A",0
154,1,400,0,1.289464," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(b*x+a)^4,x, algorithm=""maxima"")","-\frac{{\left(\frac{6 \, d^{3} e n \log\left(b x + a\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{6 \, d^{3} e n \log\left(d x + c\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} + \frac{6 \, b^{2} d^{2} e n x^{2} + 2 \, b^{2} c^{2} e n - 7 \, a b c d e n + 11 \, a^{2} d^{2} e n - 3 \, {\left(b^{2} c d e n - 5 \, a b d^{2} e n\right)} x}{a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2} + {\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} x}\right)} B}{18 \, e} - \frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}} - \frac{A}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"-1/18*(6*d^3*e*n*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) - 6*d^3*e*n*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) + (6*b^2*d^2*e*n*x^2 + 2*b^2*c^2*e*n - 7*a*b*c*d*e*n + 11*a^2*d^2*e*n - 3*(b^2*c*d*e*n - 5*a*b*d^2*e*n)*x)/(a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2 + (b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*x))*B/e - 1/3*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b) - 1/3*A/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)","B",0
155,1,618,0,1.380858," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(b*x+a)^5,x, algorithm=""maxima"")","\frac{{\left(\frac{12 \, d^{4} e n \log\left(b x + a\right)}{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}} - \frac{12 \, d^{4} e n \log\left(d x + c\right)}{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}} + \frac{12 \, b^{3} d^{3} e n x^{3} - 3 \, b^{3} c^{3} e n + 13 \, a b^{2} c^{2} d e n - 23 \, a^{2} b c d^{2} e n + 25 \, a^{3} d^{3} e n - 6 \, {\left(b^{3} c d^{2} e n - 7 \, a b^{2} d^{3} e n\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d e n - 5 \, a b^{2} c d^{2} e n + 13 \, a^{2} b d^{3} e n\right)} 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} + {\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)} 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)} 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)} 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)} x}\right)} B}{48 \, e} - \frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}} - \frac{A}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}}"," ",0,"1/48*(12*d^4*e*n*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) - 12*d^4*e*n*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) + (12*b^3*d^3*e*n*x^3 - 3*b^3*c^3*e*n + 13*a*b^2*c^2*d*e*n - 23*a^2*b*c*d^2*e*n + 25*a^3*d^3*e*n - 6*(b^3*c*d^2*e*n - 7*a*b^2*d^3*e*n)*x^2 + 4*(b^3*c^2*d*e*n - 5*a*b^2*c*d^2*e*n + 13*a^2*b*d^3*e*n)*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 + (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)*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)*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)*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)*x))*B/e - 1/4*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b) - 1/4*A/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b)","B",0
156,1,1871,0,7.070199," ","integrate((b*x+a)^3*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A B b^{3} x^{4} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{4} \, A^{2} b^{3} x^{4} + 2 \, A B a b^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} a b^{2} x^{3} + 3 \, A B a^{2} b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{3}{2} \, A^{2} a^{2} b x^{2} + 2 \, A B a^{3} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} a^{3} x + \frac{2 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A B a^{3}}{e} - \frac{3 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A B a^{2} b}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} A B a b^{2}}{e} - \frac{{\left(\frac{6 \, a^{4} e n \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} e n \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} e n - a b^{2} d^{3} e n\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d e n - a^{2} b d^{3} e n\right)} x^{2} + 6 \, {\left(b^{3} c^{3} e n - a^{3} d^{3} e n\right)} x}{b^{3} d^{3}}\right)} A B b^{3}}{12 \, e} + \frac{{\left({\left(11 \, n^{2} + 6 \, n \log\left(e\right)\right)} b^{3} c^{4} - 2 \, {\left(19 \, n^{2} + 12 \, n \log\left(e\right)\right)} a b^{2} c^{3} d + 9 \, {\left(5 \, n^{2} + 4 \, n \log\left(e\right)\right)} a^{2} b c^{2} d^{2} - 6 \, {\left(3 \, n^{2} + 4 \, n \log\left(e\right)\right)} a^{3} c d^{3}\right)} B^{2} \log\left(d x + c\right)}{12 \, d^{4}} + \frac{{\left(b^{4} c^{4} n^{2} - 4 \, a b^{3} c^{3} d n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} n^{2} - 4 \, a^{3} b c d^{3} n^{2} + a^{4} d^{4} 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 d^{4}} + \frac{3 \, B^{2} b^{4} d^{4} x^{4} \log\left(e\right)^{2} - 3 \, B^{2} a^{4} d^{4} n^{2} \log\left(b x + a\right)^{2} - 2 \, {\left(b^{4} c d^{3} n \log\left(e\right) - {\left(n \log\left(e\right) + 6 \, \log\left(e\right)^{2}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} + {\left({\left(n^{2} + 3 \, n \log\left(e\right)\right)} b^{4} c^{2} d^{2} - 2 \, {\left(n^{2} + 6 \, n \log\left(e\right)\right)} a b^{3} c d^{3} + {\left(n^{2} + 9 \, n \log\left(e\right) + 18 \, \log\left(e\right)^{2}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} - 6 \, {\left(b^{4} c^{4} n^{2} - 4 \, a b^{3} c^{3} d n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} n^{2} - 4 \, a^{3} b c d^{3} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) + 3 \, {\left(b^{4} c^{4} n^{2} - 4 \, a b^{3} c^{3} d n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} n^{2} - 4 \, a^{3} b c d^{3} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} - {\left({\left(5 \, n^{2} + 6 \, n \log\left(e\right)\right)} b^{4} c^{3} d - {\left(17 \, n^{2} + 24 \, n \log\left(e\right)\right)} a b^{3} c^{2} d^{2} + {\left(19 \, n^{2} + 36 \, n \log\left(e\right)\right)} a^{2} b^{2} c d^{3} - {\left(7 \, n^{2} + 18 \, n \log\left(e\right) + 12 \, \log\left(e\right)^{2}\right)} a^{3} b d^{4}\right)} B^{2} x - {\left(6 \, a b^{3} c^{3} d n^{2} - 21 \, a^{2} b^{2} c^{2} d^{2} n^{2} + 26 \, a^{3} b c d^{3} n^{2} - {\left(11 \, n^{2} + 6 \, 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} x^{4} + 4 \, B^{2} a b^{3} d^{4} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} x^{2} + 4 \, B^{2} a^{3} b d^{4} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} x^{4} + 4 \, B^{2} a b^{3} d^{4} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} x^{2} + 4 \, B^{2} a^{3} b d^{4} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} x^{4} \log\left(e\right) + 6 \, B^{2} a^{4} d^{4} n \log\left(b x + a\right) + 2 \, {\left(a b^{3} d^{4} {\left(n + 12 \, \log\left(e\right)\right)} - b^{4} c d^{3} n\right)} B^{2} x^{3} + 3 \, {\left(3 \, a^{2} b^{2} d^{4} {\left(n + 4 \, \log\left(e\right)\right)} + b^{4} c^{2} d^{2} n - 4 \, a b^{3} c d^{3} n\right)} B^{2} x^{2} + 6 \, {\left(a^{3} b d^{4} {\left(3 \, n + 4 \, \log\left(e\right)\right)} - b^{4} c^{3} d n + 4 \, a b^{3} c^{2} d^{2} n - 6 \, a^{2} b^{2} c d^{3} n\right)} B^{2} x + 6 \, {\left(b^{4} c^{4} n - 4 \, a b^{3} c^{3} d n + 6 \, a^{2} b^{2} c^{2} d^{2} n - 4 \, a^{3} b c d^{3} 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} x^{4} \log\left(e\right) + 6 \, B^{2} a^{4} d^{4} n \log\left(b x + a\right) + 2 \, {\left(a b^{3} d^{4} {\left(n + 12 \, \log\left(e\right)\right)} - b^{4} c d^{3} n\right)} B^{2} x^{3} + 3 \, {\left(3 \, a^{2} b^{2} d^{4} {\left(n + 4 \, \log\left(e\right)\right)} + b^{4} c^{2} d^{2} n - 4 \, a b^{3} c d^{3} n\right)} B^{2} x^{2} + 6 \, {\left(a^{3} b d^{4} {\left(3 \, n + 4 \, \log\left(e\right)\right)} - b^{4} c^{3} d n + 4 \, a b^{3} c^{2} d^{2} n - 6 \, a^{2} b^{2} c d^{3} n\right)} B^{2} x + 6 \, {\left(b^{4} c^{4} n - 4 \, a b^{3} c^{3} d n + 6 \, a^{2} b^{2} c^{2} d^{2} n - 4 \, a^{3} b c d^{3} n\right)} B^{2} \log\left(d x + c\right) + 6 \, {\left(B^{2} b^{4} d^{4} x^{4} + 4 \, B^{2} a b^{3} d^{4} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} x^{2} + 4 \, B^{2} a^{3} b d^{4} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{12 \, b d^{4}}"," ",0,"1/2*A*B*b^3*x^4*log((b*x + a)^n*e/(d*x + c)^n) + 1/4*A^2*b^3*x^4 + 2*A*B*a*b^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + A^2*a*b^2*x^3 + 3*A*B*a^2*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 3/2*A^2*a^2*b*x^2 + 2*A*B*a^3*x*log((b*x + a)^n*e/(d*x + c)^n) + A^2*a^3*x + 2*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A*B*a^3/e - 3*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A*B*a^2*b/e + (2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*A*B*a*b^2/e - 1/12*(6*a^4*e*n*log(b*x + a)/b^4 - 6*c^4*e*n*log(d*x + c)/d^4 + (2*(b^3*c*d^2*e*n - a*b^2*d^3*e*n)*x^3 - 3*(b^3*c^2*d*e*n - a^2*b*d^3*e*n)*x^2 + 6*(b^3*c^3*e*n - a^3*d^3*e*n)*x)/(b^3*d^3))*A*B*b^3/e + 1/12*((11*n^2 + 6*n*log(e))*b^3*c^4 - 2*(19*n^2 + 12*n*log(e))*a*b^2*c^3*d + 9*(5*n^2 + 4*n*log(e))*a^2*b*c^2*d^2 - 6*(3*n^2 + 4*n*log(e))*a^3*c*d^3)*B^2*log(d*x + c)/d^4 + 1/2*(b^4*c^4*n^2 - 4*a*b^3*c^3*d*n^2 + 6*a^2*b^2*c^2*d^2*n^2 - 4*a^3*b*c*d^3*n^2 + a^4*d^4*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*d^4) + 1/12*(3*B^2*b^4*d^4*x^4*log(e)^2 - 3*B^2*a^4*d^4*n^2*log(b*x + a)^2 - 2*(b^4*c*d^3*n*log(e) - (n*log(e) + 6*log(e)^2)*a*b^3*d^4)*B^2*x^3 + ((n^2 + 3*n*log(e))*b^4*c^2*d^2 - 2*(n^2 + 6*n*log(e))*a*b^3*c*d^3 + (n^2 + 9*n*log(e) + 18*log(e)^2)*a^2*b^2*d^4)*B^2*x^2 - 6*(b^4*c^4*n^2 - 4*a*b^3*c^3*d*n^2 + 6*a^2*b^2*c^2*d^2*n^2 - 4*a^3*b*c*d^3*n^2)*B^2*log(b*x + a)*log(d*x + c) + 3*(b^4*c^4*n^2 - 4*a*b^3*c^3*d*n^2 + 6*a^2*b^2*c^2*d^2*n^2 - 4*a^3*b*c*d^3*n^2)*B^2*log(d*x + c)^2 - ((5*n^2 + 6*n*log(e))*b^4*c^3*d - (17*n^2 + 24*n*log(e))*a*b^3*c^2*d^2 + (19*n^2 + 36*n*log(e))*a^2*b^2*c*d^3 - (7*n^2 + 18*n*log(e) + 12*log(e)^2)*a^3*b*d^4)*B^2*x - (6*a*b^3*c^3*d*n^2 - 21*a^2*b^2*c^2*d^2*n^2 + 26*a^3*b*c*d^3*n^2 - (11*n^2 + 6*n*log(e))*a^4*d^4)*B^2*log(b*x + a) + 3*(B^2*b^4*d^4*x^4 + 4*B^2*a*b^3*d^4*x^3 + 6*B^2*a^2*b^2*d^4*x^2 + 4*B^2*a^3*b*d^4*x)*log((b*x + a)^n)^2 + 3*(B^2*b^4*d^4*x^4 + 4*B^2*a*b^3*d^4*x^3 + 6*B^2*a^2*b^2*d^4*x^2 + 4*B^2*a^3*b*d^4*x)*log((d*x + c)^n)^2 + (6*B^2*b^4*d^4*x^4*log(e) + 6*B^2*a^4*d^4*n*log(b*x + a) + 2*(a*b^3*d^4*(n + 12*log(e)) - b^4*c*d^3*n)*B^2*x^3 + 3*(3*a^2*b^2*d^4*(n + 4*log(e)) + b^4*c^2*d^2*n - 4*a*b^3*c*d^3*n)*B^2*x^2 + 6*(a^3*b*d^4*(3*n + 4*log(e)) - b^4*c^3*d*n + 4*a*b^3*c^2*d^2*n - 6*a^2*b^2*c*d^3*n)*B^2*x + 6*(b^4*c^4*n - 4*a*b^3*c^3*d*n + 6*a^2*b^2*c^2*d^2*n - 4*a^3*b*c*d^3*n)*B^2*log(d*x + c))*log((b*x + a)^n) - (6*B^2*b^4*d^4*x^4*log(e) + 6*B^2*a^4*d^4*n*log(b*x + a) + 2*(a*b^3*d^4*(n + 12*log(e)) - b^4*c*d^3*n)*B^2*x^3 + 3*(3*a^2*b^2*d^4*(n + 4*log(e)) + b^4*c^2*d^2*n - 4*a*b^3*c*d^3*n)*B^2*x^2 + 6*(a^3*b*d^4*(3*n + 4*log(e)) - b^4*c^3*d*n + 4*a*b^3*c^2*d^2*n - 6*a^2*b^2*c*d^3*n)*B^2*x + 6*(b^4*c^4*n - 4*a*b^3*c^3*d*n + 6*a^2*b^2*c^2*d^2*n - 4*a^3*b*c*d^3*n)*B^2*log(d*x + c) + 6*(B^2*b^4*d^4*x^4 + 4*B^2*a*b^3*d^4*x^3 + 6*B^2*a^2*b^2*d^4*x^2 + 4*B^2*a^3*b*d^4*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^4)","B",0
157,1,1284,0,7.047448," ","integrate((b*x+a)^2*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","\frac{2}{3} \, A B b^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{3} \, A^{2} b^{2} x^{3} + 2 \, A B a b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} a b x^{2} + 2 \, A B a^{2} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} a^{2} x + \frac{2 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A B a^{2}}{e} - \frac{2 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A B a b}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} A B b^{2}}{3 \, e} - \frac{{\left({\left(3 \, n^{2} + 2 \, n \log\left(e\right)\right)} b^{2} c^{3} - {\left(7 \, n^{2} + 6 \, n \log\left(e\right)\right)} a b c^{2} d + 2 \, {\left(2 \, n^{2} + 3 \, n \log\left(e\right)\right)} a^{2} c d^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, d^{3}} - \frac{2 \, {\left(b^{3} c^{3} n^{2} - 3 \, a b^{2} c^{2} d n^{2} + 3 \, a^{2} b c d^{2} n^{2} - a^{3} d^{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}}{3 \, b d^{3}} + \frac{B^{2} b^{3} d^{3} x^{3} \log\left(e\right)^{2} - B^{2} a^{3} d^{3} n^{2} \log\left(b x + a\right)^{2} - {\left(b^{3} c d^{2} n \log\left(e\right) - {\left(n \log\left(e\right) + 3 \, \log\left(e\right)^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} + 2 \, {\left(b^{3} c^{3} n^{2} - 3 \, a b^{2} c^{2} d n^{2} + 3 \, a^{2} b c d^{2} n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{3} c^{3} n^{2} - 3 \, a b^{2} c^{2} d n^{2} + 3 \, a^{2} b c d^{2} n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + {\left({\left(n^{2} + 2 \, n \log\left(e\right)\right)} b^{3} c^{2} d - 2 \, {\left(n^{2} + 3 \, n \log\left(e\right)\right)} a b^{2} c d^{2} + {\left(n^{2} + 4 \, n \log\left(e\right) + 3 \, \log\left(e\right)^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + {\left(2 \, a b^{2} c^{2} d n^{2} - 5 \, a^{2} b c d^{2} n^{2} + {\left(3 \, n^{2} + 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} x^{3} + 3 \, B^{2} a b^{2} d^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{3} d^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} x^{3} \log\left(e\right) + 2 \, B^{2} a^{3} d^{3} n \log\left(b x + a\right) + {\left(a b^{2} d^{3} {\left(n + 6 \, \log\left(e\right)\right)} - b^{3} c d^{2} n\right)} B^{2} x^{2} + 2 \, {\left(a^{2} b d^{3} {\left(2 \, n + 3 \, \log\left(e\right)\right)} + b^{3} c^{2} d n - 3 \, a b^{2} c d^{2} n\right)} B^{2} x - 2 \, {\left(b^{3} c^{3} n - 3 \, a b^{2} c^{2} d n + 3 \, a^{2} b c d^{2} n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, B^{2} b^{3} d^{3} x^{3} \log\left(e\right) + 2 \, B^{2} a^{3} d^{3} n \log\left(b x + a\right) + {\left(a b^{2} d^{3} {\left(n + 6 \, \log\left(e\right)\right)} - b^{3} c d^{2} n\right)} B^{2} x^{2} + 2 \, {\left(a^{2} b d^{3} {\left(2 \, n + 3 \, \log\left(e\right)\right)} + b^{3} c^{2} d n - 3 \, a b^{2} c d^{2} n\right)} B^{2} x - 2 \, {\left(b^{3} c^{3} n - 3 \, a b^{2} c^{2} d n + 3 \, a^{2} b c d^{2} n\right)} B^{2} \log\left(d x + c\right) + 2 \, {\left(B^{2} b^{3} d^{3} x^{3} + 3 \, B^{2} a b^{2} d^{3} x^{2} + 3 \, B^{2} a^{2} b d^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{3 \, b d^{3}}"," ",0,"2/3*A*B*b^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + 1/3*A^2*b^2*x^3 + 2*A*B*a*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + A^2*a*b*x^2 + 2*A*B*a^2*x*log((b*x + a)^n*e/(d*x + c)^n) + A^2*a^2*x + 2*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A*B*a^2/e - 2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A*B*a*b/e + 1/3*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*A*B*b^2/e - 1/3*((3*n^2 + 2*n*log(e))*b^2*c^3 - (7*n^2 + 6*n*log(e))*a*b*c^2*d + 2*(2*n^2 + 3*n*log(e))*a^2*c*d^2)*B^2*log(d*x + c)/d^3 - 2/3*(b^3*c^3*n^2 - 3*a*b^2*c^2*d*n^2 + 3*a^2*b*c*d^2*n^2 - a^3*d^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*d^3) + 1/3*(B^2*b^3*d^3*x^3*log(e)^2 - B^2*a^3*d^3*n^2*log(b*x + a)^2 - (b^3*c*d^2*n*log(e) - (n*log(e) + 3*log(e)^2)*a*b^2*d^3)*B^2*x^2 + 2*(b^3*c^3*n^2 - 3*a*b^2*c^2*d*n^2 + 3*a^2*b*c*d^2*n^2)*B^2*log(b*x + a)*log(d*x + c) - (b^3*c^3*n^2 - 3*a*b^2*c^2*d*n^2 + 3*a^2*b*c*d^2*n^2)*B^2*log(d*x + c)^2 + ((n^2 + 2*n*log(e))*b^3*c^2*d - 2*(n^2 + 3*n*log(e))*a*b^2*c*d^2 + (n^2 + 4*n*log(e) + 3*log(e)^2)*a^2*b*d^3)*B^2*x + (2*a*b^2*c^2*d*n^2 - 5*a^2*b*c*d^2*n^2 + (3*n^2 + 2*n*log(e))*a^3*d^3)*B^2*log(b*x + a) + (B^2*b^3*d^3*x^3 + 3*B^2*a*b^2*d^3*x^2 + 3*B^2*a^2*b*d^3*x)*log((b*x + a)^n)^2 + (B^2*b^3*d^3*x^3 + 3*B^2*a*b^2*d^3*x^2 + 3*B^2*a^2*b*d^3*x)*log((d*x + c)^n)^2 + (2*B^2*b^3*d^3*x^3*log(e) + 2*B^2*a^3*d^3*n*log(b*x + a) + (a*b^2*d^3*(n + 6*log(e)) - b^3*c*d^2*n)*B^2*x^2 + 2*(a^2*b*d^3*(2*n + 3*log(e)) + b^3*c^2*d*n - 3*a*b^2*c*d^2*n)*B^2*x - 2*(b^3*c^3*n - 3*a*b^2*c^2*d*n + 3*a^2*b*c*d^2*n)*B^2*log(d*x + c))*log((b*x + a)^n) - (2*B^2*b^3*d^3*x^3*log(e) + 2*B^2*a^3*d^3*n*log(b*x + a) + (a*b^2*d^3*(n + 6*log(e)) - b^3*c*d^2*n)*B^2*x^2 + 2*(a^2*b*d^3*(2*n + 3*log(e)) + b^3*c^2*d*n - 3*a*b^2*c*d^2*n)*B^2*x - 2*(b^3*c^3*n - 3*a*b^2*c^2*d*n + 3*a^2*b*c*d^2*n)*B^2*log(d*x + c) + 2*(B^2*b^3*d^3*x^3 + 3*B^2*a*b^2*d^3*x^2 + 3*B^2*a^2*b*d^3*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^3)","B",0
158,1,779,0,6.912181," ","integrate((b*x+a)*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","A B b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{2} \, A^{2} b x^{2} + 2 \, A B a x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} a x + \frac{2 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A B a}{e} - \frac{{\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A B b}{e} + \frac{{\left({\left(n^{2} + n \log\left(e\right)\right)} b c^{2} - {\left(n^{2} + 2 \, n \log\left(e\right)\right)} a c d\right)} B^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b^{2} c^{2} n^{2} - 2 \, a b c d n^{2} + a^{2} d^{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}}{b d^{2}} - \frac{B^{2} a^{2} d^{2} n^{2} \log\left(b x + a\right)^{2} - B^{2} b^{2} d^{2} x^{2} \log\left(e\right)^{2} + 2 \, {\left(b^{2} c^{2} n^{2} - 2 \, a b c d n^{2}\right)} B^{2} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(b^{2} c^{2} n^{2} - 2 \, a b c d n^{2}\right)} B^{2} \log\left(d x + c\right)^{2} + 2 \, {\left(b^{2} c d n \log\left(e\right) - {\left(n \log\left(e\right) + \log\left(e\right)^{2}\right)} a b d^{2}\right)} B^{2} x + 2 \, {\left(a b c d n^{2} - {\left(n^{2} + 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} x^{2} + 2 \, B^{2} a b d^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} - {\left(B^{2} b^{2} d^{2} x^{2} + 2 \, B^{2} a b d^{2} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} - 2 \, {\left(B^{2} b^{2} d^{2} x^{2} \log\left(e\right) + B^{2} a^{2} d^{2} n \log\left(b x + a\right) + {\left(a b d^{2} {\left(n + 2 \, \log\left(e\right)\right)} - b^{2} c d n\right)} B^{2} x + {\left(b^{2} c^{2} n - 2 \, a b c d n\right)} B^{2} \log\left(d x + c\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + 2 \, {\left(B^{2} b^{2} d^{2} x^{2} \log\left(e\right) + B^{2} a^{2} d^{2} n \log\left(b x + a\right) + {\left(a b d^{2} {\left(n + 2 \, \log\left(e\right)\right)} - b^{2} c d n\right)} B^{2} x + {\left(b^{2} c^{2} n - 2 \, a b c d n\right)} B^{2} \log\left(d x + c\right) + {\left(B^{2} b^{2} d^{2} x^{2} + 2 \, B^{2} a b d^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, b d^{2}}"," ",0,"A*B*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 1/2*A^2*b*x^2 + 2*A*B*a*x*log((b*x + a)^n*e/(d*x + c)^n) + A^2*a*x + 2*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A*B*a/e - (a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A*B*b/e + ((n^2 + n*log(e))*b*c^2 - (n^2 + 2*n*log(e))*a*c*d)*B^2*log(d*x + c)/d^2 + (b^2*c^2*n^2 - 2*a*b*c*d*n^2 + a^2*d^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*d^2) - 1/2*(B^2*a^2*d^2*n^2*log(b*x + a)^2 - B^2*b^2*d^2*x^2*log(e)^2 + 2*(b^2*c^2*n^2 - 2*a*b*c*d*n^2)*B^2*log(b*x + a)*log(d*x + c) - (b^2*c^2*n^2 - 2*a*b*c*d*n^2)*B^2*log(d*x + c)^2 + 2*(b^2*c*d*n*log(e) - (n*log(e) + log(e)^2)*a*b*d^2)*B^2*x + 2*(a*b*c*d*n^2 - (n^2 + n*log(e))*a^2*d^2)*B^2*log(b*x + a) - (B^2*b^2*d^2*x^2 + 2*B^2*a*b*d^2*x)*log((b*x + a)^n)^2 - (B^2*b^2*d^2*x^2 + 2*B^2*a*b*d^2*x)*log((d*x + c)^n)^2 - 2*(B^2*b^2*d^2*x^2*log(e) + B^2*a^2*d^2*n*log(b*x + a) + (a*b*d^2*(n + 2*log(e)) - b^2*c*d*n)*B^2*x + (b^2*c^2*n - 2*a*b*c*d*n)*B^2*log(d*x + c))*log((b*x + a)^n) + 2*(B^2*b^2*d^2*x^2*log(e) + B^2*a^2*d^2*n*log(b*x + a) + (a*b*d^2*(n + 2*log(e)) - b^2*c*d*n)*B^2*x + (b^2*c^2*n - 2*a*b*c*d*n)*B^2*log(d*x + c) + (B^2*b^2*d^2*x^2 + 2*B^2*a*b*d^2*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^2)","B",0
159,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(b*x+a),x, algorithm=""maxima"")","\frac{B^{2} \log\left(b x + a\right) \log\left({\left(d x + c\right)}^{n}\right)^{2}}{b} + \frac{A^{2} \log\left(b x + a\right)}{b} - \int -\frac{B^{2} b c \log\left(e\right)^{2} + 2 \, A B b c \log\left(e\right) + {\left(B^{2} b d x + B^{2} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b d \log\left(e\right)^{2} + 2 \, A B b d \log\left(e\right)\right)} x + 2 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x + {\left(B^{2} b d n x + B^{2} a d n\right)} \log\left(b x + a\right) + {\left(B^{2} b d x + B^{2} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x}\,{d x}"," ",0,"B^2*log(b*x + a)*log((d*x + c)^n)^2/b + A^2*log(b*x + a)/b - integrate(-(B^2*b*c*log(e)^2 + 2*A*B*b*c*log(e) + (B^2*b*d*x + B^2*b*c)*log((b*x + a)^n)^2 + (B^2*b*d*log(e)^2 + 2*A*B*b*d*log(e))*x + 2*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x)*log((b*x + a)^n) - 2*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x + (B^2*b*d*n*x + B^2*a*d*n)*log(b*x + a) + (B^2*b*d*x + B^2*b*c)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x), x)","F",0
160,1,449,0,1.530606," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(b*x+a)^2,x, algorithm=""maxima"")","-B^{2} {\left(\frac{2 \, {\left(\frac{d e n \log\left(b x + a\right)}{b^{2} c - a b d} - \frac{d e n \log\left(d x + c\right)}{b^{2} c - a b d} + \frac{e n}{b^{2} x + a b}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{e} + \frac{2 \, b c e^{2} n^{2} - 2 \, a d e^{2} n^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(b d e^{2} n^{2} x + a d e^{2} n^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x\right)} e^{2}}\right)} - \frac{B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{b^{2} x + a b} - \frac{2 \, {\left(\frac{d e n \log\left(b x + a\right)}{b^{2} c - a b d} - \frac{d e n \log\left(d x + c\right)}{b^{2} c - a b d} + \frac{e n}{b^{2} x + a b}\right)} A B}{e} - \frac{2 \, A B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{b^{2} x + a b} - \frac{A^{2}}{b^{2} x + a b}"," ",0,"-B^2*(2*(d*e*n*log(b*x + a)/(b^2*c - a*b*d) - d*e*n*log(d*x + c)/(b^2*c - a*b*d) + e*n/(b^2*x + a*b))*log((b*x + a)^n*e/(d*x + c)^n)/e + (2*b*c*e^2*n^2 - 2*a*d*e^2*n^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a)^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(d*x + c)^2 + 2*(b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a) - 2*(b*d*e^2*n^2*x + a*d*e^2*n^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a))*log(d*x + c))/((a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x)*e^2)) - B^2*log((b*x + a)^n*e/(d*x + c)^n)^2/(b^2*x + a*b) - 2*(d*e*n*log(b*x + a)/(b^2*c - a*b*d) - d*e*n*log(d*x + c)/(b^2*c - a*b*d) + e*n/(b^2*x + a*b))*A*B/e - 2*A*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^2*x + a*b) - A^2/(b^2*x + a*b)","B",0
161,1,899,0,1.847661," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(b*x+a)^3,x, algorithm=""maxima"")","\frac{1}{4} \, B^{2} {\left(\frac{2 \, {\left(\frac{2 \, d^{2} e n \log\left(b x + a\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} - \frac{2 \, d^{2} e n \log\left(d x + c\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} + \frac{2 \, b d e n x - b c e n + 3 \, a d e n}{a^{2} b^{2} c - a^{3} b d + {\left(b^{4} c - a b^{3} d\right)} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{e} - \frac{b^{2} c^{2} e^{2} n^{2} - 8 \, a b c d e^{2} n^{2} + 7 \, a^{2} d^{2} e^{2} n^{2} + 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d e^{2} n^{2} - a b d^{2} e^{2} n^{2}\right)} x - 6 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} e^{2} n^{2} x^{2} + 6 \, a b d^{2} e^{2} n^{2} x + 3 \, a^{2} d^{2} e^{2} n^{2} - 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{2} + 2 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x\right)} e^{2}}\right)} - \frac{B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}} + \frac{{\left(\frac{2 \, d^{2} e n \log\left(b x + a\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} - \frac{2 \, d^{2} e n \log\left(d x + c\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} + \frac{2 \, b d e n x - b c e n + 3 \, a d e n}{a^{2} b^{2} c - a^{3} b d + {\left(b^{4} c - a b^{3} d\right)} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x}\right)} A B}{2 \, e} - \frac{A B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b} - \frac{A^{2}}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"1/4*B^2*(2*(2*d^2*e*n*log(b*x + a)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - 2*d^2*e*n*log(d*x + c)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) + (2*b*d*e*n*x - b*c*e*n + 3*a*d*e*n)/(a^2*b^2*c - a^3*b*d + (b^4*c - a*b^3*d)*x^2 + 2*(a*b^3*c - a^2*b^2*d)*x))*log((b*x + a)^n*e/(d*x + c)^n)/e - (b^2*c^2*e^2*n^2 - 8*a*b*c*d*e^2*n^2 + 7*a^2*d^2*e^2*n^2 + 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a)^2 + 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(d*x + c)^2 - 6*(b^2*c*d*e^2*n^2 - a*b*d^2*e^2*n^2)*x - 6*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a) + 2*(3*b^2*d^2*e^2*n^2*x^2 + 6*a*b*d^2*e^2*n^2*x + 3*a^2*d^2*e^2*n^2 - 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a))*log(d*x + c))/((a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^2 + 2*(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x)*e^2)) - 1/2*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2/(b^3*x^2 + 2*a*b^2*x + a^2*b) + 1/2*(2*d^2*e*n*log(b*x + a)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - 2*d^2*e*n*log(d*x + c)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) + (2*b*d*e*n*x - b*c*e*n + 3*a*d*e*n)/(a^2*b^2*c - a^3*b*d + (b^4*c - a*b^3*d)*x^2 + 2*(a*b^3*c - a^2*b^2*d)*x))*A*B/e - A*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^3*x^2 + 2*a*b^2*x + a^2*b) - 1/2*A^2/(b^3*x^2 + 2*a*b^2*x + a^2*b)","B",0
162,1,1500,0,2.434673," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(b*x+a)^4,x, algorithm=""maxima"")","-\frac{1}{54} \, B^{2} {\left(\frac{6 \, {\left(\frac{6 \, d^{3} e n \log\left(b x + a\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{6 \, d^{3} e n \log\left(d x + c\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} + \frac{6 \, b^{2} d^{2} e n x^{2} + 2 \, b^{2} c^{2} e n - 7 \, a b c d e n + 11 \, a^{2} d^{2} e n - 3 \, {\left(b^{2} c d e n - 5 \, a b d^{2} e n\right)} x}{a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2} + {\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{e} + \frac{4 \, b^{3} c^{3} e^{2} n^{2} - 27 \, a b^{2} c^{2} d e^{2} n^{2} + 108 \, a^{2} b c d^{2} e^{2} n^{2} - 85 \, a^{3} d^{3} e^{2} n^{2} + 66 \, {\left(b^{3} c d^{2} e^{2} n^{2} - a b^{2} d^{3} e^{2} n^{2}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d e^{2} n^{2} - 54 \, a b^{2} c d^{2} e^{2} n^{2} + 49 \, a^{2} b d^{3} e^{2} n^{2}\right)} x + 66 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} e^{2} n^{2} x^{3} + 33 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 33 \, a^{2} b d^{3} e^{2} n^{2} x + 11 \, a^{3} d^{3} e^{2} n^{2} - 6 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3} + {\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} x^{3} + 3 \, {\left(a b^{6} c^{3} - 3 \, a^{2} b^{5} c^{2} d + 3 \, a^{3} b^{4} c d^{2} - a^{4} b^{3} d^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} x\right)} e^{2}}\right)} - \frac{B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}} - \frac{{\left(\frac{6 \, d^{3} e n \log\left(b x + a\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{6 \, d^{3} e n \log\left(d x + c\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} + \frac{6 \, b^{2} d^{2} e n x^{2} + 2 \, b^{2} c^{2} e n - 7 \, a b c d e n + 11 \, a^{2} d^{2} e n - 3 \, {\left(b^{2} c d e n - 5 \, a b d^{2} e n\right)} x}{a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2} + {\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} x}\right)} A B}{9 \, e} - \frac{2 \, A B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}} - \frac{A^{2}}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"-1/54*B^2*(6*(6*d^3*e*n*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) - 6*d^3*e*n*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) + (6*b^2*d^2*e*n*x^2 + 2*b^2*c^2*e*n - 7*a*b*c*d*e*n + 11*a^2*d^2*e*n - 3*(b^2*c*d*e*n - 5*a*b*d^2*e*n)*x)/(a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2 + (b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*x))*log((b*x + a)^n*e/(d*x + c)^n)/e + (4*b^3*c^3*e^2*n^2 - 27*a*b^2*c^2*d*e^2*n^2 + 108*a^2*b*c*d^2*e^2*n^2 - 85*a^3*d^3*e^2*n^2 + 66*(b^3*c*d^2*e^2*n^2 - a*b^2*d^3*e^2*n^2)*x^2 - 18*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a)^2 - 18*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(d*x + c)^2 - 3*(5*b^3*c^2*d*e^2*n^2 - 54*a*b^2*c*d^2*e^2*n^2 + 49*a^2*b*d^3*e^2*n^2)*x + 66*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a) - 6*(11*b^3*d^3*e^2*n^2*x^3 + 33*a*b^2*d^3*e^2*n^2*x^2 + 33*a^2*b*d^3*e^2*n^2*x + 11*a^3*d^3*e^2*n^2 - 6*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a))*log(d*x + c))/((a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3 + (b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*x^3 + 3*(a*b^6*c^3 - 3*a^2*b^5*c^2*d + 3*a^3*b^4*c*d^2 - a^4*b^3*d^3)*x^2 + 3*(a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*x)*e^2)) - 1/3*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b) - 1/9*(6*d^3*e*n*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) - 6*d^3*e*n*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) + (6*b^2*d^2*e*n*x^2 + 2*b^2*c^2*e*n - 7*a*b*c*d*e*n + 11*a^2*d^2*e*n - 3*(b^2*c*d*e*n - 5*a*b*d^2*e*n)*x)/(a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2 + (b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*x))*A*B/e - 2/3*A*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b) - 1/3*A^2/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)","B",0
163,1,2238,0,2.995691," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(b*x+a)^5,x, algorithm=""maxima"")","\frac{1}{288} \, B^{2} {\left(\frac{12 \, {\left(\frac{12 \, d^{4} e n \log\left(b x + a\right)}{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}} - \frac{12 \, d^{4} e n \log\left(d x + c\right)}{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}} + \frac{12 \, b^{3} d^{3} e n x^{3} - 3 \, b^{3} c^{3} e n + 13 \, a b^{2} c^{2} d e n - 23 \, a^{2} b c d^{2} e n + 25 \, a^{3} d^{3} e n - 6 \, {\left(b^{3} c d^{2} e n - 7 \, a b^{2} d^{3} e n\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d e n - 5 \, a b^{2} c d^{2} e n + 13 \, a^{2} b d^{3} e n\right)} 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} + {\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)} 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)} 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)} 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)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{e} - \frac{9 \, b^{4} c^{4} e^{2} n^{2} - 64 \, a b^{3} c^{3} d e^{2} n^{2} + 216 \, a^{2} b^{2} c^{2} d^{2} e^{2} n^{2} - 576 \, a^{3} b c d^{3} e^{2} n^{2} + 415 \, a^{4} d^{4} e^{2} n^{2} - 300 \, {\left(b^{4} c d^{3} e^{2} n^{2} - a b^{3} d^{4} e^{2} n^{2}\right)} x^{3} + 6 \, {\left(13 \, b^{4} c^{2} d^{2} e^{2} n^{2} - 176 \, a b^{3} c d^{3} e^{2} n^{2} + 163 \, a^{2} b^{2} d^{4} e^{2} n^{2}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(7 \, b^{4} c^{3} d e^{2} n^{2} - 60 \, a b^{3} c^{2} d^{2} e^{2} n^{2} + 324 \, a^{2} b^{2} c d^{3} e^{2} n^{2} - 271 \, a^{3} b d^{4} e^{2} n^{2}\right)} x - 300 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right) + 12 \, {\left(25 \, b^{4} d^{4} e^{2} n^{2} x^{4} + 100 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 150 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 100 \, a^{3} b d^{4} e^{2} n^{2} x + 25 \, a^{4} d^{4} e^{2} n^{2} - 12 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{4} b^{5} c^{4} - 4 \, a^{5} b^{4} c^{3} d + 6 \, a^{6} b^{3} c^{2} d^{2} - 4 \, a^{7} b^{2} c d^{3} + a^{8} b d^{4} + {\left(b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} - 4 \, a^{2} b^{7} c^{3} d + 6 \, a^{3} b^{6} c^{2} d^{2} - 4 \, a^{4} b^{5} c d^{3} + a^{5} b^{4} d^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} - 4 \, a^{3} b^{6} c^{3} d + 6 \, a^{4} b^{5} c^{2} d^{2} - 4 \, a^{5} b^{4} c d^{3} + a^{6} b^{3} d^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} - 4 \, a^{4} b^{5} c^{3} d + 6 \, a^{5} b^{4} c^{2} d^{2} - 4 \, a^{6} b^{3} c d^{3} + a^{7} b^{2} d^{4}\right)} x\right)} e^{2}}\right)} - \frac{B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}} + \frac{{\left(\frac{12 \, d^{4} e n \log\left(b x + a\right)}{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}} - \frac{12 \, d^{4} e n \log\left(d x + c\right)}{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}} + \frac{12 \, b^{3} d^{3} e n x^{3} - 3 \, b^{3} c^{3} e n + 13 \, a b^{2} c^{2} d e n - 23 \, a^{2} b c d^{2} e n + 25 \, a^{3} d^{3} e n - 6 \, {\left(b^{3} c d^{2} e n - 7 \, a b^{2} d^{3} e n\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d e n - 5 \, a b^{2} c d^{2} e n + 13 \, a^{2} b d^{3} e n\right)} 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} + {\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)} 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)} 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)} 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)} x}\right)} A B}{24 \, e} - \frac{A B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{2 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}} - \frac{A^{2}}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}}"," ",0,"1/288*B^2*(12*(12*d^4*e*n*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) - 12*d^4*e*n*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) + (12*b^3*d^3*e*n*x^3 - 3*b^3*c^3*e*n + 13*a*b^2*c^2*d*e*n - 23*a^2*b*c*d^2*e*n + 25*a^3*d^3*e*n - 6*(b^3*c*d^2*e*n - 7*a*b^2*d^3*e*n)*x^2 + 4*(b^3*c^2*d*e*n - 5*a*b^2*c*d^2*e*n + 13*a^2*b*d^3*e*n)*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 + (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)*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)*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)*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)*x))*log((b*x + a)^n*e/(d*x + c)^n)/e - (9*b^4*c^4*e^2*n^2 - 64*a*b^3*c^3*d*e^2*n^2 + 216*a^2*b^2*c^2*d^2*e^2*n^2 - 576*a^3*b*c*d^3*e^2*n^2 + 415*a^4*d^4*e^2*n^2 - 300*(b^4*c*d^3*e^2*n^2 - a*b^3*d^4*e^2*n^2)*x^3 + 6*(13*b^4*c^2*d^2*e^2*n^2 - 176*a*b^3*c*d^3*e^2*n^2 + 163*a^2*b^2*d^4*e^2*n^2)*x^2 + 72*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a)^2 + 72*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(d*x + c)^2 - 4*(7*b^4*c^3*d*e^2*n^2 - 60*a*b^3*c^2*d^2*e^2*n^2 + 324*a^2*b^2*c*d^3*e^2*n^2 - 271*a^3*b*d^4*e^2*n^2)*x - 300*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a) + 12*(25*b^4*d^4*e^2*n^2*x^4 + 100*a*b^3*d^4*e^2*n^2*x^3 + 150*a^2*b^2*d^4*e^2*n^2*x^2 + 100*a^3*b*d^4*e^2*n^2*x + 25*a^4*d^4*e^2*n^2 - 12*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a))*log(d*x + c))/((a^4*b^5*c^4 - 4*a^5*b^4*c^3*d + 6*a^6*b^3*c^2*d^2 - 4*a^7*b^2*c*d^3 + a^8*b*d^4 + (b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4)*x^4 + 4*(a*b^8*c^4 - 4*a^2*b^7*c^3*d + 6*a^3*b^6*c^2*d^2 - 4*a^4*b^5*c*d^3 + a^5*b^4*d^4)*x^3 + 6*(a^2*b^7*c^4 - 4*a^3*b^6*c^3*d + 6*a^4*b^5*c^2*d^2 - 4*a^5*b^4*c*d^3 + a^6*b^3*d^4)*x^2 + 4*(a^3*b^6*c^4 - 4*a^4*b^5*c^3*d + 6*a^5*b^4*c^2*d^2 - 4*a^6*b^3*c*d^3 + a^7*b^2*d^4)*x)*e^2)) - 1/4*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b) + 1/24*(12*d^4*e*n*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) - 12*d^4*e*n*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) + (12*b^3*d^3*e*n*x^3 - 3*b^3*c^3*e*n + 13*a*b^2*c^2*d*e*n - 23*a^2*b*c*d^2*e*n + 25*a^3*d^3*e*n - 6*(b^3*c*d^2*e*n - 7*a*b^2*d^3*e*n)*x^2 + 4*(b^3*c^2*d*e*n - 5*a*b^2*c*d^2*e*n + 13*a^2*b*d^3*e*n)*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 + (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)*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)*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)*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)*x))*A*B/e - 1/2*A*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b) - 1/4*A^2/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b)","B",0
164,0,0,0,0.000000," ","integrate((b*x+a)^3*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3,x, algorithm=""maxima"")","\frac{3}{4} \, A^{2} B b^{3} x^{4} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{4} \, A^{3} b^{3} x^{4} + 3 \, A^{2} B a b^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} a b^{2} x^{3} + \frac{9}{2} \, A^{2} B a^{2} b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{3}{2} \, A^{3} a^{2} b x^{2} + 3 \, A^{2} B a^{3} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} a^{3} x + \frac{3 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A^{2} B a^{3}}{e} - \frac{9 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A^{2} B a^{2} b}{2 \, e} + \frac{3 \, {\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} A^{2} B a b^{2}}{2 \, e} - \frac{{\left(\frac{6 \, a^{4} e n \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} e n \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} e n - a b^{2} d^{3} e n\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d e n - a^{2} b d^{3} e n\right)} x^{2} + 6 \, {\left(b^{3} c^{3} e n - a^{3} d^{3} e n\right)} x}{b^{3} d^{3}}\right)} A^{2} B b^{3}}{8 \, e} - \frac{2 \, {\left(B^{3} b^{4} d^{4} x^{4} + 4 \, B^{3} a b^{3} d^{4} x^{3} + 6 \, B^{3} a^{2} b^{2} d^{4} x^{2} + 4 \, B^{3} a^{3} b d^{4} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{3} - {\left(6 \, B^{3} a^{4} d^{4} n \log\left(b x + a\right) + 6 \, {\left(B^{3} b^{4} d^{4} \log\left(e\right) + A B^{2} b^{4} d^{4}\right)} x^{4} + 6 \, {\left(b^{4} c^{4} n - 4 \, a b^{3} c^{3} d n + 6 \, a^{2} b^{2} c^{2} d^{2} n - 4 \, a^{3} b c d^{3} n\right)} B^{3} \log\left(d x + c\right) + 2 \, {\left(12 \, A B^{2} a b^{3} d^{4} + {\left(a b^{3} d^{4} {\left(n + 12 \, \log\left(e\right)\right)} - b^{4} c d^{3} n\right)} B^{3}\right)} x^{3} + 3 \, {\left(12 \, A B^{2} a^{2} b^{2} d^{4} + {\left(3 \, a^{2} b^{2} d^{4} {\left(n + 4 \, \log\left(e\right)\right)} + b^{4} c^{2} d^{2} n - 4 \, a b^{3} c d^{3} n\right)} B^{3}\right)} x^{2} + 6 \, {\left(4 \, A B^{2} a^{3} b d^{4} + {\left(a^{3} b d^{4} {\left(3 \, n + 4 \, \log\left(e\right)\right)} - b^{4} c^{3} d n + 4 \, a b^{3} c^{2} d^{2} n - 6 \, a^{2} b^{2} c d^{3} n\right)} B^{3}\right)} x + 6 \, {\left(B^{3} b^{4} d^{4} x^{4} + 4 \, B^{3} a b^{3} d^{4} x^{3} + 6 \, B^{3} a^{2} b^{2} d^{4} x^{2} + 4 \, B^{3} a^{3} b d^{4} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{8 \, b d^{4}} - \int -\frac{4 \, B^{3} a^{3} b c d^{3} \log\left(e\right)^{3} + 12 \, A B^{2} a^{3} b c d^{3} \log\left(e\right)^{2} + 4 \, {\left(B^{3} b^{4} d^{4} \log\left(e\right)^{3} + 3 \, A B^{2} b^{4} d^{4} \log\left(e\right)^{2}\right)} x^{4} + 4 \, {\left(3 \, {\left(b^{4} c d^{3} \log\left(e\right)^{2} + 3 \, a b^{3} d^{4} \log\left(e\right)^{2}\right)} A B^{2} + {\left(b^{4} c d^{3} \log\left(e\right)^{3} + 3 \, a b^{3} d^{4} \log\left(e\right)^{3}\right)} B^{3}\right)} x^{3} + 4 \, {\left(B^{3} b^{4} d^{4} x^{4} + B^{3} a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} B^{3} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} B^{3} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} B^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + 12 \, {\left(3 \, {\left(a b^{3} c d^{3} \log\left(e\right)^{2} + a^{2} b^{2} d^{4} \log\left(e\right)^{2}\right)} A B^{2} + {\left(a b^{3} c d^{3} \log\left(e\right)^{3} + a^{2} b^{2} d^{4} \log\left(e\right)^{3}\right)} B^{3}\right)} x^{2} + 12 \, {\left(B^{3} a^{3} b c d^{3} \log\left(e\right) + A B^{2} a^{3} b c d^{3} + {\left(B^{3} b^{4} d^{4} \log\left(e\right) + A B^{2} b^{4} d^{4}\right)} x^{4} + {\left({\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} A B^{2} + {\left(b^{4} c d^{3} \log\left(e\right) + 3 \, a b^{3} d^{4} \log\left(e\right)\right)} B^{3}\right)} x^{3} + 3 \, {\left({\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} A B^{2} + {\left(a b^{3} c d^{3} \log\left(e\right) + a^{2} b^{2} d^{4} \log\left(e\right)\right)} B^{3}\right)} x^{2} + {\left({\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} A B^{2} + {\left(3 \, a^{2} b^{2} c d^{3} \log\left(e\right) + a^{3} b d^{4} \log\left(e\right)\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 4 \, {\left(3 \, {\left(3 \, a^{2} b^{2} c d^{3} \log\left(e\right)^{2} + a^{3} b d^{4} \log\left(e\right)^{2}\right)} A B^{2} + {\left(3 \, a^{2} b^{2} c d^{3} \log\left(e\right)^{3} + a^{3} b d^{4} \log\left(e\right)^{3}\right)} B^{3}\right)} x + 12 \, {\left(B^{3} a^{3} b c d^{3} \log\left(e\right)^{2} + 2 \, A B^{2} a^{3} b c d^{3} \log\left(e\right) + {\left(B^{3} b^{4} d^{4} \log\left(e\right)^{2} + 2 \, A B^{2} b^{4} d^{4} \log\left(e\right)\right)} x^{4} + {\left(2 \, {\left(b^{4} c d^{3} \log\left(e\right) + 3 \, a b^{3} d^{4} \log\left(e\right)\right)} A B^{2} + {\left(b^{4} c d^{3} \log\left(e\right)^{2} + 3 \, a b^{3} d^{4} \log\left(e\right)^{2}\right)} B^{3}\right)} x^{3} + 3 \, {\left(2 \, {\left(a b^{3} c d^{3} \log\left(e\right) + a^{2} b^{2} d^{4} \log\left(e\right)\right)} A B^{2} + {\left(a b^{3} c d^{3} \log\left(e\right)^{2} + a^{2} b^{2} d^{4} \log\left(e\right)^{2}\right)} B^{3}\right)} x^{2} + {\left(2 \, {\left(3 \, a^{2} b^{2} c d^{3} \log\left(e\right) + a^{3} b d^{4} \log\left(e\right)\right)} A B^{2} + {\left(3 \, a^{2} b^{2} c d^{3} \log\left(e\right)^{2} + a^{3} b d^{4} \log\left(e\right)^{2}\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(6 \, B^{3} a^{4} d^{4} n^{2} \log\left(b x + a\right) + 12 \, B^{3} a^{3} b c d^{3} \log\left(e\right)^{2} + 24 \, A B^{2} a^{3} b c d^{3} \log\left(e\right) + 6 \, {\left({\left(n \log\left(e\right) + 2 \, \log\left(e\right)^{2}\right)} B^{3} b^{4} d^{4} + A B^{2} b^{4} d^{4} {\left(n + 4 \, \log\left(e\right)\right)}\right)} x^{4} + 6 \, {\left(b^{4} c^{4} n^{2} - 4 \, a b^{3} c^{3} d n^{2} + 6 \, a^{2} b^{2} c^{2} d^{2} n^{2} - 4 \, a^{3} b c d^{3} n^{2}\right)} B^{3} \log\left(d x + c\right) + 2 \, {\left(12 \, {\left(a b^{3} d^{4} {\left(n + 3 \, \log\left(e\right)\right)} + b^{4} c d^{3} \log\left(e\right)\right)} A B^{2} - {\left({\left(n^{2} - 6 \, \log\left(e\right)^{2}\right)} b^{4} c d^{3} - {\left(n^{2} + 12 \, n \log\left(e\right) + 18 \, \log\left(e\right)^{2}\right)} a b^{3} d^{4}\right)} B^{3}\right)} x^{3} + 3 \, {\left(12 \, {\left(a^{2} b^{2} d^{4} {\left(n + 2 \, \log\left(e\right)\right)} + 2 \, a b^{3} c d^{3} \log\left(e\right)\right)} A B^{2} + {\left(b^{4} c^{2} d^{2} n^{2} - 4 \, {\left(n^{2} - 3 \, \log\left(e\right)^{2}\right)} a b^{3} c d^{3} + 3 \, {\left(n^{2} + 4 \, n \log\left(e\right) + 4 \, \log\left(e\right)^{2}\right)} a^{2} b^{2} d^{4}\right)} B^{3}\right)} x^{2} + 12 \, {\left(B^{3} b^{4} d^{4} x^{4} + B^{3} a^{3} b c d^{3} + {\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} B^{3} x^{3} + 3 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} B^{3} x^{2} + {\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} B^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 6 \, {\left(4 \, {\left(a^{3} b d^{4} {\left(n + \log\left(e\right)\right)} + 3 \, a^{2} b^{2} c d^{3} \log\left(e\right)\right)} A B^{2} - {\left(b^{4} c^{3} d n^{2} - 4 \, a b^{3} c^{2} d^{2} n^{2} + 6 \, {\left(n^{2} - \log\left(e\right)^{2}\right)} a^{2} b^{2} c d^{3} - {\left(3 \, n^{2} + 4 \, n \log\left(e\right) + 2 \, \log\left(e\right)^{2}\right)} a^{3} b d^{4}\right)} B^{3}\right)} x + 6 \, {\left(4 \, B^{3} a^{3} b c d^{3} \log\left(e\right) + 4 \, A B^{2} a^{3} b c d^{3} + {\left(B^{3} b^{4} d^{4} {\left(n + 4 \, \log\left(e\right)\right)} + 4 \, A B^{2} b^{4} d^{4}\right)} x^{4} + 4 \, {\left({\left(b^{4} c d^{3} + 3 \, a b^{3} d^{4}\right)} A B^{2} + {\left(a b^{3} d^{4} {\left(n + 3 \, \log\left(e\right)\right)} + b^{4} c d^{3} \log\left(e\right)\right)} B^{3}\right)} x^{3} + 6 \, {\left(2 \, {\left(a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} A B^{2} + {\left(a^{2} b^{2} d^{4} {\left(n + 2 \, \log\left(e\right)\right)} + 2 \, a b^{3} c d^{3} \log\left(e\right)\right)} B^{3}\right)} x^{2} + 4 \, {\left({\left(3 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} A B^{2} + {\left(a^{3} b d^{4} {\left(n + \log\left(e\right)\right)} + 3 \, a^{2} b^{2} c d^{3} \log\left(e\right)\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{4 \, {\left(b d^{4} x + b c d^{3}\right)}}\,{d x}"," ",0,"3/4*A^2*B*b^3*x^4*log((b*x + a)^n*e/(d*x + c)^n) + 1/4*A^3*b^3*x^4 + 3*A^2*B*a*b^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + A^3*a*b^2*x^3 + 9/2*A^2*B*a^2*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 3/2*A^3*a^2*b*x^2 + 3*A^2*B*a^3*x*log((b*x + a)^n*e/(d*x + c)^n) + A^3*a^3*x + 3*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A^2*B*a^3/e - 9/2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A^2*B*a^2*b/e + 3/2*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*A^2*B*a*b^2/e - 1/8*(6*a^4*e*n*log(b*x + a)/b^4 - 6*c^4*e*n*log(d*x + c)/d^4 + (2*(b^3*c*d^2*e*n - a*b^2*d^3*e*n)*x^3 - 3*(b^3*c^2*d*e*n - a^2*b*d^3*e*n)*x^2 + 6*(b^3*c^3*e*n - a^3*d^3*e*n)*x)/(b^3*d^3))*A^2*B*b^3/e - 1/8*(2*(B^3*b^4*d^4*x^4 + 4*B^3*a*b^3*d^4*x^3 + 6*B^3*a^2*b^2*d^4*x^2 + 4*B^3*a^3*b*d^4*x)*log((d*x + c)^n)^3 - (6*B^3*a^4*d^4*n*log(b*x + a) + 6*(B^3*b^4*d^4*log(e) + A*B^2*b^4*d^4)*x^4 + 6*(b^4*c^4*n - 4*a*b^3*c^3*d*n + 6*a^2*b^2*c^2*d^2*n - 4*a^3*b*c*d^3*n)*B^3*log(d*x + c) + 2*(12*A*B^2*a*b^3*d^4 + (a*b^3*d^4*(n + 12*log(e)) - b^4*c*d^3*n)*B^3)*x^3 + 3*(12*A*B^2*a^2*b^2*d^4 + (3*a^2*b^2*d^4*(n + 4*log(e)) + b^4*c^2*d^2*n - 4*a*b^3*c*d^3*n)*B^3)*x^2 + 6*(4*A*B^2*a^3*b*d^4 + (a^3*b*d^4*(3*n + 4*log(e)) - b^4*c^3*d*n + 4*a*b^3*c^2*d^2*n - 6*a^2*b^2*c*d^3*n)*B^3)*x + 6*(B^3*b^4*d^4*x^4 + 4*B^3*a*b^3*d^4*x^3 + 6*B^3*a^2*b^2*d^4*x^2 + 4*B^3*a^3*b*d^4*x)*log((b*x + a)^n))*log((d*x + c)^n)^2)/(b*d^4) - integrate(-1/4*(4*B^3*a^3*b*c*d^3*log(e)^3 + 12*A*B^2*a^3*b*c*d^3*log(e)^2 + 4*(B^3*b^4*d^4*log(e)^3 + 3*A*B^2*b^4*d^4*log(e)^2)*x^4 + 4*(3*(b^4*c*d^3*log(e)^2 + 3*a*b^3*d^4*log(e)^2)*A*B^2 + (b^4*c*d^3*log(e)^3 + 3*a*b^3*d^4*log(e)^3)*B^3)*x^3 + 4*(B^3*b^4*d^4*x^4 + B^3*a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*B^3*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*B^3*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*B^3*x)*log((b*x + a)^n)^3 + 12*(3*(a*b^3*c*d^3*log(e)^2 + a^2*b^2*d^4*log(e)^2)*A*B^2 + (a*b^3*c*d^3*log(e)^3 + a^2*b^2*d^4*log(e)^3)*B^3)*x^2 + 12*(B^3*a^3*b*c*d^3*log(e) + A*B^2*a^3*b*c*d^3 + (B^3*b^4*d^4*log(e) + A*B^2*b^4*d^4)*x^4 + ((b^4*c*d^3 + 3*a*b^3*d^4)*A*B^2 + (b^4*c*d^3*log(e) + 3*a*b^3*d^4*log(e))*B^3)*x^3 + 3*((a*b^3*c*d^3 + a^2*b^2*d^4)*A*B^2 + (a*b^3*c*d^3*log(e) + a^2*b^2*d^4*log(e))*B^3)*x^2 + ((3*a^2*b^2*c*d^3 + a^3*b*d^4)*A*B^2 + (3*a^2*b^2*c*d^3*log(e) + a^3*b*d^4*log(e))*B^3)*x)*log((b*x + a)^n)^2 + 4*(3*(3*a^2*b^2*c*d^3*log(e)^2 + a^3*b*d^4*log(e)^2)*A*B^2 + (3*a^2*b^2*c*d^3*log(e)^3 + a^3*b*d^4*log(e)^3)*B^3)*x + 12*(B^3*a^3*b*c*d^3*log(e)^2 + 2*A*B^2*a^3*b*c*d^3*log(e) + (B^3*b^4*d^4*log(e)^2 + 2*A*B^2*b^4*d^4*log(e))*x^4 + (2*(b^4*c*d^3*log(e) + 3*a*b^3*d^4*log(e))*A*B^2 + (b^4*c*d^3*log(e)^2 + 3*a*b^3*d^4*log(e)^2)*B^3)*x^3 + 3*(2*(a*b^3*c*d^3*log(e) + a^2*b^2*d^4*log(e))*A*B^2 + (a*b^3*c*d^3*log(e)^2 + a^2*b^2*d^4*log(e)^2)*B^3)*x^2 + (2*(3*a^2*b^2*c*d^3*log(e) + a^3*b*d^4*log(e))*A*B^2 + (3*a^2*b^2*c*d^3*log(e)^2 + a^3*b*d^4*log(e)^2)*B^3)*x)*log((b*x + a)^n) - (6*B^3*a^4*d^4*n^2*log(b*x + a) + 12*B^3*a^3*b*c*d^3*log(e)^2 + 24*A*B^2*a^3*b*c*d^3*log(e) + 6*((n*log(e) + 2*log(e)^2)*B^3*b^4*d^4 + A*B^2*b^4*d^4*(n + 4*log(e)))*x^4 + 6*(b^4*c^4*n^2 - 4*a*b^3*c^3*d*n^2 + 6*a^2*b^2*c^2*d^2*n^2 - 4*a^3*b*c*d^3*n^2)*B^3*log(d*x + c) + 2*(12*(a*b^3*d^4*(n + 3*log(e)) + b^4*c*d^3*log(e))*A*B^2 - ((n^2 - 6*log(e)^2)*b^4*c*d^3 - (n^2 + 12*n*log(e) + 18*log(e)^2)*a*b^3*d^4)*B^3)*x^3 + 3*(12*(a^2*b^2*d^4*(n + 2*log(e)) + 2*a*b^3*c*d^3*log(e))*A*B^2 + (b^4*c^2*d^2*n^2 - 4*(n^2 - 3*log(e)^2)*a*b^3*c*d^3 + 3*(n^2 + 4*n*log(e) + 4*log(e)^2)*a^2*b^2*d^4)*B^3)*x^2 + 12*(B^3*b^4*d^4*x^4 + B^3*a^3*b*c*d^3 + (b^4*c*d^3 + 3*a*b^3*d^4)*B^3*x^3 + 3*(a*b^3*c*d^3 + a^2*b^2*d^4)*B^3*x^2 + (3*a^2*b^2*c*d^3 + a^3*b*d^4)*B^3*x)*log((b*x + a)^n)^2 + 6*(4*(a^3*b*d^4*(n + log(e)) + 3*a^2*b^2*c*d^3*log(e))*A*B^2 - (b^4*c^3*d*n^2 - 4*a*b^3*c^2*d^2*n^2 + 6*(n^2 - log(e)^2)*a^2*b^2*c*d^3 - (3*n^2 + 4*n*log(e) + 2*log(e)^2)*a^3*b*d^4)*B^3)*x + 6*(4*B^3*a^3*b*c*d^3*log(e) + 4*A*B^2*a^3*b*c*d^3 + (B^3*b^4*d^4*(n + 4*log(e)) + 4*A*B^2*b^4*d^4)*x^4 + 4*((b^4*c*d^3 + 3*a*b^3*d^4)*A*B^2 + (a*b^3*d^4*(n + 3*log(e)) + b^4*c*d^3*log(e))*B^3)*x^3 + 6*(2*(a*b^3*c*d^3 + a^2*b^2*d^4)*A*B^2 + (a^2*b^2*d^4*(n + 2*log(e)) + 2*a*b^3*c*d^3*log(e))*B^3)*x^2 + 4*((3*a^2*b^2*c*d^3 + a^3*b*d^4)*A*B^2 + (a^3*b*d^4*(n + log(e)) + 3*a^2*b^2*c*d^3*log(e))*B^3)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^4*x + b*c*d^3), x)","F",0
165,0,0,0,0.000000," ","integrate((b*x+a)^2*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3,x, algorithm=""maxima"")","A^{2} B b^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{3} \, A^{3} b^{2} x^{3} + 3 \, A^{2} B a b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} a b x^{2} + 3 \, A^{2} B a^{2} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} a^{2} x + \frac{3 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A^{2} B a^{2}}{e} - \frac{3 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A^{2} B a b}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} A^{2} B b^{2}}{2 \, e} - \frac{2 \, {\left(B^{3} b^{3} d^{3} x^{3} + 3 \, B^{3} a b^{2} d^{3} x^{2} + 3 \, B^{3} a^{2} b d^{3} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{3} - 3 \, {\left(2 \, B^{3} a^{3} d^{3} n \log\left(b x + a\right) - 2 \, {\left(b^{3} c^{3} n - 3 \, a b^{2} c^{2} d n + 3 \, a^{2} b c d^{2} n\right)} B^{3} \log\left(d x + c\right) + 2 \, {\left(B^{3} b^{3} d^{3} \log\left(e\right) + A B^{2} b^{3} d^{3}\right)} x^{3} + {\left(6 \, A B^{2} a b^{2} d^{3} + {\left(a b^{2} d^{3} {\left(n + 6 \, \log\left(e\right)\right)} - b^{3} c d^{2} n\right)} B^{3}\right)} x^{2} + 2 \, {\left(3 \, A B^{2} a^{2} b d^{3} + {\left(a^{2} b d^{3} {\left(2 \, n + 3 \, \log\left(e\right)\right)} + b^{3} c^{2} d n - 3 \, a b^{2} c d^{2} n\right)} B^{3}\right)} x + 2 \, {\left(B^{3} b^{3} d^{3} x^{3} + 3 \, B^{3} a b^{2} d^{3} x^{2} + 3 \, B^{3} a^{2} b d^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{6 \, b d^{3}} - \int -\frac{B^{3} a^{2} b c d^{2} \log\left(e\right)^{3} + 3 \, A B^{2} a^{2} b c d^{2} \log\left(e\right)^{2} + {\left(B^{3} b^{3} d^{3} \log\left(e\right)^{3} + 3 \, A B^{2} b^{3} d^{3} \log\left(e\right)^{2}\right)} x^{3} + {\left(B^{3} b^{3} d^{3} x^{3} + B^{3} a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} B^{3} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} B^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + {\left(3 \, {\left(b^{3} c d^{2} \log\left(e\right)^{2} + 2 \, a b^{2} d^{3} \log\left(e\right)^{2}\right)} A B^{2} + {\left(b^{3} c d^{2} \log\left(e\right)^{3} + 2 \, a b^{2} d^{3} \log\left(e\right)^{3}\right)} B^{3}\right)} x^{2} + 3 \, {\left(B^{3} a^{2} b c d^{2} \log\left(e\right) + A B^{2} a^{2} b c d^{2} + {\left(B^{3} b^{3} d^{3} \log\left(e\right) + A B^{2} b^{3} d^{3}\right)} x^{3} + {\left({\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} A B^{2} + {\left(b^{3} c d^{2} \log\left(e\right) + 2 \, a b^{2} d^{3} \log\left(e\right)\right)} B^{3}\right)} x^{2} + {\left({\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} A B^{2} + {\left(2 \, a b^{2} c d^{2} \log\left(e\right) + a^{2} b d^{3} \log\left(e\right)\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(3 \, {\left(2 \, a b^{2} c d^{2} \log\left(e\right)^{2} + a^{2} b d^{3} \log\left(e\right)^{2}\right)} A B^{2} + {\left(2 \, a b^{2} c d^{2} \log\left(e\right)^{3} + a^{2} b d^{3} \log\left(e\right)^{3}\right)} B^{3}\right)} x + 3 \, {\left(B^{3} a^{2} b c d^{2} \log\left(e\right)^{2} + 2 \, A B^{2} a^{2} b c d^{2} \log\left(e\right) + {\left(B^{3} b^{3} d^{3} \log\left(e\right)^{2} + 2 \, A B^{2} b^{3} d^{3} \log\left(e\right)\right)} x^{3} + {\left(2 \, {\left(b^{3} c d^{2} \log\left(e\right) + 2 \, a b^{2} d^{3} \log\left(e\right)\right)} A B^{2} + {\left(b^{3} c d^{2} \log\left(e\right)^{2} + 2 \, a b^{2} d^{3} \log\left(e\right)^{2}\right)} B^{3}\right)} x^{2} + {\left(2 \, {\left(2 \, a b^{2} c d^{2} \log\left(e\right) + a^{2} b d^{3} \log\left(e\right)\right)} A B^{2} + {\left(2 \, a b^{2} c d^{2} \log\left(e\right)^{2} + a^{2} b d^{3} \log\left(e\right)^{2}\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(2 \, B^{3} a^{3} d^{3} n^{2} \log\left(b x + a\right) + 3 \, B^{3} a^{2} b c d^{2} \log\left(e\right)^{2} + 6 \, A B^{2} a^{2} b c d^{2} \log\left(e\right) - 2 \, {\left(b^{3} c^{3} n^{2} - 3 \, a b^{2} c^{2} d n^{2} + 3 \, a^{2} b c d^{2} n^{2}\right)} B^{3} \log\left(d x + c\right) + {\left({\left(2 \, n \log\left(e\right) + 3 \, \log\left(e\right)^{2}\right)} B^{3} b^{3} d^{3} + 2 \, A B^{2} b^{3} d^{3} {\left(n + 3 \, \log\left(e\right)\right)}\right)} x^{3} + {\left(6 \, {\left(a b^{2} d^{3} {\left(n + 2 \, \log\left(e\right)\right)} + b^{3} c d^{2} \log\left(e\right)\right)} A B^{2} - {\left({\left(n^{2} - 3 \, \log\left(e\right)^{2}\right)} b^{3} c d^{2} - {\left(n^{2} + 6 \, n \log\left(e\right) + 6 \, \log\left(e\right)^{2}\right)} a b^{2} d^{3}\right)} B^{3}\right)} x^{2} + 3 \, {\left(B^{3} b^{3} d^{3} x^{3} + B^{3} a^{2} b c d^{2} + {\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} B^{3} x^{2} + {\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} B^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(6 \, {\left(a^{2} b d^{3} {\left(n + \log\left(e\right)\right)} + 2 \, a b^{2} c d^{2} \log\left(e\right)\right)} A B^{2} + {\left(2 \, b^{3} c^{2} d n^{2} - 6 \, {\left(n^{2} - \log\left(e\right)^{2}\right)} a b^{2} c d^{2} + {\left(4 \, n^{2} + 6 \, n \log\left(e\right) + 3 \, \log\left(e\right)^{2}\right)} a^{2} b d^{3}\right)} B^{3}\right)} x + 2 \, {\left(3 \, B^{3} a^{2} b c d^{2} \log\left(e\right) + 3 \, A B^{2} a^{2} b c d^{2} + {\left(B^{3} b^{3} d^{3} {\left(n + 3 \, \log\left(e\right)\right)} + 3 \, A B^{2} b^{3} d^{3}\right)} x^{3} + 3 \, {\left({\left(b^{3} c d^{2} + 2 \, a b^{2} d^{3}\right)} A B^{2} + {\left(a b^{2} d^{3} {\left(n + 2 \, \log\left(e\right)\right)} + b^{3} c d^{2} \log\left(e\right)\right)} B^{3}\right)} x^{2} + 3 \, {\left({\left(2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} A B^{2} + {\left(a^{2} b d^{3} {\left(n + \log\left(e\right)\right)} + 2 \, a b^{2} c d^{2} \log\left(e\right)\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b d^{3} x + b c d^{2}}\,{d x}"," ",0,"A^2*B*b^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + 1/3*A^3*b^2*x^3 + 3*A^2*B*a*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + A^3*a*b*x^2 + 3*A^2*B*a^2*x*log((b*x + a)^n*e/(d*x + c)^n) + A^3*a^2*x + 3*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A^2*B*a^2/e - 3*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A^2*B*a*b/e + 1/2*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*A^2*B*b^2/e - 1/6*(2*(B^3*b^3*d^3*x^3 + 3*B^3*a*b^2*d^3*x^2 + 3*B^3*a^2*b*d^3*x)*log((d*x + c)^n)^3 - 3*(2*B^3*a^3*d^3*n*log(b*x + a) - 2*(b^3*c^3*n - 3*a*b^2*c^2*d*n + 3*a^2*b*c*d^2*n)*B^3*log(d*x + c) + 2*(B^3*b^3*d^3*log(e) + A*B^2*b^3*d^3)*x^3 + (6*A*B^2*a*b^2*d^3 + (a*b^2*d^3*(n + 6*log(e)) - b^3*c*d^2*n)*B^3)*x^2 + 2*(3*A*B^2*a^2*b*d^3 + (a^2*b*d^3*(2*n + 3*log(e)) + b^3*c^2*d*n - 3*a*b^2*c*d^2*n)*B^3)*x + 2*(B^3*b^3*d^3*x^3 + 3*B^3*a*b^2*d^3*x^2 + 3*B^3*a^2*b*d^3*x)*log((b*x + a)^n))*log((d*x + c)^n)^2)/(b*d^3) - integrate(-(B^3*a^2*b*c*d^2*log(e)^3 + 3*A*B^2*a^2*b*c*d^2*log(e)^2 + (B^3*b^3*d^3*log(e)^3 + 3*A*B^2*b^3*d^3*log(e)^2)*x^3 + (B^3*b^3*d^3*x^3 + B^3*a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*B^3*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*B^3*x)*log((b*x + a)^n)^3 + (3*(b^3*c*d^2*log(e)^2 + 2*a*b^2*d^3*log(e)^2)*A*B^2 + (b^3*c*d^2*log(e)^3 + 2*a*b^2*d^3*log(e)^3)*B^3)*x^2 + 3*(B^3*a^2*b*c*d^2*log(e) + A*B^2*a^2*b*c*d^2 + (B^3*b^3*d^3*log(e) + A*B^2*b^3*d^3)*x^3 + ((b^3*c*d^2 + 2*a*b^2*d^3)*A*B^2 + (b^3*c*d^2*log(e) + 2*a*b^2*d^3*log(e))*B^3)*x^2 + ((2*a*b^2*c*d^2 + a^2*b*d^3)*A*B^2 + (2*a*b^2*c*d^2*log(e) + a^2*b*d^3*log(e))*B^3)*x)*log((b*x + a)^n)^2 + (3*(2*a*b^2*c*d^2*log(e)^2 + a^2*b*d^3*log(e)^2)*A*B^2 + (2*a*b^2*c*d^2*log(e)^3 + a^2*b*d^3*log(e)^3)*B^3)*x + 3*(B^3*a^2*b*c*d^2*log(e)^2 + 2*A*B^2*a^2*b*c*d^2*log(e) + (B^3*b^3*d^3*log(e)^2 + 2*A*B^2*b^3*d^3*log(e))*x^3 + (2*(b^3*c*d^2*log(e) + 2*a*b^2*d^3*log(e))*A*B^2 + (b^3*c*d^2*log(e)^2 + 2*a*b^2*d^3*log(e)^2)*B^3)*x^2 + (2*(2*a*b^2*c*d^2*log(e) + a^2*b*d^3*log(e))*A*B^2 + (2*a*b^2*c*d^2*log(e)^2 + a^2*b*d^3*log(e)^2)*B^3)*x)*log((b*x + a)^n) - (2*B^3*a^3*d^3*n^2*log(b*x + a) + 3*B^3*a^2*b*c*d^2*log(e)^2 + 6*A*B^2*a^2*b*c*d^2*log(e) - 2*(b^3*c^3*n^2 - 3*a*b^2*c^2*d*n^2 + 3*a^2*b*c*d^2*n^2)*B^3*log(d*x + c) + ((2*n*log(e) + 3*log(e)^2)*B^3*b^3*d^3 + 2*A*B^2*b^3*d^3*(n + 3*log(e)))*x^3 + (6*(a*b^2*d^3*(n + 2*log(e)) + b^3*c*d^2*log(e))*A*B^2 - ((n^2 - 3*log(e)^2)*b^3*c*d^2 - (n^2 + 6*n*log(e) + 6*log(e)^2)*a*b^2*d^3)*B^3)*x^2 + 3*(B^3*b^3*d^3*x^3 + B^3*a^2*b*c*d^2 + (b^3*c*d^2 + 2*a*b^2*d^3)*B^3*x^2 + (2*a*b^2*c*d^2 + a^2*b*d^3)*B^3*x)*log((b*x + a)^n)^2 + (6*(a^2*b*d^3*(n + log(e)) + 2*a*b^2*c*d^2*log(e))*A*B^2 + (2*b^3*c^2*d*n^2 - 6*(n^2 - log(e)^2)*a*b^2*c*d^2 + (4*n^2 + 6*n*log(e) + 3*log(e)^2)*a^2*b*d^3)*B^3)*x + 2*(3*B^3*a^2*b*c*d^2*log(e) + 3*A*B^2*a^2*b*c*d^2 + (B^3*b^3*d^3*(n + 3*log(e)) + 3*A*B^2*b^3*d^3)*x^3 + 3*((b^3*c*d^2 + 2*a*b^2*d^3)*A*B^2 + (a*b^2*d^3*(n + 2*log(e)) + b^3*c*d^2*log(e))*B^3)*x^2 + 3*((2*a*b^2*c*d^2 + a^2*b*d^3)*A*B^2 + (a^2*b*d^3*(n + log(e)) + 2*a*b^2*c*d^2*log(e))*B^3)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^3*x + b*c*d^2), x)","F",0
166,0,0,0,0.000000," ","integrate((b*x+a)*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3,x, algorithm=""maxima"")","\frac{3}{2} \, A^{2} B b x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{2} \, A^{3} b x^{2} + 3 \, A^{2} B a x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} a x + \frac{3 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A^{2} B a}{e} - \frac{3 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A^{2} B b}{2 \, e} - \frac{{\left(B^{3} b^{2} d^{2} x^{2} + 2 \, B^{3} a b d^{2} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{3} - 3 \, {\left(B^{3} a^{2} d^{2} n \log\left(b x + a\right) + {\left(b^{2} c^{2} n - 2 \, a b c d n\right)} B^{3} \log\left(d x + c\right) + {\left(B^{3} b^{2} d^{2} \log\left(e\right) + A B^{2} b^{2} d^{2}\right)} x^{2} + {\left(2 \, A B^{2} a b d^{2} + {\left(a b d^{2} {\left(n + 2 \, \log\left(e\right)\right)} - b^{2} c d n\right)} B^{3}\right)} x + {\left(B^{3} b^{2} d^{2} x^{2} + 2 \, B^{3} a b d^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, b d^{2}} - \int -\frac{B^{3} a b c d \log\left(e\right)^{3} + 3 \, A B^{2} a b c d \log\left(e\right)^{2} + {\left(B^{3} b^{2} d^{2} x^{2} + B^{3} a b c d + {\left(b^{2} c d + a b d^{2}\right)} B^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + {\left(B^{3} b^{2} d^{2} \log\left(e\right)^{3} + 3 \, A B^{2} b^{2} d^{2} \log\left(e\right)^{2}\right)} x^{2} + 3 \, {\left(B^{3} a b c d \log\left(e\right) + A B^{2} a b c d + {\left(B^{3} b^{2} d^{2} \log\left(e\right) + A B^{2} b^{2} d^{2}\right)} x^{2} + {\left({\left(b^{2} c d + a b d^{2}\right)} A B^{2} + {\left(b^{2} c d \log\left(e\right) + a b d^{2} \log\left(e\right)\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(3 \, {\left(b^{2} c d \log\left(e\right)^{2} + a b d^{2} \log\left(e\right)^{2}\right)} A B^{2} + {\left(b^{2} c d \log\left(e\right)^{3} + a b d^{2} \log\left(e\right)^{3}\right)} B^{3}\right)} x + 3 \, {\left(B^{3} a b c d \log\left(e\right)^{2} + 2 \, A B^{2} a b c d \log\left(e\right) + {\left(B^{3} b^{2} d^{2} \log\left(e\right)^{2} + 2 \, A B^{2} b^{2} d^{2} \log\left(e\right)\right)} x^{2} + {\left(2 \, {\left(b^{2} c d \log\left(e\right) + a b d^{2} \log\left(e\right)\right)} A B^{2} + {\left(b^{2} c d \log\left(e\right)^{2} + a b d^{2} \log\left(e\right)^{2}\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 3 \, {\left(B^{3} a^{2} d^{2} n^{2} \log\left(b x + a\right) + B^{3} a b c d \log\left(e\right)^{2} + 2 \, A B^{2} a b c d \log\left(e\right) + {\left(b^{2} c^{2} n^{2} - 2 \, a b c d n^{2}\right)} B^{3} \log\left(d x + c\right) + {\left({\left(n \log\left(e\right) + \log\left(e\right)^{2}\right)} B^{3} b^{2} d^{2} + A B^{2} b^{2} d^{2} {\left(n + 2 \, \log\left(e\right)\right)}\right)} x^{2} + {\left(B^{3} b^{2} d^{2} x^{2} + B^{3} a b c d + {\left(b^{2} c d + a b d^{2}\right)} B^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(2 \, {\left(a b d^{2} {\left(n + \log\left(e\right)\right)} + b^{2} c d \log\left(e\right)\right)} A B^{2} - {\left({\left(n^{2} - \log\left(e\right)^{2}\right)} b^{2} c d - {\left(n^{2} + 2 \, n \log\left(e\right) + \log\left(e\right)^{2}\right)} a b d^{2}\right)} B^{3}\right)} x + {\left(2 \, B^{3} a b c d \log\left(e\right) + 2 \, A B^{2} a b c d + {\left(B^{3} b^{2} d^{2} {\left(n + 2 \, \log\left(e\right)\right)} + 2 \, A B^{2} b^{2} d^{2}\right)} x^{2} + 2 \, {\left({\left(b^{2} c d + a b d^{2}\right)} A B^{2} + {\left(a b d^{2} {\left(n + \log\left(e\right)\right)} + b^{2} c d \log\left(e\right)\right)} B^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b d^{2} x + b c d}\,{d x}"," ",0,"3/2*A^2*B*b*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 1/2*A^3*b*x^2 + 3*A^2*B*a*x*log((b*x + a)^n*e/(d*x + c)^n) + A^3*a*x + 3*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A^2*B*a/e - 3/2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A^2*B*b/e - 1/2*((B^3*b^2*d^2*x^2 + 2*B^3*a*b*d^2*x)*log((d*x + c)^n)^3 - 3*(B^3*a^2*d^2*n*log(b*x + a) + (b^2*c^2*n - 2*a*b*c*d*n)*B^3*log(d*x + c) + (B^3*b^2*d^2*log(e) + A*B^2*b^2*d^2)*x^2 + (2*A*B^2*a*b*d^2 + (a*b*d^2*(n + 2*log(e)) - b^2*c*d*n)*B^3)*x + (B^3*b^2*d^2*x^2 + 2*B^3*a*b*d^2*x)*log((b*x + a)^n))*log((d*x + c)^n)^2)/(b*d^2) - integrate(-(B^3*a*b*c*d*log(e)^3 + 3*A*B^2*a*b*c*d*log(e)^2 + (B^3*b^2*d^2*x^2 + B^3*a*b*c*d + (b^2*c*d + a*b*d^2)*B^3*x)*log((b*x + a)^n)^3 + (B^3*b^2*d^2*log(e)^3 + 3*A*B^2*b^2*d^2*log(e)^2)*x^2 + 3*(B^3*a*b*c*d*log(e) + A*B^2*a*b*c*d + (B^3*b^2*d^2*log(e) + A*B^2*b^2*d^2)*x^2 + ((b^2*c*d + a*b*d^2)*A*B^2 + (b^2*c*d*log(e) + a*b*d^2*log(e))*B^3)*x)*log((b*x + a)^n)^2 + (3*(b^2*c*d*log(e)^2 + a*b*d^2*log(e)^2)*A*B^2 + (b^2*c*d*log(e)^3 + a*b*d^2*log(e)^3)*B^3)*x + 3*(B^3*a*b*c*d*log(e)^2 + 2*A*B^2*a*b*c*d*log(e) + (B^3*b^2*d^2*log(e)^2 + 2*A*B^2*b^2*d^2*log(e))*x^2 + (2*(b^2*c*d*log(e) + a*b*d^2*log(e))*A*B^2 + (b^2*c*d*log(e)^2 + a*b*d^2*log(e)^2)*B^3)*x)*log((b*x + a)^n) - 3*(B^3*a^2*d^2*n^2*log(b*x + a) + B^3*a*b*c*d*log(e)^2 + 2*A*B^2*a*b*c*d*log(e) + (b^2*c^2*n^2 - 2*a*b*c*d*n^2)*B^3*log(d*x + c) + ((n*log(e) + log(e)^2)*B^3*b^2*d^2 + A*B^2*b^2*d^2*(n + 2*log(e)))*x^2 + (B^3*b^2*d^2*x^2 + B^3*a*b*c*d + (b^2*c*d + a*b*d^2)*B^3*x)*log((b*x + a)^n)^2 + (2*(a*b*d^2*(n + log(e)) + b^2*c*d*log(e))*A*B^2 - ((n^2 - log(e)^2)*b^2*c*d - (n^2 + 2*n*log(e) + log(e)^2)*a*b*d^2)*B^3)*x + (2*B^3*a*b*c*d*log(e) + 2*A*B^2*a*b*c*d + (B^3*b^2*d^2*(n + 2*log(e)) + 2*A*B^2*b^2*d^2)*x^2 + 2*((b^2*c*d + a*b*d^2)*A*B^2 + (a*b*d^2*(n + log(e)) + b^2*c*d*log(e))*B^3)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d^2*x + b*c*d), x)","F",0
167,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(b*x+a),x, algorithm=""maxima"")","-\frac{B^{3} \log\left(b x + a\right) \log\left({\left(d x + c\right)}^{n}\right)^{3}}{b} + \frac{A^{3} \log\left(b x + a\right)}{b} + \int \frac{B^{3} b c \log\left(e\right)^{3} + 3 \, A B^{2} b c \log\left(e\right)^{2} + 3 \, A^{2} B b c \log\left(e\right) + {\left(B^{3} b d x + B^{3} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + 3 \, {\left(B^{3} b c \log\left(e\right) + A B^{2} b c + {\left(B^{3} b d \log\left(e\right) + A B^{2} b d\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(B^{3} b c \log\left(e\right) + A B^{2} b c + {\left(B^{3} b d \log\left(e\right) + A B^{2} b d\right)} x + {\left(B^{3} b d n x + B^{3} a d n\right)} \log\left(b x + a\right) + {\left(B^{3} b d x + B^{3} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(B^{3} b d \log\left(e\right)^{3} + 3 \, A B^{2} b d \log\left(e\right)^{2} + 3 \, A^{2} B b d \log\left(e\right)\right)} x + 3 \, {\left(B^{3} b c \log\left(e\right)^{2} + 2 \, A B^{2} b c \log\left(e\right) + A^{2} B b c + {\left(B^{3} b d \log\left(e\right)^{2} + 2 \, A B^{2} b d \log\left(e\right) + A^{2} B b d\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 3 \, {\left(B^{3} b c \log\left(e\right)^{2} + 2 \, A B^{2} b c \log\left(e\right) + A^{2} B b c + {\left(B^{3} b d x + B^{3} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{3} b d \log\left(e\right)^{2} + 2 \, A B^{2} b d \log\left(e\right) + A^{2} B b d\right)} x + 2 \, {\left(B^{3} b c \log\left(e\right) + A B^{2} b c + {\left(B^{3} b d \log\left(e\right) + A B^{2} b d\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x}\,{d x}"," ",0,"-B^3*log(b*x + a)*log((d*x + c)^n)^3/b + A^3*log(b*x + a)/b + integrate((B^3*b*c*log(e)^3 + 3*A*B^2*b*c*log(e)^2 + 3*A^2*B*b*c*log(e) + (B^3*b*d*x + B^3*b*c)*log((b*x + a)^n)^3 + 3*(B^3*b*c*log(e) + A*B^2*b*c + (B^3*b*d*log(e) + A*B^2*b*d)*x)*log((b*x + a)^n)^2 + 3*(B^3*b*c*log(e) + A*B^2*b*c + (B^3*b*d*log(e) + A*B^2*b*d)*x + (B^3*b*d*n*x + B^3*a*d*n)*log(b*x + a) + (B^3*b*d*x + B^3*b*c)*log((b*x + a)^n))*log((d*x + c)^n)^2 + (B^3*b*d*log(e)^3 + 3*A*B^2*b*d*log(e)^2 + 3*A^2*B*b*d*log(e))*x + 3*(B^3*b*c*log(e)^2 + 2*A*B^2*b*c*log(e) + A^2*B*b*c + (B^3*b*d*log(e)^2 + 2*A*B^2*b*d*log(e) + A^2*B*b*d)*x)*log((b*x + a)^n) - 3*(B^3*b*c*log(e)^2 + 2*A*B^2*b*c*log(e) + A^2*B*b*c + (B^3*b*d*x + B^3*b*c)*log((b*x + a)^n)^2 + (B^3*b*d*log(e)^2 + 2*A*B^2*b*d*log(e) + A^2*B*b*d)*x + 2*(B^3*b*c*log(e) + A*B^2*b*c + (B^3*b*d*log(e) + A*B^2*b*d)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x), x)","F",0
168,1,1129,0,2.160854," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(b*x+a)^2,x, algorithm=""maxima"")","-\frac{B^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{3}}{b^{2} x + a b} - {\left(\frac{3 \, {\left(\frac{d e n \log\left(b x + a\right)}{b^{2} c - a b d} - \frac{d e n \log\left(d x + c\right)}{b^{2} c - a b d} + \frac{e n}{b^{2} x + a b}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{e} + \frac{\frac{3 \, {\left(2 \, b c e^{2} n^{2} - 2 \, a d e^{2} n^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(b d e^{2} n^{2} x + a d e^{2} n^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{{\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x\right)} e} + \frac{6 \, b c e^{3} n^{3} - 6 \, a d e^{3} n^{3} + {\left(b d e^{3} n^{3} x + a d e^{3} n^{3}\right)} \log\left(b x + a\right)^{3} - {\left(b d e^{3} n^{3} x + a d e^{3} n^{3}\right)} \log\left(d x + c\right)^{3} - 3 \, {\left(b d e^{3} n^{3} x + a d e^{3} n^{3}\right)} \log\left(b x + a\right)^{2} - 3 \, {\left(b d e^{3} n^{3} x + a d e^{3} n^{3} - {\left(b d e^{3} n^{3} x + a d e^{3} n^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 6 \, {\left(b d e^{3} n^{3} x + a d e^{3} n^{3}\right)} \log\left(b x + a\right) - 3 \, {\left(2 \, b d e^{3} n^{3} x + 2 \, a d e^{3} n^{3} + {\left(b d e^{3} n^{3} x + a d e^{3} n^{3}\right)} \log\left(b x + a\right)^{2} - 2 \, {\left(b d e^{3} n^{3} x + a d e^{3} n^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x\right)} e^{2}}}{e}\right)} B^{3} - 3 \, A B^{2} {\left(\frac{2 \, {\left(\frac{d e n \log\left(b x + a\right)}{b^{2} c - a b d} - \frac{d e n \log\left(d x + c\right)}{b^{2} c - a b d} + \frac{e n}{b^{2} x + a b}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{e} + \frac{2 \, b c e^{2} n^{2} - 2 \, a d e^{2} n^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(b d e^{2} n^{2} x + a d e^{2} n^{2} - {\left(b d e^{2} n^{2} x + a d e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a b^{2} c - a^{2} b d + {\left(b^{3} c - a b^{2} d\right)} x\right)} e^{2}}\right)} - \frac{3 \, A B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{b^{2} x + a b} - \frac{3 \, {\left(\frac{d e n \log\left(b x + a\right)}{b^{2} c - a b d} - \frac{d e n \log\left(d x + c\right)}{b^{2} c - a b d} + \frac{e n}{b^{2} x + a b}\right)} A^{2} B}{e} - \frac{3 \, A^{2} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{b^{2} x + a b} - \frac{A^{3}}{b^{2} x + a b}"," ",0,"-B^3*log((b*x + a)^n*e/(d*x + c)^n)^3/(b^2*x + a*b) - (3*(d*e*n*log(b*x + a)/(b^2*c - a*b*d) - d*e*n*log(d*x + c)/(b^2*c - a*b*d) + e*n/(b^2*x + a*b))*log((b*x + a)^n*e/(d*x + c)^n)^2/e + (3*(2*b*c*e^2*n^2 - 2*a*d*e^2*n^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a)^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(d*x + c)^2 + 2*(b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a) - 2*(b*d*e^2*n^2*x + a*d*e^2*n^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a))*log(d*x + c))*log((b*x + a)^n*e/(d*x + c)^n)/((a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x)*e) + (6*b*c*e^3*n^3 - 6*a*d*e^3*n^3 + (b*d*e^3*n^3*x + a*d*e^3*n^3)*log(b*x + a)^3 - (b*d*e^3*n^3*x + a*d*e^3*n^3)*log(d*x + c)^3 - 3*(b*d*e^3*n^3*x + a*d*e^3*n^3)*log(b*x + a)^2 - 3*(b*d*e^3*n^3*x + a*d*e^3*n^3 - (b*d*e^3*n^3*x + a*d*e^3*n^3)*log(b*x + a))*log(d*x + c)^2 + 6*(b*d*e^3*n^3*x + a*d*e^3*n^3)*log(b*x + a) - 3*(2*b*d*e^3*n^3*x + 2*a*d*e^3*n^3 + (b*d*e^3*n^3*x + a*d*e^3*n^3)*log(b*x + a)^2 - 2*(b*d*e^3*n^3*x + a*d*e^3*n^3)*log(b*x + a))*log(d*x + c))/((a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x)*e^2))/e)*B^3 - 3*A*B^2*(2*(d*e*n*log(b*x + a)/(b^2*c - a*b*d) - d*e*n*log(d*x + c)/(b^2*c - a*b*d) + e*n/(b^2*x + a*b))*log((b*x + a)^n*e/(d*x + c)^n)/e + (2*b*c*e^2*n^2 - 2*a*d*e^2*n^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a)^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(d*x + c)^2 + 2*(b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a) - 2*(b*d*e^2*n^2*x + a*d*e^2*n^2 - (b*d*e^2*n^2*x + a*d*e^2*n^2)*log(b*x + a))*log(d*x + c))/((a*b^2*c - a^2*b*d + (b^3*c - a*b^2*d)*x)*e^2)) - 3*A*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2/(b^2*x + a*b) - 3*(d*e*n*log(b*x + a)/(b^2*c - a*b*d) - d*e*n*log(d*x + c)/(b^2*c - a*b*d) + e*n/(b^2*x + a*b))*A^2*B/e - 3*A^2*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^2*x + a*b) - A^3/(b^2*x + a*b)","B",0
169,1,2246,0,2.762439," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(b*x+a)^3,x, algorithm=""maxima"")","-\frac{B^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{3}}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}} + \frac{1}{8} \, {\left(\frac{6 \, {\left(\frac{2 \, d^{2} e n \log\left(b x + a\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} - \frac{2 \, d^{2} e n \log\left(d x + c\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} + \frac{2 \, b d e n x - b c e n + 3 \, a d e n}{a^{2} b^{2} c - a^{3} b d + {\left(b^{4} c - a b^{3} d\right)} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{e} - \frac{\frac{6 \, {\left(b^{2} c^{2} e^{2} n^{2} - 8 \, a b c d e^{2} n^{2} + 7 \, a^{2} d^{2} e^{2} n^{2} + 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d e^{2} n^{2} - a b d^{2} e^{2} n^{2}\right)} x - 6 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} e^{2} n^{2} x^{2} + 6 \, a b d^{2} e^{2} n^{2} x + 3 \, a^{2} d^{2} e^{2} n^{2} - 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{{\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{2} + 2 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x\right)} e} + \frac{3 \, b^{2} c^{2} e^{3} n^{3} - 48 \, a b c d e^{3} n^{3} + 45 \, a^{2} d^{2} e^{3} n^{3} - 4 \, {\left(b^{2} d^{2} e^{3} n^{3} x^{2} + 2 \, a b d^{2} e^{3} n^{3} x + a^{2} d^{2} e^{3} n^{3}\right)} \log\left(b x + a\right)^{3} + 4 \, {\left(b^{2} d^{2} e^{3} n^{3} x^{2} + 2 \, a b d^{2} e^{3} n^{3} x + a^{2} d^{2} e^{3} n^{3}\right)} \log\left(d x + c\right)^{3} + 18 \, {\left(b^{2} d^{2} e^{3} n^{3} x^{2} + 2 \, a b d^{2} e^{3} n^{3} x + a^{2} d^{2} e^{3} n^{3}\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(3 \, b^{2} d^{2} e^{3} n^{3} x^{2} + 6 \, a b d^{2} e^{3} n^{3} x + 3 \, a^{2} d^{2} e^{3} n^{3} - 2 \, {\left(b^{2} d^{2} e^{3} n^{3} x^{2} + 2 \, a b d^{2} e^{3} n^{3} x + a^{2} d^{2} e^{3} n^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 42 \, {\left(b^{2} c d e^{3} n^{3} - a b d^{2} e^{3} n^{3}\right)} x - 42 \, {\left(b^{2} d^{2} e^{3} n^{3} x^{2} + 2 \, a b d^{2} e^{3} n^{3} x + a^{2} d^{2} e^{3} n^{3}\right)} \log\left(b x + a\right) + 6 \, {\left(7 \, b^{2} d^{2} e^{3} n^{3} x^{2} + 14 \, a b d^{2} e^{3} n^{3} x + 7 \, a^{2} d^{2} e^{3} n^{3} + 2 \, {\left(b^{2} d^{2} e^{3} n^{3} x^{2} + 2 \, a b d^{2} e^{3} n^{3} x + a^{2} d^{2} e^{3} n^{3}\right)} \log\left(b x + a\right)^{2} - 6 \, {\left(b^{2} d^{2} e^{3} n^{3} x^{2} + 2 \, a b d^{2} e^{3} n^{3} x + a^{2} d^{2} e^{3} n^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{2} + 2 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x\right)} e^{2}}}{e}\right)} B^{3} + \frac{3}{4} \, A B^{2} {\left(\frac{2 \, {\left(\frac{2 \, d^{2} e n \log\left(b x + a\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} - \frac{2 \, d^{2} e n \log\left(d x + c\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} + \frac{2 \, b d e n x - b c e n + 3 \, a d e n}{a^{2} b^{2} c - a^{3} b d + {\left(b^{4} c - a b^{3} d\right)} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{e} - \frac{b^{2} c^{2} e^{2} n^{2} - 8 \, a b c d e^{2} n^{2} + 7 \, a^{2} d^{2} e^{2} n^{2} + 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 6 \, {\left(b^{2} c d e^{2} n^{2} - a b d^{2} e^{2} n^{2}\right)} x - 6 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(3 \, b^{2} d^{2} e^{2} n^{2} x^{2} + 6 \, a b d^{2} e^{2} n^{2} x + 3 \, a^{2} d^{2} e^{2} n^{2} - 2 \, {\left(b^{2} d^{2} e^{2} n^{2} x^{2} + 2 \, a b d^{2} e^{2} n^{2} x + a^{2} d^{2} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{2} b^{3} c^{2} - 2 \, a^{3} b^{2} c d + a^{4} b d^{2} + {\left(b^{5} c^{2} - 2 \, a b^{4} c d + a^{2} b^{3} d^{2}\right)} x^{2} + 2 \, {\left(a b^{4} c^{2} - 2 \, a^{2} b^{3} c d + a^{3} b^{2} d^{2}\right)} x\right)} e^{2}}\right)} - \frac{3 \, A B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}} + \frac{3 \, {\left(\frac{2 \, d^{2} e n \log\left(b x + a\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} - \frac{2 \, d^{2} e n \log\left(d x + c\right)}{b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}} + \frac{2 \, b d e n x - b c e n + 3 \, a d e n}{a^{2} b^{2} c - a^{3} b d + {\left(b^{4} c - a b^{3} d\right)} x^{2} + 2 \, {\left(a b^{3} c - a^{2} b^{2} d\right)} x}\right)} A^{2} B}{4 \, e} - \frac{3 \, A^{2} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}} - \frac{A^{3}}{2 \, {\left(b^{3} x^{2} + 2 \, a b^{2} x + a^{2} b\right)}}"," ",0,"-1/2*B^3*log((b*x + a)^n*e/(d*x + c)^n)^3/(b^3*x^2 + 2*a*b^2*x + a^2*b) + 1/8*(6*(2*d^2*e*n*log(b*x + a)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - 2*d^2*e*n*log(d*x + c)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) + (2*b*d*e*n*x - b*c*e*n + 3*a*d*e*n)/(a^2*b^2*c - a^3*b*d + (b^4*c - a*b^3*d)*x^2 + 2*(a*b^3*c - a^2*b^2*d)*x))*log((b*x + a)^n*e/(d*x + c)^n)^2/e - (6*(b^2*c^2*e^2*n^2 - 8*a*b*c*d*e^2*n^2 + 7*a^2*d^2*e^2*n^2 + 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a)^2 + 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(d*x + c)^2 - 6*(b^2*c*d*e^2*n^2 - a*b*d^2*e^2*n^2)*x - 6*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a) + 2*(3*b^2*d^2*e^2*n^2*x^2 + 6*a*b*d^2*e^2*n^2*x + 3*a^2*d^2*e^2*n^2 - 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a))*log(d*x + c))*log((b*x + a)^n*e/(d*x + c)^n)/((a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^2 + 2*(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x)*e) + (3*b^2*c^2*e^3*n^3 - 48*a*b*c*d*e^3*n^3 + 45*a^2*d^2*e^3*n^3 - 4*(b^2*d^2*e^3*n^3*x^2 + 2*a*b*d^2*e^3*n^3*x + a^2*d^2*e^3*n^3)*log(b*x + a)^3 + 4*(b^2*d^2*e^3*n^3*x^2 + 2*a*b*d^2*e^3*n^3*x + a^2*d^2*e^3*n^3)*log(d*x + c)^3 + 18*(b^2*d^2*e^3*n^3*x^2 + 2*a*b*d^2*e^3*n^3*x + a^2*d^2*e^3*n^3)*log(b*x + a)^2 + 6*(3*b^2*d^2*e^3*n^3*x^2 + 6*a*b*d^2*e^3*n^3*x + 3*a^2*d^2*e^3*n^3 - 2*(b^2*d^2*e^3*n^3*x^2 + 2*a*b*d^2*e^3*n^3*x + a^2*d^2*e^3*n^3)*log(b*x + a))*log(d*x + c)^2 - 42*(b^2*c*d*e^3*n^3 - a*b*d^2*e^3*n^3)*x - 42*(b^2*d^2*e^3*n^3*x^2 + 2*a*b*d^2*e^3*n^3*x + a^2*d^2*e^3*n^3)*log(b*x + a) + 6*(7*b^2*d^2*e^3*n^3*x^2 + 14*a*b*d^2*e^3*n^3*x + 7*a^2*d^2*e^3*n^3 + 2*(b^2*d^2*e^3*n^3*x^2 + 2*a*b*d^2*e^3*n^3*x + a^2*d^2*e^3*n^3)*log(b*x + a)^2 - 6*(b^2*d^2*e^3*n^3*x^2 + 2*a*b*d^2*e^3*n^3*x + a^2*d^2*e^3*n^3)*log(b*x + a))*log(d*x + c))/((a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^2 + 2*(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x)*e^2))/e)*B^3 + 3/4*A*B^2*(2*(2*d^2*e*n*log(b*x + a)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - 2*d^2*e*n*log(d*x + c)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) + (2*b*d*e*n*x - b*c*e*n + 3*a*d*e*n)/(a^2*b^2*c - a^3*b*d + (b^4*c - a*b^3*d)*x^2 + 2*(a*b^3*c - a^2*b^2*d)*x))*log((b*x + a)^n*e/(d*x + c)^n)/e - (b^2*c^2*e^2*n^2 - 8*a*b*c*d*e^2*n^2 + 7*a^2*d^2*e^2*n^2 + 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a)^2 + 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(d*x + c)^2 - 6*(b^2*c*d*e^2*n^2 - a*b*d^2*e^2*n^2)*x - 6*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a) + 2*(3*b^2*d^2*e^2*n^2*x^2 + 6*a*b*d^2*e^2*n^2*x + 3*a^2*d^2*e^2*n^2 - 2*(b^2*d^2*e^2*n^2*x^2 + 2*a*b*d^2*e^2*n^2*x + a^2*d^2*e^2*n^2)*log(b*x + a))*log(d*x + c))/((a^2*b^3*c^2 - 2*a^3*b^2*c*d + a^4*b*d^2 + (b^5*c^2 - 2*a*b^4*c*d + a^2*b^3*d^2)*x^2 + 2*(a*b^4*c^2 - 2*a^2*b^3*c*d + a^3*b^2*d^2)*x)*e^2)) - 3/2*A*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2/(b^3*x^2 + 2*a*b^2*x + a^2*b) + 3/4*(2*d^2*e*n*log(b*x + a)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) - 2*d^2*e*n*log(d*x + c)/(b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2) + (2*b*d*e*n*x - b*c*e*n + 3*a*d*e*n)/(a^2*b^2*c - a^3*b*d + (b^4*c - a*b^3*d)*x^2 + 2*(a*b^3*c - a^2*b^2*d)*x))*A^2*B/e - 3/2*A^2*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^3*x^2 + 2*a*b^2*x + a^2*b) - 1/2*A^3/(b^3*x^2 + 2*a*b^2*x + a^2*b)","B",0
170,1,3630,0,4.173587," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(b*x+a)^4,x, algorithm=""maxima"")","-\frac{B^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{3}}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}} - \frac{1}{108} \, {\left(\frac{18 \, {\left(\frac{6 \, d^{3} e n \log\left(b x + a\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{6 \, d^{3} e n \log\left(d x + c\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} + \frac{6 \, b^{2} d^{2} e n x^{2} + 2 \, b^{2} c^{2} e n - 7 \, a b c d e n + 11 \, a^{2} d^{2} e n - 3 \, {\left(b^{2} c d e n - 5 \, a b d^{2} e n\right)} x}{a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2} + {\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{e} + \frac{\frac{6 \, {\left(4 \, b^{3} c^{3} e^{2} n^{2} - 27 \, a b^{2} c^{2} d e^{2} n^{2} + 108 \, a^{2} b c d^{2} e^{2} n^{2} - 85 \, a^{3} d^{3} e^{2} n^{2} + 66 \, {\left(b^{3} c d^{2} e^{2} n^{2} - a b^{2} d^{3} e^{2} n^{2}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d e^{2} n^{2} - 54 \, a b^{2} c d^{2} e^{2} n^{2} + 49 \, a^{2} b d^{3} e^{2} n^{2}\right)} x + 66 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} e^{2} n^{2} x^{3} + 33 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 33 \, a^{2} b d^{3} e^{2} n^{2} x + 11 \, a^{3} d^{3} e^{2} n^{2} - 6 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{{\left(a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3} + {\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} x^{3} + 3 \, {\left(a b^{6} c^{3} - 3 \, a^{2} b^{5} c^{2} d + 3 \, a^{3} b^{4} c d^{2} - a^{4} b^{3} d^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} x\right)} e} + \frac{8 \, b^{3} c^{3} e^{3} n^{3} - 81 \, a b^{2} c^{2} d e^{3} n^{3} + 648 \, a^{2} b c d^{2} e^{3} n^{3} - 575 \, a^{3} d^{3} e^{3} n^{3} + 36 \, {\left(b^{3} d^{3} e^{3} n^{3} x^{3} + 3 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 3 \, a^{2} b d^{3} e^{3} n^{3} x + a^{3} d^{3} e^{3} n^{3}\right)} \log\left(b x + a\right)^{3} - 36 \, {\left(b^{3} d^{3} e^{3} n^{3} x^{3} + 3 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 3 \, a^{2} b d^{3} e^{3} n^{3} x + a^{3} d^{3} e^{3} n^{3}\right)} \log\left(d x + c\right)^{3} + 510 \, {\left(b^{3} c d^{2} e^{3} n^{3} - a b^{2} d^{3} e^{3} n^{3}\right)} x^{2} - 198 \, {\left(b^{3} d^{3} e^{3} n^{3} x^{3} + 3 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 3 \, a^{2} b d^{3} e^{3} n^{3} x + a^{3} d^{3} e^{3} n^{3}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(11 \, b^{3} d^{3} e^{3} n^{3} x^{3} + 33 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 33 \, a^{2} b d^{3} e^{3} n^{3} x + 11 \, a^{3} d^{3} e^{3} n^{3} - 6 \, {\left(b^{3} d^{3} e^{3} n^{3} x^{3} + 3 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 3 \, a^{2} b d^{3} e^{3} n^{3} x + a^{3} d^{3} e^{3} n^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(19 \, b^{3} c^{2} d e^{3} n^{3} - 378 \, a b^{2} c d^{2} e^{3} n^{3} + 359 \, a^{2} b d^{3} e^{3} n^{3}\right)} x + 510 \, {\left(b^{3} d^{3} e^{3} n^{3} x^{3} + 3 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 3 \, a^{2} b d^{3} e^{3} n^{3} x + a^{3} d^{3} e^{3} n^{3}\right)} \log\left(b x + a\right) - 6 \, {\left(85 \, b^{3} d^{3} e^{3} n^{3} x^{3} + 255 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 255 \, a^{2} b d^{3} e^{3} n^{3} x + 85 \, a^{3} d^{3} e^{3} n^{3} + 18 \, {\left(b^{3} d^{3} e^{3} n^{3} x^{3} + 3 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 3 \, a^{2} b d^{3} e^{3} n^{3} x + a^{3} d^{3} e^{3} n^{3}\right)} \log\left(b x + a\right)^{2} - 66 \, {\left(b^{3} d^{3} e^{3} n^{3} x^{3} + 3 \, a b^{2} d^{3} e^{3} n^{3} x^{2} + 3 \, a^{2} b d^{3} e^{3} n^{3} x + a^{3} d^{3} e^{3} n^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3} + {\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} x^{3} + 3 \, {\left(a b^{6} c^{3} - 3 \, a^{2} b^{5} c^{2} d + 3 \, a^{3} b^{4} c d^{2} - a^{4} b^{3} d^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} x\right)} e^{2}}}{e}\right)} B^{3} - \frac{1}{18} \, A B^{2} {\left(\frac{6 \, {\left(\frac{6 \, d^{3} e n \log\left(b x + a\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{6 \, d^{3} e n \log\left(d x + c\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} + \frac{6 \, b^{2} d^{2} e n x^{2} + 2 \, b^{2} c^{2} e n - 7 \, a b c d e n + 11 \, a^{2} d^{2} e n - 3 \, {\left(b^{2} c d e n - 5 \, a b d^{2} e n\right)} x}{a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2} + {\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{e} + \frac{4 \, b^{3} c^{3} e^{2} n^{2} - 27 \, a b^{2} c^{2} d e^{2} n^{2} + 108 \, a^{2} b c d^{2} e^{2} n^{2} - 85 \, a^{3} d^{3} e^{2} n^{2} + 66 \, {\left(b^{3} c d^{2} e^{2} n^{2} - a b^{2} d^{3} e^{2} n^{2}\right)} x^{2} - 18 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} - 18 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 3 \, {\left(5 \, b^{3} c^{2} d e^{2} n^{2} - 54 \, a b^{2} c d^{2} e^{2} n^{2} + 49 \, a^{2} b d^{3} e^{2} n^{2}\right)} x + 66 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right) - 6 \, {\left(11 \, b^{3} d^{3} e^{2} n^{2} x^{3} + 33 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 33 \, a^{2} b d^{3} e^{2} n^{2} x + 11 \, a^{3} d^{3} e^{2} n^{2} - 6 \, {\left(b^{3} d^{3} e^{2} n^{2} x^{3} + 3 \, a b^{2} d^{3} e^{2} n^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} n^{2} x + a^{3} d^{3} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{3} b^{4} c^{3} - 3 \, a^{4} b^{3} c^{2} d + 3 \, a^{5} b^{2} c d^{2} - a^{6} b d^{3} + {\left(b^{7} c^{3} - 3 \, a b^{6} c^{2} d + 3 \, a^{2} b^{5} c d^{2} - a^{3} b^{4} d^{3}\right)} x^{3} + 3 \, {\left(a b^{6} c^{3} - 3 \, a^{2} b^{5} c^{2} d + 3 \, a^{3} b^{4} c d^{2} - a^{4} b^{3} d^{3}\right)} x^{2} + 3 \, {\left(a^{2} b^{5} c^{3} - 3 \, a^{3} b^{4} c^{2} d + 3 \, a^{4} b^{3} c d^{2} - a^{5} b^{2} d^{3}\right)} x\right)} e^{2}}\right)} - \frac{A B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b} - \frac{{\left(\frac{6 \, d^{3} e n \log\left(b x + a\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} - \frac{6 \, d^{3} e n \log\left(d x + c\right)}{b^{4} c^{3} - 3 \, a b^{3} c^{2} d + 3 \, a^{2} b^{2} c d^{2} - a^{3} b d^{3}} + \frac{6 \, b^{2} d^{2} e n x^{2} + 2 \, b^{2} c^{2} e n - 7 \, a b c d e n + 11 \, a^{2} d^{2} e n - 3 \, {\left(b^{2} c d e n - 5 \, a b d^{2} e n\right)} x}{a^{3} b^{3} c^{2} - 2 \, a^{4} b^{2} c d + a^{5} b d^{2} + {\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} x^{3} + 3 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} x^{2} + 3 \, {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} x}\right)} A^{2} B}{6 \, e} - \frac{A^{2} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b} - \frac{A^{3}}{3 \, {\left(b^{4} x^{3} + 3 \, a b^{3} x^{2} + 3 \, a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"-1/3*B^3*log((b*x + a)^n*e/(d*x + c)^n)^3/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b) - 1/108*(18*(6*d^3*e*n*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) - 6*d^3*e*n*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) + (6*b^2*d^2*e*n*x^2 + 2*b^2*c^2*e*n - 7*a*b*c*d*e*n + 11*a^2*d^2*e*n - 3*(b^2*c*d*e*n - 5*a*b*d^2*e*n)*x)/(a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2 + (b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*x))*log((b*x + a)^n*e/(d*x + c)^n)^2/e + (6*(4*b^3*c^3*e^2*n^2 - 27*a*b^2*c^2*d*e^2*n^2 + 108*a^2*b*c*d^2*e^2*n^2 - 85*a^3*d^3*e^2*n^2 + 66*(b^3*c*d^2*e^2*n^2 - a*b^2*d^3*e^2*n^2)*x^2 - 18*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a)^2 - 18*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(d*x + c)^2 - 3*(5*b^3*c^2*d*e^2*n^2 - 54*a*b^2*c*d^2*e^2*n^2 + 49*a^2*b*d^3*e^2*n^2)*x + 66*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a) - 6*(11*b^3*d^3*e^2*n^2*x^3 + 33*a*b^2*d^3*e^2*n^2*x^2 + 33*a^2*b*d^3*e^2*n^2*x + 11*a^3*d^3*e^2*n^2 - 6*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a))*log(d*x + c))*log((b*x + a)^n*e/(d*x + c)^n)/((a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3 + (b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*x^3 + 3*(a*b^6*c^3 - 3*a^2*b^5*c^2*d + 3*a^3*b^4*c*d^2 - a^4*b^3*d^3)*x^2 + 3*(a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*x)*e) + (8*b^3*c^3*e^3*n^3 - 81*a*b^2*c^2*d*e^3*n^3 + 648*a^2*b*c*d^2*e^3*n^3 - 575*a^3*d^3*e^3*n^3 + 36*(b^3*d^3*e^3*n^3*x^3 + 3*a*b^2*d^3*e^3*n^3*x^2 + 3*a^2*b*d^3*e^3*n^3*x + a^3*d^3*e^3*n^3)*log(b*x + a)^3 - 36*(b^3*d^3*e^3*n^3*x^3 + 3*a*b^2*d^3*e^3*n^3*x^2 + 3*a^2*b*d^3*e^3*n^3*x + a^3*d^3*e^3*n^3)*log(d*x + c)^3 + 510*(b^3*c*d^2*e^3*n^3 - a*b^2*d^3*e^3*n^3)*x^2 - 198*(b^3*d^3*e^3*n^3*x^3 + 3*a*b^2*d^3*e^3*n^3*x^2 + 3*a^2*b*d^3*e^3*n^3*x + a^3*d^3*e^3*n^3)*log(b*x + a)^2 - 18*(11*b^3*d^3*e^3*n^3*x^3 + 33*a*b^2*d^3*e^3*n^3*x^2 + 33*a^2*b*d^3*e^3*n^3*x + 11*a^3*d^3*e^3*n^3 - 6*(b^3*d^3*e^3*n^3*x^3 + 3*a*b^2*d^3*e^3*n^3*x^2 + 3*a^2*b*d^3*e^3*n^3*x + a^3*d^3*e^3*n^3)*log(b*x + a))*log(d*x + c)^2 - 3*(19*b^3*c^2*d*e^3*n^3 - 378*a*b^2*c*d^2*e^3*n^3 + 359*a^2*b*d^3*e^3*n^3)*x + 510*(b^3*d^3*e^3*n^3*x^3 + 3*a*b^2*d^3*e^3*n^3*x^2 + 3*a^2*b*d^3*e^3*n^3*x + a^3*d^3*e^3*n^3)*log(b*x + a) - 6*(85*b^3*d^3*e^3*n^3*x^3 + 255*a*b^2*d^3*e^3*n^3*x^2 + 255*a^2*b*d^3*e^3*n^3*x + 85*a^3*d^3*e^3*n^3 + 18*(b^3*d^3*e^3*n^3*x^3 + 3*a*b^2*d^3*e^3*n^3*x^2 + 3*a^2*b*d^3*e^3*n^3*x + a^3*d^3*e^3*n^3)*log(b*x + a)^2 - 66*(b^3*d^3*e^3*n^3*x^3 + 3*a*b^2*d^3*e^3*n^3*x^2 + 3*a^2*b*d^3*e^3*n^3*x + a^3*d^3*e^3*n^3)*log(b*x + a))*log(d*x + c))/((a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3 + (b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*x^3 + 3*(a*b^6*c^3 - 3*a^2*b^5*c^2*d + 3*a^3*b^4*c*d^2 - a^4*b^3*d^3)*x^2 + 3*(a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*x)*e^2))/e)*B^3 - 1/18*A*B^2*(6*(6*d^3*e*n*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) - 6*d^3*e*n*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) + (6*b^2*d^2*e*n*x^2 + 2*b^2*c^2*e*n - 7*a*b*c*d*e*n + 11*a^2*d^2*e*n - 3*(b^2*c*d*e*n - 5*a*b*d^2*e*n)*x)/(a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2 + (b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*x))*log((b*x + a)^n*e/(d*x + c)^n)/e + (4*b^3*c^3*e^2*n^2 - 27*a*b^2*c^2*d*e^2*n^2 + 108*a^2*b*c*d^2*e^2*n^2 - 85*a^3*d^3*e^2*n^2 + 66*(b^3*c*d^2*e^2*n^2 - a*b^2*d^3*e^2*n^2)*x^2 - 18*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a)^2 - 18*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(d*x + c)^2 - 3*(5*b^3*c^2*d*e^2*n^2 - 54*a*b^2*c*d^2*e^2*n^2 + 49*a^2*b*d^3*e^2*n^2)*x + 66*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a) - 6*(11*b^3*d^3*e^2*n^2*x^3 + 33*a*b^2*d^3*e^2*n^2*x^2 + 33*a^2*b*d^3*e^2*n^2*x + 11*a^3*d^3*e^2*n^2 - 6*(b^3*d^3*e^2*n^2*x^3 + 3*a*b^2*d^3*e^2*n^2*x^2 + 3*a^2*b*d^3*e^2*n^2*x + a^3*d^3*e^2*n^2)*log(b*x + a))*log(d*x + c))/((a^3*b^4*c^3 - 3*a^4*b^3*c^2*d + 3*a^5*b^2*c*d^2 - a^6*b*d^3 + (b^7*c^3 - 3*a*b^6*c^2*d + 3*a^2*b^5*c*d^2 - a^3*b^4*d^3)*x^3 + 3*(a*b^6*c^3 - 3*a^2*b^5*c^2*d + 3*a^3*b^4*c*d^2 - a^4*b^3*d^3)*x^2 + 3*(a^2*b^5*c^3 - 3*a^3*b^4*c^2*d + 3*a^4*b^3*c*d^2 - a^5*b^2*d^3)*x)*e^2)) - A*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b) - 1/6*(6*d^3*e*n*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) - 6*d^3*e*n*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) + (6*b^2*d^2*e*n*x^2 + 2*b^2*c^2*e*n - 7*a*b*c*d*e*n + 11*a^2*d^2*e*n - 3*(b^2*c*d*e*n - 5*a*b*d^2*e*n)*x)/(a^3*b^3*c^2 - 2*a^4*b^2*c*d + a^5*b*d^2 + (b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*x^3 + 3*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*x^2 + 3*(a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*x))*A^2*B/e - A^2*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b) - 1/3*A^3/(b^4*x^3 + 3*a*b^3*x^2 + 3*a^2*b^2*x + a^3*b)","B",0
171,1,5280,0,5.792561," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(b*x+a)^5,x, algorithm=""maxima"")","-\frac{B^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{3}}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}} + \frac{1}{1152} \, {\left(\frac{72 \, {\left(\frac{12 \, d^{4} e n \log\left(b x + a\right)}{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}} - \frac{12 \, d^{4} e n \log\left(d x + c\right)}{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}} + \frac{12 \, b^{3} d^{3} e n x^{3} - 3 \, b^{3} c^{3} e n + 13 \, a b^{2} c^{2} d e n - 23 \, a^{2} b c d^{2} e n + 25 \, a^{3} d^{3} e n - 6 \, {\left(b^{3} c d^{2} e n - 7 \, a b^{2} d^{3} e n\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d e n - 5 \, a b^{2} c d^{2} e n + 13 \, a^{2} b d^{3} e n\right)} 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} + {\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)} 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)} 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)} 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)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{e} - \frac{\frac{12 \, {\left(9 \, b^{4} c^{4} e^{2} n^{2} - 64 \, a b^{3} c^{3} d e^{2} n^{2} + 216 \, a^{2} b^{2} c^{2} d^{2} e^{2} n^{2} - 576 \, a^{3} b c d^{3} e^{2} n^{2} + 415 \, a^{4} d^{4} e^{2} n^{2} - 300 \, {\left(b^{4} c d^{3} e^{2} n^{2} - a b^{3} d^{4} e^{2} n^{2}\right)} x^{3} + 6 \, {\left(13 \, b^{4} c^{2} d^{2} e^{2} n^{2} - 176 \, a b^{3} c d^{3} e^{2} n^{2} + 163 \, a^{2} b^{2} d^{4} e^{2} n^{2}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(7 \, b^{4} c^{3} d e^{2} n^{2} - 60 \, a b^{3} c^{2} d^{2} e^{2} n^{2} + 324 \, a^{2} b^{2} c d^{3} e^{2} n^{2} - 271 \, a^{3} b d^{4} e^{2} n^{2}\right)} x - 300 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right) + 12 \, {\left(25 \, b^{4} d^{4} e^{2} n^{2} x^{4} + 100 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 150 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 100 \, a^{3} b d^{4} e^{2} n^{2} x + 25 \, a^{4} d^{4} e^{2} n^{2} - 12 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{{\left(a^{4} b^{5} c^{4} - 4 \, a^{5} b^{4} c^{3} d + 6 \, a^{6} b^{3} c^{2} d^{2} - 4 \, a^{7} b^{2} c d^{3} + a^{8} b d^{4} + {\left(b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} - 4 \, a^{2} b^{7} c^{3} d + 6 \, a^{3} b^{6} c^{2} d^{2} - 4 \, a^{4} b^{5} c d^{3} + a^{5} b^{4} d^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} - 4 \, a^{3} b^{6} c^{3} d + 6 \, a^{4} b^{5} c^{2} d^{2} - 4 \, a^{5} b^{4} c d^{3} + a^{6} b^{3} d^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} - 4 \, a^{4} b^{5} c^{3} d + 6 \, a^{5} b^{4} c^{2} d^{2} - 4 \, a^{6} b^{3} c d^{3} + a^{7} b^{2} d^{4}\right)} x\right)} e} + \frac{27 \, b^{4} c^{4} e^{3} n^{3} - 256 \, a b^{3} c^{3} d e^{3} n^{3} + 1296 \, a^{2} b^{2} c^{2} d^{2} e^{3} n^{3} - 6912 \, a^{3} b c d^{3} e^{3} n^{3} + 5845 \, a^{4} d^{4} e^{3} n^{3} - 4980 \, {\left(b^{4} c d^{3} e^{3} n^{3} - a b^{3} d^{4} e^{3} n^{3}\right)} x^{3} - 288 \, {\left(b^{4} d^{4} e^{3} n^{3} x^{4} + 4 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 4 \, a^{3} b d^{4} e^{3} n^{3} x + a^{4} d^{4} e^{3} n^{3}\right)} \log\left(b x + a\right)^{3} + 288 \, {\left(b^{4} d^{4} e^{3} n^{3} x^{4} + 4 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 4 \, a^{3} b d^{4} e^{3} n^{3} x + a^{4} d^{4} e^{3} n^{3}\right)} \log\left(d x + c\right)^{3} + 30 \, {\left(23 \, b^{4} c^{2} d^{2} e^{3} n^{3} - 544 \, a b^{3} c d^{3} e^{3} n^{3} + 521 \, a^{2} b^{2} d^{4} e^{3} n^{3}\right)} x^{2} + 1800 \, {\left(b^{4} d^{4} e^{3} n^{3} x^{4} + 4 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 4 \, a^{3} b d^{4} e^{3} n^{3} x + a^{4} d^{4} e^{3} n^{3}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(25 \, b^{4} d^{4} e^{3} n^{3} x^{4} + 100 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 150 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 100 \, a^{3} b d^{4} e^{3} n^{3} x + 25 \, a^{4} d^{4} e^{3} n^{3} - 12 \, {\left(b^{4} d^{4} e^{3} n^{3} x^{4} + 4 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 4 \, a^{3} b d^{4} e^{3} n^{3} x + a^{4} d^{4} e^{3} n^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(37 \, b^{4} c^{3} d e^{3} n^{3} - 456 \, a b^{3} c^{2} d^{2} e^{3} n^{3} + 4536 \, a^{2} b^{2} c d^{3} e^{3} n^{3} - 4117 \, a^{3} b d^{4} e^{3} n^{3}\right)} x - 4980 \, {\left(b^{4} d^{4} e^{3} n^{3} x^{4} + 4 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 4 \, a^{3} b d^{4} e^{3} n^{3} x + a^{4} d^{4} e^{3} n^{3}\right)} \log\left(b x + a\right) + 12 \, {\left(415 \, b^{4} d^{4} e^{3} n^{3} x^{4} + 1660 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 2490 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 1660 \, a^{3} b d^{4} e^{3} n^{3} x + 415 \, a^{4} d^{4} e^{3} n^{3} + 72 \, {\left(b^{4} d^{4} e^{3} n^{3} x^{4} + 4 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 4 \, a^{3} b d^{4} e^{3} n^{3} x + a^{4} d^{4} e^{3} n^{3}\right)} \log\left(b x + a\right)^{2} - 300 \, {\left(b^{4} d^{4} e^{3} n^{3} x^{4} + 4 \, a b^{3} d^{4} e^{3} n^{3} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{3} n^{3} x^{2} + 4 \, a^{3} b d^{4} e^{3} n^{3} x + a^{4} d^{4} e^{3} n^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{4} b^{5} c^{4} - 4 \, a^{5} b^{4} c^{3} d + 6 \, a^{6} b^{3} c^{2} d^{2} - 4 \, a^{7} b^{2} c d^{3} + a^{8} b d^{4} + {\left(b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} - 4 \, a^{2} b^{7} c^{3} d + 6 \, a^{3} b^{6} c^{2} d^{2} - 4 \, a^{4} b^{5} c d^{3} + a^{5} b^{4} d^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} - 4 \, a^{3} b^{6} c^{3} d + 6 \, a^{4} b^{5} c^{2} d^{2} - 4 \, a^{5} b^{4} c d^{3} + a^{6} b^{3} d^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} - 4 \, a^{4} b^{5} c^{3} d + 6 \, a^{5} b^{4} c^{2} d^{2} - 4 \, a^{6} b^{3} c d^{3} + a^{7} b^{2} d^{4}\right)} x\right)} e^{2}}}{e}\right)} B^{3} + \frac{1}{96} \, A B^{2} {\left(\frac{12 \, {\left(\frac{12 \, d^{4} e n \log\left(b x + a\right)}{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}} - \frac{12 \, d^{4} e n \log\left(d x + c\right)}{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}} + \frac{12 \, b^{3} d^{3} e n x^{3} - 3 \, b^{3} c^{3} e n + 13 \, a b^{2} c^{2} d e n - 23 \, a^{2} b c d^{2} e n + 25 \, a^{3} d^{3} e n - 6 \, {\left(b^{3} c d^{2} e n - 7 \, a b^{2} d^{3} e n\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d e n - 5 \, a b^{2} c d^{2} e n + 13 \, a^{2} b d^{3} e n\right)} 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} + {\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)} 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)} 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)} 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)} x}\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{e} - \frac{9 \, b^{4} c^{4} e^{2} n^{2} - 64 \, a b^{3} c^{3} d e^{2} n^{2} + 216 \, a^{2} b^{2} c^{2} d^{2} e^{2} n^{2} - 576 \, a^{3} b c d^{3} e^{2} n^{2} + 415 \, a^{4} d^{4} e^{2} n^{2} - 300 \, {\left(b^{4} c d^{3} e^{2} n^{2} - a b^{3} d^{4} e^{2} n^{2}\right)} x^{3} + 6 \, {\left(13 \, b^{4} c^{2} d^{2} e^{2} n^{2} - 176 \, a b^{3} c d^{3} e^{2} n^{2} + 163 \, a^{2} b^{2} d^{4} e^{2} n^{2}\right)} x^{2} + 72 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right)^{2} + 72 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(7 \, b^{4} c^{3} d e^{2} n^{2} - 60 \, a b^{3} c^{2} d^{2} e^{2} n^{2} + 324 \, a^{2} b^{2} c d^{3} e^{2} n^{2} - 271 \, a^{3} b d^{4} e^{2} n^{2}\right)} x - 300 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right) + 12 \, {\left(25 \, b^{4} d^{4} e^{2} n^{2} x^{4} + 100 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 150 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 100 \, a^{3} b d^{4} e^{2} n^{2} x + 25 \, a^{4} d^{4} e^{2} n^{2} - 12 \, {\left(b^{4} d^{4} e^{2} n^{2} x^{4} + 4 \, a b^{3} d^{4} e^{2} n^{2} x^{3} + 6 \, a^{2} b^{2} d^{4} e^{2} n^{2} x^{2} + 4 \, a^{3} b d^{4} e^{2} n^{2} x + a^{4} d^{4} e^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{{\left(a^{4} b^{5} c^{4} - 4 \, a^{5} b^{4} c^{3} d + 6 \, a^{6} b^{3} c^{2} d^{2} - 4 \, a^{7} b^{2} c d^{3} + a^{8} b d^{4} + {\left(b^{9} c^{4} - 4 \, a b^{8} c^{3} d + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{3} b^{6} c d^{3} + a^{4} b^{5} d^{4}\right)} x^{4} + 4 \, {\left(a b^{8} c^{4} - 4 \, a^{2} b^{7} c^{3} d + 6 \, a^{3} b^{6} c^{2} d^{2} - 4 \, a^{4} b^{5} c d^{3} + a^{5} b^{4} d^{4}\right)} x^{3} + 6 \, {\left(a^{2} b^{7} c^{4} - 4 \, a^{3} b^{6} c^{3} d + 6 \, a^{4} b^{5} c^{2} d^{2} - 4 \, a^{5} b^{4} c d^{3} + a^{6} b^{3} d^{4}\right)} x^{2} + 4 \, {\left(a^{3} b^{6} c^{4} - 4 \, a^{4} b^{5} c^{3} d + 6 \, a^{5} b^{4} c^{2} d^{2} - 4 \, a^{6} b^{3} c d^{3} + a^{7} b^{2} d^{4}\right)} x\right)} e^{2}}\right)} - \frac{3 \, A B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2}}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}} + \frac{{\left(\frac{12 \, d^{4} e n \log\left(b x + a\right)}{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}} - \frac{12 \, d^{4} e n \log\left(d x + c\right)}{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}} + \frac{12 \, b^{3} d^{3} e n x^{3} - 3 \, b^{3} c^{3} e n + 13 \, a b^{2} c^{2} d e n - 23 \, a^{2} b c d^{2} e n + 25 \, a^{3} d^{3} e n - 6 \, {\left(b^{3} c d^{2} e n - 7 \, a b^{2} d^{3} e n\right)} x^{2} + 4 \, {\left(b^{3} c^{2} d e n - 5 \, a b^{2} c d^{2} e n + 13 \, a^{2} b d^{3} e n\right)} 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} + {\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)} 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)} 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)} 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)} x}\right)} A^{2} B}{16 \, e} - \frac{3 \, A^{2} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}} - \frac{A^{3}}{4 \, {\left(b^{5} x^{4} + 4 \, a b^{4} x^{3} + 6 \, a^{2} b^{3} x^{2} + 4 \, a^{3} b^{2} x + a^{4} b\right)}}"," ",0,"-1/4*B^3*log((b*x + a)^n*e/(d*x + c)^n)^3/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b) + 1/1152*(72*(12*d^4*e*n*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) - 12*d^4*e*n*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) + (12*b^3*d^3*e*n*x^3 - 3*b^3*c^3*e*n + 13*a*b^2*c^2*d*e*n - 23*a^2*b*c*d^2*e*n + 25*a^3*d^3*e*n - 6*(b^3*c*d^2*e*n - 7*a*b^2*d^3*e*n)*x^2 + 4*(b^3*c^2*d*e*n - 5*a*b^2*c*d^2*e*n + 13*a^2*b*d^3*e*n)*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 + (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)*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)*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)*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)*x))*log((b*x + a)^n*e/(d*x + c)^n)^2/e - (12*(9*b^4*c^4*e^2*n^2 - 64*a*b^3*c^3*d*e^2*n^2 + 216*a^2*b^2*c^2*d^2*e^2*n^2 - 576*a^3*b*c*d^3*e^2*n^2 + 415*a^4*d^4*e^2*n^2 - 300*(b^4*c*d^3*e^2*n^2 - a*b^3*d^4*e^2*n^2)*x^3 + 6*(13*b^4*c^2*d^2*e^2*n^2 - 176*a*b^3*c*d^3*e^2*n^2 + 163*a^2*b^2*d^4*e^2*n^2)*x^2 + 72*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a)^2 + 72*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(d*x + c)^2 - 4*(7*b^4*c^3*d*e^2*n^2 - 60*a*b^3*c^2*d^2*e^2*n^2 + 324*a^2*b^2*c*d^3*e^2*n^2 - 271*a^3*b*d^4*e^2*n^2)*x - 300*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a) + 12*(25*b^4*d^4*e^2*n^2*x^4 + 100*a*b^3*d^4*e^2*n^2*x^3 + 150*a^2*b^2*d^4*e^2*n^2*x^2 + 100*a^3*b*d^4*e^2*n^2*x + 25*a^4*d^4*e^2*n^2 - 12*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a))*log(d*x + c))*log((b*x + a)^n*e/(d*x + c)^n)/((a^4*b^5*c^4 - 4*a^5*b^4*c^3*d + 6*a^6*b^3*c^2*d^2 - 4*a^7*b^2*c*d^3 + a^8*b*d^4 + (b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4)*x^4 + 4*(a*b^8*c^4 - 4*a^2*b^7*c^3*d + 6*a^3*b^6*c^2*d^2 - 4*a^4*b^5*c*d^3 + a^5*b^4*d^4)*x^3 + 6*(a^2*b^7*c^4 - 4*a^3*b^6*c^3*d + 6*a^4*b^5*c^2*d^2 - 4*a^5*b^4*c*d^3 + a^6*b^3*d^4)*x^2 + 4*(a^3*b^6*c^4 - 4*a^4*b^5*c^3*d + 6*a^5*b^4*c^2*d^2 - 4*a^6*b^3*c*d^3 + a^7*b^2*d^4)*x)*e) + (27*b^4*c^4*e^3*n^3 - 256*a*b^3*c^3*d*e^3*n^3 + 1296*a^2*b^2*c^2*d^2*e^3*n^3 - 6912*a^3*b*c*d^3*e^3*n^3 + 5845*a^4*d^4*e^3*n^3 - 4980*(b^4*c*d^3*e^3*n^3 - a*b^3*d^4*e^3*n^3)*x^3 - 288*(b^4*d^4*e^3*n^3*x^4 + 4*a*b^3*d^4*e^3*n^3*x^3 + 6*a^2*b^2*d^4*e^3*n^3*x^2 + 4*a^3*b*d^4*e^3*n^3*x + a^4*d^4*e^3*n^3)*log(b*x + a)^3 + 288*(b^4*d^4*e^3*n^3*x^4 + 4*a*b^3*d^4*e^3*n^3*x^3 + 6*a^2*b^2*d^4*e^3*n^3*x^2 + 4*a^3*b*d^4*e^3*n^3*x + a^4*d^4*e^3*n^3)*log(d*x + c)^3 + 30*(23*b^4*c^2*d^2*e^3*n^3 - 544*a*b^3*c*d^3*e^3*n^3 + 521*a^2*b^2*d^4*e^3*n^3)*x^2 + 1800*(b^4*d^4*e^3*n^3*x^4 + 4*a*b^3*d^4*e^3*n^3*x^3 + 6*a^2*b^2*d^4*e^3*n^3*x^2 + 4*a^3*b*d^4*e^3*n^3*x + a^4*d^4*e^3*n^3)*log(b*x + a)^2 + 72*(25*b^4*d^4*e^3*n^3*x^4 + 100*a*b^3*d^4*e^3*n^3*x^3 + 150*a^2*b^2*d^4*e^3*n^3*x^2 + 100*a^3*b*d^4*e^3*n^3*x + 25*a^4*d^4*e^3*n^3 - 12*(b^4*d^4*e^3*n^3*x^4 + 4*a*b^3*d^4*e^3*n^3*x^3 + 6*a^2*b^2*d^4*e^3*n^3*x^2 + 4*a^3*b*d^4*e^3*n^3*x + a^4*d^4*e^3*n^3)*log(b*x + a))*log(d*x + c)^2 - 4*(37*b^4*c^3*d*e^3*n^3 - 456*a*b^3*c^2*d^2*e^3*n^3 + 4536*a^2*b^2*c*d^3*e^3*n^3 - 4117*a^3*b*d^4*e^3*n^3)*x - 4980*(b^4*d^4*e^3*n^3*x^4 + 4*a*b^3*d^4*e^3*n^3*x^3 + 6*a^2*b^2*d^4*e^3*n^3*x^2 + 4*a^3*b*d^4*e^3*n^3*x + a^4*d^4*e^3*n^3)*log(b*x + a) + 12*(415*b^4*d^4*e^3*n^3*x^4 + 1660*a*b^3*d^4*e^3*n^3*x^3 + 2490*a^2*b^2*d^4*e^3*n^3*x^2 + 1660*a^3*b*d^4*e^3*n^3*x + 415*a^4*d^4*e^3*n^3 + 72*(b^4*d^4*e^3*n^3*x^4 + 4*a*b^3*d^4*e^3*n^3*x^3 + 6*a^2*b^2*d^4*e^3*n^3*x^2 + 4*a^3*b*d^4*e^3*n^3*x + a^4*d^4*e^3*n^3)*log(b*x + a)^2 - 300*(b^4*d^4*e^3*n^3*x^4 + 4*a*b^3*d^4*e^3*n^3*x^3 + 6*a^2*b^2*d^4*e^3*n^3*x^2 + 4*a^3*b*d^4*e^3*n^3*x + a^4*d^4*e^3*n^3)*log(b*x + a))*log(d*x + c))/((a^4*b^5*c^4 - 4*a^5*b^4*c^3*d + 6*a^6*b^3*c^2*d^2 - 4*a^7*b^2*c*d^3 + a^8*b*d^4 + (b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4)*x^4 + 4*(a*b^8*c^4 - 4*a^2*b^7*c^3*d + 6*a^3*b^6*c^2*d^2 - 4*a^4*b^5*c*d^3 + a^5*b^4*d^4)*x^3 + 6*(a^2*b^7*c^4 - 4*a^3*b^6*c^3*d + 6*a^4*b^5*c^2*d^2 - 4*a^5*b^4*c*d^3 + a^6*b^3*d^4)*x^2 + 4*(a^3*b^6*c^4 - 4*a^4*b^5*c^3*d + 6*a^5*b^4*c^2*d^2 - 4*a^6*b^3*c*d^3 + a^7*b^2*d^4)*x)*e^2))/e)*B^3 + 1/96*A*B^2*(12*(12*d^4*e*n*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) - 12*d^4*e*n*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) + (12*b^3*d^3*e*n*x^3 - 3*b^3*c^3*e*n + 13*a*b^2*c^2*d*e*n - 23*a^2*b*c*d^2*e*n + 25*a^3*d^3*e*n - 6*(b^3*c*d^2*e*n - 7*a*b^2*d^3*e*n)*x^2 + 4*(b^3*c^2*d*e*n - 5*a*b^2*c*d^2*e*n + 13*a^2*b*d^3*e*n)*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 + (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)*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)*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)*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)*x))*log((b*x + a)^n*e/(d*x + c)^n)/e - (9*b^4*c^4*e^2*n^2 - 64*a*b^3*c^3*d*e^2*n^2 + 216*a^2*b^2*c^2*d^2*e^2*n^2 - 576*a^3*b*c*d^3*e^2*n^2 + 415*a^4*d^4*e^2*n^2 - 300*(b^4*c*d^3*e^2*n^2 - a*b^3*d^4*e^2*n^2)*x^3 + 6*(13*b^4*c^2*d^2*e^2*n^2 - 176*a*b^3*c*d^3*e^2*n^2 + 163*a^2*b^2*d^4*e^2*n^2)*x^2 + 72*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a)^2 + 72*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(d*x + c)^2 - 4*(7*b^4*c^3*d*e^2*n^2 - 60*a*b^3*c^2*d^2*e^2*n^2 + 324*a^2*b^2*c*d^3*e^2*n^2 - 271*a^3*b*d^4*e^2*n^2)*x - 300*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a) + 12*(25*b^4*d^4*e^2*n^2*x^4 + 100*a*b^3*d^4*e^2*n^2*x^3 + 150*a^2*b^2*d^4*e^2*n^2*x^2 + 100*a^3*b*d^4*e^2*n^2*x + 25*a^4*d^4*e^2*n^2 - 12*(b^4*d^4*e^2*n^2*x^4 + 4*a*b^3*d^4*e^2*n^2*x^3 + 6*a^2*b^2*d^4*e^2*n^2*x^2 + 4*a^3*b*d^4*e^2*n^2*x + a^4*d^4*e^2*n^2)*log(b*x + a))*log(d*x + c))/((a^4*b^5*c^4 - 4*a^5*b^4*c^3*d + 6*a^6*b^3*c^2*d^2 - 4*a^7*b^2*c*d^3 + a^8*b*d^4 + (b^9*c^4 - 4*a*b^8*c^3*d + 6*a^2*b^7*c^2*d^2 - 4*a^3*b^6*c*d^3 + a^4*b^5*d^4)*x^4 + 4*(a*b^8*c^4 - 4*a^2*b^7*c^3*d + 6*a^3*b^6*c^2*d^2 - 4*a^4*b^5*c*d^3 + a^5*b^4*d^4)*x^3 + 6*(a^2*b^7*c^4 - 4*a^3*b^6*c^3*d + 6*a^4*b^5*c^2*d^2 - 4*a^5*b^4*c*d^3 + a^6*b^3*d^4)*x^2 + 4*(a^3*b^6*c^4 - 4*a^4*b^5*c^3*d + 6*a^5*b^4*c^2*d^2 - 4*a^6*b^3*c*d^3 + a^7*b^2*d^4)*x)*e^2)) - 3/4*A*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b) + 1/16*(12*d^4*e*n*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) - 12*d^4*e*n*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) + (12*b^3*d^3*e*n*x^3 - 3*b^3*c^3*e*n + 13*a*b^2*c^2*d*e*n - 23*a^2*b*c*d^2*e*n + 25*a^3*d^3*e*n - 6*(b^3*c*d^2*e*n - 7*a*b^2*d^3*e*n)*x^2 + 4*(b^3*c^2*d*e*n - 5*a*b^2*c*d^2*e*n + 13*a^2*b*d^3*e*n)*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 + (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)*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)*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)*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)*x))*A^2*B/e - 3/4*A^2*B*log((b*x + a)^n*e/(d*x + c)^n)/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b) - 1/4*A^3/(b^5*x^4 + 4*a*b^4*x^3 + 6*a^2*b^3*x^2 + 4*a^3*b^2*x + a^4*b)","B",0
172,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{2} {\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*x + a*g)^2*(B*log((b*x + a)^n*e/(d*x + c)^n) + A)), x)","F",0
173,1,619,0,1.259382," ","integrate((b*g*x+a*g)^4*(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\frac{1}{5} \, A b^{4} g^{4} x^{5} + A a b^{3} g^{4} x^{4} + 2 \, A a^{2} b^{2} g^{4} x^{3} + 2 \, A a^{3} b g^{4} x^{2} + {\left(x \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) - \frac{a \log\left(b x + a\right)}{b} + \frac{c \log\left(d x + c\right)}{d}\right)} B a^{4} g^{4} + 2 \, {\left(x^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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} b g^{4} + {\left(2 \, x^{3} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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^{2} g^{4} + \frac{1}{6} \, {\left(6 \, x^{4} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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^{3} g^{4} + \frac{1}{60} \, {\left(12 \, x^{5} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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^{4} g^{4} + A a^{4} g^{4} x"," ",0,"1/5*A*b^4*g^4*x^5 + A*a*b^3*g^4*x^4 + 2*A*a^2*b^2*g^4*x^3 + 2*A*a^3*b*g^4*x^2 + (x*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - a*log(b*x + a)/b + c*log(d*x + c)/d)*B*a^4*g^4 + 2*(x^2*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*b*g^4 + (2*x^3*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - 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^2*g^4 + 1/6*(6*x^4*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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^3*g^4 + 1/60*(12*x^5*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - 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^4*g^4 + A*a^4*g^4*x","B",0
174,1,436,0,1.304571," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\frac{1}{4} \, A b^{3} g^{3} x^{4} + A a b^{2} g^{3} x^{3} + \frac{3}{2} \, A a^{2} b g^{3} x^{2} + {\left(x \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) - \frac{a \log\left(b x + a\right)}{b} + \frac{c \log\left(d x + c\right)}{d}\right)} B a^{3} g^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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 g^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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} g^{3} + \frac{1}{24} \, {\left(6 \, x^{4} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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} g^{3} + A a^{3} g^{3} x"," ",0,"1/4*A*b^3*g^3*x^4 + A*a*b^2*g^3*x^3 + 3/2*A*a^2*b*g^3*x^2 + (x*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - a*log(b*x + a)/b + c*log(d*x + c)/d)*B*a^3*g^3 + 3/2*(x^2*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*g^3 + 1/2*(2*x^3*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - 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*g^3 + 1/24*(6*x^4*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*g^3 + A*a^3*g^3*x","B",0
175,1,278,0,1.162605," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\frac{1}{3} \, A b^{2} g^{2} x^{3} + A a b g^{2} x^{2} + {\left(x \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) - \frac{a \log\left(b x + a\right)}{b} + \frac{c \log\left(d x + c\right)}{d}\right)} B a^{2} g^{2} + {\left(x^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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 g^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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} g^{2} + A a^{2} g^{2} x"," ",0,"1/3*A*b^2*g^2*x^3 + A*a*b*g^2*x^2 + (x*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - a*log(b*x + a)/b + c*log(d*x + c)/d)*B*a^2*g^2 + (x^2*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*g^2 + 1/6*(2*x^3*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - 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*g^2 + A*a^2*g^2*x","B",0
176,1,143,0,1.118599," ","integrate((b*g*x+a*g)*(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\frac{1}{2} \, A b g x^{2} + {\left(x \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) - \frac{a \log\left(b x + a\right)}{b} + \frac{c \log\left(d x + c\right)}{d}\right)} B a g + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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 g + A a g x"," ",0,"1/2*A*b*g*x^2 + (x*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - a*log(b*x + a)/b + c*log(d*x + c)/d)*B*a*g + 1/2*(x^2*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*g + A*a*g*x","A",0
177,0,0,0,0.000000," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))/(b*g*x+a*g),x, algorithm=""maxima"")","B {\left(\frac{\log\left(b x + a\right) \log\left(d x + c\right)}{b g} - \int -\frac{b d x \log\left(e\right) + b c \log\left(e\right) - {\left(2 \, b d x + b c + a d\right)} \log\left(b x + a\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}\right)} + \frac{A \log\left(b g x + a g\right)}{b g}"," ",0,"B*(log(b*x + a)*log(d*x + c)/(b*g) - integrate(-(b*d*x*log(e) + b*c*log(e) - (2*b*d*x + b*c + a*d)*log(b*x + a))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)) + A*log(b*g*x + a*g)/(b*g)","F",0
178,1,134,0,1.070620," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B {\left(\frac{\log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-B*(log(d*e*x/(b*x + a) + c*e/(b*x + a))/(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/(b^2*g^2*x + a*b*g^2)","B",0
179,1,255,0,1.279616," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{1}{4} \, B {\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{d e x}{b x + a} + \frac{c e}{b x + a}\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{A}{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*((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(d*e*x/(b*x + a) + c*e/(b*x + a))/(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*A/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","A",0
180,1,428,0,1.372370," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","\frac{1}{18} \, 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^{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{d e x}{b x + a} + \frac{c e}{b x + a}\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{A}{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*((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(d*e*x/(b*x + a) + c*e/(b*x + a))/(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*A/(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
181,1,647,0,1.514928," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{1}{48} \, B {\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{d e x}{b x + a} + \frac{c e}{b x + a}\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{A}{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*((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(d*e*x/(b*x + a) + c*e/(b*x + a))/(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*A/(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
182,1,2395,0,2.527549," ","integrate((b*g*x+a*g)^4*(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","\frac{1}{5} \, A^{2} b^{4} g^{4} x^{5} + A^{2} a b^{3} g^{4} x^{4} + 2 \, A^{2} a^{2} b^{2} g^{4} x^{3} + 2 \, A^{2} a^{3} b g^{4} x^{2} + 2 \, {\left(x \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) - \frac{a \log\left(b x + a\right)}{b} + \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{4} g^{4} + 4 \, {\left(x^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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} b g^{4} + 2 \, {\left(2 \, x^{3} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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^{2} g^{4} + \frac{1}{3} \, {\left(6 \, x^{4} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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^{3} g^{4} + \frac{1}{30} \, {\left(12 \, x^{5} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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^{4} g^{4} + A^{2} a^{4} g^{4} x + \frac{{\left({\left(12 \, g^{4} \log\left(e\right) - 25 \, g^{4}\right)} b^{4} c^{5} - {\left(60 \, g^{4} \log\left(e\right) - 113 \, g^{4}\right)} a b^{3} c^{4} d + 4 \, {\left(30 \, g^{4} \log\left(e\right) - 49 \, g^{4}\right)} a^{2} b^{2} c^{3} d^{2} - 12 \, {\left(10 \, g^{4} \log\left(e\right) - 13 \, g^{4}\right)} a^{3} b c^{2} d^{3} + 12 \, {\left(5 \, g^{4} \log\left(e\right) - 4 \, g^{4}\right)} a^{4} c d^{4}\right)} B^{2} \log\left(d x + c\right)}{30 \, d^{5}} - \frac{2 \, {\left(b^{5} c^{5} g^{4} - 5 \, a b^{4} c^{4} d g^{4} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} + 5 \, a^{4} b c d^{4} g^{4} - a^{5} d^{5} g^{4}\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}}{5 \, b d^{5}} + \frac{12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right)^{2} + 6 \, {\left(b^{5} c d^{4} g^{4} \log\left(e\right) + {\left(10 \, g^{4} \log\left(e\right)^{2} - g^{4} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 2 \, {\left({\left(4 \, g^{4} \log\left(e\right) - g^{4}\right)} b^{5} c^{2} d^{3} - 2 \, {\left(10 \, g^{4} \log\left(e\right) - g^{4}\right)} a b^{4} c d^{4} - {\left(60 \, g^{4} \log\left(e\right)^{2} - 16 \, g^{4} \log\left(e\right) + g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + {\left({\left(12 \, g^{4} \log\left(e\right) - 7 \, g^{4}\right)} b^{5} c^{3} d^{2} - 3 \, {\left(20 \, g^{4} \log\left(e\right) - 9 \, g^{4}\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(40 \, g^{4} \log\left(e\right) - 11 \, g^{4}\right)} a^{2} b^{3} c d^{4} + {\left(120 \, g^{4} \log\left(e\right)^{2} - 72 \, g^{4} \log\left(e\right) + 13 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 2 \, {\left({\left(12 \, g^{4} \log\left(e\right) - 13 \, g^{4}\right)} b^{5} c^{4} d - {\left(60 \, g^{4} \log\left(e\right) - 59 \, g^{4}\right)} a b^{4} c^{3} d^{2} + 6 \, {\left(20 \, g^{4} \log\left(e\right) - 17 \, g^{4}\right)} a^{2} b^{3} c^{2} d^{3} - {\left(120 \, g^{4} \log\left(e\right) - 79 \, g^{4}\right)} a^{3} b^{2} c d^{4} - {\left(30 \, g^{4} \log\left(e\right)^{2} - 48 \, g^{4} \log\left(e\right) + 23 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + B^{2} a^{5} d^{5} g^{4}\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + {\left(b^{5} c^{5} g^{4} - 5 \, a b^{4} c^{4} d g^{4} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} + 5 \, a^{4} b c d^{4} g^{4}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) + 3 \, {\left(b^{5} c d^{4} g^{4} + {\left(20 \, g^{4} \log\left(e\right) - g^{4}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 4 \, {\left(b^{5} c^{2} d^{3} g^{4} - 5 \, a b^{4} c d^{4} g^{4} - 2 \, {\left(15 \, g^{4} \log\left(e\right) - 2 \, g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + 6 \, {\left(b^{5} c^{3} d^{2} g^{4} - 5 \, a b^{4} c^{2} d^{3} g^{4} + 10 \, a^{2} b^{3} c d^{4} g^{4} + 2 \, {\left(10 \, g^{4} \log\left(e\right) - 3 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 12 \, {\left(b^{5} c^{4} d g^{4} - 5 \, a b^{4} c^{3} d^{2} g^{4} + 10 \, a^{2} b^{3} c^{2} d^{3} g^{4} - 10 \, a^{3} b^{2} c d^{4} g^{4} - {\left(5 \, g^{4} \log\left(e\right) - 4 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x - {\left(12 \, a b^{4} c^{4} d g^{4} - 54 \, a^{2} b^{3} c^{3} d^{2} g^{4} + 94 \, a^{3} b^{2} c^{2} d^{3} g^{4} - 77 \, a^{4} b c d^{4} g^{4} - {\left(12 \, g^{4} \log\left(e\right) - 25 \, g^{4}\right)} a^{5} d^{5}\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(12 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) + 3 \, {\left(b^{5} c d^{4} g^{4} + {\left(20 \, g^{4} \log\left(e\right) - g^{4}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 4 \, {\left(b^{5} c^{2} d^{3} g^{4} - 5 \, a b^{4} c d^{4} g^{4} - 2 \, {\left(15 \, g^{4} \log\left(e\right) - 2 \, g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + 6 \, {\left(b^{5} c^{3} d^{2} g^{4} - 5 \, a b^{4} c^{2} d^{3} g^{4} + 10 \, a^{2} b^{3} c d^{4} g^{4} + 2 \, {\left(10 \, g^{4} \log\left(e\right) - 3 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 12 \, {\left(b^{5} c^{4} d g^{4} - 5 \, a b^{4} c^{3} d^{2} g^{4} + 10 \, a^{2} b^{3} c^{2} d^{3} g^{4} - 10 \, a^{3} b^{2} c d^{4} g^{4} - {\left(5 \, g^{4} \log\left(e\right) - 4 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x - 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + B^{2} a^{5} d^{5} g^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{60 \, b d^{5}}"," ",0,"1/5*A^2*b^4*g^4*x^5 + A^2*a*b^3*g^4*x^4 + 2*A^2*a^2*b^2*g^4*x^3 + 2*A^2*a^3*b*g^4*x^2 + 2*(x*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - a*log(b*x + a)/b + c*log(d*x + c)/d)*A*B*a^4*g^4 + 4*(x^2*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*b*g^4 + 2*(2*x^3*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - 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^2*g^4 + 1/3*(6*x^4*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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^3*g^4 + 1/30*(12*x^5*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - 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^4*g^4 + A^2*a^4*g^4*x + 1/30*((12*g^4*log(e) - 25*g^4)*b^4*c^5 - (60*g^4*log(e) - 113*g^4)*a*b^3*c^4*d + 4*(30*g^4*log(e) - 49*g^4)*a^2*b^2*c^3*d^2 - 12*(10*g^4*log(e) - 13*g^4)*a^3*b*c^2*d^3 + 12*(5*g^4*log(e) - 4*g^4)*a^4*c*d^4)*B^2*log(d*x + c)/d^5 - 2/5*(b^5*c^5*g^4 - 5*a*b^4*c^4*d*g^4 + 10*a^2*b^3*c^3*d^2*g^4 - 10*a^3*b^2*c^2*d^3*g^4 + 5*a^4*b*c*d^4*g^4 - a^5*d^5*g^4)*(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*d^5) + 1/60*(12*B^2*b^5*d^5*g^4*x^5*log(e)^2 + 6*(b^5*c*d^4*g^4*log(e) + (10*g^4*log(e)^2 - g^4*log(e))*a*b^4*d^5)*B^2*x^4 - 2*((4*g^4*log(e) - g^4)*b^5*c^2*d^3 - 2*(10*g^4*log(e) - g^4)*a*b^4*c*d^4 - (60*g^4*log(e)^2 - 16*g^4*log(e) + g^4)*a^2*b^3*d^5)*B^2*x^3 + ((12*g^4*log(e) - 7*g^4)*b^5*c^3*d^2 - 3*(20*g^4*log(e) - 9*g^4)*a*b^4*c^2*d^3 + 3*(40*g^4*log(e) - 11*g^4)*a^2*b^3*c*d^4 + (120*g^4*log(e)^2 - 72*g^4*log(e) + 13*g^4)*a^3*b^2*d^5)*B^2*x^2 - 2*((12*g^4*log(e) - 13*g^4)*b^5*c^4*d - (60*g^4*log(e) - 59*g^4)*a*b^4*c^3*d^2 + 6*(20*g^4*log(e) - 17*g^4)*a^2*b^3*c^2*d^3 - (120*g^4*log(e) - 79*g^4)*a^3*b^2*c*d^4 - (30*g^4*log(e)^2 - 48*g^4*log(e) + 23*g^4)*a^4*b*d^5)*B^2*x + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + B^2*a^5*d^5*g^4)*log(b*x + a)^2 + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + (b^5*c^5*g^4 - 5*a*b^4*c^4*d*g^4 + 10*a^2*b^3*c^3*d^2*g^4 - 10*a^3*b^2*c^2*d^3*g^4 + 5*a^4*b*c*d^4*g^4)*B^2)*log(d*x + c)^2 - 2*(12*B^2*b^5*d^5*g^4*x^5*log(e) + 3*(b^5*c*d^4*g^4 + (20*g^4*log(e) - g^4)*a*b^4*d^5)*B^2*x^4 - 4*(b^5*c^2*d^3*g^4 - 5*a*b^4*c*d^4*g^4 - 2*(15*g^4*log(e) - 2*g^4)*a^2*b^3*d^5)*B^2*x^3 + 6*(b^5*c^3*d^2*g^4 - 5*a*b^4*c^2*d^3*g^4 + 10*a^2*b^3*c*d^4*g^4 + 2*(10*g^4*log(e) - 3*g^4)*a^3*b^2*d^5)*B^2*x^2 - 12*(b^5*c^4*d*g^4 - 5*a*b^4*c^3*d^2*g^4 + 10*a^2*b^3*c^2*d^3*g^4 - 10*a^3*b^2*c*d^4*g^4 - (5*g^4*log(e) - 4*g^4)*a^4*b*d^5)*B^2*x - (12*a*b^4*c^4*d*g^4 - 54*a^2*b^3*c^3*d^2*g^4 + 94*a^3*b^2*c^2*d^3*g^4 - 77*a^4*b*c*d^4*g^4 - (12*g^4*log(e) - 25*g^4)*a^5*d^5)*B^2)*log(b*x + a) + 2*(12*B^2*b^5*d^5*g^4*x^5*log(e) + 3*(b^5*c*d^4*g^4 + (20*g^4*log(e) - g^4)*a*b^4*d^5)*B^2*x^4 - 4*(b^5*c^2*d^3*g^4 - 5*a*b^4*c*d^4*g^4 - 2*(15*g^4*log(e) - 2*g^4)*a^2*b^3*d^5)*B^2*x^3 + 6*(b^5*c^3*d^2*g^4 - 5*a*b^4*c^2*d^3*g^4 + 10*a^2*b^3*c*d^4*g^4 + 2*(10*g^4*log(e) - 3*g^4)*a^3*b^2*d^5)*B^2*x^2 - 12*(b^5*c^4*d*g^4 - 5*a*b^4*c^3*d^2*g^4 + 10*a^2*b^3*c^2*d^3*g^4 - 10*a^3*b^2*c*d^4*g^4 - (5*g^4*log(e) - 4*g^4)*a^4*b*d^5)*B^2*x - 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + B^2*a^5*d^5*g^4)*log(b*x + a))*log(d*x + c))/(b*d^5)","B",0
183,1,1735,0,2.159639," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} b^{3} g^{3} x^{4} + A^{2} a b^{2} g^{3} x^{3} + \frac{3}{2} \, A^{2} a^{2} b g^{3} x^{2} + 2 \, {\left(x \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) - \frac{a \log\left(b x + a\right)}{b} + \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{3} g^{3} + 3 \, {\left(x^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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 g^{3} + {\left(2 \, x^{3} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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} g^{3} + \frac{1}{12} \, {\left(6 \, x^{4} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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} g^{3} + A^{2} a^{3} g^{3} x - \frac{{\left({\left(6 \, g^{3} \log\left(e\right) - 11 \, g^{3}\right)} b^{3} c^{4} - 2 \, {\left(12 \, g^{3} \log\left(e\right) - 19 \, g^{3}\right)} a b^{2} c^{3} d + 9 \, {\left(4 \, g^{3} \log\left(e\right) - 5 \, g^{3}\right)} a^{2} b c^{2} d^{2} - 6 \, {\left(4 \, g^{3} \log\left(e\right) - 3 \, g^{3}\right)} a^{3} c d^{3}\right)} B^{2} \log\left(d x + c\right)}{12 \, d^{4}} + \frac{{\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} - 4 \, a^{3} b c d^{3} g^{3} + a^{4} d^{4} 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^{2}}{2 \, b d^{4}} + \frac{3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right)^{2} + 2 \, {\left(b^{4} c d^{3} g^{3} \log\left(e\right) + {\left(6 \, g^{3} \log\left(e\right)^{2} - g^{3} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - {\left({\left(3 \, g^{3} \log\left(e\right) - g^{3}\right)} b^{4} c^{2} d^{2} - 2 \, {\left(6 \, g^{3} \log\left(e\right) - g^{3}\right)} a b^{3} c d^{3} - {\left(18 \, g^{3} \log\left(e\right)^{2} - 9 \, g^{3} \log\left(e\right) + g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + {\left({\left(6 \, g^{3} \log\left(e\right) - 5 \, g^{3}\right)} b^{4} c^{3} d - {\left(24 \, g^{3} \log\left(e\right) - 17 \, g^{3}\right)} a b^{3} c^{2} d^{2} + {\left(36 \, g^{3} \log\left(e\right) - 19 \, g^{3}\right)} a^{2} b^{2} c d^{3} + {\left(12 \, g^{3} \log\left(e\right)^{2} - 18 \, g^{3} \log\left(e\right) + 7 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x + B^{2} a^{4} d^{4} g^{3}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x - {\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} - 4 \, a^{3} b c d^{3} g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} - {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 2 \, {\left(b^{4} c d^{3} g^{3} + {\left(12 \, g^{3} \log\left(e\right) - g^{3}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 4 \, a b^{3} c d^{3} g^{3} - 3 \, {\left(4 \, g^{3} \log\left(e\right) - g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 6 \, {\left(b^{4} c^{3} d g^{3} - 4 \, a b^{3} c^{2} d^{2} g^{3} + 6 \, a^{2} b^{2} c d^{3} g^{3} + {\left(4 \, g^{3} \log\left(e\right) - 3 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + {\left(6 \, a b^{3} c^{3} d g^{3} - 21 \, a^{2} b^{2} c^{2} d^{2} g^{3} + 26 \, a^{3} b c d^{3} g^{3} + {\left(6 \, g^{3} \log\left(e\right) - 11 \, g^{3}\right)} a^{4} d^{4}\right)} B^{2}\right)} \log\left(b x + a\right) + {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 2 \, {\left(b^{4} c d^{3} g^{3} + {\left(12 \, g^{3} \log\left(e\right) - g^{3}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 4 \, a b^{3} c d^{3} g^{3} - 3 \, {\left(4 \, g^{3} \log\left(e\right) - g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 6 \, {\left(b^{4} c^{3} d g^{3} - 4 \, a b^{3} c^{2} d^{2} g^{3} + 6 \, a^{2} b^{2} c d^{3} g^{3} + {\left(4 \, g^{3} \log\left(e\right) - 3 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x - 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x + B^{2} a^{4} d^{4} g^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b d^{4}}"," ",0,"1/4*A^2*b^3*g^3*x^4 + A^2*a*b^2*g^3*x^3 + 3/2*A^2*a^2*b*g^3*x^2 + 2*(x*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - a*log(b*x + a)/b + c*log(d*x + c)/d)*A*B*a^3*g^3 + 3*(x^2*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*g^3 + (2*x^3*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - 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*g^3 + 1/12*(6*x^4*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*g^3 + A^2*a^3*g^3*x - 1/12*((6*g^3*log(e) - 11*g^3)*b^3*c^4 - 2*(12*g^3*log(e) - 19*g^3)*a*b^2*c^3*d + 9*(4*g^3*log(e) - 5*g^3)*a^2*b*c^2*d^2 - 6*(4*g^3*log(e) - 3*g^3)*a^3*c*d^3)*B^2*log(d*x + c)/d^4 + 1/2*(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 - 4*a^3*b*c*d^3*g^3 + a^4*d^4*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^2/(b*d^4) + 1/12*(3*B^2*b^4*d^4*g^3*x^4*log(e)^2 + 2*(b^4*c*d^3*g^3*log(e) + (6*g^3*log(e)^2 - g^3*log(e))*a*b^3*d^4)*B^2*x^3 - ((3*g^3*log(e) - g^3)*b^4*c^2*d^2 - 2*(6*g^3*log(e) - g^3)*a*b^3*c*d^3 - (18*g^3*log(e)^2 - 9*g^3*log(e) + g^3)*a^2*b^2*d^4)*B^2*x^2 + ((6*g^3*log(e) - 5*g^3)*b^4*c^3*d - (24*g^3*log(e) - 17*g^3)*a*b^3*c^2*d^2 + (36*g^3*log(e) - 19*g^3)*a^2*b^2*c*d^3 + (12*g^3*log(e)^2 - 18*g^3*log(e) + 7*g^3)*a^3*b*d^4)*B^2*x + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x + B^2*a^4*d^4*g^3)*log(b*x + a)^2 + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x - (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 - 4*a^3*b*c*d^3*g^3)*B^2)*log(d*x + c)^2 - (6*B^2*b^4*d^4*g^3*x^4*log(e) + 2*(b^4*c*d^3*g^3 + (12*g^3*log(e) - g^3)*a*b^3*d^4)*B^2*x^3 - 3*(b^4*c^2*d^2*g^3 - 4*a*b^3*c*d^3*g^3 - 3*(4*g^3*log(e) - g^3)*a^2*b^2*d^4)*B^2*x^2 + 6*(b^4*c^3*d*g^3 - 4*a*b^3*c^2*d^2*g^3 + 6*a^2*b^2*c*d^3*g^3 + (4*g^3*log(e) - 3*g^3)*a^3*b*d^4)*B^2*x + (6*a*b^3*c^3*d*g^3 - 21*a^2*b^2*c^2*d^2*g^3 + 26*a^3*b*c*d^3*g^3 + (6*g^3*log(e) - 11*g^3)*a^4*d^4)*B^2)*log(b*x + a) + (6*B^2*b^4*d^4*g^3*x^4*log(e) + 2*(b^4*c*d^3*g^3 + (12*g^3*log(e) - g^3)*a*b^3*d^4)*B^2*x^3 - 3*(b^4*c^2*d^2*g^3 - 4*a*b^3*c*d^3*g^3 - 3*(4*g^3*log(e) - g^3)*a^2*b^2*d^4)*B^2*x^2 + 6*(b^4*c^3*d*g^3 - 4*a*b^3*c^2*d^2*g^3 + 6*a^2*b^2*c*d^3*g^3 + (4*g^3*log(e) - 3*g^3)*a^3*b*d^4)*B^2*x - 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x + B^2*a^4*d^4*g^3)*log(b*x + a))*log(d*x + c))/(b*d^4)","B",0
184,1,1172,0,2.086037," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A^{2} b^{2} g^{2} x^{3} + A^{2} a b g^{2} x^{2} + 2 \, {\left(x \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) - \frac{a \log\left(b x + a\right)}{b} + \frac{c \log\left(d x + c\right)}{d}\right)} A B a^{2} g^{2} + 2 \, {\left(x^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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 g^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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} g^{2} + A^{2} a^{2} g^{2} x + \frac{{\left({\left(2 \, g^{2} \log\left(e\right) - 3 \, g^{2}\right)} b^{2} c^{3} - {\left(6 \, g^{2} \log\left(e\right) - 7 \, g^{2}\right)} a b c^{2} d + 2 \, {\left(3 \, g^{2} \log\left(e\right) - 2 \, g^{2}\right)} a^{2} c d^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, d^{3}} - \frac{2 \, {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 3 \, a^{2} b c d^{2} g^{2} - a^{3} d^{3} 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^{2}}{3 \, b d^{3}} + \frac{B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right)^{2} + {\left(b^{3} c d^{2} g^{2} \log\left(e\right) + {\left(3 \, g^{2} \log\left(e\right)^{2} - g^{2} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - {\left({\left(2 \, g^{2} \log\left(e\right) - g^{2}\right)} b^{3} c^{2} d - 2 \, {\left(3 \, g^{2} \log\left(e\right) - g^{2}\right)} a b^{2} c d^{2} - {\left(3 \, g^{2} \log\left(e\right)^{2} - 4 \, g^{2} \log\left(e\right) + g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + B^{2} a^{3} d^{3} g^{2}\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 3 \, a^{2} b c d^{2} g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} - {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + {\left(b^{3} c d^{2} g^{2} + {\left(6 \, g^{2} \log\left(e\right) - g^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - 2 \, {\left(b^{3} c^{2} d g^{2} - 3 \, a b^{2} c d^{2} g^{2} - {\left(3 \, g^{2} \log\left(e\right) - 2 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x - {\left(2 \, a b^{2} c^{2} d g^{2} - 5 \, a^{2} b c d^{2} g^{2} - {\left(2 \, g^{2} \log\left(e\right) - 3 \, g^{2}\right)} a^{3} d^{3}\right)} B^{2}\right)} \log\left(b x + a\right) + {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + {\left(b^{3} c d^{2} g^{2} + {\left(6 \, g^{2} \log\left(e\right) - g^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - 2 \, {\left(b^{3} c^{2} d g^{2} - 3 \, a b^{2} c d^{2} g^{2} - {\left(3 \, g^{2} \log\left(e\right) - 2 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x - 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + B^{2} a^{3} d^{3} g^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, b d^{3}}"," ",0,"1/3*A^2*b^2*g^2*x^3 + A^2*a*b*g^2*x^2 + 2*(x*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - a*log(b*x + a)/b + c*log(d*x + c)/d)*A*B*a^2*g^2 + 2*(x^2*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*g^2 + 1/3*(2*x^3*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - 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*g^2 + A^2*a^2*g^2*x + 1/3*((2*g^2*log(e) - 3*g^2)*b^2*c^3 - (6*g^2*log(e) - 7*g^2)*a*b*c^2*d + 2*(3*g^2*log(e) - 2*g^2)*a^2*c*d^2)*B^2*log(d*x + c)/d^3 - 2/3*(b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 3*a^2*b*c*d^2*g^2 - a^3*d^3*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^2/(b*d^3) + 1/3*(B^2*b^3*d^3*g^2*x^3*log(e)^2 + (b^3*c*d^2*g^2*log(e) + (3*g^2*log(e)^2 - g^2*log(e))*a*b^2*d^3)*B^2*x^2 - ((2*g^2*log(e) - g^2)*b^3*c^2*d - 2*(3*g^2*log(e) - g^2)*a*b^2*c*d^2 - (3*g^2*log(e)^2 - 4*g^2*log(e) + g^2)*a^2*b*d^3)*B^2*x + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + B^2*a^3*d^3*g^2)*log(b*x + a)^2 + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + (b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 3*a^2*b*c*d^2*g^2)*B^2)*log(d*x + c)^2 - (2*B^2*b^3*d^3*g^2*x^3*log(e) + (b^3*c*d^2*g^2 + (6*g^2*log(e) - g^2)*a*b^2*d^3)*B^2*x^2 - 2*(b^3*c^2*d*g^2 - 3*a*b^2*c*d^2*g^2 - (3*g^2*log(e) - 2*g^2)*a^2*b*d^3)*B^2*x - (2*a*b^2*c^2*d*g^2 - 5*a^2*b*c*d^2*g^2 - (2*g^2*log(e) - 3*g^2)*a^3*d^3)*B^2)*log(b*x + a) + (2*B^2*b^3*d^3*g^2*x^3*log(e) + (b^3*c*d^2*g^2 + (6*g^2*log(e) - g^2)*a*b^2*d^3)*B^2*x^2 - 2*(b^3*c^2*d*g^2 - 3*a*b^2*c*d^2*g^2 - (3*g^2*log(e) - 2*g^2)*a^2*b*d^3)*B^2*x - 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + B^2*a^3*d^3*g^2)*log(b*x + a))*log(d*x + c))/(b*d^3)","B",0
185,1,619,0,1.968852," ","integrate((b*g*x+a*g)*(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A^{2} b g x^{2} + 2 \, {\left(x \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) - \frac{a \log\left(b x + a\right)}{b} + \frac{c \log\left(d x + c\right)}{d}\right)} A B a g + {\left(x^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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 g + A^{2} a g x - \frac{{\left({\left(g \log\left(e\right) - g\right)} b c^{2} - {\left(2 \, g \log\left(e\right) - g\right)} a c d\right)} B^{2} \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b^{2} c^{2} g - 2 \, a b c d g + a^{2} d^{2} 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^{2}}{b d^{2}} + \frac{B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} + 2 \, {\left(b^{2} c d g \log\left(e\right) + {\left(g \log\left(e\right)^{2} - g \log\left(e\right)\right)} a b d^{2}\right)} B^{2} x + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x + B^{2} a^{2} d^{2} g\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x - {\left(b^{2} c^{2} g - 2 \, a b c d g\right)} B^{2}\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + {\left({\left(2 \, g \log\left(e\right) - g\right)} a b d^{2} + b^{2} c d g\right)} B^{2} x + {\left({\left(g \log\left(e\right) - g\right)} a^{2} d^{2} + a b c d g\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + {\left({\left(2 \, g \log\left(e\right) - g\right)} a b d^{2} + b^{2} c d g\right)} B^{2} x - {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x + B^{2} a^{2} d^{2} g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b d^{2}}"," ",0,"1/2*A^2*b*g*x^2 + 2*(x*log(d*e*x/(b*x + a) + c*e/(b*x + a)) - a*log(b*x + a)/b + c*log(d*x + c)/d)*A*B*a*g + (x^2*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + 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*g + A^2*a*g*x - ((g*log(e) - g)*b*c^2 - (2*g*log(e) - g)*a*c*d)*B^2*log(d*x + c)/d^2 + (b^2*c^2*g - 2*a*b*c*d*g + a^2*d^2*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^2/(b*d^2) + 1/2*(B^2*b^2*d^2*g*x^2*log(e)^2 + 2*(b^2*c*d*g*log(e) + (g*log(e)^2 - g*log(e))*a*b*d^2)*B^2*x + (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x + B^2*a^2*d^2*g)*log(b*x + a)^2 + (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x - (b^2*c^2*g - 2*a*b*c*d*g)*B^2)*log(d*x + c)^2 - 2*(B^2*b^2*d^2*g*x^2*log(e) + ((2*g*log(e) - g)*a*b*d^2 + b^2*c*d*g)*B^2*x + ((g*log(e) - g)*a^2*d^2 + a*b*c*d*g)*B^2)*log(b*x + a) + 2*(B^2*b^2*d^2*g*x^2*log(e) + ((2*g*log(e) - g)*a*b*d^2 + b^2*c*d*g)*B^2*x - (B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x + B^2*a^2*d^2*g)*log(b*x + a))*log(d*x + c))/(b*d^2)","B",0
186,0,0,0,0.000000," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))^2/(b*g*x+a*g),x, algorithm=""maxima"")","\frac{B^{2} \log\left(b x + a\right) \log\left(d x + c\right)^{2}}{b g} + \frac{A^{2} \log\left(b g x + a g\right)}{b g} - \int -\frac{B^{2} b c \log\left(e\right)^{2} + 2 \, A B b c \log\left(e\right) + {\left(B^{2} b d x + B^{2} b c\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b d \log\left(e\right)^{2} + 2 \, A B b d \log\left(e\right)\right)} x - 2 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x\right)} \log\left(b x + a\right) + 2 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x - {\left(2 \, B^{2} b d x + {\left(b c + a d\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}"," ",0,"B^2*log(b*x + a)*log(d*x + c)^2/(b*g) + A^2*log(b*g*x + a*g)/(b*g) - integrate(-(B^2*b*c*log(e)^2 + 2*A*B*b*c*log(e) + (B^2*b*d*x + B^2*b*c)*log(b*x + a)^2 + (B^2*b*d*log(e)^2 + 2*A*B*b*d*log(e))*x - 2*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x)*log(b*x + a) + 2*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x - (2*B^2*b*d*x + (b*c + a*d)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)","F",0
187,1,416,0,1.254213," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","{\left(2 \, {\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)} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right) + \frac{{\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)}{a b^{2} c g^{2} - a^{2} b d g^{2} + {\left(b^{3} c g^{2} - a b^{2} d g^{2}\right)} x}\right)} B^{2} - 2 \, A B {\left(\frac{\log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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{B^{2} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right)^{2}}{b^{2} g^{2} x + a b g^{2}} - \frac{A^{2}}{b^{2} g^{2} x + a b g^{2}}"," ",0,"(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))*log(d*e*x/(b*x + a) + c*e/(b*x + a)) + ((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^2*c*g^2 - a^2*b*d*g^2 + (b^3*c*g^2 - a*b^2*d*g^2)*x))*B^2 - 2*A*B*(log(d*e*x/(b*x + a) + c*e/(b*x + a))/(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)) - B^2*log(d*e*x/(b*x + a) + c*e/(b*x + a))^2/(b^2*g^2*x + a*b*g^2) - A^2/(b^2*g^2*x + a*b*g^2)","B",0
188,1,847,0,1.517318," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\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{d e x}{b x + a} + \frac{c e}{b x + a}\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} - \frac{1}{2} \, A B {\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{d e x}{b x + a} + \frac{c e}{b x + a}\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} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\right)^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{A^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"-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(d*e*x/(b*x + a) + c*e/(b*x + a)) + (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 - 1/2*A*B*((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(d*e*x/(b*x + a) + c*e/(b*x + a))/(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*log(d*e*x/(b*x + a) + c*e/(b*x + a))^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
189,1,1420,0,2.171647," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","\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{d e x}{b x + a} + \frac{c e}{b x + a}\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} + \frac{1}{9} \, 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^{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{d e x}{b x + a} + \frac{c e}{b x + a}\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} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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{A^{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,"1/54*(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(d*e*x/(b*x + a) + c*e/(b*x + a)) - (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 + 1/9*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^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(d*e*x/(b*x + a) + c*e/(b*x + a))/(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*log(d*e*x/(b*x + a) + c*e/(b*x + a))^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*A^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
190,1,2122,0,2.907641," ","integrate((A+B*log(e*(d*x+c)/(b*x+a)))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\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{d e x}{b x + a} + \frac{c e}{b x + a}\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} - \frac{1}{24} \, A B {\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{d e x}{b x + a} + \frac{c e}{b x + a}\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} \log\left(\frac{d e x}{b x + a} + \frac{c e}{b x + a}\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{A^{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,"-1/288*(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(d*e*x/(b*x + a) + c*e/(b*x + a)) + (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 - 1/24*A*B*((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(d*e*x/(b*x + a) + c*e/(b*x + a))/(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*log(d*e*x/(b*x + a) + c*e/(b*x + a))^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*A^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
191,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\int \frac{{\left(b g x + a g\right)}^{2}}{B \log\left(\frac{{\left(d x + c\right)} e}{b x + a}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)^2/(B*log((d*x + c)*e/(b*x + a)) + A), x)","F",0
192,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\int \frac{b g x + a g}{B \log\left(\frac{{\left(d x + c\right)} e}{b x + a}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)/(B*log((d*x + c)*e/(b*x + a)) + A), x)","F",0
193,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)} {\left(B \log\left(\frac{{\left(d x + c\right)} e}{b x + a}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)*(B*log((d*x + c)*e/(b*x + a)) + A)), x)","F",0
194,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{2} {\left(B \log\left(\frac{{\left(d x + c\right)} e}{b x + a}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^2*(B*log((d*x + c)*e/(b*x + a)) + A)), x)","F",0
195,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*(d*x+c)/(b*x+a))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{3} {\left(B \log\left(\frac{{\left(d x + c\right)} e}{b x + a}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^3*(B*log((d*x + c)*e/(b*x + a)) + A)), x)","F",0
196,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","-\frac{b^{3} d g^{2} x^{4} + a^{3} c g^{2} + {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{3} + 3 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x^{2} + {\left(3 \, a^{2} b c g^{2} + a^{3} d g^{2}\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) - {\left(b c - a d\right)} A B - {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}} + \int \frac{4 \, b^{3} d g^{2} x^{3} + 3 \, a^{2} b c g^{2} + a^{3} d g^{2} + 3 \, {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{2} + 6 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) - {\left(b c - a d\right)} A B - {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}}\,{d x}"," ",0,"-(b^3*d*g^2*x^4 + a^3*c*g^2 + (b^3*c*g^2 + 3*a*b^2*d*g^2)*x^3 + 3*(a*b^2*c*g^2 + a^2*b*d*g^2)*x^2 + (3*a^2*b*c*g^2 + a^3*d*g^2)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) - (b*c - a*d)*A*B - (b*c*log(e) - a*d*log(e))*B^2) + integrate((4*b^3*d*g^2*x^3 + 3*a^2*b*c*g^2 + a^3*d*g^2 + 3*(b^3*c*g^2 + 3*a*b^2*d*g^2)*x^2 + 6*(a*b^2*c*g^2 + a^2*b*d*g^2)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) - (b*c - a*d)*A*B - (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
197,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","-\frac{b^{2} d g x^{3} + a^{2} c g + {\left(b^{2} c g + 2 \, a b d g\right)} x^{2} + {\left(2 \, a b c g + a^{2} d g\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) - {\left(b c - a d\right)} A B - {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}} + \int \frac{3 \, b^{2} d g x^{2} + 2 \, a b c g + a^{2} d g + 2 \, {\left(b^{2} c g + 2 \, a b d g\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) - {\left(b c - a d\right)} A B - {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}}\,{d x}"," ",0,"-(b^2*d*g*x^3 + a^2*c*g + (b^2*c*g + 2*a*b*d*g)*x^2 + (2*a*b*c*g + a^2*d*g)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) - (b*c - a*d)*A*B - (b*c*log(e) - a*d*log(e))*B^2) + integrate((3*b^2*d*g*x^2 + 2*a*b*c*g + a^2*d*g + 2*(b^2*c*g + 2*a*b*d*g)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) - (b*c - a*d)*A*B - (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
198,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","d \int \frac{1}{{\left(b c g - a d g\right)} B^{2} \log\left(b x + a\right) - {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right) - {\left(b c g - a d g\right)} A B - {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}}\,{d x} - \frac{d x + c}{{\left(b c g - a d g\right)} B^{2} \log\left(b x + a\right) - {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right) - {\left(b c g - a d g\right)} A B - {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}}"," ",0,"d*integrate(1/((b*c*g - a*d*g)*B^2*log(b*x + a) - (b*c*g - a*d*g)*B^2*log(d*x + c) - (b*c*g - a*d*g)*A*B - (b*c*g*log(e) - a*d*g*log(e))*B^2), x) - (d*x + c)/((b*c*g - a*d*g)*B^2*log(b*x + a) - (b*c*g - a*d*g)*B^2*log(d*x + c) - (b*c*g - a*d*g)*A*B - (b*c*g*log(e) - a*d*g*log(e))*B^2)","F",0
199,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","\frac{d x + c}{{\left(a b c g^{2} - a^{2} d g^{2}\right)} A B + {\left(a b c g^{2} \log\left(e\right) - a^{2} d g^{2} \log\left(e\right)\right)} B^{2} + {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} A B + {\left(b^{2} c g^{2} \log\left(e\right) - a b d g^{2} \log\left(e\right)\right)} B^{2}\right)} x - {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} B^{2} x + {\left(a b c g^{2} - a^{2} d g^{2}\right)} B^{2}\right)} \log\left(b x + a\right) + {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} B^{2} x + {\left(a b c g^{2} - a^{2} d g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)} + \int \frac{1}{B^{2} a^{2} g^{2} \log\left(e\right) + A B a^{2} g^{2} + {\left(B^{2} b^{2} g^{2} \log\left(e\right) + A B b^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} a b g^{2} \log\left(e\right) + A B a b g^{2}\right)} x - {\left(B^{2} b^{2} g^{2} x^{2} + 2 \, B^{2} a b g^{2} x + B^{2} a^{2} g^{2}\right)} \log\left(b x + a\right) + {\left(B^{2} b^{2} g^{2} x^{2} + 2 \, B^{2} a b g^{2} x + B^{2} a^{2} g^{2}\right)} \log\left(d x + c\right)}\,{d x}"," ",0,"(d*x + c)/((a*b*c*g^2 - a^2*d*g^2)*A*B + (a*b*c*g^2*log(e) - a^2*d*g^2*log(e))*B^2 + ((b^2*c*g^2 - a*b*d*g^2)*A*B + (b^2*c*g^2*log(e) - a*b*d*g^2*log(e))*B^2)*x - ((b^2*c*g^2 - a*b*d*g^2)*B^2*x + (a*b*c*g^2 - a^2*d*g^2)*B^2)*log(b*x + a) + ((b^2*c*g^2 - a*b*d*g^2)*B^2*x + (a*b*c*g^2 - a^2*d*g^2)*B^2)*log(d*x + c)) + integrate(1/(B^2*a^2*g^2*log(e) + A*B*a^2*g^2 + (B^2*b^2*g^2*log(e) + A*B*b^2*g^2)*x^2 + 2*(B^2*a*b*g^2*log(e) + A*B*a*b*g^2)*x - (B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(b*x + a) + (B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(d*x + c)), x)","F",0
200,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*(d*x+c)/(b*x+a)))^2,x, algorithm=""maxima"")","\frac{d x + c}{{\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} A B + {\left(a^{2} b c g^{3} \log\left(e\right) - a^{3} d g^{3} \log\left(e\right)\right)} B^{2} + {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} A B + {\left(b^{3} c g^{3} \log\left(e\right) - a b^{2} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} A B + {\left(a b^{2} c g^{3} \log\left(e\right) - a^{2} b d g^{3} \log\left(e\right)\right)} B^{2}\right)} x - {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} B^{2} x + {\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} B^{2}\right)} \log\left(b x + a\right) + {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} B^{2} x + {\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)} - \int -\frac{b d x + 2 \, b c - a d}{{\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} A B + {\left(b^{4} c g^{3} \log\left(e\right) - a b^{3} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} A B + {\left(a^{3} b c g^{3} \log\left(e\right) - a^{4} d g^{3} \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} A B + {\left(a b^{3} c g^{3} \log\left(e\right) - a^{2} b^{2} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} A B + {\left(a^{2} b^{2} c g^{3} \log\left(e\right) - a^{3} b d g^{3} \log\left(e\right)\right)} B^{2}\right)} x - {\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} B^{2} x + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} B^{2}\right)} \log\left(b x + a\right) + {\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} B^{2} x + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)}\,{d x}"," ",0,"(d*x + c)/((a^2*b*c*g^3 - a^3*d*g^3)*A*B + (a^2*b*c*g^3*log(e) - a^3*d*g^3*log(e))*B^2 + ((b^3*c*g^3 - a*b^2*d*g^3)*A*B + (b^3*c*g^3*log(e) - a*b^2*d*g^3*log(e))*B^2)*x^2 + 2*((a*b^2*c*g^3 - a^2*b*d*g^3)*A*B + (a*b^2*c*g^3*log(e) - a^2*b*d*g^3*log(e))*B^2)*x - ((b^3*c*g^3 - a*b^2*d*g^3)*B^2*x^2 + 2*(a*b^2*c*g^3 - a^2*b*d*g^3)*B^2*x + (a^2*b*c*g^3 - a^3*d*g^3)*B^2)*log(b*x + a) + ((b^3*c*g^3 - a*b^2*d*g^3)*B^2*x^2 + 2*(a*b^2*c*g^3 - a^2*b*d*g^3)*B^2*x + (a^2*b*c*g^3 - a^3*d*g^3)*B^2)*log(d*x + c)) - integrate(-(b*d*x + 2*b*c - a*d)/(((b^4*c*g^3 - a*b^3*d*g^3)*A*B + (b^4*c*g^3*log(e) - a*b^3*d*g^3*log(e))*B^2)*x^3 + (a^3*b*c*g^3 - a^4*d*g^3)*A*B + (a^3*b*c*g^3*log(e) - a^4*d*g^3*log(e))*B^2 + 3*((a*b^3*c*g^3 - a^2*b^2*d*g^3)*A*B + (a*b^3*c*g^3*log(e) - a^2*b^2*d*g^3*log(e))*B^2)*x^2 + 3*((a^2*b^2*c*g^3 - a^3*b*d*g^3)*A*B + (a^2*b^2*c*g^3*log(e) - a^3*b*d*g^3*log(e))*B^2)*x - ((b^4*c*g^3 - a*b^3*d*g^3)*B^2*x^3 + 3*(a*b^3*c*g^3 - a^2*b^2*d*g^3)*B^2*x^2 + 3*(a^2*b^2*c*g^3 - a^3*b*d*g^3)*B^2*x + (a^3*b*c*g^3 - a^4*d*g^3)*B^2)*log(b*x + a) + ((b^4*c*g^3 - a*b^3*d*g^3)*B^2*x^3 + 3*(a*b^3*c*g^3 - a^2*b^2*d*g^3)*B^2*x^2 + 3*(a^2*b^2*c*g^3 - a^3*b*d*g^3)*B^2*x + (a^3*b*c*g^3 - a^4*d*g^3)*B^2)*log(d*x + c)), x)","F",0
201,1,882,0,1.396740," ","integrate((b*g*x+a*g)^4*(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\frac{1}{5} \, A b^{4} g^{4} x^{5} + A a b^{3} g^{4} x^{4} + 2 \, A a^{2} b^{2} g^{4} x^{3} + 2 \, A a^{3} b g^{4} x^{2} + {\left(x \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) - \frac{2 \, a \log\left(b x + a\right)}{b} + \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B a^{4} g^{4} + 2 \, {\left(x^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B a^{3} b g^{4} + 2 \, {\left(x^{3} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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^{2} g^{4} + \frac{1}{3} \, {\left(3 \, x^{4} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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^{3} g^{4} + \frac{1}{30} \, {\left(6 \, x^{5} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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^{4} g^{4} + A a^{4} g^{4} x"," ",0,"1/5*A*b^4*g^4*x^5 + A*a*b^3*g^4*x^4 + 2*A*a^2*b^2*g^4*x^3 + 2*A*a^3*b*g^4*x^2 + (x*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 2*a*log(b*x + a)/b + 2*c*log(d*x + c)/d)*B*a^4*g^4 + 2*(x^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 2*a^2*log(b*x + a)/b^2 - 2*c^2*log(d*x + c)/d^2 + 2*(b*c - a*d)*x/(b*d))*B*a^3*b*g^4 + 2*(x^3*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 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^2*g^4 + 1/3*(3*x^4*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 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^3*g^4 + 1/30*(6*x^5*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 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^4*g^4 + A*a^4*g^4*x","B",0
202,1,645,0,1.306359," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\frac{1}{4} \, A b^{3} g^{3} x^{4} + A a b^{2} g^{3} x^{3} + \frac{3}{2} \, A a^{2} b g^{3} x^{2} + {\left(x \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) - \frac{2 \, a \log\left(b x + a\right)}{b} + \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B a^{3} g^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B a^{2} b g^{3} + {\left(x^{3} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} g^{3} + \frac{1}{12} \, {\left(3 \, x^{4} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} g^{3} + A a^{3} g^{3} x"," ",0,"1/4*A*b^3*g^3*x^4 + A*a*b^2*g^3*x^3 + 3/2*A*a^2*b*g^3*x^2 + (x*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 2*a*log(b*x + a)/b + 2*c*log(d*x + c)/d)*B*a^3*g^3 + 3/2*(x^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 2*a^2*log(b*x + a)/b^2 - 2*c^2*log(d*x + c)/d^2 + 2*(b*c - a*d)*x/(b*d))*B*a^2*b*g^3 + (x^3*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 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*g^3 + 1/12*(3*x^4*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 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*g^3 + A*a^3*g^3*x","B",0
203,1,436,0,1.511321," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\frac{1}{3} \, A b^{2} g^{2} x^{3} + A a b g^{2} x^{2} + {\left(x \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) - \frac{2 \, a \log\left(b x + a\right)}{b} + \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B a^{2} g^{2} + {\left(x^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B a b g^{2} + \frac{1}{3} \, {\left(x^{3} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} g^{2} + A a^{2} g^{2} x"," ",0,"1/3*A*b^2*g^2*x^3 + A*a*b*g^2*x^2 + (x*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 2*a*log(b*x + a)/b + 2*c*log(d*x + c)/d)*B*a^2*g^2 + (x^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 2*a^2*log(b*x + a)/b^2 - 2*c^2*log(d*x + c)/d^2 + 2*(b*c - a*d)*x/(b*d))*B*a*b*g^2 + 1/3*(x^3*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 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*g^2 + A*a^2*g^2*x","B",0
204,1,250,0,1.442222," ","integrate((b*g*x+a*g)*(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\frac{1}{2} \, A b g x^{2} + {\left(x \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) - \frac{2 \, a \log\left(b x + a\right)}{b} + \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B a g + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B b g + A a g x"," ",0,"1/2*A*b*g*x^2 + (x*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 2*a*log(b*x + a)/b + 2*c*log(d*x + c)/d)*B*a*g + 1/2*(x^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 2*a^2*log(b*x + a)/b^2 - 2*c^2*log(d*x + c)/d^2 + 2*(b*c - a*d)*x/(b*d))*B*b*g + A*a*g*x","B",0
205,0,0,0,0.000000," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))/(b*g*x+a*g),x, algorithm=""maxima"")","B {\left(\frac{2 \, \log\left(b x + a\right) \log\left(d x + c\right)}{b g} - \int -\frac{b d x \log\left(e\right) + b c \log\left(e\right) - 2 \, {\left(2 \, b d x + b c + a d\right)} \log\left(b x + a\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}\right)} + \frac{A \log\left(b g x + a g\right)}{b g}"," ",0,"B*(2*log(b*x + a)*log(d*x + c)/(b*g) - integrate(-(b*d*x*log(e) + b*c*log(e) - 2*(2*b*d*x + b*c + a*d)*log(b*x + a))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)) + A*log(b*g*x + a*g)/(b*g)","F",0
206,1,187,0,1.077944," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))/(b*g*x+a*g)^2,x, algorithm=""maxima"")","-B {\left(\frac{\log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}{b^{2} g^{2} x + a b g^{2}} - \frac{2}{b^{2} g^{2} x + a b g^{2}} - \frac{2 \, d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} + \frac{2 \, d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{A}{b^{2} g^{2} x + a b g^{2}}"," ",0,"-B*(log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2))/(b^2*g^2*x + a*b*g^2) - 2/(b^2*g^2*x + a*b*g^2) - 2*d*log(b*x + a)/((b^2*c - a*b*d)*g^2) + 2*d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - A/(b^2*g^2*x + a*b*g^2)","A",0
207,1,306,0,1.155101," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B {\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{\log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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{A}{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*((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) + log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2))/(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*A/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
208,1,480,0,1.223155," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))/(b*g*x+a*g)^4,x, algorithm=""maxima"")","\frac{1}{9} \, 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^{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{3 \, \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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{A}{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*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^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) - 3*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^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) + 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*A/(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
209,1,699,0,1.376965," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{1}{24} \, B {\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{6 \, \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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{A}{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*B*((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) + 6*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^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) + 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*A/(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
210,1,2660,0,2.597420," ","integrate((b*g*x+a*g)^4*(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","\frac{1}{5} \, A^{2} b^{4} g^{4} x^{5} + A^{2} a b^{3} g^{4} x^{4} + 2 \, A^{2} a^{2} b^{2} g^{4} x^{3} + 2 \, A^{2} a^{3} b g^{4} x^{2} + 2 \, {\left(x \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) - \frac{2 \, a \log\left(b x + a\right)}{b} + \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B a^{4} g^{4} + 4 \, {\left(x^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B a^{3} b g^{4} + 4 \, {\left(x^{3} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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^{2} g^{4} + \frac{2}{3} \, {\left(3 \, x^{4} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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^{3} g^{4} + \frac{1}{15} \, {\left(6 \, x^{5} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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^{4} g^{4} + A^{2} a^{4} g^{4} x + \frac{2 \, {\left({\left(6 \, g^{4} \log\left(e\right) - 25 \, g^{4}\right)} b^{4} c^{5} - {\left(30 \, g^{4} \log\left(e\right) - 113 \, g^{4}\right)} a b^{3} c^{4} d + 4 \, {\left(15 \, g^{4} \log\left(e\right) - 49 \, g^{4}\right)} a^{2} b^{2} c^{3} d^{2} - 12 \, {\left(5 \, g^{4} \log\left(e\right) - 13 \, g^{4}\right)} a^{3} b c^{2} d^{3} + 6 \, {\left(5 \, g^{4} \log\left(e\right) - 8 \, g^{4}\right)} a^{4} c d^{4}\right)} B^{2} \log\left(d x + c\right)}{15 \, d^{5}} - \frac{8 \, {\left(b^{5} c^{5} g^{4} - 5 \, a b^{4} c^{4} d g^{4} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} + 5 \, a^{4} b c d^{4} g^{4} - a^{5} d^{5} g^{4}\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}}{5 \, b d^{5}} + \frac{3 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right)^{2} + 3 \, {\left(b^{5} c d^{4} g^{4} \log\left(e\right) + {\left(5 \, g^{4} \log\left(e\right)^{2} - g^{4} \log\left(e\right)\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 2 \, {\left({\left(2 \, g^{4} \log\left(e\right) - g^{4}\right)} b^{5} c^{2} d^{3} - 2 \, {\left(5 \, g^{4} \log\left(e\right) - g^{4}\right)} a b^{4} c d^{4} - {\left(15 \, g^{4} \log\left(e\right)^{2} - 8 \, g^{4} \log\left(e\right) + g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + {\left({\left(6 \, g^{4} \log\left(e\right) - 7 \, g^{4}\right)} b^{5} c^{3} d^{2} - 3 \, {\left(10 \, g^{4} \log\left(e\right) - 9 \, g^{4}\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(20 \, g^{4} \log\left(e\right) - 11 \, g^{4}\right)} a^{2} b^{3} c d^{4} + {\left(30 \, g^{4} \log\left(e\right)^{2} - 36 \, g^{4} \log\left(e\right) + 13 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - {\left(2 \, {\left(6 \, g^{4} \log\left(e\right) - 13 \, g^{4}\right)} b^{5} c^{4} d - 2 \, {\left(30 \, g^{4} \log\left(e\right) - 59 \, g^{4}\right)} a b^{4} c^{3} d^{2} + 12 \, {\left(10 \, g^{4} \log\left(e\right) - 17 \, g^{4}\right)} a^{2} b^{3} c^{2} d^{3} - 2 \, {\left(60 \, g^{4} \log\left(e\right) - 79 \, g^{4}\right)} a^{3} b^{2} c d^{4} - {\left(15 \, g^{4} \log\left(e\right)^{2} - 48 \, g^{4} \log\left(e\right) + 46 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + B^{2} a^{5} d^{5} g^{4}\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + {\left(b^{5} c^{5} g^{4} - 5 \, a b^{4} c^{4} d g^{4} + 10 \, a^{2} b^{3} c^{3} d^{2} g^{4} - 10 \, a^{3} b^{2} c^{2} d^{3} g^{4} + 5 \, a^{4} b c d^{4} g^{4}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) + 3 \, {\left(b^{5} c d^{4} g^{4} + {\left(10 \, g^{4} \log\left(e\right) - g^{4}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 4 \, {\left(b^{5} c^{2} d^{3} g^{4} - 5 \, a b^{4} c d^{4} g^{4} - {\left(15 \, g^{4} \log\left(e\right) - 4 \, g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + 6 \, {\left(b^{5} c^{3} d^{2} g^{4} - 5 \, a b^{4} c^{2} d^{3} g^{4} + 10 \, a^{2} b^{3} c d^{4} g^{4} + 2 \, {\left(5 \, g^{4} \log\left(e\right) - 3 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 6 \, {\left(2 \, b^{5} c^{4} d g^{4} - 10 \, a b^{4} c^{3} d^{2} g^{4} + 20 \, a^{2} b^{3} c^{2} d^{3} g^{4} - 20 \, a^{3} b^{2} c d^{4} g^{4} - {\left(5 \, g^{4} \log\left(e\right) - 8 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x - {\left(12 \, a b^{4} c^{4} d g^{4} - 54 \, a^{2} b^{3} c^{3} d^{2} g^{4} + 94 \, a^{3} b^{2} c^{2} d^{3} g^{4} - 77 \, a^{4} b c d^{4} g^{4} - {\left(6 \, g^{4} \log\left(e\right) - 25 \, g^{4}\right)} a^{5} d^{5}\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(6 \, B^{2} b^{5} d^{5} g^{4} x^{5} \log\left(e\right) + 3 \, {\left(b^{5} c d^{4} g^{4} + {\left(10 \, g^{4} \log\left(e\right) - g^{4}\right)} a b^{4} d^{5}\right)} B^{2} x^{4} - 4 \, {\left(b^{5} c^{2} d^{3} g^{4} - 5 \, a b^{4} c d^{4} g^{4} - {\left(15 \, g^{4} \log\left(e\right) - 4 \, g^{4}\right)} a^{2} b^{3} d^{5}\right)} B^{2} x^{3} + 6 \, {\left(b^{5} c^{3} d^{2} g^{4} - 5 \, a b^{4} c^{2} d^{3} g^{4} + 10 \, a^{2} b^{3} c d^{4} g^{4} + 2 \, {\left(5 \, g^{4} \log\left(e\right) - 3 \, g^{4}\right)} a^{3} b^{2} d^{5}\right)} B^{2} x^{2} - 6 \, {\left(2 \, b^{5} c^{4} d g^{4} - 10 \, a b^{4} c^{3} d^{2} g^{4} + 20 \, a^{2} b^{3} c^{2} d^{3} g^{4} - 20 \, a^{3} b^{2} c d^{4} g^{4} - {\left(5 \, g^{4} \log\left(e\right) - 8 \, g^{4}\right)} a^{4} b d^{5}\right)} B^{2} x - 12 \, {\left(B^{2} b^{5} d^{5} g^{4} x^{5} + 5 \, B^{2} a b^{4} d^{5} g^{4} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} g^{4} x^{3} + 10 \, B^{2} a^{3} b^{2} d^{5} g^{4} x^{2} + 5 \, B^{2} a^{4} b d^{5} g^{4} x + B^{2} a^{5} d^{5} g^{4}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{15 \, b d^{5}}"," ",0,"1/5*A^2*b^4*g^4*x^5 + A^2*a*b^3*g^4*x^4 + 2*A^2*a^2*b^2*g^4*x^3 + 2*A^2*a^3*b*g^4*x^2 + 2*(x*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 2*a*log(b*x + a)/b + 2*c*log(d*x + c)/d)*A*B*a^4*g^4 + 4*(x^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 2*a^2*log(b*x + a)/b^2 - 2*c^2*log(d*x + c)/d^2 + 2*(b*c - a*d)*x/(b*d))*A*B*a^3*b*g^4 + 4*(x^3*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 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^2*g^4 + 2/3*(3*x^4*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 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^3*g^4 + 1/15*(6*x^5*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 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^4*g^4 + A^2*a^4*g^4*x + 2/15*((6*g^4*log(e) - 25*g^4)*b^4*c^5 - (30*g^4*log(e) - 113*g^4)*a*b^3*c^4*d + 4*(15*g^4*log(e) - 49*g^4)*a^2*b^2*c^3*d^2 - 12*(5*g^4*log(e) - 13*g^4)*a^3*b*c^2*d^3 + 6*(5*g^4*log(e) - 8*g^4)*a^4*c*d^4)*B^2*log(d*x + c)/d^5 - 8/5*(b^5*c^5*g^4 - 5*a*b^4*c^4*d*g^4 + 10*a^2*b^3*c^3*d^2*g^4 - 10*a^3*b^2*c^2*d^3*g^4 + 5*a^4*b*c*d^4*g^4 - a^5*d^5*g^4)*(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*d^5) + 1/15*(3*B^2*b^5*d^5*g^4*x^5*log(e)^2 + 3*(b^5*c*d^4*g^4*log(e) + (5*g^4*log(e)^2 - g^4*log(e))*a*b^4*d^5)*B^2*x^4 - 2*((2*g^4*log(e) - g^4)*b^5*c^2*d^3 - 2*(5*g^4*log(e) - g^4)*a*b^4*c*d^4 - (15*g^4*log(e)^2 - 8*g^4*log(e) + g^4)*a^2*b^3*d^5)*B^2*x^3 + ((6*g^4*log(e) - 7*g^4)*b^5*c^3*d^2 - 3*(10*g^4*log(e) - 9*g^4)*a*b^4*c^2*d^3 + 3*(20*g^4*log(e) - 11*g^4)*a^2*b^3*c*d^4 + (30*g^4*log(e)^2 - 36*g^4*log(e) + 13*g^4)*a^3*b^2*d^5)*B^2*x^2 - (2*(6*g^4*log(e) - 13*g^4)*b^5*c^4*d - 2*(30*g^4*log(e) - 59*g^4)*a*b^4*c^3*d^2 + 12*(10*g^4*log(e) - 17*g^4)*a^2*b^3*c^2*d^3 - 2*(60*g^4*log(e) - 79*g^4)*a^3*b^2*c*d^4 - (15*g^4*log(e)^2 - 48*g^4*log(e) + 46*g^4)*a^4*b*d^5)*B^2*x + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + B^2*a^5*d^5*g^4)*log(b*x + a)^2 + 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + (b^5*c^5*g^4 - 5*a*b^4*c^4*d*g^4 + 10*a^2*b^3*c^3*d^2*g^4 - 10*a^3*b^2*c^2*d^3*g^4 + 5*a^4*b*c*d^4*g^4)*B^2)*log(d*x + c)^2 - 2*(6*B^2*b^5*d^5*g^4*x^5*log(e) + 3*(b^5*c*d^4*g^4 + (10*g^4*log(e) - g^4)*a*b^4*d^5)*B^2*x^4 - 4*(b^5*c^2*d^3*g^4 - 5*a*b^4*c*d^4*g^4 - (15*g^4*log(e) - 4*g^4)*a^2*b^3*d^5)*B^2*x^3 + 6*(b^5*c^3*d^2*g^4 - 5*a*b^4*c^2*d^3*g^4 + 10*a^2*b^3*c*d^4*g^4 + 2*(5*g^4*log(e) - 3*g^4)*a^3*b^2*d^5)*B^2*x^2 - 6*(2*b^5*c^4*d*g^4 - 10*a*b^4*c^3*d^2*g^4 + 20*a^2*b^3*c^2*d^3*g^4 - 20*a^3*b^2*c*d^4*g^4 - (5*g^4*log(e) - 8*g^4)*a^4*b*d^5)*B^2*x - (12*a*b^4*c^4*d*g^4 - 54*a^2*b^3*c^3*d^2*g^4 + 94*a^3*b^2*c^2*d^3*g^4 - 77*a^4*b*c*d^4*g^4 - (6*g^4*log(e) - 25*g^4)*a^5*d^5)*B^2)*log(b*x + a) + 2*(6*B^2*b^5*d^5*g^4*x^5*log(e) + 3*(b^5*c*d^4*g^4 + (10*g^4*log(e) - g^4)*a*b^4*d^5)*B^2*x^4 - 4*(b^5*c^2*d^3*g^4 - 5*a*b^4*c*d^4*g^4 - (15*g^4*log(e) - 4*g^4)*a^2*b^3*d^5)*B^2*x^3 + 6*(b^5*c^3*d^2*g^4 - 5*a*b^4*c^2*d^3*g^4 + 10*a^2*b^3*c*d^4*g^4 + 2*(5*g^4*log(e) - 3*g^4)*a^3*b^2*d^5)*B^2*x^2 - 6*(2*b^5*c^4*d*g^4 - 10*a*b^4*c^3*d^2*g^4 + 20*a^2*b^3*c^2*d^3*g^4 - 20*a^3*b^2*c*d^4*g^4 - (5*g^4*log(e) - 8*g^4)*a^4*b*d^5)*B^2*x - 12*(B^2*b^5*d^5*g^4*x^5 + 5*B^2*a*b^4*d^5*g^4*x^4 + 10*B^2*a^2*b^3*d^5*g^4*x^3 + 10*B^2*a^3*b^2*d^5*g^4*x^2 + 5*B^2*a^4*b*d^5*g^4*x + B^2*a^5*d^5*g^4)*log(b*x + a))*log(d*x + c))/(b*d^5)","B",0
211,1,1950,0,2.596603," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} b^{3} g^{3} x^{4} + A^{2} a b^{2} g^{3} x^{3} + \frac{3}{2} \, A^{2} a^{2} b g^{3} x^{2} + 2 \, {\left(x \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) - \frac{2 \, a \log\left(b x + a\right)}{b} + \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B a^{3} g^{3} + 3 \, {\left(x^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B a^{2} b g^{3} + 2 \, {\left(x^{3} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} g^{3} + \frac{1}{6} \, {\left(3 \, x^{4} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} g^{3} + A^{2} a^{3} g^{3} x - \frac{{\left({\left(3 \, g^{3} \log\left(e\right) - 11 \, g^{3}\right)} b^{3} c^{4} - 2 \, {\left(6 \, g^{3} \log\left(e\right) - 19 \, g^{3}\right)} a b^{2} c^{3} d + 9 \, {\left(2 \, g^{3} \log\left(e\right) - 5 \, g^{3}\right)} a^{2} b c^{2} d^{2} - 6 \, {\left(2 \, g^{3} \log\left(e\right) - 3 \, g^{3}\right)} a^{3} c d^{3}\right)} B^{2} \log\left(d x + c\right)}{3 \, d^{4}} + \frac{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} - 4 \, a^{3} b c d^{3} g^{3} + a^{4} d^{4} 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^{2}}{b d^{4}} + \frac{3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right)^{2} + 4 \, {\left(b^{4} c d^{3} g^{3} \log\left(e\right) + {\left(3 \, g^{3} \log\left(e\right)^{2} - g^{3} \log\left(e\right)\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - 2 \, {\left({\left(3 \, g^{3} \log\left(e\right) - 2 \, g^{3}\right)} b^{4} c^{2} d^{2} - 4 \, {\left(3 \, g^{3} \log\left(e\right) - g^{3}\right)} a b^{3} c d^{3} - {\left(9 \, g^{3} \log\left(e\right)^{2} - 9 \, g^{3} \log\left(e\right) + 2 \, g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 4 \, {\left({\left(3 \, g^{3} \log\left(e\right) - 5 \, g^{3}\right)} b^{4} c^{3} d - {\left(12 \, g^{3} \log\left(e\right) - 17 \, g^{3}\right)} a b^{3} c^{2} d^{2} + {\left(18 \, g^{3} \log\left(e\right) - 19 \, g^{3}\right)} a^{2} b^{2} c d^{3} + {\left(3 \, g^{3} \log\left(e\right)^{2} - 9 \, g^{3} \log\left(e\right) + 7 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + 12 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x + B^{2} a^{4} d^{4} g^{3}\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x - {\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} - 4 \, a^{3} b c d^{3} g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 2 \, {\left(b^{4} c d^{3} g^{3} + {\left(6 \, g^{3} \log\left(e\right) - g^{3}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 4 \, a b^{3} c d^{3} g^{3} - 3 \, {\left(2 \, g^{3} \log\left(e\right) - g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 6 \, {\left(b^{4} c^{3} d g^{3} - 4 \, a b^{3} c^{2} d^{2} g^{3} + 6 \, a^{2} b^{2} c d^{3} g^{3} + {\left(2 \, g^{3} \log\left(e\right) - 3 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x + {\left(6 \, a b^{3} c^{3} d g^{3} - 21 \, a^{2} b^{2} c^{2} d^{2} g^{3} + 26 \, a^{3} b c d^{3} g^{3} + {\left(3 \, g^{3} \log\left(e\right) - 11 \, g^{3}\right)} a^{4} d^{4}\right)} B^{2}\right)} \log\left(b x + a\right) + 4 \, {\left(3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 2 \, {\left(b^{4} c d^{3} g^{3} + {\left(6 \, g^{3} \log\left(e\right) - g^{3}\right)} a b^{3} d^{4}\right)} B^{2} x^{3} - 3 \, {\left(b^{4} c^{2} d^{2} g^{3} - 4 \, a b^{3} c d^{3} g^{3} - 3 \, {\left(2 \, g^{3} \log\left(e\right) - g^{3}\right)} a^{2} b^{2} d^{4}\right)} B^{2} x^{2} + 6 \, {\left(b^{4} c^{3} d g^{3} - 4 \, a b^{3} c^{2} d^{2} g^{3} + 6 \, a^{2} b^{2} c d^{3} g^{3} + {\left(2 \, g^{3} \log\left(e\right) - 3 \, g^{3}\right)} a^{3} b d^{4}\right)} B^{2} x - 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} a b^{3} d^{4} g^{3} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} g^{3} x^{2} + 4 \, B^{2} a^{3} b d^{4} g^{3} x + B^{2} a^{4} d^{4} g^{3}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b d^{4}}"," ",0,"1/4*A^2*b^3*g^3*x^4 + A^2*a*b^2*g^3*x^3 + 3/2*A^2*a^2*b*g^3*x^2 + 2*(x*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 2*a*log(b*x + a)/b + 2*c*log(d*x + c)/d)*A*B*a^3*g^3 + 3*(x^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 2*a^2*log(b*x + a)/b^2 - 2*c^2*log(d*x + c)/d^2 + 2*(b*c - a*d)*x/(b*d))*A*B*a^2*b*g^3 + 2*(x^3*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 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*g^3 + 1/6*(3*x^4*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 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*g^3 + A^2*a^3*g^3*x - 1/3*((3*g^3*log(e) - 11*g^3)*b^3*c^4 - 2*(6*g^3*log(e) - 19*g^3)*a*b^2*c^3*d + 9*(2*g^3*log(e) - 5*g^3)*a^2*b*c^2*d^2 - 6*(2*g^3*log(e) - 3*g^3)*a^3*c*d^3)*B^2*log(d*x + c)/d^4 + 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 - 4*a^3*b*c*d^3*g^3 + a^4*d^4*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^2/(b*d^4) + 1/12*(3*B^2*b^4*d^4*g^3*x^4*log(e)^2 + 4*(b^4*c*d^3*g^3*log(e) + (3*g^3*log(e)^2 - g^3*log(e))*a*b^3*d^4)*B^2*x^3 - 2*((3*g^3*log(e) - 2*g^3)*b^4*c^2*d^2 - 4*(3*g^3*log(e) - g^3)*a*b^3*c*d^3 - (9*g^3*log(e)^2 - 9*g^3*log(e) + 2*g^3)*a^2*b^2*d^4)*B^2*x^2 + 4*((3*g^3*log(e) - 5*g^3)*b^4*c^3*d - (12*g^3*log(e) - 17*g^3)*a*b^3*c^2*d^2 + (18*g^3*log(e) - 19*g^3)*a^2*b^2*c*d^3 + (3*g^3*log(e)^2 - 9*g^3*log(e) + 7*g^3)*a^3*b*d^4)*B^2*x + 12*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x + B^2*a^4*d^4*g^3)*log(b*x + a)^2 + 12*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x - (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 - 4*a^3*b*c*d^3*g^3)*B^2)*log(d*x + c)^2 - 4*(3*B^2*b^4*d^4*g^3*x^4*log(e) + 2*(b^4*c*d^3*g^3 + (6*g^3*log(e) - g^3)*a*b^3*d^4)*B^2*x^3 - 3*(b^4*c^2*d^2*g^3 - 4*a*b^3*c*d^3*g^3 - 3*(2*g^3*log(e) - g^3)*a^2*b^2*d^4)*B^2*x^2 + 6*(b^4*c^3*d*g^3 - 4*a*b^3*c^2*d^2*g^3 + 6*a^2*b^2*c*d^3*g^3 + (2*g^3*log(e) - 3*g^3)*a^3*b*d^4)*B^2*x + (6*a*b^3*c^3*d*g^3 - 21*a^2*b^2*c^2*d^2*g^3 + 26*a^3*b*c*d^3*g^3 + (3*g^3*log(e) - 11*g^3)*a^4*d^4)*B^2)*log(b*x + a) + 4*(3*B^2*b^4*d^4*g^3*x^4*log(e) + 2*(b^4*c*d^3*g^3 + (6*g^3*log(e) - g^3)*a*b^3*d^4)*B^2*x^3 - 3*(b^4*c^2*d^2*g^3 - 4*a*b^3*c*d^3*g^3 - 3*(2*g^3*log(e) - g^3)*a^2*b^2*d^4)*B^2*x^2 + 6*(b^4*c^3*d*g^3 - 4*a*b^3*c^2*d^2*g^3 + 6*a^2*b^2*c*d^3*g^3 + (2*g^3*log(e) - 3*g^3)*a^3*b*d^4)*B^2*x - 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*a*b^3*d^4*g^3*x^3 + 6*B^2*a^2*b^2*d^4*g^3*x^2 + 4*B^2*a^3*b*d^4*g^3*x + B^2*a^4*d^4*g^3)*log(b*x + a))*log(d*x + c))/(b*d^4)","B",0
212,1,1333,0,1.699479," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A^{2} b^{2} g^{2} x^{3} + A^{2} a b g^{2} x^{2} + 2 \, {\left(x \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) - \frac{2 \, a \log\left(b x + a\right)}{b} + \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B a^{2} g^{2} + 2 \, {\left(x^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B a b g^{2} + \frac{2}{3} \, {\left(x^{3} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} g^{2} + A^{2} a^{2} g^{2} x + \frac{4 \, {\left({\left(g^{2} \log\left(e\right) - 3 \, g^{2}\right)} b^{2} c^{3} - {\left(3 \, g^{2} \log\left(e\right) - 7 \, g^{2}\right)} a b c^{2} d + {\left(3 \, g^{2} \log\left(e\right) - 4 \, g^{2}\right)} a^{2} c d^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, d^{3}} - \frac{8 \, {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 3 \, a^{2} b c d^{2} g^{2} - a^{3} d^{3} 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^{2}}{3 \, b d^{3}} + \frac{B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right)^{2} + {\left(2 \, b^{3} c d^{2} g^{2} \log\left(e\right) + {\left(3 \, g^{2} \log\left(e\right)^{2} - 2 \, g^{2} \log\left(e\right)\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - {\left(4 \, {\left(g^{2} \log\left(e\right) - g^{2}\right)} b^{3} c^{2} d - 4 \, {\left(3 \, g^{2} \log\left(e\right) - 2 \, g^{2}\right)} a b^{2} c d^{2} - {\left(3 \, g^{2} \log\left(e\right)^{2} - 8 \, g^{2} \log\left(e\right) + 4 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + B^{2} a^{3} d^{3} g^{2}\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + {\left(b^{3} c^{3} g^{2} - 3 \, a b^{2} c^{2} d g^{2} + 3 \, a^{2} b c d^{2} g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + {\left(b^{3} c d^{2} g^{2} + {\left(3 \, g^{2} \log\left(e\right) - g^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - {\left(2 \, b^{3} c^{2} d g^{2} - 6 \, a b^{2} c d^{2} g^{2} - {\left(3 \, g^{2} \log\left(e\right) - 4 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x - {\left(2 \, a b^{2} c^{2} d g^{2} - 5 \, a^{2} b c d^{2} g^{2} - {\left(g^{2} \log\left(e\right) - 3 \, g^{2}\right)} a^{3} d^{3}\right)} B^{2}\right)} \log\left(b x + a\right) + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + {\left(b^{3} c d^{2} g^{2} + {\left(3 \, g^{2} \log\left(e\right) - g^{2}\right)} a b^{2} d^{3}\right)} B^{2} x^{2} - {\left(2 \, b^{3} c^{2} d g^{2} - 6 \, a b^{2} c d^{2} g^{2} - {\left(3 \, g^{2} \log\left(e\right) - 4 \, g^{2}\right)} a^{2} b d^{3}\right)} B^{2} x - 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} g^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} g^{2} x + B^{2} a^{3} d^{3} g^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, b d^{3}}"," ",0,"1/3*A^2*b^2*g^2*x^3 + A^2*a*b*g^2*x^2 + 2*(x*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 2*a*log(b*x + a)/b + 2*c*log(d*x + c)/d)*A*B*a^2*g^2 + 2*(x^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 2*a^2*log(b*x + a)/b^2 - 2*c^2*log(d*x + c)/d^2 + 2*(b*c - a*d)*x/(b*d))*A*B*a*b*g^2 + 2/3*(x^3*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 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*g^2 + A^2*a^2*g^2*x + 4/3*((g^2*log(e) - 3*g^2)*b^2*c^3 - (3*g^2*log(e) - 7*g^2)*a*b*c^2*d + (3*g^2*log(e) - 4*g^2)*a^2*c*d^2)*B^2*log(d*x + c)/d^3 - 8/3*(b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 3*a^2*b*c*d^2*g^2 - a^3*d^3*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^2/(b*d^3) + 1/3*(B^2*b^3*d^3*g^2*x^3*log(e)^2 + (2*b^3*c*d^2*g^2*log(e) + (3*g^2*log(e)^2 - 2*g^2*log(e))*a*b^2*d^3)*B^2*x^2 - (4*(g^2*log(e) - g^2)*b^3*c^2*d - 4*(3*g^2*log(e) - 2*g^2)*a*b^2*c*d^2 - (3*g^2*log(e)^2 - 8*g^2*log(e) + 4*g^2)*a^2*b*d^3)*B^2*x + 4*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + B^2*a^3*d^3*g^2)*log(b*x + a)^2 + 4*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + (b^3*c^3*g^2 - 3*a*b^2*c^2*d*g^2 + 3*a^2*b*c*d^2*g^2)*B^2)*log(d*x + c)^2 - 4*(B^2*b^3*d^3*g^2*x^3*log(e) + (b^3*c*d^2*g^2 + (3*g^2*log(e) - g^2)*a*b^2*d^3)*B^2*x^2 - (2*b^3*c^2*d*g^2 - 6*a*b^2*c*d^2*g^2 - (3*g^2*log(e) - 4*g^2)*a^2*b*d^3)*B^2*x - (2*a*b^2*c^2*d*g^2 - 5*a^2*b*c*d^2*g^2 - (g^2*log(e) - 3*g^2)*a^3*d^3)*B^2)*log(b*x + a) + 4*(B^2*b^3*d^3*g^2*x^3*log(e) + (b^3*c*d^2*g^2 + (3*g^2*log(e) - g^2)*a*b^2*d^3)*B^2*x^2 - (2*b^3*c^2*d*g^2 - 6*a*b^2*c*d^2*g^2 - (3*g^2*log(e) - 4*g^2)*a^2*b*d^3)*B^2*x - 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*a*b^2*d^3*g^2*x^2 + 3*B^2*a^2*b*d^3*g^2*x + B^2*a^3*d^3*g^2)*log(b*x + a))*log(d*x + c))/(b*d^3)","B",0
213,1,730,0,2.085881," ","integrate((b*g*x+a*g)*(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A^{2} b g x^{2} + 2 \, {\left(x \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) - \frac{2 \, a \log\left(b x + a\right)}{b} + \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B a g + {\left(x^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} - \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} + \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B b g + A^{2} a g x - \frac{2 \, {\left({\left(g \log\left(e\right) - 2 \, g\right)} b c^{2} - 2 \, {\left(g \log\left(e\right) - g\right)} a c d\right)} B^{2} \log\left(d x + c\right)}{d^{2}} + \frac{4 \, {\left(b^{2} c^{2} g - 2 \, a b c d g + a^{2} d^{2} 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^{2}}{b d^{2}} + \frac{B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} + 2 \, {\left(2 \, b^{2} c d g \log\left(e\right) + {\left(g \log\left(e\right)^{2} - 2 \, g \log\left(e\right)\right)} a b d^{2}\right)} B^{2} x + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x + B^{2} a^{2} d^{2} g\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x - {\left(b^{2} c^{2} g - 2 \, a b c d g\right)} B^{2}\right)} \log\left(d x + c\right)^{2} - 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + 2 \, {\left({\left(g \log\left(e\right) - g\right)} a b d^{2} + b^{2} c d g\right)} B^{2} x + {\left({\left(g \log\left(e\right) - 2 \, g\right)} a^{2} d^{2} + 2 \, a b c d g\right)} B^{2}\right)} \log\left(b x + a\right) + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + 2 \, {\left({\left(g \log\left(e\right) - g\right)} a b d^{2} + b^{2} c d g\right)} B^{2} x - 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} a b d^{2} g x + B^{2} a^{2} d^{2} g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b d^{2}}"," ",0,"1/2*A^2*b*g*x^2 + 2*(x*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - 2*a*log(b*x + a)/b + 2*c*log(d*x + c)/d)*A*B*a*g + (x^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + 2*a^2*log(b*x + a)/b^2 - 2*c^2*log(d*x + c)/d^2 + 2*(b*c - a*d)*x/(b*d))*A*B*b*g + A^2*a*g*x - 2*((g*log(e) - 2*g)*b*c^2 - 2*(g*log(e) - g)*a*c*d)*B^2*log(d*x + c)/d^2 + 4*(b^2*c^2*g - 2*a*b*c*d*g + a^2*d^2*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^2/(b*d^2) + 1/2*(B^2*b^2*d^2*g*x^2*log(e)^2 + 2*(2*b^2*c*d*g*log(e) + (g*log(e)^2 - 2*g*log(e))*a*b*d^2)*B^2*x + 4*(B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x + B^2*a^2*d^2*g)*log(b*x + a)^2 + 4*(B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x - (b^2*c^2*g - 2*a*b*c*d*g)*B^2)*log(d*x + c)^2 - 4*(B^2*b^2*d^2*g*x^2*log(e) + 2*((g*log(e) - g)*a*b*d^2 + b^2*c*d*g)*B^2*x + ((g*log(e) - 2*g)*a^2*d^2 + 2*a*b*c*d*g)*B^2)*log(b*x + a) + 4*(B^2*b^2*d^2*g*x^2*log(e) + 2*((g*log(e) - g)*a*b*d^2 + b^2*c*d*g)*B^2*x - 2*(B^2*b^2*d^2*g*x^2 + 2*B^2*a*b*d^2*g*x + B^2*a^2*d^2*g)*log(b*x + a))*log(d*x + c))/(b*d^2)","B",0
214,0,0,0,0.000000," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2/(b*g*x+a*g),x, algorithm=""maxima"")","\frac{4 \, B^{2} \log\left(b x + a\right) \log\left(d x + c\right)^{2}}{b g} + \frac{A^{2} \log\left(b g x + a g\right)}{b g} - \int -\frac{B^{2} b c \log\left(e\right)^{2} + 2 \, A B b c \log\left(e\right) + 4 \, {\left(B^{2} b d x + B^{2} b c\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b d \log\left(e\right)^{2} + 2 \, A B b d \log\left(e\right)\right)} x - 4 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x\right)} \log\left(b x + a\right) + 4 \, {\left(B^{2} b c \log\left(e\right) + A B b c + {\left(B^{2} b d \log\left(e\right) + A B b d\right)} x - 2 \, {\left(2 \, B^{2} b d x + {\left(b c + a d\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b^{2} d g x^{2} + a b c g + {\left(b^{2} c g + a b d g\right)} x}\,{d x}"," ",0,"4*B^2*log(b*x + a)*log(d*x + c)^2/(b*g) + A^2*log(b*g*x + a*g)/(b*g) - integrate(-(B^2*b*c*log(e)^2 + 2*A*B*b*c*log(e) + 4*(B^2*b*d*x + B^2*b*c)*log(b*x + a)^2 + (B^2*b*d*log(e)^2 + 2*A*B*b*d*log(e))*x - 4*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x)*log(b*x + a) + 4*(B^2*b*c*log(e) + A*B*b*c + (B^2*b*d*log(e) + A*B*b*d)*x - 2*(2*B^2*b*d*x + (b*c + a*d)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d*g*x^2 + a*b*c*g + (b^2*c*g + a*b*d*g)*x), x)","F",0
215,1,573,0,1.159901," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2/(b*g*x+a*g)^2,x, algorithm=""maxima"")","4 \, {\left({\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)} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right) + \frac{{\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)}{a b^{2} c g^{2} - a^{2} b d g^{2} + {\left(b^{3} c g^{2} - a b^{2} d g^{2}\right)} x}\right)} B^{2} - 2 \, A B {\left(\frac{\log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)}{b^{2} g^{2} x + a b g^{2}} - \frac{2}{b^{2} g^{2} x + a b g^{2}} - \frac{2 \, d \log\left(b x + a\right)}{{\left(b^{2} c - a b d\right)} g^{2}} + \frac{2 \, d \log\left(d x + c\right)}{{\left(b^{2} c - a b d\right)} g^{2}}\right)} - \frac{B^{2} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)^{2}}{b^{2} g^{2} x + a b g^{2}} - \frac{A^{2}}{b^{2} g^{2} x + a b g^{2}}"," ",0,"4*((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))*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^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^2*c*g^2 - a^2*b*d*g^2 + (b^3*c*g^2 - a*b^2*d*g^2)*x))*B^2 - 2*A*B*(log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2))/(b^2*g^2*x + a*b*g^2) - 2/(b^2*g^2*x + a*b*g^2) - 2*d*log(b*x + a)/((b^2*c - a*b*d)*g^2) + 2*d*log(d*x + c)/((b^2*c - a*b*d)*g^2)) - B^2*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2))^2/(b^2*g^2*x + a*b*g^2) - A^2/(b^2*g^2*x + a*b*g^2)","B",0
216,1,1001,0,1.481514," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2/(b*g*x+a*g)^3,x, algorithm=""maxima"")","-{\left({\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{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} - A B {\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{\log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\right)^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}} - \frac{A^{2}}{2 \, {\left(b^{3} g^{3} x^{2} + 2 \, a b^{2} g^{3} x + a^{2} b g^{3}\right)}}"," ",0,"-(((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(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^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^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 - A*B*((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) + log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2))/(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*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2))^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3) - 1/2*A^2/(b^3*g^3*x^2 + 2*a*b^2*g^3*x + a^2*b*g^3)","B",0
217,1,1576,0,1.895458," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2/(b*g*x+a*g)^4,x, algorithm=""maxima"")","\frac{2}{27} \, {\left(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 \, 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{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} + \frac{2}{9} \, 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^{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{3 \, \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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{A^{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,"2/27*(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*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(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) - (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 + 2/9*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^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) - 3*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^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) + 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*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2))^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*A^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
218,1,2278,0,2.507852," ","integrate((A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2/(b*g*x+a*g)^5,x, algorithm=""maxima"")","-\frac{1}{72} \, {\left(6 \, {\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{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} - \frac{1}{12} \, A B {\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{6 \, \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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} \log\left(\frac{d^{2} e x^{2}}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{2 \, c d e x}{b^{2} x^{2} + 2 \, a b x + a^{2}} + \frac{c^{2} e}{b^{2} x^{2} + 2 \, a b x + a^{2}}\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{A^{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,"-1/72*(6*((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(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2)) + (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 - 1/12*A*B*((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) + 6*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^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) + 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*log(d^2*e*x^2/(b^2*x^2 + 2*a*b*x + a^2) + 2*c*d*e*x/(b^2*x^2 + 2*a*b*x + a^2) + c^2*e/(b^2*x^2 + 2*a*b*x + a^2))^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*A^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
219,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\int \frac{{\left(b g x + a g\right)}^{2}}{B \log\left(\frac{{\left(d x + c\right)}^{2} e}{{\left(b x + a\right)}^{2}}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)^2/(B*log((d*x + c)^2*e/(b*x + a)^2) + A), x)","F",0
220,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\int \frac{b g x + a g}{B \log\left(\frac{{\left(d x + c\right)}^{2} e}{{\left(b x + a\right)}^{2}}\right) + A}\,{d x}"," ",0,"integrate((b*g*x + a*g)/(B*log((d*x + c)^2*e/(b*x + a)^2) + A), x)","F",0
221,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)} {\left(B \log\left(\frac{{\left(d x + c\right)}^{2} e}{{\left(b x + a\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)*(B*log((d*x + c)^2*e/(b*x + a)^2) + A)), x)","F",0
222,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{2} {\left(B \log\left(\frac{{\left(d x + c\right)}^{2} e}{{\left(b x + a\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^2*(B*log((d*x + c)^2*e/(b*x + a)^2) + A)), x)","F",0
223,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*(d*x+c)^2/(b*x+a)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{3} {\left(B \log\left(\frac{{\left(d x + c\right)}^{2} e}{{\left(b x + a\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((b*g*x + a*g)^3*(B*log((d*x + c)^2*e/(b*x + a)^2) + A)), x)","F",0
224,0,0,0,0.000000," ","integrate((b*g*x+a*g)^2/(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","-\frac{b^{3} d g^{2} x^{4} + a^{3} c g^{2} + {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{3} + 3 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x^{2} + {\left(3 \, a^{2} b c g^{2} + a^{3} d g^{2}\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) - {\left(b c - a d\right)} A B - {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}} + \int \frac{4 \, b^{3} d g^{2} x^{3} + 3 \, a^{2} b c g^{2} + a^{3} d g^{2} + 3 \, {\left(b^{3} c g^{2} + 3 \, a b^{2} d g^{2}\right)} x^{2} + 6 \, {\left(a b^{2} c g^{2} + a^{2} b d g^{2}\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) - {\left(b c - a d\right)} A B - {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}}\,{d x}"," ",0,"-1/2*(b^3*d*g^2*x^4 + a^3*c*g^2 + (b^3*c*g^2 + 3*a*b^2*d*g^2)*x^3 + 3*(a*b^2*c*g^2 + a^2*b*d*g^2)*x^2 + (3*a^2*b*c*g^2 + a^3*d*g^2)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) - (b*c - a*d)*A*B - (b*c*log(e) - a*d*log(e))*B^2) + integrate(1/2*(4*b^3*d*g^2*x^3 + 3*a^2*b*c*g^2 + a^3*d*g^2 + 3*(b^3*c*g^2 + 3*a*b^2*d*g^2)*x^2 + 6*(a*b^2*c*g^2 + a^2*b*d*g^2)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) - (b*c - a*d)*A*B - (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
225,0,0,0,0.000000," ","integrate((b*g*x+a*g)/(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","-\frac{b^{2} d g x^{3} + a^{2} c g + {\left(b^{2} c g + 2 \, a b d g\right)} x^{2} + {\left(2 \, a b c g + a^{2} d g\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) - {\left(b c - a d\right)} A B - {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}} + \int \frac{3 \, b^{2} d g x^{2} + 2 \, a b c g + a^{2} d g + 2 \, {\left(b^{2} c g + 2 \, a b d g\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) - {\left(b c - a d\right)} A B - {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}}\,{d x}"," ",0,"-1/2*(b^2*d*g*x^3 + a^2*c*g + (b^2*c*g + 2*a*b*d*g)*x^2 + (2*a*b*c*g + a^2*d*g)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) - (b*c - a*d)*A*B - (b*c*log(e) - a*d*log(e))*B^2) + integrate(1/2*(3*b^2*d*g*x^2 + 2*a*b*c*g + a^2*d*g + 2*(b^2*c*g + 2*a*b*d*g)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) - (b*c - a*d)*A*B - (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
226,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)/(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","d \int \frac{1}{2 \, {\left(2 \, {\left(b c g - a d g\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right) - {\left(b c g - a d g\right)} A B - {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}\right)}}\,{d x} - \frac{d x + c}{2 \, {\left(2 \, {\left(b c g - a d g\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c g - a d g\right)} B^{2} \log\left(d x + c\right) - {\left(b c g - a d g\right)} A B - {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}\right)}}"," ",0,"d*integrate(1/2/(2*(b*c*g - a*d*g)*B^2*log(b*x + a) - 2*(b*c*g - a*d*g)*B^2*log(d*x + c) - (b*c*g - a*d*g)*A*B - (b*c*g*log(e) - a*d*g*log(e))*B^2), x) - 1/2*(d*x + c)/(2*(b*c*g - a*d*g)*B^2*log(b*x + a) - 2*(b*c*g - a*d*g)*B^2*log(d*x + c) - (b*c*g - a*d*g)*A*B - (b*c*g*log(e) - a*d*g*log(e))*B^2)","F",0
227,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","\frac{d x + c}{2 \, {\left({\left(a b c g^{2} - a^{2} d g^{2}\right)} A B + {\left(a b c g^{2} \log\left(e\right) - a^{2} d g^{2} \log\left(e\right)\right)} B^{2} + {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} A B + {\left(b^{2} c g^{2} \log\left(e\right) - a b d g^{2} \log\left(e\right)\right)} B^{2}\right)} x - 2 \, {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} B^{2} x + {\left(a b c g^{2} - a^{2} d g^{2}\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left({\left(b^{2} c g^{2} - a b d g^{2}\right)} B^{2} x + {\left(a b c g^{2} - a^{2} d g^{2}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}} + \int \frac{1}{2 \, {\left(B^{2} a^{2} g^{2} \log\left(e\right) + A B a^{2} g^{2} + {\left(B^{2} b^{2} g^{2} \log\left(e\right) + A B b^{2} g^{2}\right)} x^{2} + 2 \, {\left(B^{2} a b g^{2} \log\left(e\right) + A B a b g^{2}\right)} x - 2 \, {\left(B^{2} b^{2} g^{2} x^{2} + 2 \, B^{2} a b g^{2} x + B^{2} a^{2} g^{2}\right)} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{2} g^{2} x^{2} + 2 \, B^{2} a b g^{2} x + B^{2} a^{2} g^{2}\right)} \log\left(d x + c\right)\right)}}\,{d x}"," ",0,"1/2*(d*x + c)/((a*b*c*g^2 - a^2*d*g^2)*A*B + (a*b*c*g^2*log(e) - a^2*d*g^2*log(e))*B^2 + ((b^2*c*g^2 - a*b*d*g^2)*A*B + (b^2*c*g^2*log(e) - a*b*d*g^2*log(e))*B^2)*x - 2*((b^2*c*g^2 - a*b*d*g^2)*B^2*x + (a*b*c*g^2 - a^2*d*g^2)*B^2)*log(b*x + a) + 2*((b^2*c*g^2 - a*b*d*g^2)*B^2*x + (a*b*c*g^2 - a^2*d*g^2)*B^2)*log(d*x + c)) + integrate(1/2/(B^2*a^2*g^2*log(e) + A*B*a^2*g^2 + (B^2*b^2*g^2*log(e) + A*B*b^2*g^2)*x^2 + 2*(B^2*a*b*g^2*log(e) + A*B*a*b*g^2)*x - 2*(B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(b*x + a) + 2*(B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(d*x + c)), x)","F",0
228,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^3/(A+B*log(e*(d*x+c)^2/(b*x+a)^2))^2,x, algorithm=""maxima"")","\frac{d x + c}{2 \, {\left({\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} A B + {\left(a^{2} b c g^{3} \log\left(e\right) - a^{3} d g^{3} \log\left(e\right)\right)} B^{2} + {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} A B + {\left(b^{3} c g^{3} \log\left(e\right) - a b^{2} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} A B + {\left(a b^{2} c g^{3} \log\left(e\right) - a^{2} b d g^{3} \log\left(e\right)\right)} B^{2}\right)} x - 2 \, {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} B^{2} x + {\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left({\left(b^{3} c g^{3} - a b^{2} d g^{3}\right)} B^{2} x^{2} + 2 \, {\left(a b^{2} c g^{3} - a^{2} b d g^{3}\right)} B^{2} x + {\left(a^{2} b c g^{3} - a^{3} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}} - \int -\frac{b d x + 2 \, b c - a d}{2 \, {\left({\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} A B + {\left(b^{4} c g^{3} \log\left(e\right) - a b^{3} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} A B + {\left(a^{3} b c g^{3} \log\left(e\right) - a^{4} d g^{3} \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} A B + {\left(a b^{3} c g^{3} \log\left(e\right) - a^{2} b^{2} d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} A B + {\left(a^{2} b^{2} c g^{3} \log\left(e\right) - a^{3} b d g^{3} \log\left(e\right)\right)} B^{2}\right)} x - 2 \, {\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} B^{2} x + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} B^{2}\right)} \log\left(b x + a\right) + 2 \, {\left({\left(b^{4} c g^{3} - a b^{3} d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(a b^{3} c g^{3} - a^{2} b^{2} d g^{3}\right)} B^{2} x^{2} + 3 \, {\left(a^{2} b^{2} c g^{3} - a^{3} b d g^{3}\right)} B^{2} x + {\left(a^{3} b c g^{3} - a^{4} d g^{3}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}}\,{d x}"," ",0,"1/2*(d*x + c)/((a^2*b*c*g^3 - a^3*d*g^3)*A*B + (a^2*b*c*g^3*log(e) - a^3*d*g^3*log(e))*B^2 + ((b^3*c*g^3 - a*b^2*d*g^3)*A*B + (b^3*c*g^3*log(e) - a*b^2*d*g^3*log(e))*B^2)*x^2 + 2*((a*b^2*c*g^3 - a^2*b*d*g^3)*A*B + (a*b^2*c*g^3*log(e) - a^2*b*d*g^3*log(e))*B^2)*x - 2*((b^3*c*g^3 - a*b^2*d*g^3)*B^2*x^2 + 2*(a*b^2*c*g^3 - a^2*b*d*g^3)*B^2*x + (a^2*b*c*g^3 - a^3*d*g^3)*B^2)*log(b*x + a) + 2*((b^3*c*g^3 - a*b^2*d*g^3)*B^2*x^2 + 2*(a*b^2*c*g^3 - a^2*b*d*g^3)*B^2*x + (a^2*b*c*g^3 - a^3*d*g^3)*B^2)*log(d*x + c)) - integrate(-1/2*(b*d*x + 2*b*c - a*d)/(((b^4*c*g^3 - a*b^3*d*g^3)*A*B + (b^4*c*g^3*log(e) - a*b^3*d*g^3*log(e))*B^2)*x^3 + (a^3*b*c*g^3 - a^4*d*g^3)*A*B + (a^3*b*c*g^3*log(e) - a^4*d*g^3*log(e))*B^2 + 3*((a*b^3*c*g^3 - a^2*b^2*d*g^3)*A*B + (a*b^3*c*g^3*log(e) - a^2*b^2*d*g^3*log(e))*B^2)*x^2 + 3*((a^2*b^2*c*g^3 - a^3*b*d*g^3)*A*B + (a^2*b^2*c*g^3*log(e) - a^3*b*d*g^3*log(e))*B^2)*x - 2*((b^4*c*g^3 - a*b^3*d*g^3)*B^2*x^3 + 3*(a*b^3*c*g^3 - a^2*b^2*d*g^3)*B^2*x^2 + 3*(a^2*b^2*c*g^3 - a^3*b*d*g^3)*B^2*x + (a^3*b*c*g^3 - a^4*d*g^3)*B^2)*log(b*x + a) + 2*((b^4*c*g^3 - a*b^3*d*g^3)*B^2*x^3 + 3*(a*b^3*c*g^3 - a^2*b^2*d*g^3)*B^2*x^2 + 3*(a^2*b^2*c*g^3 - a^3*b*d*g^3)*B^2*x + (a^3*b*c*g^3 - a^4*d*g^3)*B^2)*log(d*x + c)), x)","F",0
229,0,0,0,0.000000," ","integrate(1/(b*g*x+a*g)^2/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\int \frac{1}{{\left(b g x + a g\right)}^{2} {\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*x + a*g)^2*(B*log((b*x + a)^n*e/(d*x + c)^n) + A)), x)","F",0
230,1,593,0,0.823036," ","integrate((g*x+f)^4*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{5} \, A g^{4} x^{5} + A f g^{3} x^{4} + 2 \, A f^{2} g^{2} x^{3} + 2 \, A f^{3} g 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 f^{4} + 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 f^{3} g + {\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 f^{2} g^{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)} B f g^{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 g^{4} + A f^{4} x"," ",0,"1/5*A*g^4*x^5 + A*f*g^3*x^4 + 2*A*f^2*g^2*x^3 + 2*A*f^3*g*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*f^4 + 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*f^3*g + (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*f^2*g^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))*B*f*g^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*g^4 + A*f^4*x","A",0
231,1,415,0,0.976387," ","integrate((g*x+f)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{4} \, A g^{3} x^{4} + A f g^{2} x^{3} + \frac{3}{2} \, A f^{2} g 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 f^{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 f^{2} g + \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 f g^{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 g^{3} + A f^{3} x"," ",0,"1/4*A*g^3*x^4 + A*f*g^2*x^3 + 3/2*A*f^2*g*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*f^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*f^2*g + 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*f*g^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*g^3 + A*f^3*x","A",0
232,1,262,0,0.636120," ","integrate((g*x+f)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{3} \, A g^{2} x^{3} + A f g 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 f^{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 f g + \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 g^{2} + A f^{2} x"," ",0,"1/3*A*g^2*x^3 + A*f*g*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*f^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*f*g + 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*g^2 + A*f^2*x","A",0
233,1,140,0,0.906158," ","integrate((g*x+f)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\frac{1}{2} \, A g 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 f + \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 g + A f x"," ",0,"1/2*A*g*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*f + 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*g + A*f*x","A",0
234,1,54,0,0.617082," ","integrate(A+B*log(e*(b*x+a)/(d*x+c)),x, algorithm=""maxima"")","{\left(x \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + \frac{\frac{a e \log\left(b x + a\right)}{b} - \frac{c e \log\left(d x + c\right)}{d}}{e}\right)} B + A x"," ",0,"(x*log((b*x + a)*e/(d*x + c)) + (a*e*log(b*x + a)/b - c*e*log(d*x + c)/d)/e)*B + A*x","A",0
235,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(g*x+f),x, algorithm=""maxima"")","-B \int -\frac{\log\left(b x + a\right) - \log\left(d x + c\right) + \log\left(e\right)}{g x + f}\,{d x} + \frac{A \log\left(g x + f\right)}{g}"," ",0,"-B*integrate(-(log(b*x + a) - log(d*x + c) + log(e))/(g*x + f), x) + A*log(g*x + f)/g","F",0
236,1,138,0,0.766525," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(g*x+f)^2,x, algorithm=""maxima"")","B {\left(\frac{b \log\left(b x + a\right)}{b f g - a g^{2}} - \frac{d \log\left(d x + c\right)}{d f g - c g^{2}} + \frac{{\left(b c - a d\right)} \log\left(g x + f\right)}{b d f^{2} + a c g^{2} - {\left(b c + a d\right)} f g} - \frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{g^{2} x + f g}\right)} - \frac{A}{g^{2} x + f g}"," ",0,"B*(b*log(b*x + a)/(b*f*g - a*g^2) - d*log(d*x + c)/(d*f*g - c*g^2) + (b*c - a*d)*log(g*x + f)/(b*d*f^2 + a*c*g^2 - (b*c + a*d)*f*g) - log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^2*x + f*g)) - A/(g^2*x + f*g)","A",0
237,1,351,0,0.990606," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(g*x+f)^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{b^{2} \log\left(b x + a\right)}{b^{2} f^{2} g - 2 \, a b f g^{2} + a^{2} g^{3}} - \frac{d^{2} \log\left(d x + c\right)}{d^{2} f^{2} g - 2 \, c d f g^{2} + c^{2} g^{3}} + \frac{{\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g\right)} \log\left(g x + f\right)}{b^{2} d^{2} f^{4} + a^{2} c^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{3}} - \frac{b c - a d}{b d f^{3} + a c f g^{2} - {\left(b c + a d\right)} f^{2} g + {\left(b d f^{2} g + a c g^{3} - {\left(b c + a d\right)} f g^{2}\right)} x} - \frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g}\right)} B - \frac{A}{2 \, {\left(g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g\right)}}"," ",0,"1/2*(b^2*log(b*x + a)/(b^2*f^2*g - 2*a*b*f*g^2 + a^2*g^3) - d^2*log(d*x + c)/(d^2*f^2*g - 2*c*d*f*g^2 + c^2*g^3) + (2*(b^2*c*d - a*b*d^2)*f - (b^2*c^2 - a^2*d^2)*g)*log(g*x + f)/(b^2*d^2*f^4 + a^2*c^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^3*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^2 - 2*(a*b*c^2 + a^2*c*d)*f*g^3) - (b*c - a*d)/(b*d*f^3 + a*c*f*g^2 - (b*c + a*d)*f^2*g + (b*d*f^2*g + a*c*g^3 - (b*c + a*d)*f*g^2)*x) - log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^3*x^2 + 2*f*g^2*x + f^2*g))*B - 1/2*A/(g^3*x^2 + 2*f*g^2*x + f^2*g)","B",0
238,1,848,0,1.285121," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(g*x+f)^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{2 \, b^{3} \log\left(b x + a\right)}{b^{3} f^{3} g - 3 \, a b^{2} f^{2} g^{2} + 3 \, a^{2} b f g^{3} - a^{3} g^{4}} - \frac{2 \, d^{3} \log\left(d x + c\right)}{d^{3} f^{3} g - 3 \, c d^{2} f^{2} g^{2} + 3 \, c^{2} d f g^{3} - c^{3} g^{4}} + \frac{2 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{2}\right)} \log\left(g x + f\right)}{b^{3} d^{3} f^{6} + a^{3} c^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{5}} - \frac{5 \, {\left(b^{2} c d - a b d^{2}\right)} f^{2} - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} f g + {\left(a b c^{2} - a^{2} c d\right)} g^{2} + 2 \, {\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f g - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g^{2}\right)} x}{b^{2} d^{2} f^{6} + a^{2} c^{2} f^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{5} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{4} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{3} g^{3} + {\left(b^{2} d^{2} f^{4} g^{2} + a^{2} c^{2} g^{6} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g^{3} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{4} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} f^{5} g + a^{2} c^{2} f g^{5} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{4} g^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{3} g^{3} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2} g^{4}\right)} x} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g}\right)} B - \frac{A}{3 \, {\left(g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g\right)}}"," ",0,"1/6*(2*b^3*log(b*x + a)/(b^3*f^3*g - 3*a*b^2*f^2*g^2 + 3*a^2*b*f*g^3 - a^3*g^4) - 2*d^3*log(d*x + c)/(d^3*f^3*g - 3*c*d^2*f^2*g^2 + 3*c^2*d*f*g^3 - c^3*g^4) + 2*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g + (b^3*c^3 - a^3*d^3)*g^2)*log(g*x + f)/(b^3*d^3*f^6 + a^3*c^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^5) - (5*(b^2*c*d - a*b*d^2)*f^2 - 3*(b^2*c^2 - a^2*d^2)*f*g + (a*b*c^2 - a^2*c*d)*g^2 + 2*(2*(b^2*c*d - a*b*d^2)*f*g - (b^2*c^2 - a^2*d^2)*g^2)*x)/(b^2*d^2*f^6 + a^2*c^2*f^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^5*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^4*g^2 - 2*(a*b*c^2 + a^2*c*d)*f^3*g^3 + (b^2*d^2*f^4*g^2 + a^2*c^2*g^6 - 2*(b^2*c*d + a*b*d^2)*f^3*g^3 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^4 - 2*(a*b*c^2 + a^2*c*d)*f*g^5)*x^2 + 2*(b^2*d^2*f^5*g + a^2*c^2*f*g^5 - 2*(b^2*c*d + a*b*d^2)*f^4*g^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^3*g^3 - 2*(a*b*c^2 + a^2*c*d)*f^2*g^4)*x) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g))*B - 1/3*A/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g)","B",0
239,1,1757,0,1.989195," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(g*x+f)^5,x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{6 \, b^{4} \log\left(b x + a\right)}{b^{4} f^{4} g - 4 \, a b^{3} f^{3} g^{2} + 6 \, a^{2} b^{2} f^{2} g^{3} - 4 \, a^{3} b f g^{4} + a^{4} g^{5}} - \frac{6 \, d^{4} \log\left(d x + c\right)}{d^{4} f^{4} g - 4 \, c d^{3} f^{3} g^{2} + 6 \, c^{2} d^{2} f^{2} g^{3} - 4 \, c^{3} d f g^{4} + c^{4} g^{5}} + \frac{6 \, {\left(4 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f^{3} - 6 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} f^{2} g + 4 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} f g^{2} - {\left(b^{4} c^{4} - a^{4} d^{4}\right)} g^{3}\right)} \log\left(g x + f\right)}{b^{4} d^{4} f^{8} + a^{4} c^{4} g^{8} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} f^{7} g + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} f^{6} g^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} f^{5} g^{3} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} f^{4} g^{4} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} f^{3} g^{5} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f^{2} g^{6} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} f g^{7}} - \frac{26 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{4} - 31 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{3} g + {\left(11 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 15 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3}\right)} f^{2} g^{2} - 7 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} f g^{3} + 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} g^{4} + 6 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} g^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g^{3} + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{4}\right)} x^{2} + 3 \, {\left(14 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{3} g - 15 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{2} g^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f g^{3} - {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} g^{4}\right)} x}{b^{3} d^{3} f^{9} + a^{3} c^{3} f^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{8} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{7} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{5} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{4} g^{5} + {\left(b^{3} d^{3} f^{6} g^{3} + a^{3} c^{3} g^{9} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{5} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{6} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{7} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{8}\right)} x^{3} + 3 \, {\left(b^{3} d^{3} f^{7} g^{2} + a^{3} c^{3} f g^{8} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{5} g^{4} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{4} g^{5} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{3} g^{6} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{2} g^{7}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} f^{8} g + a^{3} c^{3} f^{2} g^{7} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{7} g^{2} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{6} g^{3} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{4} g^{5} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{3} g^{6}\right)} x} - \frac{6 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g}\right)} B - \frac{A}{4 \, {\left(g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g\right)}}"," ",0,"1/24*(6*b^4*log(b*x + a)/(b^4*f^4*g - 4*a*b^3*f^3*g^2 + 6*a^2*b^2*f^2*g^3 - 4*a^3*b*f*g^4 + a^4*g^5) - 6*d^4*log(d*x + c)/(d^4*f^4*g - 4*c*d^3*f^3*g^2 + 6*c^2*d^2*f^2*g^3 - 4*c^3*d*f*g^4 + c^4*g^5) + 6*(4*(b^4*c*d^3 - a*b^3*d^4)*f^3 - 6*(b^4*c^2*d^2 - a^2*b^2*d^4)*f^2*g + 4*(b^4*c^3*d - a^3*b*d^4)*f*g^2 - (b^4*c^4 - a^4*d^4)*g^3)*log(g*x + f)/(b^4*d^4*f^8 + a^4*c^4*g^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*f^7*g + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*f^6*g^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*f^5*g^3 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*f^4*g^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*f^3*g^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f^2*g^6 - 4*(a^3*b*c^4 + a^4*c^3*d)*f*g^7) - (26*(b^3*c*d^2 - a*b^2*d^3)*f^4 - 31*(b^3*c^2*d - a^2*b*d^3)*f^3*g + (11*b^3*c^3 + 15*a*b^2*c^2*d - 15*a^2*b*c*d^2 - 11*a^3*d^3)*f^2*g^2 - 7*(a*b^2*c^3 - a^3*c*d^2)*f*g^3 + 2*(a^2*b*c^3 - a^3*c^2*d)*g^4 + 6*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2*g^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g^3 + (b^3*c^3 - a^3*d^3)*g^4)*x^2 + 3*(14*(b^3*c*d^2 - a*b^2*d^3)*f^3*g - 15*(b^3*c^2*d - a^2*b*d^3)*f^2*g^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f*g^3 - (a*b^2*c^3 - a^3*c*d^2)*g^4)*x)/(b^3*d^3*f^9 + a^3*c^3*f^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^8*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^7*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^6*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^5*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^4*g^5 + (b^3*d^3*f^6*g^3 + a^3*c^3*g^9 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g^4 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^5 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^6 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^7 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^8)*x^3 + 3*(b^3*d^3*f^7*g^2 + a^3*c^3*f*g^8 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^6*g^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^5*g^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^4*g^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3*g^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^2*g^7)*x^2 + 3*(b^3*d^3*f^8*g + a^3*c^3*f^2*g^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^7*g^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^6*g^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^5*g^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^4*g^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^3*g^6)*x) - 6*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g))*B - 1/4*A/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g)","B",0
240,1,2140,0,1.907449," ","integrate((g*x+f)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} g^{3} x^{4} + A^{2} f g^{2} x^{3} + \frac{3}{2} \, A^{2} f^{2} g 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 f^{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 f^{2} g + {\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 f g^{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 g^{3} + A^{2} f^{3} x - \frac{{\left(6 \, a^{3} c d^{3} g^{3} - 3 \, {\left(8 \, c d^{3} f g^{2} - c^{2} d^{2} g^{3}\right)} a^{2} b + 2 \, {\left(18 \, c d^{3} f^{2} g - 6 \, c^{2} d^{2} f g^{2} + c^{3} d g^{3}\right)} a b^{2} + {\left(24 \, c d^{3} f^{3} \log\left(e\right) - {\left(6 \, g^{3} \log\left(e\right) + 11 \, g^{3}\right)} c^{4} + 12 \, {\left(2 \, f g^{2} \log\left(e\right) + 3 \, f g^{2}\right)} c^{3} d - 36 \, {\left(f^{2} g \log\left(e\right) + f^{2} g\right)} c^{2} d^{2}\right)} b^{3}\right)} B^{2} \log\left(d x + c\right)}{12 \, b^{3} d^{4}} + \frac{{\left(4 \, a b^{3} d^{4} f^{3} - 6 \, a^{2} b^{2} d^{4} f^{2} g + 4 \, a^{3} b d^{4} f g^{2} - a^{4} d^{4} g^{3} - {\left(4 \, c d^{3} f^{3} - 6 \, c^{2} d^{2} f^{2} g + 4 \, c^{3} d f g^{2} - c^{4} g^{3}\right)} b^{4}\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^{4}} + \frac{3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right)^{2} + 2 \, {\left(a b^{3} d^{4} g^{3} \log\left(e\right) + {\left(6 \, d^{4} f g^{2} \log\left(e\right)^{2} - c d^{3} g^{3} \log\left(e\right)\right)} b^{4}\right)} B^{2} x^{3} - {\left({\left(3 \, g^{3} \log\left(e\right) - g^{3}\right)} a^{2} b^{2} d^{4} - 2 \, {\left(6 \, d^{4} f g^{2} \log\left(e\right) - c d^{3} g^{3}\right)} a b^{3} - {\left(18 \, d^{4} f^{2} g \log\left(e\right)^{2} - 12 \, c d^{3} f g^{2} \log\left(e\right) + {\left(3 \, g^{3} \log\left(e\right) + g^{3}\right)} c^{2} d^{2}\right)} b^{4}\right)} B^{2} x^{2} + {\left({\left(6 \, g^{3} \log\left(e\right) - 5 \, g^{3}\right)} a^{3} b d^{4} + {\left(5 \, c d^{3} g^{3} - 12 \, {\left(2 \, f g^{2} \log\left(e\right) - f g^{2}\right)} d^{4}\right)} a^{2} b^{2} + {\left(36 \, d^{4} f^{2} g \log\left(e\right) - 24 \, c d^{3} f g^{2} + 5 \, c^{2} d^{2} g^{3}\right)} a b^{3} + {\left(12 \, d^{4} f^{3} \log\left(e\right)^{2} - 36 \, c d^{3} f^{2} g \log\left(e\right) - {\left(6 \, g^{3} \log\left(e\right) + 5 \, g^{3}\right)} c^{3} d + 12 \, {\left(2 \, f g^{2} \log\left(e\right) + f g^{2}\right)} c^{2} d^{2}\right)} b^{4}\right)} B^{2} x + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{3} x + {\left(4 \, a b^{3} d^{4} f^{3} - 6 \, a^{2} b^{2} d^{4} f^{2} g + 4 \, a^{3} b d^{4} f g^{2} - a^{4} d^{4} g^{3}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{3} x + {\left(4 \, c d^{3} f^{3} - 6 \, c^{2} d^{2} f^{2} g + 4 \, c^{3} d f g^{2} - c^{4} g^{3}\right)} B^{2} b^{4}\right)} \log\left(d x + c\right)^{2} + {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 2 \, {\left(a b^{3} d^{4} g^{3} + {\left(12 \, d^{4} f g^{2} \log\left(e\right) - c d^{3} g^{3}\right)} b^{4}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} d^{4} f g^{2} - a^{2} b^{2} d^{4} g^{3} + {\left(12 \, d^{4} f^{2} g \log\left(e\right) - 4 \, c d^{3} f g^{2} + c^{2} d^{2} g^{3}\right)} b^{4}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} d^{4} f^{2} g - 4 \, a^{2} b^{2} d^{4} f g^{2} + a^{3} b d^{4} g^{3} + {\left(4 \, d^{4} f^{3} \log\left(e\right) - 6 \, c d^{3} f^{2} g + 4 \, c^{2} d^{2} f g^{2} - c^{3} d g^{3}\right)} b^{4}\right)} B^{2} x - {\left({\left(6 \, g^{3} \log\left(e\right) - 11 \, g^{3}\right)} a^{4} d^{4} + 2 \, {\left(c d^{3} g^{3} - 6 \, {\left(2 \, f g^{2} \log\left(e\right) - 3 \, f g^{2}\right)} d^{4}\right)} a^{3} b - 3 \, {\left(4 \, c d^{3} f g^{2} - c^{2} d^{2} g^{3} - 12 \, {\left(f^{2} g \log\left(e\right) - f^{2} g\right)} d^{4}\right)} a^{2} b^{2} - 6 \, {\left(4 \, d^{4} f^{3} \log\left(e\right) - 6 \, c d^{3} f^{2} g + 4 \, c^{2} d^{2} f g^{2} - c^{3} d g^{3}\right)} a b^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(6 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 2 \, {\left(a b^{3} d^{4} g^{3} + {\left(12 \, d^{4} f g^{2} \log\left(e\right) - c d^{3} g^{3}\right)} b^{4}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} d^{4} f g^{2} - a^{2} b^{2} d^{4} g^{3} + {\left(12 \, d^{4} f^{2} g \log\left(e\right) - 4 \, c d^{3} f g^{2} + c^{2} d^{2} g^{3}\right)} b^{4}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} d^{4} f^{2} g - 4 \, a^{2} b^{2} d^{4} f g^{2} + a^{3} b d^{4} g^{3} + {\left(4 \, d^{4} f^{3} \log\left(e\right) - 6 \, c d^{3} f^{2} g + 4 \, c^{2} d^{2} f g^{2} - c^{3} d g^{3}\right)} b^{4}\right)} B^{2} x + 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{3} x + {\left(4 \, a b^{3} d^{4} f^{3} - 6 \, a^{2} b^{2} d^{4} f^{2} g + 4 \, a^{3} b d^{4} f g^{2} - a^{4} d^{4} g^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b^{4} d^{4}}"," ",0,"1/4*A^2*g^3*x^4 + A^2*f*g^2*x^3 + 3/2*A^2*f^2*g*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*f^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*f^2*g + (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*f*g^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*g^3 + A^2*f^3*x - 1/12*(6*a^3*c*d^3*g^3 - 3*(8*c*d^3*f*g^2 - c^2*d^2*g^3)*a^2*b + 2*(18*c*d^3*f^2*g - 6*c^2*d^2*f*g^2 + c^3*d*g^3)*a*b^2 + (24*c*d^3*f^3*log(e) - (6*g^3*log(e) + 11*g^3)*c^4 + 12*(2*f*g^2*log(e) + 3*f*g^2)*c^3*d - 36*(f^2*g*log(e) + f^2*g)*c^2*d^2)*b^3)*B^2*log(d*x + c)/(b^3*d^4) + 1/2*(4*a*b^3*d^4*f^3 - 6*a^2*b^2*d^4*f^2*g + 4*a^3*b*d^4*f*g^2 - a^4*d^4*g^3 - (4*c*d^3*f^3 - 6*c^2*d^2*f^2*g + 4*c^3*d*f*g^2 - c^4*g^3)*b^4)*(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) + 1/12*(3*B^2*b^4*d^4*g^3*x^4*log(e)^2 + 2*(a*b^3*d^4*g^3*log(e) + (6*d^4*f*g^2*log(e)^2 - c*d^3*g^3*log(e))*b^4)*B^2*x^3 - ((3*g^3*log(e) - g^3)*a^2*b^2*d^4 - 2*(6*d^4*f*g^2*log(e) - c*d^3*g^3)*a*b^3 - (18*d^4*f^2*g*log(e)^2 - 12*c*d^3*f*g^2*log(e) + (3*g^3*log(e) + g^3)*c^2*d^2)*b^4)*B^2*x^2 + ((6*g^3*log(e) - 5*g^3)*a^3*b*d^4 + (5*c*d^3*g^3 - 12*(2*f*g^2*log(e) - f*g^2)*d^4)*a^2*b^2 + (36*d^4*f^2*g*log(e) - 24*c*d^3*f*g^2 + 5*c^2*d^2*g^3)*a*b^3 + (12*d^4*f^3*log(e)^2 - 36*c*d^3*f^2*g*log(e) - (6*g^3*log(e) + 5*g^3)*c^3*d + 12*(2*f*g^2*log(e) + f*g^2)*c^2*d^2)*b^4)*B^2*x + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x + (4*a*b^3*d^4*f^3 - 6*a^2*b^2*d^4*f^2*g + 4*a^3*b*d^4*f*g^2 - a^4*d^4*g^3)*B^2)*log(b*x + a)^2 + 3*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x + (4*c*d^3*f^3 - 6*c^2*d^2*f^2*g + 4*c^3*d*f*g^2 - c^4*g^3)*B^2*b^4)*log(d*x + c)^2 + (6*B^2*b^4*d^4*g^3*x^4*log(e) + 2*(a*b^3*d^4*g^3 + (12*d^4*f*g^2*log(e) - c*d^3*g^3)*b^4)*B^2*x^3 + 3*(4*a*b^3*d^4*f*g^2 - a^2*b^2*d^4*g^3 + (12*d^4*f^2*g*log(e) - 4*c*d^3*f*g^2 + c^2*d^2*g^3)*b^4)*B^2*x^2 + 6*(6*a*b^3*d^4*f^2*g - 4*a^2*b^2*d^4*f*g^2 + a^3*b*d^4*g^3 + (4*d^4*f^3*log(e) - 6*c*d^3*f^2*g + 4*c^2*d^2*f*g^2 - c^3*d*g^3)*b^4)*B^2*x - ((6*g^3*log(e) - 11*g^3)*a^4*d^4 + 2*(c*d^3*g^3 - 6*(2*f*g^2*log(e) - 3*f*g^2)*d^4)*a^3*b - 3*(4*c*d^3*f*g^2 - c^2*d^2*g^3 - 12*(f^2*g*log(e) - f^2*g)*d^4)*a^2*b^2 - 6*(4*d^4*f^3*log(e) - 6*c*d^3*f^2*g + 4*c^2*d^2*f*g^2 - c^3*d*g^3)*a*b^3)*B^2)*log(b*x + a) - (6*B^2*b^4*d^4*g^3*x^4*log(e) + 2*(a*b^3*d^4*g^3 + (12*d^4*f*g^2*log(e) - c*d^3*g^3)*b^4)*B^2*x^3 + 3*(4*a*b^3*d^4*f*g^2 - a^2*b^2*d^4*g^3 + (12*d^4*f^2*g*log(e) - 4*c*d^3*f*g^2 + c^2*d^2*g^3)*b^4)*B^2*x^2 + 6*(6*a*b^3*d^4*f^2*g - 4*a^2*b^2*d^4*f*g^2 + a^3*b*d^4*g^3 + (4*d^4*f^3*log(e) - 6*c*d^3*f^2*g + 4*c^2*d^2*f*g^2 - c^3*d*g^3)*b^4)*B^2*x + 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x + (4*a*b^3*d^4*f^3 - 6*a^2*b^2*d^4*f^2*g + 4*a^3*b*d^4*f*g^2 - a^4*d^4*g^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d^4)","B",0
241,1,1300,0,2.043760," ","integrate((g*x+f)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A^{2} g^{2} x^{3} + A^{2} f g 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 f^{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 f g + \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 g^{2} + A^{2} f^{2} x + \frac{{\left(2 \, a^{2} c d^{2} g^{2} - {\left(6 \, c d^{2} f g - c^{2} d g^{2}\right)} a b - {\left(6 \, c d^{2} f^{2} \log\left(e\right) + {\left(2 \, g^{2} \log\left(e\right) + 3 \, g^{2}\right)} c^{3} - 6 \, {\left(f g \log\left(e\right) + f g\right)} c^{2} d\right)} b^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, b^{2} d^{3}} + \frac{2 \, {\left(3 \, a b^{2} d^{3} f^{2} - 3 \, a^{2} b d^{3} f g + a^{3} d^{3} g^{2} - {\left(3 \, c d^{2} f^{2} - 3 \, c^{2} d f g + c^{3} g^{2}\right)} b^{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}}{3 \, b^{3} d^{3}} + \frac{B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right)^{2} + {\left(a b^{2} d^{3} g^{2} \log\left(e\right) + {\left(3 \, d^{3} f g \log\left(e\right)^{2} - c d^{2} g^{2} \log\left(e\right)\right)} b^{3}\right)} B^{2} x^{2} - {\left({\left(2 \, g^{2} \log\left(e\right) - g^{2}\right)} a^{2} b d^{3} - 2 \, {\left(3 \, d^{3} f g \log\left(e\right) - c d^{2} g^{2}\right)} a b^{2} - {\left(3 \, d^{3} f^{2} \log\left(e\right)^{2} - 6 \, c d^{2} f g \log\left(e\right) + {\left(2 \, g^{2} \log\left(e\right) + g^{2}\right)} c^{2} d\right)} b^{3}\right)} B^{2} x + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{2} x + {\left(3 \, a b^{2} d^{3} f^{2} - 3 \, a^{2} b d^{3} f g + a^{3} d^{3} g^{2}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{2} x + {\left(3 \, c d^{2} f^{2} - 3 \, c^{2} d f g + c^{3} g^{2}\right)} B^{2} b^{3}\right)} \log\left(d x + c\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + {\left(a b^{2} d^{3} g^{2} + {\left(6 \, d^{3} f g \log\left(e\right) - c d^{2} g^{2}\right)} b^{3}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f g - a^{2} b d^{3} g^{2} + {\left(3 \, d^{3} f^{2} \log\left(e\right) - 3 \, c d^{2} f g + c^{2} d g^{2}\right)} b^{3}\right)} B^{2} x + {\left({\left(2 \, g^{2} \log\left(e\right) - 3 \, g^{2}\right)} a^{3} d^{3} + {\left(c d^{2} g^{2} - 6 \, {\left(f g \log\left(e\right) - f g\right)} d^{3}\right)} a^{2} b + 2 \, {\left(3 \, d^{3} f^{2} \log\left(e\right) - 3 \, c d^{2} f g + c^{2} d g^{2}\right)} a b^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left(2 \, B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + {\left(a b^{2} d^{3} g^{2} + {\left(6 \, d^{3} f g \log\left(e\right) - c d^{2} g^{2}\right)} b^{3}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} d^{3} f g - a^{2} b d^{3} g^{2} + {\left(3 \, d^{3} f^{2} \log\left(e\right) - 3 \, c d^{2} f g + c^{2} d g^{2}\right)} b^{3}\right)} B^{2} x + 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{2} x + {\left(3 \, a b^{2} d^{3} f^{2} - 3 \, a^{2} b d^{3} f g + a^{3} d^{3} g^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, b^{3} d^{3}}"," ",0,"1/3*A^2*g^2*x^3 + A^2*f*g*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*f^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*f*g + 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*g^2 + A^2*f^2*x + 1/3*(2*a^2*c*d^2*g^2 - (6*c*d^2*f*g - c^2*d*g^2)*a*b - (6*c*d^2*f^2*log(e) + (2*g^2*log(e) + 3*g^2)*c^3 - 6*(f*g*log(e) + f*g)*c^2*d)*b^2)*B^2*log(d*x + c)/(b^2*d^3) + 2/3*(3*a*b^2*d^3*f^2 - 3*a^2*b*d^3*f*g + a^3*d^3*g^2 - (3*c*d^2*f^2 - 3*c^2*d*f*g + c^3*g^2)*b^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^3*d^3) + 1/3*(B^2*b^3*d^3*g^2*x^3*log(e)^2 + (a*b^2*d^3*g^2*log(e) + (3*d^3*f*g*log(e)^2 - c*d^2*g^2*log(e))*b^3)*B^2*x^2 - ((2*g^2*log(e) - g^2)*a^2*b*d^3 - 2*(3*d^3*f*g*log(e) - c*d^2*g^2)*a*b^2 - (3*d^3*f^2*log(e)^2 - 6*c*d^2*f*g*log(e) + (2*g^2*log(e) + g^2)*c^2*d)*b^3)*B^2*x + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x + (3*a*b^2*d^3*f^2 - 3*a^2*b*d^3*f*g + a^3*d^3*g^2)*B^2)*log(b*x + a)^2 + (B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x + (3*c*d^2*f^2 - 3*c^2*d*f*g + c^3*g^2)*B^2*b^3)*log(d*x + c)^2 + (2*B^2*b^3*d^3*g^2*x^3*log(e) + (a*b^2*d^3*g^2 + (6*d^3*f*g*log(e) - c*d^2*g^2)*b^3)*B^2*x^2 + 2*(3*a*b^2*d^3*f*g - a^2*b*d^3*g^2 + (3*d^3*f^2*log(e) - 3*c*d^2*f*g + c^2*d*g^2)*b^3)*B^2*x + ((2*g^2*log(e) - 3*g^2)*a^3*d^3 + (c*d^2*g^2 - 6*(f*g*log(e) - f*g)*d^3)*a^2*b + 2*(3*d^3*f^2*log(e) - 3*c*d^2*f*g + c^2*d*g^2)*a*b^2)*B^2)*log(b*x + a) - (2*B^2*b^3*d^3*g^2*x^3*log(e) + (a*b^2*d^3*g^2 + (6*d^3*f*g*log(e) - c*d^2*g^2)*b^3)*B^2*x^2 + 2*(3*a*b^2*d^3*f*g - a^2*b*d^3*g^2 + (3*d^3*f^2*log(e) - 3*c*d^2*f*g + c^2*d*g^2)*b^3)*B^2*x + 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x + (3*a*b^2*d^3*f^2 - 3*a^2*b*d^3*f*g + a^3*d^3*g^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^3*d^3)","B",0
242,1,673,0,1.915137," ","integrate((g*x+f)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A^{2} g 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 f + {\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 g + A^{2} f x - \frac{{\left(a c d g + {\left(2 \, c d f \log\left(e\right) - {\left(g \log\left(e\right) + g\right)} c^{2}\right)} b\right)} B^{2} \log\left(d x + c\right)}{b d^{2}} + \frac{{\left(2 \, a b d^{2} f - a^{2} d^{2} g - {\left(2 \, c d f - c^{2} g\right)} b^{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^{2}} + \frac{B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} + 2 \, {\left(a b d^{2} g \log\left(e\right) + {\left(d^{2} f \log\left(e\right)^{2} - c d g \log\left(e\right)\right)} b^{2}\right)} B^{2} x + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f x + {\left(2 \, a b d^{2} f - a^{2} d^{2} g\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f x + {\left(2 \, c d f - c^{2} g\right)} B^{2} b^{2}\right)} \log\left(d x + c\right)^{2} + 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + {\left(a b d^{2} g + {\left(2 \, d^{2} f \log\left(e\right) - c d g\right)} b^{2}\right)} B^{2} x - {\left({\left(g \log\left(e\right) - g\right)} a^{2} d^{2} - {\left(2 \, d^{2} f \log\left(e\right) - c d g\right)} a b\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + {\left(a b d^{2} g + {\left(2 \, d^{2} f \log\left(e\right) - c d g\right)} b^{2}\right)} B^{2} x + {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f x + {\left(2 \, a b d^{2} f - a^{2} d^{2} g\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b^{2} d^{2}}"," ",0,"1/2*A^2*g*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*f + (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*g + A^2*f*x - (a*c*d*g + (2*c*d*f*log(e) - (g*log(e) + g)*c^2)*b)*B^2*log(d*x + c)/(b*d^2) + (2*a*b*d^2*f - a^2*d^2*g - (2*c*d*f - c^2*g)*b^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) + 1/2*(B^2*b^2*d^2*g*x^2*log(e)^2 + 2*(a*b*d^2*g*log(e) + (d^2*f*log(e)^2 - c*d*g*log(e))*b^2)*B^2*x + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x + (2*a*b*d^2*f - a^2*d^2*g)*B^2)*log(b*x + a)^2 + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x + (2*c*d*f - c^2*g)*B^2*b^2)*log(d*x + c)^2 + 2*(B^2*b^2*d^2*g*x^2*log(e) + (a*b*d^2*g + (2*d^2*f*log(e) - c*d*g)*b^2)*B^2*x - ((g*log(e) - g)*a^2*d^2 - (2*d^2*f*log(e) - c*d*g)*a*b)*B^2)*log(b*x + a) - 2*(B^2*b^2*d^2*g*x^2*log(e) + (a*b*d^2*g + (2*d^2*f*log(e) - c*d*g)*b^2)*B^2*x + (B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x + (2*a*b*d^2*f - a^2*d^2*g)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d^2)","B",0
243,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","2 \, {\left(x \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + \frac{\frac{a e \log\left(b x + a\right)}{b} - \frac{c e \log\left(d x + c\right)}{d}}{e}\right)} A B + A^{2} x + B^{2} {\left(\frac{b d x \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} - 2 \, {\left(b d x \log\left(e\right) + {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{b d} + \int \frac{{\left(\log\left(e\right)^{2} + 2 \, \log\left(e\right)\right)} b^{2} d x^{2} + a b c \log\left(e\right)^{2} + {\left(b^{2} c \log\left(e\right)^{2} + {\left(\log\left(e\right)^{2} + 2 \, \log\left(e\right)\right)} a b d\right)} x + 2 \, {\left(b^{2} d x^{2} \log\left(e\right) + a b c \log\left(e\right) + a^{2} d + {\left(a b d {\left(\log\left(e\right) + 2\right)} + b^{2} c {\left(\log\left(e\right) - 1\right)}\right)} x\right)} \log\left(b x + a\right)}{b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x}\,{d x}\right)}"," ",0,"2*(x*log((b*x + a)*e/(d*x + c)) + (a*e*log(b*x + a)/b - c*e*log(d*x + c)/d)/e)*A*B + A^2*x + B^2*((b*d*x*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 - 2*(b*d*x*log(e) + (b*d*x + a*d)*log(b*x + a))*log(d*x + c))/(b*d) + integrate(((log(e)^2 + 2*log(e))*b^2*d*x^2 + a*b*c*log(e)^2 + (b^2*c*log(e)^2 + (log(e)^2 + 2*log(e))*a*b*d)*x + 2*(b^2*d*x^2*log(e) + a*b*c*log(e) + a^2*d + (a*b*d*(log(e) + 2) + b^2*c*(log(e) - 1))*x)*log(b*x + a))/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x), x))","F",0
244,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(g*x+f),x, algorithm=""maxima"")","\frac{A^{2} \log\left(g x + f\right)}{g} - \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)}{g x + f}\,{d x}"," ",0,"A^2*log(g*x + f)/g - 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))/(g*x + f), x)","F",0
245,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(g*x+f)^2,x, algorithm=""maxima"")","2 \, A B {\left(\frac{b \log\left(b x + a\right)}{b f g - a g^{2}} - \frac{d \log\left(d x + c\right)}{d f g - c g^{2}} + \frac{{\left(b c - a d\right)} \log\left(g x + f\right)}{b d f^{2} + a c g^{2} - {\left(b c + a d\right)} f g} - \frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{g^{2} x + f g}\right)} - B^{2} {\left(\frac{\log\left(d x + c\right)^{2}}{g^{2} x + f g} + \int -\frac{d g x \log\left(e\right)^{2} + c g \log\left(e\right)^{2} + {\left(d g x + c g\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left(b x + a\right) - 2 \, {\left({\left(g \log\left(e\right) - g\right)} d x + c g \log\left(e\right) - d f + {\left(d g x + c g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d g^{3} x^{3} + c f^{2} g + {\left(2 \, d f g^{2} + c g^{3}\right)} x^{2} + {\left(d f^{2} g + 2 \, c f g^{2}\right)} x}\,{d x}\right)} - \frac{A^{2}}{g^{2} x + f g}"," ",0,"2*A*B*(b*log(b*x + a)/(b*f*g - a*g^2) - d*log(d*x + c)/(d*f*g - c*g^2) + (b*c - a*d)*log(g*x + f)/(b*d*f^2 + a*c*g^2 - (b*c + a*d)*f*g) - log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^2*x + f*g)) - B^2*(log(d*x + c)^2/(g^2*x + f*g) + integrate(-(d*g*x*log(e)^2 + c*g*log(e)^2 + (d*g*x + c*g)*log(b*x + a)^2 + 2*(d*g*x*log(e) + c*g*log(e))*log(b*x + a) - 2*((g*log(e) - g)*d*x + c*g*log(e) - d*f + (d*g*x + c*g)*log(b*x + a))*log(d*x + c))/(d*g^3*x^3 + c*f^2*g + (2*d*f*g^2 + c*g^3)*x^2 + (d*f^2*g + 2*c*f*g^2)*x), x)) - A^2/(g^2*x + f*g)","F",0
246,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(g*x+f)^3,x, algorithm=""maxima"")","{\left(\frac{b^{2} \log\left(b x + a\right)}{b^{2} f^{2} g - 2 \, a b f g^{2} + a^{2} g^{3}} - \frac{d^{2} \log\left(d x + c\right)}{d^{2} f^{2} g - 2 \, c d f g^{2} + c^{2} g^{3}} + \frac{{\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g\right)} \log\left(g x + f\right)}{b^{2} d^{2} f^{4} + a^{2} c^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{3}} - \frac{b c - a d}{b d f^{3} + a c f g^{2} - {\left(b c + a d\right)} f^{2} g + {\left(b d f^{2} g + a c g^{3} - {\left(b c + a d\right)} f g^{2}\right)} x} - \frac{\log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g}\right)} A B - \frac{1}{2} \, B^{2} {\left(\frac{\log\left(d x + c\right)^{2}}{g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g} + 2 \, \int -\frac{d g x \log\left(e\right)^{2} + c g \log\left(e\right)^{2} + {\left(d g x + c g\right)} \log\left(b x + a\right)^{2} + 2 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left(b x + a\right) - {\left({\left(2 \, g \log\left(e\right) - g\right)} d x + 2 \, c g \log\left(e\right) - d f + 2 \, {\left(d g x + c g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d g^{4} x^{4} + c f^{3} g + {\left(3 \, d f g^{3} + c g^{4}\right)} x^{3} + 3 \, {\left(d f^{2} g^{2} + c f g^{3}\right)} x^{2} + {\left(d f^{3} g + 3 \, c f^{2} g^{2}\right)} x}\,{d x}\right)} - \frac{A^{2}}{2 \, {\left(g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g\right)}}"," ",0,"(b^2*log(b*x + a)/(b^2*f^2*g - 2*a*b*f*g^2 + a^2*g^3) - d^2*log(d*x + c)/(d^2*f^2*g - 2*c*d*f*g^2 + c^2*g^3) + (2*(b^2*c*d - a*b*d^2)*f - (b^2*c^2 - a^2*d^2)*g)*log(g*x + f)/(b^2*d^2*f^4 + a^2*c^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^3*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^2 - 2*(a*b*c^2 + a^2*c*d)*f*g^3) - (b*c - a*d)/(b*d*f^3 + a*c*f*g^2 - (b*c + a*d)*f^2*g + (b*d*f^2*g + a*c*g^3 - (b*c + a*d)*f*g^2)*x) - log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^3*x^2 + 2*f*g^2*x + f^2*g))*A*B - 1/2*B^2*(log(d*x + c)^2/(g^3*x^2 + 2*f*g^2*x + f^2*g) + 2*integrate(-(d*g*x*log(e)^2 + c*g*log(e)^2 + (d*g*x + c*g)*log(b*x + a)^2 + 2*(d*g*x*log(e) + c*g*log(e))*log(b*x + a) - ((2*g*log(e) - g)*d*x + 2*c*g*log(e) - d*f + 2*(d*g*x + c*g)*log(b*x + a))*log(d*x + c))/(d*g^4*x^4 + c*f^3*g + (3*d*f*g^3 + c*g^4)*x^3 + 3*(d*f^2*g^2 + c*f*g^3)*x^2 + (d*f^3*g + 3*c*f^2*g^2)*x), x)) - 1/2*A^2/(g^3*x^2 + 2*f*g^2*x + f^2*g)","F",0
247,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(g*x+f)^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, b^{3} \log\left(b x + a\right)}{b^{3} f^{3} g - 3 \, a b^{2} f^{2} g^{2} + 3 \, a^{2} b f g^{3} - a^{3} g^{4}} - \frac{2 \, d^{3} \log\left(d x + c\right)}{d^{3} f^{3} g - 3 \, c d^{2} f^{2} g^{2} + 3 \, c^{2} d f g^{3} - c^{3} g^{4}} + \frac{2 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{2}\right)} \log\left(g x + f\right)}{b^{3} d^{3} f^{6} + a^{3} c^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{5}} - \frac{5 \, {\left(b^{2} c d - a b d^{2}\right)} f^{2} - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} f g + {\left(a b c^{2} - a^{2} c d\right)} g^{2} + 2 \, {\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f g - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g^{2}\right)} x}{b^{2} d^{2} f^{6} + a^{2} c^{2} f^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{5} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{4} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{3} g^{3} + {\left(b^{2} d^{2} f^{4} g^{2} + a^{2} c^{2} g^{6} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g^{3} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{4} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} f^{5} g + a^{2} c^{2} f g^{5} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{4} g^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{3} g^{3} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2} g^{4}\right)} x} - \frac{2 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g}\right)} A B - \frac{1}{3} \, B^{2} {\left(\frac{\log\left(d x + c\right)^{2}}{g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g} + 3 \, \int -\frac{3 \, d g x \log\left(e\right)^{2} + 3 \, c g \log\left(e\right)^{2} + 3 \, {\left(d g x + c g\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left(b x + a\right) - 2 \, {\left({\left(3 \, g \log\left(e\right) - g\right)} d x + 3 \, c g \log\left(e\right) - d f + 3 \, {\left(d g x + c g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, {\left(d g^{5} x^{5} + c f^{4} g + {\left(4 \, d f g^{4} + c g^{5}\right)} x^{4} + 2 \, {\left(3 \, d f^{2} g^{3} + 2 \, c f g^{4}\right)} x^{3} + 2 \, {\left(2 \, d f^{3} g^{2} + 3 \, c f^{2} g^{3}\right)} x^{2} + {\left(d f^{4} g + 4 \, c f^{3} g^{2}\right)} x\right)}}\,{d x}\right)} - \frac{A^{2}}{3 \, {\left(g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g\right)}}"," ",0,"1/3*(2*b^3*log(b*x + a)/(b^3*f^3*g - 3*a*b^2*f^2*g^2 + 3*a^2*b*f*g^3 - a^3*g^4) - 2*d^3*log(d*x + c)/(d^3*f^3*g - 3*c*d^2*f^2*g^2 + 3*c^2*d*f*g^3 - c^3*g^4) + 2*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g + (b^3*c^3 - a^3*d^3)*g^2)*log(g*x + f)/(b^3*d^3*f^6 + a^3*c^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^5) - (5*(b^2*c*d - a*b*d^2)*f^2 - 3*(b^2*c^2 - a^2*d^2)*f*g + (a*b*c^2 - a^2*c*d)*g^2 + 2*(2*(b^2*c*d - a*b*d^2)*f*g - (b^2*c^2 - a^2*d^2)*g^2)*x)/(b^2*d^2*f^6 + a^2*c^2*f^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^5*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^4*g^2 - 2*(a*b*c^2 + a^2*c*d)*f^3*g^3 + (b^2*d^2*f^4*g^2 + a^2*c^2*g^6 - 2*(b^2*c*d + a*b*d^2)*f^3*g^3 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^4 - 2*(a*b*c^2 + a^2*c*d)*f*g^5)*x^2 + 2*(b^2*d^2*f^5*g + a^2*c^2*f*g^5 - 2*(b^2*c*d + a*b*d^2)*f^4*g^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^3*g^3 - 2*(a*b*c^2 + a^2*c*d)*f^2*g^4)*x) - 2*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g))*A*B - 1/3*B^2*(log(d*x + c)^2/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g) + 3*integrate(-1/3*(3*d*g*x*log(e)^2 + 3*c*g*log(e)^2 + 3*(d*g*x + c*g)*log(b*x + a)^2 + 6*(d*g*x*log(e) + c*g*log(e))*log(b*x + a) - 2*((3*g*log(e) - g)*d*x + 3*c*g*log(e) - d*f + 3*(d*g*x + c*g)*log(b*x + a))*log(d*x + c))/(d*g^5*x^5 + c*f^4*g + (4*d*f*g^4 + c*g^5)*x^4 + 2*(3*d*f^2*g^3 + 2*c*f*g^4)*x^3 + 2*(2*d*f^3*g^2 + 3*c*f^2*g^3)*x^2 + (d*f^4*g + 4*c*f^3*g^2)*x), x)) - 1/3*A^2/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g)","F",0
248,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(g*x+f)^5,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(\frac{6 \, b^{4} \log\left(b x + a\right)}{b^{4} f^{4} g - 4 \, a b^{3} f^{3} g^{2} + 6 \, a^{2} b^{2} f^{2} g^{3} - 4 \, a^{3} b f g^{4} + a^{4} g^{5}} - \frac{6 \, d^{4} \log\left(d x + c\right)}{d^{4} f^{4} g - 4 \, c d^{3} f^{3} g^{2} + 6 \, c^{2} d^{2} f^{2} g^{3} - 4 \, c^{3} d f g^{4} + c^{4} g^{5}} + \frac{6 \, {\left(4 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f^{3} - 6 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} f^{2} g + 4 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} f g^{2} - {\left(b^{4} c^{4} - a^{4} d^{4}\right)} g^{3}\right)} \log\left(g x + f\right)}{b^{4} d^{4} f^{8} + a^{4} c^{4} g^{8} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} f^{7} g + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} f^{6} g^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} f^{5} g^{3} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} f^{4} g^{4} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} f^{3} g^{5} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f^{2} g^{6} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} f g^{7}} - \frac{26 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{4} - 31 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{3} g + {\left(11 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 15 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3}\right)} f^{2} g^{2} - 7 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} f g^{3} + 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} g^{4} + 6 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} g^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g^{3} + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{4}\right)} x^{2} + 3 \, {\left(14 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{3} g - 15 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{2} g^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f g^{3} - {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} g^{4}\right)} x}{b^{3} d^{3} f^{9} + a^{3} c^{3} f^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{8} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{7} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{5} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{4} g^{5} + {\left(b^{3} d^{3} f^{6} g^{3} + a^{3} c^{3} g^{9} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{5} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{6} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{7} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{8}\right)} x^{3} + 3 \, {\left(b^{3} d^{3} f^{7} g^{2} + a^{3} c^{3} f g^{8} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{5} g^{4} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{4} g^{5} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{3} g^{6} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{2} g^{7}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} f^{8} g + a^{3} c^{3} f^{2} g^{7} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{7} g^{2} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{6} g^{3} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{4} g^{5} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{3} g^{6}\right)} x} - \frac{6 \, \log\left(\frac{b e x}{d x + c} + \frac{a e}{d x + c}\right)}{g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g}\right)} A B - \frac{1}{4} \, B^{2} {\left(\frac{\log\left(d x + c\right)^{2}}{g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g} + 4 \, \int -\frac{2 \, d g x \log\left(e\right)^{2} + 2 \, c g \log\left(e\right)^{2} + 2 \, {\left(d g x + c g\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left(b x + a\right) - {\left({\left(4 \, g \log\left(e\right) - g\right)} d x + 4 \, c g \log\left(e\right) - d f + 4 \, {\left(d g x + c g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, {\left(d g^{6} x^{6} + c f^{5} g + {\left(5 \, d f g^{5} + c g^{6}\right)} x^{5} + 5 \, {\left(2 \, d f^{2} g^{4} + c f g^{5}\right)} x^{4} + 10 \, {\left(d f^{3} g^{3} + c f^{2} g^{4}\right)} x^{3} + 5 \, {\left(d f^{4} g^{2} + 2 \, c f^{3} g^{3}\right)} x^{2} + {\left(d f^{5} g + 5 \, c f^{4} g^{2}\right)} x\right)}}\,{d x}\right)} - \frac{A^{2}}{4 \, {\left(g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g\right)}}"," ",0,"1/12*(6*b^4*log(b*x + a)/(b^4*f^4*g - 4*a*b^3*f^3*g^2 + 6*a^2*b^2*f^2*g^3 - 4*a^3*b*f*g^4 + a^4*g^5) - 6*d^4*log(d*x + c)/(d^4*f^4*g - 4*c*d^3*f^3*g^2 + 6*c^2*d^2*f^2*g^3 - 4*c^3*d*f*g^4 + c^4*g^5) + 6*(4*(b^4*c*d^3 - a*b^3*d^4)*f^3 - 6*(b^4*c^2*d^2 - a^2*b^2*d^4)*f^2*g + 4*(b^4*c^3*d - a^3*b*d^4)*f*g^2 - (b^4*c^4 - a^4*d^4)*g^3)*log(g*x + f)/(b^4*d^4*f^8 + a^4*c^4*g^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*f^7*g + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*f^6*g^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*f^5*g^3 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*f^4*g^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*f^3*g^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f^2*g^6 - 4*(a^3*b*c^4 + a^4*c^3*d)*f*g^7) - (26*(b^3*c*d^2 - a*b^2*d^3)*f^4 - 31*(b^3*c^2*d - a^2*b*d^3)*f^3*g + (11*b^3*c^3 + 15*a*b^2*c^2*d - 15*a^2*b*c*d^2 - 11*a^3*d^3)*f^2*g^2 - 7*(a*b^2*c^3 - a^3*c*d^2)*f*g^3 + 2*(a^2*b*c^3 - a^3*c^2*d)*g^4 + 6*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2*g^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g^3 + (b^3*c^3 - a^3*d^3)*g^4)*x^2 + 3*(14*(b^3*c*d^2 - a*b^2*d^3)*f^3*g - 15*(b^3*c^2*d - a^2*b*d^3)*f^2*g^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f*g^3 - (a*b^2*c^3 - a^3*c*d^2)*g^4)*x)/(b^3*d^3*f^9 + a^3*c^3*f^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^8*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^7*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^6*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^5*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^4*g^5 + (b^3*d^3*f^6*g^3 + a^3*c^3*g^9 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g^4 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^5 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^6 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^7 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^8)*x^3 + 3*(b^3*d^3*f^7*g^2 + a^3*c^3*f*g^8 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^6*g^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^5*g^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^4*g^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3*g^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^2*g^7)*x^2 + 3*(b^3*d^3*f^8*g + a^3*c^3*f^2*g^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^7*g^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^6*g^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^5*g^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^4*g^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^3*g^6)*x) - 6*log(b*e*x/(d*x + c) + a*e/(d*x + c))/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g))*A*B - 1/4*B^2*(log(d*x + c)^2/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g) + 4*integrate(-1/2*(2*d*g*x*log(e)^2 + 2*c*g*log(e)^2 + 2*(d*g*x + c*g)*log(b*x + a)^2 + 4*(d*g*x*log(e) + c*g*log(e))*log(b*x + a) - ((4*g*log(e) - g)*d*x + 4*c*g*log(e) - d*f + 4*(d*g*x + c*g)*log(b*x + a))*log(d*x + c))/(d*g^6*x^6 + c*f^5*g + (5*d*f*g^5 + c*g^6)*x^5 + 5*(2*d*f^2*g^4 + c*f*g^5)*x^4 + 10*(d*f^3*g^3 + c*f^2*g^4)*x^3 + 5*(d*f^4*g^2 + 2*c*f^3*g^3)*x^2 + (d*f^5*g + 5*c*f^4*g^2)*x), x)) - 1/4*A^2/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g)","F",0
249,1,32,0,0.477673," ","integrate(log((1+x)/(-1+x))/x^2,x, algorithm=""maxima"")","-\frac{\log\left(\frac{x + 1}{x - 1}\right)}{x} - \log\left(x + 1\right) - \log\left(x - 1\right) + 2 \, \log\left(x\right)"," ",0,"-log((x + 1)/(x - 1))/x - log(x + 1) - log(x - 1) + 2*log(x)","A",0
250,0,0,0,0.000000," ","integrate((g*x+f)^2/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{{\left(g x + f\right)}^{2}}{B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A}\,{d x}"," ",0,"integrate((g*x + f)^2/(B*log((b*x + a)*e/(d*x + c)) + A), x)","F",0
251,0,0,0,0.000000," ","integrate((g*x+f)/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{g x + f}{B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A}\,{d x}"," ",0,"integrate((g*x + f)/(B*log((b*x + a)*e/(d*x + c)) + A), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{1}{B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A}\,{d x}"," ",0,"integrate(1/(B*log((b*x + a)*e/(d*x + c)) + A), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(g*x+f)/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)} {\left(B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)*(B*log((b*x + a)*e/(d*x + c)) + A)), x)","F",0
254,0,0,0,0.000000," ","integrate(1/(g*x+f)^2/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)}^{2} {\left(B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)^2*(B*log((b*x + a)*e/(d*x + c)) + A)), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(g*x+f)^3/(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)}^{3} {\left(B \log\left(\frac{{\left(b x + a\right)} e}{d x + c}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)^3*(B*log((b*x + a)*e/(d*x + c)) + A)), x)","F",0
256,0,0,0,0.000000," ","integrate((g*x+f)^2/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{b d g^{2} x^{4} + a c f^{2} + {\left(a d g^{2} + {\left(2 \, d f g + c g^{2}\right)} b\right)} x^{3} + {\left({\left(2 \, d f g + c g^{2}\right)} a + {\left(d f^{2} + 2 \, c f g\right)} b\right)} x^{2} + {\left(b c f^{2} + {\left(d f^{2} + 2 \, c f g\right)} a\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}} + \int \frac{4 \, b d g^{2} x^{3} + b c f^{2} + 3 \, {\left(a d g^{2} + {\left(2 \, d f g + c g^{2}\right)} b\right)} x^{2} + {\left(d f^{2} + 2 \, c f g\right)} a + 2 \, {\left({\left(2 \, d f g + c g^{2}\right)} a + {\left(d f^{2} + 2 \, c f g\right)} b\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}}\,{d x}"," ",0,"-(b*d*g^2*x^4 + a*c*f^2 + (a*d*g^2 + (2*d*f*g + c*g^2)*b)*x^3 + ((2*d*f*g + c*g^2)*a + (d*f^2 + 2*c*f*g)*b)*x^2 + (b*c*f^2 + (d*f^2 + 2*c*f*g)*a)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate((4*b*d*g^2*x^3 + b*c*f^2 + 3*(a*d*g^2 + (2*d*f*g + c*g^2)*b)*x^2 + (d*f^2 + 2*c*f*g)*a + 2*((2*d*f*g + c*g^2)*a + (d*f^2 + 2*c*f*g)*b)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
257,0,0,0,0.000000," ","integrate((g*x+f)/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{b d g x^{3} + a c f + {\left(a d g + {\left(d f + c g\right)} b\right)} x^{2} + {\left(b c f + {\left(d f + c g\right)} a\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}} + \int \frac{3 \, b d g x^{2} + b c f + {\left(d f + c g\right)} a + 2 \, {\left(a d g + {\left(d f + c g\right)} b\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}}\,{d x}"," ",0,"-(b*d*g*x^3 + a*c*f + (a*d*g + (d*f + c*g)*b)*x^2 + (b*c*f + (d*f + c*g)*a)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate((3*b*d*g*x^2 + b*c*f + (d*f + c*g)*a + 2*(a*d*g + (d*f + c*g)*b)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
258,0,0,0,0.000000," ","integrate(1/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}} + \int \frac{2 \, b d x + b c + a d}{{\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}}\,{d x}"," ",0,"-(b*d*x^2 + a*c + (b*c + a*d)*x)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate((2*b*d*x + b*c + a*d)/((b*c - a*d)*B^2*log(b*x + a) - (b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
259,0,0,0,0.000000," ","integrate(1/(g*x+f)/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{{\left(b c f - a d f\right)} A B + {\left(b c f \log\left(e\right) - a d f \log\left(e\right)\right)} B^{2} + {\left({\left(b c g - a d g\right)} A B + {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g - a d g\right)} B^{2} x + {\left(b c f - a d f\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b c g - a d g\right)} B^{2} x + {\left(b c f - a d f\right)} B^{2}\right)} \log\left(d x + c\right)} + \int \frac{b d g x^{2} + 2 \, b d f x + b c f + {\left(d f - c g\right)} a}{{\left(b c f^{2} - a d f^{2}\right)} A B + {\left(b c f^{2} \log\left(e\right) - a d f^{2} \log\left(e\right)\right)} B^{2} + {\left({\left(b c g^{2} - a d g^{2}\right)} A B + {\left(b c g^{2} \log\left(e\right) - a d g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c f g - a d f g\right)} A B + {\left(b c f g \log\left(e\right) - a d f g \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{2} - a d g^{2}\right)} B^{2} x^{2} + 2 \, {\left(b c f g - a d f g\right)} B^{2} x + {\left(b c f^{2} - a d f^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b c g^{2} - a d g^{2}\right)} B^{2} x^{2} + 2 \, {\left(b c f g - a d f g\right)} B^{2} x + {\left(b c f^{2} - a d f^{2}\right)} B^{2}\right)} \log\left(d x + c\right)}\,{d x}"," ",0,"-(b*d*x^2 + a*c + (b*c + a*d)*x)/((b*c*f - a*d*f)*A*B + (b*c*f*log(e) - a*d*f*log(e))*B^2 + ((b*c*g - a*d*g)*A*B + (b*c*g*log(e) - a*d*g*log(e))*B^2)*x + ((b*c*g - a*d*g)*B^2*x + (b*c*f - a*d*f)*B^2)*log(b*x + a) - ((b*c*g - a*d*g)*B^2*x + (b*c*f - a*d*f)*B^2)*log(d*x + c)) + integrate((b*d*g*x^2 + 2*b*d*f*x + b*c*f + (d*f - c*g)*a)/((b*c*f^2 - a*d*f^2)*A*B + (b*c*f^2*log(e) - a*d*f^2*log(e))*B^2 + ((b*c*g^2 - a*d*g^2)*A*B + (b*c*g^2*log(e) - a*d*g^2*log(e))*B^2)*x^2 + 2*((b*c*f*g - a*d*f*g)*A*B + (b*c*f*g*log(e) - a*d*f*g*log(e))*B^2)*x + ((b*c*g^2 - a*d*g^2)*B^2*x^2 + 2*(b*c*f*g - a*d*f*g)*B^2*x + (b*c*f^2 - a*d*f^2)*B^2)*log(b*x + a) - ((b*c*g^2 - a*d*g^2)*B^2*x^2 + 2*(b*c*f*g - a*d*f*g)*B^2*x + (b*c*f^2 - a*d*f^2)*B^2)*log(d*x + c)), x)","F",0
260,0,0,0,0.000000," ","integrate(1/(g*x+f)^2/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{{\left(b c f^{2} - a d f^{2}\right)} A B + {\left(b c f^{2} \log\left(e\right) - a d f^{2} \log\left(e\right)\right)} B^{2} + {\left({\left(b c g^{2} - a d g^{2}\right)} A B + {\left(b c g^{2} \log\left(e\right) - a d g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c f g - a d f g\right)} A B + {\left(b c f g \log\left(e\right) - a d f g \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{2} - a d g^{2}\right)} B^{2} x^{2} + 2 \, {\left(b c f g - a d f g\right)} B^{2} x + {\left(b c f^{2} - a d f^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b c g^{2} - a d g^{2}\right)} B^{2} x^{2} + 2 \, {\left(b c f g - a d f g\right)} B^{2} x + {\left(b c f^{2} - a d f^{2}\right)} B^{2}\right)} \log\left(d x + c\right)} - \int -\frac{b c f + {\left(d f - 2 \, c g\right)} a - {\left(a d g - {\left(2 \, d f - c g\right)} b\right)} x}{{\left({\left(b c g^{3} - a d g^{3}\right)} A B + {\left(b c g^{3} \log\left(e\right) - a d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{3} - a d f^{3}\right)} A B + {\left(b c f^{3} \log\left(e\right) - a d f^{3} \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(b c f g^{2} - a d f g^{2}\right)} A B + {\left(b c f g^{2} \log\left(e\right) - a d f g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(b c f^{2} g - a d f^{2} g\right)} A B + {\left(b c f^{2} g \log\left(e\right) - a d f^{2} g \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{3} - a d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} - a d f g^{2}\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g - a d f^{2} g\right)} B^{2} x + {\left(b c f^{3} - a d f^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b c g^{3} - a d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} - a d f g^{2}\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g - a d f^{2} g\right)} B^{2} x + {\left(b c f^{3} - a d f^{3}\right)} B^{2}\right)} \log\left(d x + c\right)}\,{d x}"," ",0,"-(b*d*x^2 + a*c + (b*c + a*d)*x)/((b*c*f^2 - a*d*f^2)*A*B + (b*c*f^2*log(e) - a*d*f^2*log(e))*B^2 + ((b*c*g^2 - a*d*g^2)*A*B + (b*c*g^2*log(e) - a*d*g^2*log(e))*B^2)*x^2 + 2*((b*c*f*g - a*d*f*g)*A*B + (b*c*f*g*log(e) - a*d*f*g*log(e))*B^2)*x + ((b*c*g^2 - a*d*g^2)*B^2*x^2 + 2*(b*c*f*g - a*d*f*g)*B^2*x + (b*c*f^2 - a*d*f^2)*B^2)*log(b*x + a) - ((b*c*g^2 - a*d*g^2)*B^2*x^2 + 2*(b*c*f*g - a*d*f*g)*B^2*x + (b*c*f^2 - a*d*f^2)*B^2)*log(d*x + c)) - integrate(-(b*c*f + (d*f - 2*c*g)*a - (a*d*g - (2*d*f - c*g)*b)*x)/(((b*c*g^3 - a*d*g^3)*A*B + (b*c*g^3*log(e) - a*d*g^3*log(e))*B^2)*x^3 + (b*c*f^3 - a*d*f^3)*A*B + (b*c*f^3*log(e) - a*d*f^3*log(e))*B^2 + 3*((b*c*f*g^2 - a*d*f*g^2)*A*B + (b*c*f*g^2*log(e) - a*d*f*g^2*log(e))*B^2)*x^2 + 3*((b*c*f^2*g - a*d*f^2*g)*A*B + (b*c*f^2*g*log(e) - a*d*f^2*g*log(e))*B^2)*x + ((b*c*g^3 - a*d*g^3)*B^2*x^3 + 3*(b*c*f*g^2 - a*d*f*g^2)*B^2*x^2 + 3*(b*c*f^2*g - a*d*f^2*g)*B^2*x + (b*c*f^3 - a*d*f^3)*B^2)*log(b*x + a) - ((b*c*g^3 - a*d*g^3)*B^2*x^3 + 3*(b*c*f*g^2 - a*d*f*g^2)*B^2*x^2 + 3*(b*c*f^2*g - a*d*f^2*g)*B^2*x + (b*c*f^3 - a*d*f^3)*B^2)*log(d*x + c)), x)","F",0
261,0,0,0,0.000000," ","integrate(1/(g*x+f)^3/(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{{\left({\left(b c g^{3} - a d g^{3}\right)} A B + {\left(b c g^{3} \log\left(e\right) - a d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{3} - a d f^{3}\right)} A B + {\left(b c f^{3} \log\left(e\right) - a d f^{3} \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(b c f g^{2} - a d f g^{2}\right)} A B + {\left(b c f g^{2} \log\left(e\right) - a d f g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(b c f^{2} g - a d f^{2} g\right)} A B + {\left(b c f^{2} g \log\left(e\right) - a d f^{2} g \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{3} - a d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} - a d f g^{2}\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g - a d f^{2} g\right)} B^{2} x + {\left(b c f^{3} - a d f^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b c g^{3} - a d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} - a d f g^{2}\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g - a d f^{2} g\right)} B^{2} x + {\left(b c f^{3} - a d f^{3}\right)} B^{2}\right)} \log\left(d x + c\right)} - \int \frac{b d g x^{2} - b c f - {\left(d f - 3 \, c g\right)} a + 2 \, {\left(a d g - {\left(d f - c g\right)} b\right)} x}{{\left({\left(b c g^{4} - a d g^{4}\right)} A B + {\left(b c g^{4} \log\left(e\right) - a d g^{4} \log\left(e\right)\right)} B^{2}\right)} x^{4} + 4 \, {\left({\left(b c f g^{3} - a d f g^{3}\right)} A B + {\left(b c f g^{3} \log\left(e\right) - a d f g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{4} - a d f^{4}\right)} A B + {\left(b c f^{4} \log\left(e\right) - a d f^{4} \log\left(e\right)\right)} B^{2} + 6 \, {\left({\left(b c f^{2} g^{2} - a d f^{2} g^{2}\right)} A B + {\left(b c f^{2} g^{2} \log\left(e\right) - a d f^{2} g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 4 \, {\left({\left(b c f^{3} g - a d f^{3} g\right)} A B + {\left(b c f^{3} g \log\left(e\right) - a d f^{3} g \log\left(e\right)\right)} B^{2}\right)} x + {\left({\left(b c g^{4} - a d g^{4}\right)} B^{2} x^{4} + 4 \, {\left(b c f g^{3} - a d f g^{3}\right)} B^{2} x^{3} + 6 \, {\left(b c f^{2} g^{2} - a d f^{2} g^{2}\right)} B^{2} x^{2} + 4 \, {\left(b c f^{3} g - a d f^{3} g\right)} B^{2} x + {\left(b c f^{4} - a d f^{4}\right)} B^{2}\right)} \log\left(b x + a\right) - {\left({\left(b c g^{4} - a d g^{4}\right)} B^{2} x^{4} + 4 \, {\left(b c f g^{3} - a d f g^{3}\right)} B^{2} x^{3} + 6 \, {\left(b c f^{2} g^{2} - a d f^{2} g^{2}\right)} B^{2} x^{2} + 4 \, {\left(b c f^{3} g - a d f^{3} g\right)} B^{2} x + {\left(b c f^{4} - a d f^{4}\right)} B^{2}\right)} \log\left(d x + c\right)}\,{d x}"," ",0,"-(b*d*x^2 + a*c + (b*c + a*d)*x)/(((b*c*g^3 - a*d*g^3)*A*B + (b*c*g^3*log(e) - a*d*g^3*log(e))*B^2)*x^3 + (b*c*f^3 - a*d*f^3)*A*B + (b*c*f^3*log(e) - a*d*f^3*log(e))*B^2 + 3*((b*c*f*g^2 - a*d*f*g^2)*A*B + (b*c*f*g^2*log(e) - a*d*f*g^2*log(e))*B^2)*x^2 + 3*((b*c*f^2*g - a*d*f^2*g)*A*B + (b*c*f^2*g*log(e) - a*d*f^2*g*log(e))*B^2)*x + ((b*c*g^3 - a*d*g^3)*B^2*x^3 + 3*(b*c*f*g^2 - a*d*f*g^2)*B^2*x^2 + 3*(b*c*f^2*g - a*d*f^2*g)*B^2*x + (b*c*f^3 - a*d*f^3)*B^2)*log(b*x + a) - ((b*c*g^3 - a*d*g^3)*B^2*x^3 + 3*(b*c*f*g^2 - a*d*f*g^2)*B^2*x^2 + 3*(b*c*f^2*g - a*d*f^2*g)*B^2*x + (b*c*f^3 - a*d*f^3)*B^2)*log(d*x + c)) - integrate((b*d*g*x^2 - b*c*f - (d*f - 3*c*g)*a + 2*(a*d*g - (d*f - c*g)*b)*x)/(((b*c*g^4 - a*d*g^4)*A*B + (b*c*g^4*log(e) - a*d*g^4*log(e))*B^2)*x^4 + 4*((b*c*f*g^3 - a*d*f*g^3)*A*B + (b*c*f*g^3*log(e) - a*d*f*g^3*log(e))*B^2)*x^3 + (b*c*f^4 - a*d*f^4)*A*B + (b*c*f^4*log(e) - a*d*f^4*log(e))*B^2 + 6*((b*c*f^2*g^2 - a*d*f^2*g^2)*A*B + (b*c*f^2*g^2*log(e) - a*d*f^2*g^2*log(e))*B^2)*x^2 + 4*((b*c*f^3*g - a*d*f^3*g)*A*B + (b*c*f^3*g*log(e) - a*d*f^3*g*log(e))*B^2)*x + ((b*c*g^4 - a*d*g^4)*B^2*x^4 + 4*(b*c*f*g^3 - a*d*f*g^3)*B^2*x^3 + 6*(b*c*f^2*g^2 - a*d*f^2*g^2)*B^2*x^2 + 4*(b*c*f^3*g - a*d*f^3*g)*B^2*x + (b*c*f^4 - a*d*f^4)*B^2)*log(b*x + a) - ((b*c*g^4 - a*d*g^4)*B^2*x^4 + 4*(b*c*f*g^3 - a*d*f*g^3)*B^2*x^3 + 6*(b*c*f^2*g^2 - a*d*f^2*g^2)*B^2*x^2 + 4*(b*c*f^3*g - a*d*f^3*g)*B^2*x + (b*c*f^4 - a*d*f^4)*B^2)*log(d*x + c)), x)","F",0
262,1,855,0,1.173398," ","integrate((g*x+f)^4*(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\frac{1}{5} \, A g^{4} x^{5} + A f g^{3} x^{4} + 2 \, A f^{2} g^{2} x^{3} + 2 \, A f^{3} g x^{2} + {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B f^{4} + 2 \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B f^{3} g + 2 \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 f^{2} g^{2} + \frac{1}{3} \, {\left(3 \, x^{4} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 f g^{3} + \frac{1}{30} \, {\left(6 \, x^{5} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 g^{4} + A f^{4} x"," ",0,"1/5*A*g^4*x^5 + A*f*g^3*x^4 + 2*A*f^2*g^2*x^3 + 2*A*f^3*g*x^2 + (x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*B*f^4 + 2*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*B*f^3*g + 2*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*f^2*g^2 + 1/3*(3*x^4*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 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*f*g^3 + 1/30*(6*x^5*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*g^4 + A*f^4*x","B",0
263,1,623,0,1.055054," ","integrate((g*x+f)^3*(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\frac{1}{4} \, A g^{3} x^{4} + A f g^{2} x^{3} + \frac{3}{2} \, A f^{2} g x^{2} + {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B f^{3} + \frac{3}{2} \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B f^{2} g + {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 f g^{2} + \frac{1}{12} \, {\left(3 \, x^{4} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 g^{3} + A f^{3} x"," ",0,"1/4*A*g^3*x^4 + A*f*g^2*x^3 + 3/2*A*f^2*g*x^2 + (x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*B*f^3 + 3/2*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*B*f^2*g + (x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*f*g^2 + 1/12*(3*x^4*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 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*g^3 + A*f^3*x","B",0
264,1,419,0,0.794637," ","integrate((g*x+f)^2*(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\frac{1}{3} \, A g^{2} x^{3} + A f g x^{2} + {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B f^{2} + {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B f g + \frac{1}{3} \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 g^{2} + A f^{2} x"," ",0,"1/3*A*g^2*x^3 + A*f*g*x^2 + (x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*B*f^2 + (x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*B*f*g + 1/3*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*g^2 + A*f^2*x","B",0
265,1,246,0,0.758365," ","integrate((g*x+f)*(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\frac{1}{2} \, A g x^{2} + {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} B f + \frac{1}{2} \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} B g + A f x"," ",0,"1/2*A*g*x^2 + (x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*B*f + 1/2*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*B*g + A*f*x","B",0
266,1,57,0,0.633614," ","integrate(A+B*log(e*(b*x+a)^2/(d*x+c)^2),x, algorithm=""maxima"")","{\left(x \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + \frac{2 \, {\left(\frac{a e \log\left(b x + a\right)}{b} - \frac{c e \log\left(d x + c\right)}{d}\right)}}{e}\right)} B + A x"," ",0,"(x*log((b*x + a)^2*e/(d*x + c)^2) + 2*(a*e*log(b*x + a)/b - c*e*log(d*x + c)/d)/e)*B + A*x","A",0
267,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(g*x+f),x, algorithm=""maxima"")","-B \int -\frac{2 \, \log\left(b x + a\right) - 2 \, \log\left(d x + c\right) + \log\left(e\right)}{g x + f}\,{d x} + \frac{A \log\left(g x + f\right)}{g}"," ",0,"-B*integrate(-(2*log(b*x + a) - 2*log(d*x + c) + log(e))/(g*x + f), x) + A*log(g*x + f)/g","F",0
268,1,192,0,0.700279," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(g*x+f)^2,x, algorithm=""maxima"")","B {\left(\frac{2 \, b \log\left(b x + a\right)}{b f g - a g^{2}} - \frac{2 \, d \log\left(d x + c\right)}{d f g - c g^{2}} + \frac{2 \, {\left(b c - a d\right)} \log\left(g x + f\right)}{b d f^{2} + a c g^{2} - {\left(b c + a d\right)} f g} - \frac{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{g^{2} x + f g}\right)} - \frac{A}{g^{2} x + f g}"," ",0,"B*(2*b*log(b*x + a)/(b*f*g - a*g^2) - 2*d*log(d*x + c)/(d*f*g - c*g^2) + 2*(b*c - a*d)*log(g*x + f)/(b*d*f^2 + a*c*g^2 - (b*c + a*d)*f*g) - log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(g^2*x + f*g)) - A/(g^2*x + f*g)","B",0
269,1,405,0,1.051764," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(g*x+f)^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{2 \, b^{2} \log\left(b x + a\right)}{b^{2} f^{2} g - 2 \, a b f g^{2} + a^{2} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{d^{2} f^{2} g - 2 \, c d f g^{2} + c^{2} g^{3}} + \frac{2 \, {\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g\right)} \log\left(g x + f\right)}{b^{2} d^{2} f^{4} + a^{2} c^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{3}} - \frac{2 \, {\left(b c - a d\right)}}{b d f^{3} + a c f g^{2} - {\left(b c + a d\right)} f^{2} g + {\left(b d f^{2} g + a c g^{3} - {\left(b c + a d\right)} f g^{2}\right)} x} - \frac{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g}\right)} B - \frac{A}{2 \, {\left(g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g\right)}}"," ",0,"1/2*(2*b^2*log(b*x + a)/(b^2*f^2*g - 2*a*b*f*g^2 + a^2*g^3) - 2*d^2*log(d*x + c)/(d^2*f^2*g - 2*c*d*f*g^2 + c^2*g^3) + 2*(2*(b^2*c*d - a*b*d^2)*f - (b^2*c^2 - a^2*d^2)*g)*log(g*x + f)/(b^2*d^2*f^4 + a^2*c^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^3*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^2 - 2*(a*b*c^2 + a^2*c*d)*f*g^3) - 2*(b*c - a*d)/(b*d*f^3 + a*c*f*g^2 - (b*c + a*d)*f^2*g + (b*d*f^2*g + a*c*g^3 - (b*c + a*d)*f*g^2)*x) - log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(g^3*x^2 + 2*f*g^2*x + f^2*g))*B - 1/2*A/(g^3*x^2 + 2*f*g^2*x + f^2*g)","B",0
270,1,900,0,1.725384," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(g*x+f)^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, b^{3} \log\left(b x + a\right)}{b^{3} f^{3} g - 3 \, a b^{2} f^{2} g^{2} + 3 \, a^{2} b f g^{3} - a^{3} g^{4}} - \frac{2 \, d^{3} \log\left(d x + c\right)}{d^{3} f^{3} g - 3 \, c d^{2} f^{2} g^{2} + 3 \, c^{2} d f g^{3} - c^{3} g^{4}} + \frac{2 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{2}\right)} \log\left(g x + f\right)}{b^{3} d^{3} f^{6} + a^{3} c^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{5}} - \frac{5 \, {\left(b^{2} c d - a b d^{2}\right)} f^{2} - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} f g + {\left(a b c^{2} - a^{2} c d\right)} g^{2} + 2 \, {\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f g - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g^{2}\right)} x}{b^{2} d^{2} f^{6} + a^{2} c^{2} f^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{5} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{4} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{3} g^{3} + {\left(b^{2} d^{2} f^{4} g^{2} + a^{2} c^{2} g^{6} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g^{3} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{4} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} f^{5} g + a^{2} c^{2} f g^{5} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{4} g^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{3} g^{3} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2} g^{4}\right)} x} - \frac{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g}\right)} B - \frac{A}{3 \, {\left(g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g\right)}}"," ",0,"1/3*(2*b^3*log(b*x + a)/(b^3*f^3*g - 3*a*b^2*f^2*g^2 + 3*a^2*b*f*g^3 - a^3*g^4) - 2*d^3*log(d*x + c)/(d^3*f^3*g - 3*c*d^2*f^2*g^2 + 3*c^2*d*f*g^3 - c^3*g^4) + 2*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g + (b^3*c^3 - a^3*d^3)*g^2)*log(g*x + f)/(b^3*d^3*f^6 + a^3*c^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^5) - (5*(b^2*c*d - a*b*d^2)*f^2 - 3*(b^2*c^2 - a^2*d^2)*f*g + (a*b*c^2 - a^2*c*d)*g^2 + 2*(2*(b^2*c*d - a*b*d^2)*f*g - (b^2*c^2 - a^2*d^2)*g^2)*x)/(b^2*d^2*f^6 + a^2*c^2*f^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^5*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^4*g^2 - 2*(a*b*c^2 + a^2*c*d)*f^3*g^3 + (b^2*d^2*f^4*g^2 + a^2*c^2*g^6 - 2*(b^2*c*d + a*b*d^2)*f^3*g^3 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^4 - 2*(a*b*c^2 + a^2*c*d)*f*g^5)*x^2 + 2*(b^2*d^2*f^5*g + a^2*c^2*f*g^5 - 2*(b^2*c*d + a*b*d^2)*f^4*g^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^3*g^3 - 2*(a*b*c^2 + a^2*c*d)*f^2*g^4)*x) - log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g))*B - 1/3*A/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g)","B",0
271,1,1809,0,1.999712," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))/(g*x+f)^5,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(\frac{6 \, b^{4} \log\left(b x + a\right)}{b^{4} f^{4} g - 4 \, a b^{3} f^{3} g^{2} + 6 \, a^{2} b^{2} f^{2} g^{3} - 4 \, a^{3} b f g^{4} + a^{4} g^{5}} - \frac{6 \, d^{4} \log\left(d x + c\right)}{d^{4} f^{4} g - 4 \, c d^{3} f^{3} g^{2} + 6 \, c^{2} d^{2} f^{2} g^{3} - 4 \, c^{3} d f g^{4} + c^{4} g^{5}} + \frac{6 \, {\left(4 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f^{3} - 6 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} f^{2} g + 4 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} f g^{2} - {\left(b^{4} c^{4} - a^{4} d^{4}\right)} g^{3}\right)} \log\left(g x + f\right)}{b^{4} d^{4} f^{8} + a^{4} c^{4} g^{8} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} f^{7} g + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} f^{6} g^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} f^{5} g^{3} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} f^{4} g^{4} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} f^{3} g^{5} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f^{2} g^{6} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} f g^{7}} - \frac{26 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{4} - 31 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{3} g + {\left(11 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 15 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3}\right)} f^{2} g^{2} - 7 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} f g^{3} + 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} g^{4} + 6 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} g^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g^{3} + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{4}\right)} x^{2} + 3 \, {\left(14 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{3} g - 15 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{2} g^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f g^{3} - {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} g^{4}\right)} x}{b^{3} d^{3} f^{9} + a^{3} c^{3} f^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{8} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{7} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{5} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{4} g^{5} + {\left(b^{3} d^{3} f^{6} g^{3} + a^{3} c^{3} g^{9} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{5} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{6} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{7} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{8}\right)} x^{3} + 3 \, {\left(b^{3} d^{3} f^{7} g^{2} + a^{3} c^{3} f g^{8} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{5} g^{4} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{4} g^{5} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{3} g^{6} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{2} g^{7}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} f^{8} g + a^{3} c^{3} f^{2} g^{7} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{7} g^{2} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{6} g^{3} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{4} g^{5} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{3} g^{6}\right)} x} - \frac{3 \, \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g}\right)} B - \frac{A}{4 \, {\left(g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g\right)}}"," ",0,"1/12*(6*b^4*log(b*x + a)/(b^4*f^4*g - 4*a*b^3*f^3*g^2 + 6*a^2*b^2*f^2*g^3 - 4*a^3*b*f*g^4 + a^4*g^5) - 6*d^4*log(d*x + c)/(d^4*f^4*g - 4*c*d^3*f^3*g^2 + 6*c^2*d^2*f^2*g^3 - 4*c^3*d*f*g^4 + c^4*g^5) + 6*(4*(b^4*c*d^3 - a*b^3*d^4)*f^3 - 6*(b^4*c^2*d^2 - a^2*b^2*d^4)*f^2*g + 4*(b^4*c^3*d - a^3*b*d^4)*f*g^2 - (b^4*c^4 - a^4*d^4)*g^3)*log(g*x + f)/(b^4*d^4*f^8 + a^4*c^4*g^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*f^7*g + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*f^6*g^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*f^5*g^3 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*f^4*g^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*f^3*g^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f^2*g^6 - 4*(a^3*b*c^4 + a^4*c^3*d)*f*g^7) - (26*(b^3*c*d^2 - a*b^2*d^3)*f^4 - 31*(b^3*c^2*d - a^2*b*d^3)*f^3*g + (11*b^3*c^3 + 15*a*b^2*c^2*d - 15*a^2*b*c*d^2 - 11*a^3*d^3)*f^2*g^2 - 7*(a*b^2*c^3 - a^3*c*d^2)*f*g^3 + 2*(a^2*b*c^3 - a^3*c^2*d)*g^4 + 6*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2*g^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g^3 + (b^3*c^3 - a^3*d^3)*g^4)*x^2 + 3*(14*(b^3*c*d^2 - a*b^2*d^3)*f^3*g - 15*(b^3*c^2*d - a^2*b*d^3)*f^2*g^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f*g^3 - (a*b^2*c^3 - a^3*c*d^2)*g^4)*x)/(b^3*d^3*f^9 + a^3*c^3*f^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^8*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^7*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^6*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^5*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^4*g^5 + (b^3*d^3*f^6*g^3 + a^3*c^3*g^9 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g^4 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^5 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^6 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^7 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^8)*x^3 + 3*(b^3*d^3*f^7*g^2 + a^3*c^3*f*g^8 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^6*g^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^5*g^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^4*g^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3*g^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^2*g^7)*x^2 + 3*(b^3*d^3*f^8*g + a^3*c^3*f^2*g^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^7*g^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^6*g^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^5*g^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^4*g^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^3*g^6)*x) - 3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g))*B - 1/4*A/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g)","B",0
272,1,2351,0,1.958703," ","integrate((g*x+f)^3*(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","\frac{1}{4} \, A^{2} g^{3} x^{4} + A^{2} f g^{2} x^{3} + \frac{3}{2} \, A^{2} f^{2} g x^{2} + 2 \, {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B f^{3} + 3 \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B f^{2} g + 2 \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 f g^{2} + \frac{1}{6} \, {\left(3 \, x^{4} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 g^{3} + A^{2} f^{3} x - \frac{{\left(6 \, a^{3} c d^{3} g^{3} - 3 \, {\left(8 \, c d^{3} f g^{2} - c^{2} d^{2} g^{3}\right)} a^{2} b + 2 \, {\left(18 \, c d^{3} f^{2} g - 6 \, c^{2} d^{2} f g^{2} + c^{3} d g^{3}\right)} a b^{2} + {\left(12 \, c d^{3} f^{3} \log\left(e\right) - {\left(3 \, g^{3} \log\left(e\right) + 11 \, g^{3}\right)} c^{4} + 12 \, {\left(f g^{2} \log\left(e\right) + 3 \, f g^{2}\right)} c^{3} d - 18 \, {\left(f^{2} g \log\left(e\right) + 2 \, f^{2} g\right)} c^{2} d^{2}\right)} b^{3}\right)} B^{2} \log\left(d x + c\right)}{3 \, b^{3} d^{4}} + \frac{2 \, {\left(4 \, a b^{3} d^{4} f^{3} - 6 \, a^{2} b^{2} d^{4} f^{2} g + 4 \, a^{3} b d^{4} f g^{2} - a^{4} d^{4} g^{3} - {\left(4 \, c d^{3} f^{3} - 6 \, c^{2} d^{2} f^{2} g + 4 \, c^{3} d f g^{2} - c^{4} g^{3}\right)} b^{4}\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^{4} d^{4}} + \frac{3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right)^{2} + 4 \, {\left(a b^{3} d^{4} g^{3} \log\left(e\right) + {\left(3 \, d^{4} f g^{2} \log\left(e\right)^{2} - c d^{3} g^{3} \log\left(e\right)\right)} b^{4}\right)} B^{2} x^{3} - 2 \, {\left({\left(3 \, g^{3} \log\left(e\right) - 2 \, g^{3}\right)} a^{2} b^{2} d^{4} - 4 \, {\left(3 \, d^{4} f g^{2} \log\left(e\right) - c d^{3} g^{3}\right)} a b^{3} - {\left(9 \, d^{4} f^{2} g \log\left(e\right)^{2} - 12 \, c d^{3} f g^{2} \log\left(e\right) + {\left(3 \, g^{3} \log\left(e\right) + 2 \, g^{3}\right)} c^{2} d^{2}\right)} b^{4}\right)} B^{2} x^{2} + 4 \, {\left({\left(3 \, g^{3} \log\left(e\right) - 5 \, g^{3}\right)} a^{3} b d^{4} + {\left(5 \, c d^{3} g^{3} - 12 \, {\left(f g^{2} \log\left(e\right) - f g^{2}\right)} d^{4}\right)} a^{2} b^{2} + {\left(18 \, d^{4} f^{2} g \log\left(e\right) - 24 \, c d^{3} f g^{2} + 5 \, c^{2} d^{2} g^{3}\right)} a b^{3} + {\left(3 \, d^{4} f^{3} \log\left(e\right)^{2} - 18 \, c d^{3} f^{2} g \log\left(e\right) - {\left(3 \, g^{3} \log\left(e\right) + 5 \, g^{3}\right)} c^{3} d + 12 \, {\left(f g^{2} \log\left(e\right) + f g^{2}\right)} c^{2} d^{2}\right)} b^{4}\right)} B^{2} x + 12 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{3} x + {\left(4 \, a b^{3} d^{4} f^{3} - 6 \, a^{2} b^{2} d^{4} f^{2} g + 4 \, a^{3} b d^{4} f g^{2} - a^{4} d^{4} g^{3}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{3} x + {\left(4 \, c d^{3} f^{3} - 6 \, c^{2} d^{2} f^{2} g + 4 \, c^{3} d f g^{2} - c^{4} g^{3}\right)} B^{2} b^{4}\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 2 \, {\left(a b^{3} d^{4} g^{3} + {\left(6 \, d^{4} f g^{2} \log\left(e\right) - c d^{3} g^{3}\right)} b^{4}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} d^{4} f g^{2} - a^{2} b^{2} d^{4} g^{3} + {\left(6 \, d^{4} f^{2} g \log\left(e\right) - 4 \, c d^{3} f g^{2} + c^{2} d^{2} g^{3}\right)} b^{4}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} d^{4} f^{2} g - 4 \, a^{2} b^{2} d^{4} f g^{2} + a^{3} b d^{4} g^{3} + {\left(2 \, d^{4} f^{3} \log\left(e\right) - 6 \, c d^{3} f^{2} g + 4 \, c^{2} d^{2} f g^{2} - c^{3} d g^{3}\right)} b^{4}\right)} B^{2} x - {\left({\left(3 \, g^{3} \log\left(e\right) - 11 \, g^{3}\right)} a^{4} d^{4} + 2 \, {\left(c d^{3} g^{3} - 6 \, {\left(f g^{2} \log\left(e\right) - 3 \, f g^{2}\right)} d^{4}\right)} a^{3} b - 3 \, {\left(4 \, c d^{3} f g^{2} - c^{2} d^{2} g^{3} - 6 \, {\left(f^{2} g \log\left(e\right) - 2 \, f^{2} g\right)} d^{4}\right)} a^{2} b^{2} - 6 \, {\left(2 \, d^{4} f^{3} \log\left(e\right) - 6 \, c d^{3} f^{2} g + 4 \, c^{2} d^{2} f g^{2} - c^{3} d g^{3}\right)} a b^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - 4 \, {\left(3 \, B^{2} b^{4} d^{4} g^{3} x^{4} \log\left(e\right) + 2 \, {\left(a b^{3} d^{4} g^{3} + {\left(6 \, d^{4} f g^{2} \log\left(e\right) - c d^{3} g^{3}\right)} b^{4}\right)} B^{2} x^{3} + 3 \, {\left(4 \, a b^{3} d^{4} f g^{2} - a^{2} b^{2} d^{4} g^{3} + {\left(6 \, d^{4} f^{2} g \log\left(e\right) - 4 \, c d^{3} f g^{2} + c^{2} d^{2} g^{3}\right)} b^{4}\right)} B^{2} x^{2} + 6 \, {\left(6 \, a b^{3} d^{4} f^{2} g - 4 \, a^{2} b^{2} d^{4} f g^{2} + a^{3} b d^{4} g^{3} + {\left(2 \, d^{4} f^{3} \log\left(e\right) - 6 \, c d^{3} f^{2} g + 4 \, c^{2} d^{2} f g^{2} - c^{3} d g^{3}\right)} b^{4}\right)} B^{2} x + 6 \, {\left(B^{2} b^{4} d^{4} g^{3} x^{4} + 4 \, B^{2} b^{4} d^{4} f g^{2} x^{3} + 6 \, B^{2} b^{4} d^{4} f^{2} g x^{2} + 4 \, B^{2} b^{4} d^{4} f^{3} x + {\left(4 \, a b^{3} d^{4} f^{3} - 6 \, a^{2} b^{2} d^{4} f^{2} g + 4 \, a^{3} b d^{4} f g^{2} - a^{4} d^{4} g^{3}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{12 \, b^{4} d^{4}}"," ",0,"1/4*A^2*g^3*x^4 + A^2*f*g^2*x^3 + 3/2*A^2*f^2*g*x^2 + 2*(x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*A*B*f^3 + 3*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*A*B*f^2*g + 2*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*f*g^2 + 1/6*(3*x^4*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 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*g^3 + A^2*f^3*x - 1/3*(6*a^3*c*d^3*g^3 - 3*(8*c*d^3*f*g^2 - c^2*d^2*g^3)*a^2*b + 2*(18*c*d^3*f^2*g - 6*c^2*d^2*f*g^2 + c^3*d*g^3)*a*b^2 + (12*c*d^3*f^3*log(e) - (3*g^3*log(e) + 11*g^3)*c^4 + 12*(f*g^2*log(e) + 3*f*g^2)*c^3*d - 18*(f^2*g*log(e) + 2*f^2*g)*c^2*d^2)*b^3)*B^2*log(d*x + c)/(b^3*d^4) + 2*(4*a*b^3*d^4*f^3 - 6*a^2*b^2*d^4*f^2*g + 4*a^3*b*d^4*f*g^2 - a^4*d^4*g^3 - (4*c*d^3*f^3 - 6*c^2*d^2*f^2*g + 4*c^3*d*f*g^2 - c^4*g^3)*b^4)*(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) + 1/12*(3*B^2*b^4*d^4*g^3*x^4*log(e)^2 + 4*(a*b^3*d^4*g^3*log(e) + (3*d^4*f*g^2*log(e)^2 - c*d^3*g^3*log(e))*b^4)*B^2*x^3 - 2*((3*g^3*log(e) - 2*g^3)*a^2*b^2*d^4 - 4*(3*d^4*f*g^2*log(e) - c*d^3*g^3)*a*b^3 - (9*d^4*f^2*g*log(e)^2 - 12*c*d^3*f*g^2*log(e) + (3*g^3*log(e) + 2*g^3)*c^2*d^2)*b^4)*B^2*x^2 + 4*((3*g^3*log(e) - 5*g^3)*a^3*b*d^4 + (5*c*d^3*g^3 - 12*(f*g^2*log(e) - f*g^2)*d^4)*a^2*b^2 + (18*d^4*f^2*g*log(e) - 24*c*d^3*f*g^2 + 5*c^2*d^2*g^3)*a*b^3 + (3*d^4*f^3*log(e)^2 - 18*c*d^3*f^2*g*log(e) - (3*g^3*log(e) + 5*g^3)*c^3*d + 12*(f*g^2*log(e) + f*g^2)*c^2*d^2)*b^4)*B^2*x + 12*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x + (4*a*b^3*d^4*f^3 - 6*a^2*b^2*d^4*f^2*g + 4*a^3*b*d^4*f*g^2 - a^4*d^4*g^3)*B^2)*log(b*x + a)^2 + 12*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x + (4*c*d^3*f^3 - 6*c^2*d^2*f^2*g + 4*c^3*d*f*g^2 - c^4*g^3)*B^2*b^4)*log(d*x + c)^2 + 4*(3*B^2*b^4*d^4*g^3*x^4*log(e) + 2*(a*b^3*d^4*g^3 + (6*d^4*f*g^2*log(e) - c*d^3*g^3)*b^4)*B^2*x^3 + 3*(4*a*b^3*d^4*f*g^2 - a^2*b^2*d^4*g^3 + (6*d^4*f^2*g*log(e) - 4*c*d^3*f*g^2 + c^2*d^2*g^3)*b^4)*B^2*x^2 + 6*(6*a*b^3*d^4*f^2*g - 4*a^2*b^2*d^4*f*g^2 + a^3*b*d^4*g^3 + (2*d^4*f^3*log(e) - 6*c*d^3*f^2*g + 4*c^2*d^2*f*g^2 - c^3*d*g^3)*b^4)*B^2*x - ((3*g^3*log(e) - 11*g^3)*a^4*d^4 + 2*(c*d^3*g^3 - 6*(f*g^2*log(e) - 3*f*g^2)*d^4)*a^3*b - 3*(4*c*d^3*f*g^2 - c^2*d^2*g^3 - 6*(f^2*g*log(e) - 2*f^2*g)*d^4)*a^2*b^2 - 6*(2*d^4*f^3*log(e) - 6*c*d^3*f^2*g + 4*c^2*d^2*f*g^2 - c^3*d*g^3)*a*b^3)*B^2)*log(b*x + a) - 4*(3*B^2*b^4*d^4*g^3*x^4*log(e) + 2*(a*b^3*d^4*g^3 + (6*d^4*f*g^2*log(e) - c*d^3*g^3)*b^4)*B^2*x^3 + 3*(4*a*b^3*d^4*f*g^2 - a^2*b^2*d^4*g^3 + (6*d^4*f^2*g*log(e) - 4*c*d^3*f*g^2 + c^2*d^2*g^3)*b^4)*B^2*x^2 + 6*(6*a*b^3*d^4*f^2*g - 4*a^2*b^2*d^4*f*g^2 + a^3*b*d^4*g^3 + (2*d^4*f^3*log(e) - 6*c*d^3*f^2*g + 4*c^2*d^2*f*g^2 - c^3*d*g^3)*b^4)*B^2*x + 6*(B^2*b^4*d^4*g^3*x^4 + 4*B^2*b^4*d^4*f*g^2*x^3 + 6*B^2*b^4*d^4*f^2*g*x^2 + 4*B^2*b^4*d^4*f^3*x + (4*a*b^3*d^4*f^3 - 6*a^2*b^2*d^4*f^2*g + 4*a^3*b*d^4*f*g^2 - a^4*d^4*g^3)*B^2)*log(b*x + a))*log(d*x + c))/(b^4*d^4)","B",0
273,1,1458,0,1.770302," ","integrate((g*x+f)^2*(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","\frac{1}{3} \, A^{2} g^{2} x^{3} + A^{2} f g x^{2} + 2 \, {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B f^{2} + 2 \, {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B f g + \frac{2}{3} \, {\left(x^{3} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\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 g^{2} + A^{2} f^{2} x + \frac{4 \, {\left(2 \, a^{2} c d^{2} g^{2} - {\left(6 \, c d^{2} f g - c^{2} d g^{2}\right)} a b - {\left(3 \, c d^{2} f^{2} \log\left(e\right) + {\left(g^{2} \log\left(e\right) + 3 \, g^{2}\right)} c^{3} - 3 \, {\left(f g \log\left(e\right) + 2 \, f g\right)} c^{2} d\right)} b^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, b^{2} d^{3}} + \frac{8 \, {\left(3 \, a b^{2} d^{3} f^{2} - 3 \, a^{2} b d^{3} f g + a^{3} d^{3} g^{2} - {\left(3 \, c d^{2} f^{2} - 3 \, c^{2} d f g + c^{3} g^{2}\right)} b^{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}}{3 \, b^{3} d^{3}} + \frac{B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right)^{2} + {\left(2 \, a b^{2} d^{3} g^{2} \log\left(e\right) + {\left(3 \, d^{3} f g \log\left(e\right)^{2} - 2 \, c d^{2} g^{2} \log\left(e\right)\right)} b^{3}\right)} B^{2} x^{2} - {\left(4 \, {\left(g^{2} \log\left(e\right) - g^{2}\right)} a^{2} b d^{3} - 4 \, {\left(3 \, d^{3} f g \log\left(e\right) - 2 \, c d^{2} g^{2}\right)} a b^{2} - {\left(3 \, d^{3} f^{2} \log\left(e\right)^{2} - 12 \, c d^{2} f g \log\left(e\right) + 4 \, {\left(g^{2} \log\left(e\right) + g^{2}\right)} c^{2} d\right)} b^{3}\right)} B^{2} x + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{2} x + {\left(3 \, a b^{2} d^{3} f^{2} - 3 \, a^{2} b d^{3} f g + a^{3} d^{3} g^{2}\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{2} x + {\left(3 \, c d^{2} f^{2} - 3 \, c^{2} d f g + c^{3} g^{2}\right)} B^{2} b^{3}\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + {\left(a b^{2} d^{3} g^{2} + {\left(3 \, d^{3} f g \log\left(e\right) - c d^{2} g^{2}\right)} b^{3}\right)} B^{2} x^{2} + {\left(6 \, a b^{2} d^{3} f g - 2 \, a^{2} b d^{3} g^{2} + {\left(3 \, d^{3} f^{2} \log\left(e\right) - 6 \, c d^{2} f g + 2 \, c^{2} d g^{2}\right)} b^{3}\right)} B^{2} x + {\left({\left(g^{2} \log\left(e\right) - 3 \, g^{2}\right)} a^{3} d^{3} + {\left(c d^{2} g^{2} - 3 \, {\left(f g \log\left(e\right) - 2 \, f g\right)} d^{3}\right)} a^{2} b + {\left(3 \, d^{3} f^{2} \log\left(e\right) - 6 \, c d^{2} f g + 2 \, c^{2} d g^{2}\right)} a b^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - 4 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} \log\left(e\right) + {\left(a b^{2} d^{3} g^{2} + {\left(3 \, d^{3} f g \log\left(e\right) - c d^{2} g^{2}\right)} b^{3}\right)} B^{2} x^{2} + {\left(6 \, a b^{2} d^{3} f g - 2 \, a^{2} b d^{3} g^{2} + {\left(3 \, d^{3} f^{2} \log\left(e\right) - 6 \, c d^{2} f g + 2 \, c^{2} d g^{2}\right)} b^{3}\right)} B^{2} x + 2 \, {\left(B^{2} b^{3} d^{3} g^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} f g x^{2} + 3 \, B^{2} b^{3} d^{3} f^{2} x + {\left(3 \, a b^{2} d^{3} f^{2} - 3 \, a^{2} b d^{3} f g + a^{3} d^{3} g^{2}\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, b^{3} d^{3}}"," ",0,"1/3*A^2*g^2*x^3 + A^2*f*g*x^2 + 2*(x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*A*B*f^2 + 2*(x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*A*B*f*g + 2/3*(x^3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 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*g^2 + A^2*f^2*x + 4/3*(2*a^2*c*d^2*g^2 - (6*c*d^2*f*g - c^2*d*g^2)*a*b - (3*c*d^2*f^2*log(e) + (g^2*log(e) + 3*g^2)*c^3 - 3*(f*g*log(e) + 2*f*g)*c^2*d)*b^2)*B^2*log(d*x + c)/(b^2*d^3) + 8/3*(3*a*b^2*d^3*f^2 - 3*a^2*b*d^3*f*g + a^3*d^3*g^2 - (3*c*d^2*f^2 - 3*c^2*d*f*g + c^3*g^2)*b^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^3*d^3) + 1/3*(B^2*b^3*d^3*g^2*x^3*log(e)^2 + (2*a*b^2*d^3*g^2*log(e) + (3*d^3*f*g*log(e)^2 - 2*c*d^2*g^2*log(e))*b^3)*B^2*x^2 - (4*(g^2*log(e) - g^2)*a^2*b*d^3 - 4*(3*d^3*f*g*log(e) - 2*c*d^2*g^2)*a*b^2 - (3*d^3*f^2*log(e)^2 - 12*c*d^2*f*g*log(e) + 4*(g^2*log(e) + g^2)*c^2*d)*b^3)*B^2*x + 4*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x + (3*a*b^2*d^3*f^2 - 3*a^2*b*d^3*f*g + a^3*d^3*g^2)*B^2)*log(b*x + a)^2 + 4*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x + (3*c*d^2*f^2 - 3*c^2*d*f*g + c^3*g^2)*B^2*b^3)*log(d*x + c)^2 + 4*(B^2*b^3*d^3*g^2*x^3*log(e) + (a*b^2*d^3*g^2 + (3*d^3*f*g*log(e) - c*d^2*g^2)*b^3)*B^2*x^2 + (6*a*b^2*d^3*f*g - 2*a^2*b*d^3*g^2 + (3*d^3*f^2*log(e) - 6*c*d^2*f*g + 2*c^2*d*g^2)*b^3)*B^2*x + ((g^2*log(e) - 3*g^2)*a^3*d^3 + (c*d^2*g^2 - 3*(f*g*log(e) - 2*f*g)*d^3)*a^2*b + (3*d^3*f^2*log(e) - 6*c*d^2*f*g + 2*c^2*d*g^2)*a*b^2)*B^2)*log(b*x + a) - 4*(B^2*b^3*d^3*g^2*x^3*log(e) + (a*b^2*d^3*g^2 + (3*d^3*f*g*log(e) - c*d^2*g^2)*b^3)*B^2*x^2 + (6*a*b^2*d^3*f*g - 2*a^2*b*d^3*g^2 + (3*d^3*f^2*log(e) - 6*c*d^2*f*g + 2*c^2*d*g^2)*b^3)*B^2*x + 2*(B^2*b^3*d^3*g^2*x^3 + 3*B^2*b^3*d^3*f*g*x^2 + 3*B^2*b^3*d^3*f^2*x + (3*a*b^2*d^3*f^2 - 3*a^2*b*d^3*f*g + a^3*d^3*g^2)*B^2)*log(b*x + a))*log(d*x + c))/(b^3*d^3)","B",0
274,1,786,0,1.551383," ","integrate((g*x+f)*(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","\frac{1}{2} \, A^{2} g x^{2} + 2 \, {\left(x \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + \frac{2 \, a \log\left(b x + a\right)}{b} - \frac{2 \, c \log\left(d x + c\right)}{d}\right)} A B f + {\left(x^{2} \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - \frac{2 \, a^{2} \log\left(b x + a\right)}{b^{2}} + \frac{2 \, c^{2} \log\left(d x + c\right)}{d^{2}} - \frac{2 \, {\left(b c - a d\right)} x}{b d}\right)} A B g + A^{2} f x - \frac{2 \, {\left(2 \, a c d g + {\left(2 \, c d f \log\left(e\right) - {\left(g \log\left(e\right) + 2 \, g\right)} c^{2}\right)} b\right)} B^{2} \log\left(d x + c\right)}{b d^{2}} + \frac{4 \, {\left(2 \, a b d^{2} f - a^{2} d^{2} g - {\left(2 \, c d f - c^{2} g\right)} b^{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^{2}} + \frac{B^{2} b^{2} d^{2} g x^{2} \log\left(e\right)^{2} + 2 \, {\left(2 \, a b d^{2} g \log\left(e\right) + {\left(d^{2} f \log\left(e\right)^{2} - 2 \, c d g \log\left(e\right)\right)} b^{2}\right)} B^{2} x + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f x + {\left(2 \, a b d^{2} f - a^{2} d^{2} g\right)} B^{2}\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f x + {\left(2 \, c d f - c^{2} g\right)} B^{2} b^{2}\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + 2 \, {\left(a b d^{2} g + {\left(d^{2} f \log\left(e\right) - c d g\right)} b^{2}\right)} B^{2} x - {\left({\left(g \log\left(e\right) - 2 \, g\right)} a^{2} d^{2} - 2 \, {\left(d^{2} f \log\left(e\right) - c d g\right)} a b\right)} B^{2}\right)} \log\left(b x + a\right) - 4 \, {\left(B^{2} b^{2} d^{2} g x^{2} \log\left(e\right) + 2 \, {\left(a b d^{2} g + {\left(d^{2} f \log\left(e\right) - c d g\right)} b^{2}\right)} B^{2} x + 2 \, {\left(B^{2} b^{2} d^{2} g x^{2} + 2 \, B^{2} b^{2} d^{2} f x + {\left(2 \, a b d^{2} f - a^{2} d^{2} g\right)} B^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{2 \, b^{2} d^{2}}"," ",0,"1/2*A^2*g*x^2 + 2*(x*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) + 2*a*log(b*x + a)/b - 2*c*log(d*x + c)/d)*A*B*f + (x^2*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2)) - 2*a^2*log(b*x + a)/b^2 + 2*c^2*log(d*x + c)/d^2 - 2*(b*c - a*d)*x/(b*d))*A*B*g + A^2*f*x - 2*(2*a*c*d*g + (2*c*d*f*log(e) - (g*log(e) + 2*g)*c^2)*b)*B^2*log(d*x + c)/(b*d^2) + 4*(2*a*b*d^2*f - a^2*d^2*g - (2*c*d*f - c^2*g)*b^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) + 1/2*(B^2*b^2*d^2*g*x^2*log(e)^2 + 2*(2*a*b*d^2*g*log(e) + (d^2*f*log(e)^2 - 2*c*d*g*log(e))*b^2)*B^2*x + 4*(B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x + (2*a*b*d^2*f - a^2*d^2*g)*B^2)*log(b*x + a)^2 + 4*(B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x + (2*c*d*f - c^2*g)*B^2*b^2)*log(d*x + c)^2 + 4*(B^2*b^2*d^2*g*x^2*log(e) + 2*(a*b*d^2*g + (d^2*f*log(e) - c*d*g)*b^2)*B^2*x - ((g*log(e) - 2*g)*a^2*d^2 - 2*(d^2*f*log(e) - c*d*g)*a*b)*B^2)*log(b*x + a) - 4*(B^2*b^2*d^2*g*x^2*log(e) + 2*(a*b*d^2*g + (d^2*f*log(e) - c*d*g)*b^2)*B^2*x + 2*(B^2*b^2*d^2*g*x^2 + 2*B^2*b^2*d^2*f*x + (2*a*b*d^2*f - a^2*d^2*g)*B^2)*log(b*x + a))*log(d*x + c))/(b^2*d^2)","B",0
275,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","2 \, {\left(x \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + \frac{2 \, {\left(\frac{a e \log\left(b x + a\right)}{b} - \frac{c e \log\left(d x + c\right)}{d}\right)}}{e}\right)} A B + A^{2} x + B^{2} {\left(\frac{4 \, {\left(b d x \log\left(b x + a\right)^{2} + {\left(b d x + b c\right)} \log\left(d x + c\right)^{2} - {\left(b d x \log\left(e\right) + 2 \, {\left(b d x + a d\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)\right)}}{b d} + \int \frac{{\left(\log\left(e\right)^{2} + 4 \, \log\left(e\right)\right)} b^{2} d x^{2} + a b c \log\left(e\right)^{2} + {\left(b^{2} c \log\left(e\right)^{2} + {\left(\log\left(e\right)^{2} + 4 \, \log\left(e\right)\right)} a b d\right)} x + 4 \, {\left(b^{2} d x^{2} \log\left(e\right) + a b c \log\left(e\right) + 2 \, a^{2} d + {\left(a b d {\left(\log\left(e\right) + 4\right)} + b^{2} c {\left(\log\left(e\right) - 2\right)}\right)} x\right)} \log\left(b x + a\right)}{b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x}\,{d x}\right)}"," ",0,"2*(x*log((b*x + a)^2*e/(d*x + c)^2) + 2*(a*e*log(b*x + a)/b - c*e*log(d*x + c)/d)/e)*A*B + A^2*x + B^2*(4*(b*d*x*log(b*x + a)^2 + (b*d*x + b*c)*log(d*x + c)^2 - (b*d*x*log(e) + 2*(b*d*x + a*d)*log(b*x + a))*log(d*x + c))/(b*d) + integrate(((log(e)^2 + 4*log(e))*b^2*d*x^2 + a*b*c*log(e)^2 + (b^2*c*log(e)^2 + (log(e)^2 + 4*log(e))*a*b*d)*x + 4*(b^2*d*x^2*log(e) + a*b*c*log(e) + 2*a^2*d + (a*b*d*(log(e) + 4) + b^2*c*(log(e) - 2))*x)*log(b*x + a))/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x), x))","F",0
276,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(g*x+f),x, algorithm=""maxima"")","\frac{A^{2} \log\left(g x + f\right)}{g} - \int -\frac{4 \, B^{2} \log\left(b x + a\right)^{2} + B^{2} \log\left(e\right)^{2} + 2 \, A B \log\left(e\right) + 4 \, {\left(B^{2} \log\left(e\right) + A B\right)} \log\left(b x + a\right) - 4 \, {\left(2 \, B^{2} \log\left(b x + a\right) + B^{2} \log\left(e\right) + A B\right)} \log\left(d x + c\right)}{g x + f}\,{d x}"," ",0,"A^2*log(g*x + f)/g - integrate(-(4*B^2*log(b*x + a)^2 + B^2*log(e)^2 + 2*A*B*log(e) + 4*(B^2*log(e) + A*B)*log(b*x + a) - 4*(2*B^2*log(b*x + a) + B^2*log(e) + A*B)*log(d*x + c))/(g*x + f), x)","F",0
277,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(g*x+f)^2,x, algorithm=""maxima"")","2 \, A B {\left(\frac{2 \, b \log\left(b x + a\right)}{b f g - a g^{2}} - \frac{2 \, d \log\left(d x + c\right)}{d f g - c g^{2}} + \frac{2 \, {\left(b c - a d\right)} \log\left(g x + f\right)}{b d f^{2} + a c g^{2} - {\left(b c + a d\right)} f g} - \frac{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{g^{2} x + f g}\right)} - B^{2} {\left(\frac{4 \, \log\left(d x + c\right)^{2}}{g^{2} x + f g} + \int -\frac{d g x \log\left(e\right)^{2} + c g \log\left(e\right)^{2} + 4 \, {\left(d g x + c g\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left(b x + a\right) - 4 \, {\left({\left(g \log\left(e\right) - 2 \, g\right)} d x + c g \log\left(e\right) - 2 \, d f + 2 \, {\left(d g x + c g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d g^{3} x^{3} + c f^{2} g + {\left(2 \, d f g^{2} + c g^{3}\right)} x^{2} + {\left(d f^{2} g + 2 \, c f g^{2}\right)} x}\,{d x}\right)} - \frac{A^{2}}{g^{2} x + f g}"," ",0,"2*A*B*(2*b*log(b*x + a)/(b*f*g - a*g^2) - 2*d*log(d*x + c)/(d*f*g - c*g^2) + 2*(b*c - a*d)*log(g*x + f)/(b*d*f^2 + a*c*g^2 - (b*c + a*d)*f*g) - log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(g^2*x + f*g)) - B^2*(4*log(d*x + c)^2/(g^2*x + f*g) + integrate(-(d*g*x*log(e)^2 + c*g*log(e)^2 + 4*(d*g*x + c*g)*log(b*x + a)^2 + 4*(d*g*x*log(e) + c*g*log(e))*log(b*x + a) - 4*((g*log(e) - 2*g)*d*x + c*g*log(e) - 2*d*f + 2*(d*g*x + c*g)*log(b*x + a))*log(d*x + c))/(d*g^3*x^3 + c*f^2*g + (2*d*f*g^2 + c*g^3)*x^2 + (d*f^2*g + 2*c*f*g^2)*x), x)) - A^2/(g^2*x + f*g)","F",0
278,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(g*x+f)^3,x, algorithm=""maxima"")","{\left(\frac{2 \, b^{2} \log\left(b x + a\right)}{b^{2} f^{2} g - 2 \, a b f g^{2} + a^{2} g^{3}} - \frac{2 \, d^{2} \log\left(d x + c\right)}{d^{2} f^{2} g - 2 \, c d f g^{2} + c^{2} g^{3}} + \frac{2 \, {\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g\right)} \log\left(g x + f\right)}{b^{2} d^{2} f^{4} + a^{2} c^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{3}} - \frac{2 \, {\left(b c - a d\right)}}{b d f^{3} + a c f g^{2} - {\left(b c + a d\right)} f^{2} g + {\left(b d f^{2} g + a c g^{3} - {\left(b c + a d\right)} f g^{2}\right)} x} - \frac{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g}\right)} A B - B^{2} {\left(\frac{2 \, \log\left(d x + c\right)^{2}}{g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g} + \int -\frac{d g x \log\left(e\right)^{2} + c g \log\left(e\right)^{2} + 4 \, {\left(d g x + c g\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left(b x + a\right) - 4 \, {\left({\left(g \log\left(e\right) - g\right)} d x + c g \log\left(e\right) - d f + 2 \, {\left(d g x + c g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d g^{4} x^{4} + c f^{3} g + {\left(3 \, d f g^{3} + c g^{4}\right)} x^{3} + 3 \, {\left(d f^{2} g^{2} + c f g^{3}\right)} x^{2} + {\left(d f^{3} g + 3 \, c f^{2} g^{2}\right)} x}\,{d x}\right)} - \frac{A^{2}}{2 \, {\left(g^{3} x^{2} + 2 \, f g^{2} x + f^{2} g\right)}}"," ",0,"(2*b^2*log(b*x + a)/(b^2*f^2*g - 2*a*b*f*g^2 + a^2*g^3) - 2*d^2*log(d*x + c)/(d^2*f^2*g - 2*c*d*f*g^2 + c^2*g^3) + 2*(2*(b^2*c*d - a*b*d^2)*f - (b^2*c^2 - a^2*d^2)*g)*log(g*x + f)/(b^2*d^2*f^4 + a^2*c^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^3*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^2 - 2*(a*b*c^2 + a^2*c*d)*f*g^3) - 2*(b*c - a*d)/(b*d*f^3 + a*c*f*g^2 - (b*c + a*d)*f^2*g + (b*d*f^2*g + a*c*g^3 - (b*c + a*d)*f*g^2)*x) - log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(g^3*x^2 + 2*f*g^2*x + f^2*g))*A*B - B^2*(2*log(d*x + c)^2/(g^3*x^2 + 2*f*g^2*x + f^2*g) + integrate(-(d*g*x*log(e)^2 + c*g*log(e)^2 + 4*(d*g*x + c*g)*log(b*x + a)^2 + 4*(d*g*x*log(e) + c*g*log(e))*log(b*x + a) - 4*((g*log(e) - g)*d*x + c*g*log(e) - d*f + 2*(d*g*x + c*g)*log(b*x + a))*log(d*x + c))/(d*g^4*x^4 + c*f^3*g + (3*d*f*g^3 + c*g^4)*x^3 + 3*(d*f^2*g^2 + c*f*g^3)*x^2 + (d*f^3*g + 3*c*f^2*g^2)*x), x)) - 1/2*A^2/(g^3*x^2 + 2*f*g^2*x + f^2*g)","F",0
279,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(g*x+f)^4,x, algorithm=""maxima"")","\frac{2}{3} \, {\left(\frac{2 \, b^{3} \log\left(b x + a\right)}{b^{3} f^{3} g - 3 \, a b^{2} f^{2} g^{2} + 3 \, a^{2} b f g^{3} - a^{3} g^{4}} - \frac{2 \, d^{3} \log\left(d x + c\right)}{d^{3} f^{3} g - 3 \, c d^{2} f^{2} g^{2} + 3 \, c^{2} d f g^{3} - c^{3} g^{4}} + \frac{2 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{2}\right)} \log\left(g x + f\right)}{b^{3} d^{3} f^{6} + a^{3} c^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{5}} - \frac{5 \, {\left(b^{2} c d - a b d^{2}\right)} f^{2} - 3 \, {\left(b^{2} c^{2} - a^{2} d^{2}\right)} f g + {\left(a b c^{2} - a^{2} c d\right)} g^{2} + 2 \, {\left(2 \, {\left(b^{2} c d - a b d^{2}\right)} f g - {\left(b^{2} c^{2} - a^{2} d^{2}\right)} g^{2}\right)} x}{b^{2} d^{2} f^{6} + a^{2} c^{2} f^{2} g^{4} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{5} g + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{4} g^{2} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{3} g^{3} + {\left(b^{2} d^{2} f^{4} g^{2} + a^{2} c^{2} g^{6} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{3} g^{3} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{2} g^{4} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f g^{5}\right)} x^{2} + 2 \, {\left(b^{2} d^{2} f^{5} g + a^{2} c^{2} f g^{5} - 2 \, {\left(b^{2} c d + a b d^{2}\right)} f^{4} g^{2} + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f^{3} g^{3} - 2 \, {\left(a b c^{2} + a^{2} c d\right)} f^{2} g^{4}\right)} x} - \frac{\log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g}\right)} A B - \frac{1}{3} \, B^{2} {\left(\frac{4 \, \log\left(d x + c\right)^{2}}{g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g} + 3 \, \int -\frac{3 \, d g x \log\left(e\right)^{2} + 3 \, c g \log\left(e\right)^{2} + 12 \, {\left(d g x + c g\right)} \log\left(b x + a\right)^{2} + 12 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left(b x + a\right) - 4 \, {\left({\left(3 \, g \log\left(e\right) - 2 \, g\right)} d x + 3 \, c g \log\left(e\right) - 2 \, d f + 6 \, {\left(d g x + c g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, {\left(d g^{5} x^{5} + c f^{4} g + {\left(4 \, d f g^{4} + c g^{5}\right)} x^{4} + 2 \, {\left(3 \, d f^{2} g^{3} + 2 \, c f g^{4}\right)} x^{3} + 2 \, {\left(2 \, d f^{3} g^{2} + 3 \, c f^{2} g^{3}\right)} x^{2} + {\left(d f^{4} g + 4 \, c f^{3} g^{2}\right)} x\right)}}\,{d x}\right)} - \frac{A^{2}}{3 \, {\left(g^{4} x^{3} + 3 \, f g^{3} x^{2} + 3 \, f^{2} g^{2} x + f^{3} g\right)}}"," ",0,"2/3*(2*b^3*log(b*x + a)/(b^3*f^3*g - 3*a*b^2*f^2*g^2 + 3*a^2*b*f*g^3 - a^3*g^4) - 2*d^3*log(d*x + c)/(d^3*f^3*g - 3*c*d^2*f^2*g^2 + 3*c^2*d*f*g^3 - c^3*g^4) + 2*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g + (b^3*c^3 - a^3*d^3)*g^2)*log(g*x + f)/(b^3*d^3*f^6 + a^3*c^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^5) - (5*(b^2*c*d - a*b*d^2)*f^2 - 3*(b^2*c^2 - a^2*d^2)*f*g + (a*b*c^2 - a^2*c*d)*g^2 + 2*(2*(b^2*c*d - a*b*d^2)*f*g - (b^2*c^2 - a^2*d^2)*g^2)*x)/(b^2*d^2*f^6 + a^2*c^2*f^2*g^4 - 2*(b^2*c*d + a*b*d^2)*f^5*g + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^4*g^2 - 2*(a*b*c^2 + a^2*c*d)*f^3*g^3 + (b^2*d^2*f^4*g^2 + a^2*c^2*g^6 - 2*(b^2*c*d + a*b*d^2)*f^3*g^3 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^2*g^4 - 2*(a*b*c^2 + a^2*c*d)*f*g^5)*x^2 + 2*(b^2*d^2*f^5*g + a^2*c^2*f*g^5 - 2*(b^2*c*d + a*b*d^2)*f^4*g^2 + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f^3*g^3 - 2*(a*b*c^2 + a^2*c*d)*f^2*g^4)*x) - log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g))*A*B - 1/3*B^2*(4*log(d*x + c)^2/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g) + 3*integrate(-1/3*(3*d*g*x*log(e)^2 + 3*c*g*log(e)^2 + 12*(d*g*x + c*g)*log(b*x + a)^2 + 12*(d*g*x*log(e) + c*g*log(e))*log(b*x + a) - 4*((3*g*log(e) - 2*g)*d*x + 3*c*g*log(e) - 2*d*f + 6*(d*g*x + c*g)*log(b*x + a))*log(d*x + c))/(d*g^5*x^5 + c*f^4*g + (4*d*f*g^4 + c*g^5)*x^4 + 2*(3*d*f^2*g^3 + 2*c*f*g^4)*x^3 + 2*(2*d*f^3*g^2 + 3*c*f^2*g^3)*x^2 + (d*f^4*g + 4*c*f^3*g^2)*x), x)) - 1/3*A^2/(g^4*x^3 + 3*f*g^3*x^2 + 3*f^2*g^2*x + f^3*g)","F",0
280,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2/(g*x+f)^5,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{6 \, b^{4} \log\left(b x + a\right)}{b^{4} f^{4} g - 4 \, a b^{3} f^{3} g^{2} + 6 \, a^{2} b^{2} f^{2} g^{3} - 4 \, a^{3} b f g^{4} + a^{4} g^{5}} - \frac{6 \, d^{4} \log\left(d x + c\right)}{d^{4} f^{4} g - 4 \, c d^{3} f^{3} g^{2} + 6 \, c^{2} d^{2} f^{2} g^{3} - 4 \, c^{3} d f g^{4} + c^{4} g^{5}} + \frac{6 \, {\left(4 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f^{3} - 6 \, {\left(b^{4} c^{2} d^{2} - a^{2} b^{2} d^{4}\right)} f^{2} g + 4 \, {\left(b^{4} c^{3} d - a^{3} b d^{4}\right)} f g^{2} - {\left(b^{4} c^{4} - a^{4} d^{4}\right)} g^{3}\right)} \log\left(g x + f\right)}{b^{4} d^{4} f^{8} + a^{4} c^{4} g^{8} - 4 \, {\left(b^{4} c d^{3} + a b^{3} d^{4}\right)} f^{7} g + 2 \, {\left(3 \, b^{4} c^{2} d^{2} + 8 \, a b^{3} c d^{3} + 3 \, a^{2} b^{2} d^{4}\right)} f^{6} g^{2} - 4 \, {\left(b^{4} c^{3} d + 6 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} + a^{3} b d^{4}\right)} f^{5} g^{3} + {\left(b^{4} c^{4} + 16 \, a b^{3} c^{3} d + 36 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} f^{4} g^{4} - 4 \, {\left(a b^{3} c^{4} + 6 \, a^{2} b^{2} c^{3} d + 6 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} f^{3} g^{5} + 2 \, {\left(3 \, a^{2} b^{2} c^{4} + 8 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f^{2} g^{6} - 4 \, {\left(a^{3} b c^{4} + a^{4} c^{3} d\right)} f g^{7}} - \frac{26 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{4} - 31 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{3} g + {\left(11 \, b^{3} c^{3} + 15 \, a b^{2} c^{2} d - 15 \, a^{2} b c d^{2} - 11 \, a^{3} d^{3}\right)} f^{2} g^{2} - 7 \, {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} f g^{3} + 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} g^{4} + 6 \, {\left(3 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{2} g^{2} - 3 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f g^{3} + {\left(b^{3} c^{3} - a^{3} d^{3}\right)} g^{4}\right)} x^{2} + 3 \, {\left(14 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f^{3} g - 15 \, {\left(b^{3} c^{2} d - a^{2} b d^{3}\right)} f^{2} g^{2} + {\left(5 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} f g^{3} - {\left(a b^{2} c^{3} - a^{3} c d^{2}\right)} g^{4}\right)} x}{b^{3} d^{3} f^{9} + a^{3} c^{3} f^{3} g^{6} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{8} g + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{7} g^{2} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{5} g^{4} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{4} g^{5} + {\left(b^{3} d^{3} f^{6} g^{3} + a^{3} c^{3} g^{9} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{4} g^{5} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{3} g^{6} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{2} g^{7} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f g^{8}\right)} x^{3} + 3 \, {\left(b^{3} d^{3} f^{7} g^{2} + a^{3} c^{3} f g^{8} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{6} g^{3} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{5} g^{4} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{4} g^{5} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{3} g^{6} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{2} g^{7}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} f^{8} g + a^{3} c^{3} f^{2} g^{7} - 3 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} f^{7} g^{2} + 3 \, {\left(b^{3} c^{2} d + 3 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f^{6} g^{3} - {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 9 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f^{5} g^{4} + 3 \, {\left(a b^{2} c^{3} + 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f^{4} g^{5} - 3 \, {\left(a^{2} b c^{3} + a^{3} c^{2} d\right)} f^{3} g^{6}\right)} x} - \frac{3 \, \log\left(\frac{b^{2} e x^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{2 \, a b e x}{d^{2} x^{2} + 2 \, c d x + c^{2}} + \frac{a^{2} e}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g}\right)} A B - B^{2} {\left(\frac{\log\left(d x + c\right)^{2}}{g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g} + \int -\frac{d g x \log\left(e\right)^{2} + c g \log\left(e\right)^{2} + 4 \, {\left(d g x + c g\right)} \log\left(b x + a\right)^{2} + 4 \, {\left(d g x \log\left(e\right) + c g \log\left(e\right)\right)} \log\left(b x + a\right) - 2 \, {\left({\left(2 \, g \log\left(e\right) - g\right)} d x + 2 \, c g \log\left(e\right) - d f + 4 \, {\left(d g x + c g\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{d g^{6} x^{6} + c f^{5} g + {\left(5 \, d f g^{5} + c g^{6}\right)} x^{5} + 5 \, {\left(2 \, d f^{2} g^{4} + c f g^{5}\right)} x^{4} + 10 \, {\left(d f^{3} g^{3} + c f^{2} g^{4}\right)} x^{3} + 5 \, {\left(d f^{4} g^{2} + 2 \, c f^{3} g^{3}\right)} x^{2} + {\left(d f^{5} g + 5 \, c f^{4} g^{2}\right)} x}\,{d x}\right)} - \frac{A^{2}}{4 \, {\left(g^{5} x^{4} + 4 \, f g^{4} x^{3} + 6 \, f^{2} g^{3} x^{2} + 4 \, f^{3} g^{2} x + f^{4} g\right)}}"," ",0,"1/6*(6*b^4*log(b*x + a)/(b^4*f^4*g - 4*a*b^3*f^3*g^2 + 6*a^2*b^2*f^2*g^3 - 4*a^3*b*f*g^4 + a^4*g^5) - 6*d^4*log(d*x + c)/(d^4*f^4*g - 4*c*d^3*f^3*g^2 + 6*c^2*d^2*f^2*g^3 - 4*c^3*d*f*g^4 + c^4*g^5) + 6*(4*(b^4*c*d^3 - a*b^3*d^4)*f^3 - 6*(b^4*c^2*d^2 - a^2*b^2*d^4)*f^2*g + 4*(b^4*c^3*d - a^3*b*d^4)*f*g^2 - (b^4*c^4 - a^4*d^4)*g^3)*log(g*x + f)/(b^4*d^4*f^8 + a^4*c^4*g^8 - 4*(b^4*c*d^3 + a*b^3*d^4)*f^7*g + 2*(3*b^4*c^2*d^2 + 8*a*b^3*c*d^3 + 3*a^2*b^2*d^4)*f^6*g^2 - 4*(b^4*c^3*d + 6*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 + a^3*b*d^4)*f^5*g^3 + (b^4*c^4 + 16*a*b^3*c^3*d + 36*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 + a^4*d^4)*f^4*g^4 - 4*(a*b^3*c^4 + 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 + a^4*c*d^3)*f^3*g^5 + 2*(3*a^2*b^2*c^4 + 8*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f^2*g^6 - 4*(a^3*b*c^4 + a^4*c^3*d)*f*g^7) - (26*(b^3*c*d^2 - a*b^2*d^3)*f^4 - 31*(b^3*c^2*d - a^2*b*d^3)*f^3*g + (11*b^3*c^3 + 15*a*b^2*c^2*d - 15*a^2*b*c*d^2 - 11*a^3*d^3)*f^2*g^2 - 7*(a*b^2*c^3 - a^3*c*d^2)*f*g^3 + 2*(a^2*b*c^3 - a^3*c^2*d)*g^4 + 6*(3*(b^3*c*d^2 - a*b^2*d^3)*f^2*g^2 - 3*(b^3*c^2*d - a^2*b*d^3)*f*g^3 + (b^3*c^3 - a^3*d^3)*g^4)*x^2 + 3*(14*(b^3*c*d^2 - a*b^2*d^3)*f^3*g - 15*(b^3*c^2*d - a^2*b*d^3)*f^2*g^2 + (5*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 - 5*a^3*d^3)*f*g^3 - (a*b^2*c^3 - a^3*c*d^2)*g^4)*x)/(b^3*d^3*f^9 + a^3*c^3*f^3*g^6 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^8*g + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^7*g^2 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^6*g^3 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^5*g^4 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^4*g^5 + (b^3*d^3*f^6*g^3 + a^3*c^3*g^9 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^5*g^4 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^4*g^5 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^3*g^6 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^2*g^7 - 3*(a^2*b*c^3 + a^3*c^2*d)*f*g^8)*x^3 + 3*(b^3*d^3*f^7*g^2 + a^3*c^3*f*g^8 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^6*g^3 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^5*g^4 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^4*g^5 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^3*g^6 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^2*g^7)*x^2 + 3*(b^3*d^3*f^8*g + a^3*c^3*f^2*g^7 - 3*(b^3*c*d^2 + a*b^2*d^3)*f^7*g^2 + 3*(b^3*c^2*d + 3*a*b^2*c*d^2 + a^2*b*d^3)*f^6*g^3 - (b^3*c^3 + 9*a*b^2*c^2*d + 9*a^2*b*c*d^2 + a^3*d^3)*f^5*g^4 + 3*(a*b^2*c^3 + 3*a^2*b*c^2*d + a^3*c*d^2)*f^4*g^5 - 3*(a^2*b*c^3 + a^3*c^2*d)*f^3*g^6)*x) - 3*log(b^2*e*x^2/(d^2*x^2 + 2*c*d*x + c^2) + 2*a*b*e*x/(d^2*x^2 + 2*c*d*x + c^2) + a^2*e/(d^2*x^2 + 2*c*d*x + c^2))/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g))*A*B - B^2*(log(d*x + c)^2/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g) + integrate(-(d*g*x*log(e)^2 + c*g*log(e)^2 + 4*(d*g*x + c*g)*log(b*x + a)^2 + 4*(d*g*x*log(e) + c*g*log(e))*log(b*x + a) - 2*((2*g*log(e) - g)*d*x + 2*c*g*log(e) - d*f + 4*(d*g*x + c*g)*log(b*x + a))*log(d*x + c))/(d*g^6*x^6 + c*f^5*g + (5*d*f*g^5 + c*g^6)*x^5 + 5*(2*d*f^2*g^4 + c*f*g^5)*x^4 + 10*(d*f^3*g^3 + c*f^2*g^4)*x^3 + 5*(d*f^4*g^2 + 2*c*f^3*g^3)*x^2 + (d*f^5*g + 5*c*f^4*g^2)*x), x)) - 1/4*A^2/(g^5*x^4 + 4*f*g^4*x^3 + 6*f^2*g^3*x^2 + 4*f^3*g^2*x + f^4*g)","F",0
281,0,0,0,0.000000," ","integrate((g*x+f)^2/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{{\left(g x + f\right)}^{2}}{B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A}\,{d x}"," ",0,"integrate((g*x + f)^2/(B*log((b*x + a)^2*e/(d*x + c)^2) + A), x)","F",0
282,0,0,0,0.000000," ","integrate((g*x+f)/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{g x + f}{B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A}\,{d x}"," ",0,"integrate((g*x + f)/(B*log((b*x + a)^2*e/(d*x + c)^2) + A), x)","F",0
283,0,0,0,0.000000," ","integrate(1/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{1}{B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A}\,{d x}"," ",0,"integrate(1/(B*log((b*x + a)^2*e/(d*x + c)^2) + A), x)","F",0
284,0,0,0,0.000000," ","integrate(1/(g*x+f)/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)} {\left(B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)*(B*log((b*x + a)^2*e/(d*x + c)^2) + A)), x)","F",0
285,0,0,0,0.000000," ","integrate(1/(g*x+f)^2/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)}^{2} {\left(B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)^2*(B*log((b*x + a)^2*e/(d*x + c)^2) + A)), x)","F",0
286,0,0,0,0.000000," ","integrate(1/(g*x+f)^3/(A+B*log(e*(b*x+a)^2/(d*x+c)^2)),x, algorithm=""maxima"")","\int \frac{1}{{\left(g x + f\right)}^{3} {\left(B \log\left(\frac{{\left(b x + a\right)}^{2} e}{{\left(d x + c\right)}^{2}}\right) + A\right)}}\,{d x}"," ",0,"integrate(1/((g*x + f)^3*(B*log((b*x + a)^2*e/(d*x + c)^2) + A)), x)","F",0
287,0,0,0,0.000000," ","integrate((g*x+f)^2/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{b d g^{2} x^{4} + a c f^{2} + {\left(a d g^{2} + {\left(2 \, d f g + c g^{2}\right)} b\right)} x^{3} + {\left({\left(2 \, d f g + c g^{2}\right)} a + {\left(d f^{2} + 2 \, c f g\right)} b\right)} x^{2} + {\left(b c f^{2} + {\left(d f^{2} + 2 \, c f g\right)} a\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}} + \int \frac{4 \, b d g^{2} x^{3} + b c f^{2} + 3 \, {\left(a d g^{2} + {\left(2 \, d f g + c g^{2}\right)} b\right)} x^{2} + {\left(d f^{2} + 2 \, c f g\right)} a + 2 \, {\left({\left(2 \, d f g + c g^{2}\right)} a + {\left(d f^{2} + 2 \, c f g\right)} b\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}}\,{d x}"," ",0,"-1/2*(b*d*g^2*x^4 + a*c*f^2 + (a*d*g^2 + (2*d*f*g + c*g^2)*b)*x^3 + ((2*d*f*g + c*g^2)*a + (d*f^2 + 2*c*f*g)*b)*x^2 + (b*c*f^2 + (d*f^2 + 2*c*f*g)*a)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate(1/2*(4*b*d*g^2*x^3 + b*c*f^2 + 3*(a*d*g^2 + (2*d*f*g + c*g^2)*b)*x^2 + (d*f^2 + 2*c*f*g)*a + 2*((2*d*f*g + c*g^2)*a + (d*f^2 + 2*c*f*g)*b)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
288,0,0,0,0.000000," ","integrate((g*x+f)/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{b d g x^{3} + a c f + {\left(a d g + {\left(d f + c g\right)} b\right)} x^{2} + {\left(b c f + {\left(d f + c g\right)} a\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}} + \int \frac{3 \, b d g x^{2} + b c f + {\left(d f + c g\right)} a + 2 \, {\left(a d g + {\left(d f + c g\right)} b\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}}\,{d x}"," ",0,"-1/2*(b*d*g*x^3 + a*c*f + (a*d*g + (d*f + c*g)*b)*x^2 + (b*c*f + (d*f + c*g)*a)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate(1/2*(3*b*d*g*x^2 + b*c*f + (d*f + c*g)*a + 2*(a*d*g + (d*f + c*g)*b)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
289,0,0,0,0.000000," ","integrate(1/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}} + \int \frac{2 \, b d x + b c + a d}{2 \, {\left(2 \, {\left(b c - a d\right)} B^{2} \log\left(b x + a\right) - 2 \, {\left(b c - a d\right)} B^{2} \log\left(d x + c\right) + {\left(b c - a d\right)} A B + {\left(b c \log\left(e\right) - a d \log\left(e\right)\right)} B^{2}\right)}}\,{d x}"," ",0,"-1/2*(b*d*x^2 + a*c + (b*c + a*d)*x)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2) + integrate(1/2*(2*b*d*x + b*c + a*d)/(2*(b*c - a*d)*B^2*log(b*x + a) - 2*(b*c - a*d)*B^2*log(d*x + c) + (b*c - a*d)*A*B + (b*c*log(e) - a*d*log(e))*B^2), x)","F",0
290,0,0,0,0.000000," ","integrate(1/(g*x+f)/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{2 \, {\left({\left(b c f - a d f\right)} A B + {\left(b c f \log\left(e\right) - a d f \log\left(e\right)\right)} B^{2} + {\left({\left(b c g - a d g\right)} A B + {\left(b c g \log\left(e\right) - a d g \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b c g - a d g\right)} B^{2} x + {\left(b c f - a d f\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b c g - a d g\right)} B^{2} x + {\left(b c f - a d f\right)} B^{2}\right)} \log\left(d x + c\right)\right)}} + \int \frac{b d g x^{2} + 2 \, b d f x + b c f + {\left(d f - c g\right)} a}{2 \, {\left({\left(b c f^{2} - a d f^{2}\right)} A B + {\left(b c f^{2} \log\left(e\right) - a d f^{2} \log\left(e\right)\right)} B^{2} + {\left({\left(b c g^{2} - a d g^{2}\right)} A B + {\left(b c g^{2} \log\left(e\right) - a d g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c f g - a d f g\right)} A B + {\left(b c f g \log\left(e\right) - a d f g \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b c g^{2} - a d g^{2}\right)} B^{2} x^{2} + 2 \, {\left(b c f g - a d f g\right)} B^{2} x + {\left(b c f^{2} - a d f^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b c g^{2} - a d g^{2}\right)} B^{2} x^{2} + 2 \, {\left(b c f g - a d f g\right)} B^{2} x + {\left(b c f^{2} - a d f^{2}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}}\,{d x}"," ",0,"-1/2*(b*d*x^2 + a*c + (b*c + a*d)*x)/((b*c*f - a*d*f)*A*B + (b*c*f*log(e) - a*d*f*log(e))*B^2 + ((b*c*g - a*d*g)*A*B + (b*c*g*log(e) - a*d*g*log(e))*B^2)*x + 2*((b*c*g - a*d*g)*B^2*x + (b*c*f - a*d*f)*B^2)*log(b*x + a) - 2*((b*c*g - a*d*g)*B^2*x + (b*c*f - a*d*f)*B^2)*log(d*x + c)) + integrate(1/2*(b*d*g*x^2 + 2*b*d*f*x + b*c*f + (d*f - c*g)*a)/((b*c*f^2 - a*d*f^2)*A*B + (b*c*f^2*log(e) - a*d*f^2*log(e))*B^2 + ((b*c*g^2 - a*d*g^2)*A*B + (b*c*g^2*log(e) - a*d*g^2*log(e))*B^2)*x^2 + 2*((b*c*f*g - a*d*f*g)*A*B + (b*c*f*g*log(e) - a*d*f*g*log(e))*B^2)*x + 2*((b*c*g^2 - a*d*g^2)*B^2*x^2 + 2*(b*c*f*g - a*d*f*g)*B^2*x + (b*c*f^2 - a*d*f^2)*B^2)*log(b*x + a) - 2*((b*c*g^2 - a*d*g^2)*B^2*x^2 + 2*(b*c*f*g - a*d*f*g)*B^2*x + (b*c*f^2 - a*d*f^2)*B^2)*log(d*x + c)), x)","F",0
291,0,0,0,0.000000," ","integrate(1/(g*x+f)^2/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{2 \, {\left({\left(b c f^{2} - a d f^{2}\right)} A B + {\left(b c f^{2} \log\left(e\right) - a d f^{2} \log\left(e\right)\right)} B^{2} + {\left({\left(b c g^{2} - a d g^{2}\right)} A B + {\left(b c g^{2} \log\left(e\right) - a d g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 2 \, {\left({\left(b c f g - a d f g\right)} A B + {\left(b c f g \log\left(e\right) - a d f g \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b c g^{2} - a d g^{2}\right)} B^{2} x^{2} + 2 \, {\left(b c f g - a d f g\right)} B^{2} x + {\left(b c f^{2} - a d f^{2}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b c g^{2} - a d g^{2}\right)} B^{2} x^{2} + 2 \, {\left(b c f g - a d f g\right)} B^{2} x + {\left(b c f^{2} - a d f^{2}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}} - \int -\frac{b c f + {\left(d f - 2 \, c g\right)} a - {\left(a d g - {\left(2 \, d f - c g\right)} b\right)} x}{2 \, {\left({\left({\left(b c g^{3} - a d g^{3}\right)} A B + {\left(b c g^{3} \log\left(e\right) - a d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{3} - a d f^{3}\right)} A B + {\left(b c f^{3} \log\left(e\right) - a d f^{3} \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(b c f g^{2} - a d f g^{2}\right)} A B + {\left(b c f g^{2} \log\left(e\right) - a d f g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(b c f^{2} g - a d f^{2} g\right)} A B + {\left(b c f^{2} g \log\left(e\right) - a d f^{2} g \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b c g^{3} - a d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} - a d f g^{2}\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g - a d f^{2} g\right)} B^{2} x + {\left(b c f^{3} - a d f^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b c g^{3} - a d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} - a d f g^{2}\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g - a d f^{2} g\right)} B^{2} x + {\left(b c f^{3} - a d f^{3}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}}\,{d x}"," ",0,"-1/2*(b*d*x^2 + a*c + (b*c + a*d)*x)/((b*c*f^2 - a*d*f^2)*A*B + (b*c*f^2*log(e) - a*d*f^2*log(e))*B^2 + ((b*c*g^2 - a*d*g^2)*A*B + (b*c*g^2*log(e) - a*d*g^2*log(e))*B^2)*x^2 + 2*((b*c*f*g - a*d*f*g)*A*B + (b*c*f*g*log(e) - a*d*f*g*log(e))*B^2)*x + 2*((b*c*g^2 - a*d*g^2)*B^2*x^2 + 2*(b*c*f*g - a*d*f*g)*B^2*x + (b*c*f^2 - a*d*f^2)*B^2)*log(b*x + a) - 2*((b*c*g^2 - a*d*g^2)*B^2*x^2 + 2*(b*c*f*g - a*d*f*g)*B^2*x + (b*c*f^2 - a*d*f^2)*B^2)*log(d*x + c)) - integrate(-1/2*(b*c*f + (d*f - 2*c*g)*a - (a*d*g - (2*d*f - c*g)*b)*x)/(((b*c*g^3 - a*d*g^3)*A*B + (b*c*g^3*log(e) - a*d*g^3*log(e))*B^2)*x^3 + (b*c*f^3 - a*d*f^3)*A*B + (b*c*f^3*log(e) - a*d*f^3*log(e))*B^2 + 3*((b*c*f*g^2 - a*d*f*g^2)*A*B + (b*c*f*g^2*log(e) - a*d*f*g^2*log(e))*B^2)*x^2 + 3*((b*c*f^2*g - a*d*f^2*g)*A*B + (b*c*f^2*g*log(e) - a*d*f^2*g*log(e))*B^2)*x + 2*((b*c*g^3 - a*d*g^3)*B^2*x^3 + 3*(b*c*f*g^2 - a*d*f*g^2)*B^2*x^2 + 3*(b*c*f^2*g - a*d*f^2*g)*B^2*x + (b*c*f^3 - a*d*f^3)*B^2)*log(b*x + a) - 2*((b*c*g^3 - a*d*g^3)*B^2*x^3 + 3*(b*c*f*g^2 - a*d*f*g^2)*B^2*x^2 + 3*(b*c*f^2*g - a*d*f^2*g)*B^2*x + (b*c*f^3 - a*d*f^3)*B^2)*log(d*x + c)), x)","F",0
292,0,0,0,0.000000," ","integrate(1/(g*x+f)^3/(A+B*log(e*(b*x+a)^2/(d*x+c)^2))^2,x, algorithm=""maxima"")","-\frac{b d x^{2} + a c + {\left(b c + a d\right)} x}{2 \, {\left({\left({\left(b c g^{3} - a d g^{3}\right)} A B + {\left(b c g^{3} \log\left(e\right) - a d g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{3} - a d f^{3}\right)} A B + {\left(b c f^{3} \log\left(e\right) - a d f^{3} \log\left(e\right)\right)} B^{2} + 3 \, {\left({\left(b c f g^{2} - a d f g^{2}\right)} A B + {\left(b c f g^{2} \log\left(e\right) - a d f g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 3 \, {\left({\left(b c f^{2} g - a d f^{2} g\right)} A B + {\left(b c f^{2} g \log\left(e\right) - a d f^{2} g \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b c g^{3} - a d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} - a d f g^{2}\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g - a d f^{2} g\right)} B^{2} x + {\left(b c f^{3} - a d f^{3}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b c g^{3} - a d g^{3}\right)} B^{2} x^{3} + 3 \, {\left(b c f g^{2} - a d f g^{2}\right)} B^{2} x^{2} + 3 \, {\left(b c f^{2} g - a d f^{2} g\right)} B^{2} x + {\left(b c f^{3} - a d f^{3}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}} - \int \frac{b d g x^{2} - b c f - {\left(d f - 3 \, c g\right)} a + 2 \, {\left(a d g - {\left(d f - c g\right)} b\right)} x}{2 \, {\left({\left({\left(b c g^{4} - a d g^{4}\right)} A B + {\left(b c g^{4} \log\left(e\right) - a d g^{4} \log\left(e\right)\right)} B^{2}\right)} x^{4} + 4 \, {\left({\left(b c f g^{3} - a d f g^{3}\right)} A B + {\left(b c f g^{3} \log\left(e\right) - a d f g^{3} \log\left(e\right)\right)} B^{2}\right)} x^{3} + {\left(b c f^{4} - a d f^{4}\right)} A B + {\left(b c f^{4} \log\left(e\right) - a d f^{4} \log\left(e\right)\right)} B^{2} + 6 \, {\left({\left(b c f^{2} g^{2} - a d f^{2} g^{2}\right)} A B + {\left(b c f^{2} g^{2} \log\left(e\right) - a d f^{2} g^{2} \log\left(e\right)\right)} B^{2}\right)} x^{2} + 4 \, {\left({\left(b c f^{3} g - a d f^{3} g\right)} A B + {\left(b c f^{3} g \log\left(e\right) - a d f^{3} g \log\left(e\right)\right)} B^{2}\right)} x + 2 \, {\left({\left(b c g^{4} - a d g^{4}\right)} B^{2} x^{4} + 4 \, {\left(b c f g^{3} - a d f g^{3}\right)} B^{2} x^{3} + 6 \, {\left(b c f^{2} g^{2} - a d f^{2} g^{2}\right)} B^{2} x^{2} + 4 \, {\left(b c f^{3} g - a d f^{3} g\right)} B^{2} x + {\left(b c f^{4} - a d f^{4}\right)} B^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(b c g^{4} - a d g^{4}\right)} B^{2} x^{4} + 4 \, {\left(b c f g^{3} - a d f g^{3}\right)} B^{2} x^{3} + 6 \, {\left(b c f^{2} g^{2} - a d f^{2} g^{2}\right)} B^{2} x^{2} + 4 \, {\left(b c f^{3} g - a d f^{3} g\right)} B^{2} x + {\left(b c f^{4} - a d f^{4}\right)} B^{2}\right)} \log\left(d x + c\right)\right)}}\,{d x}"," ",0,"-1/2*(b*d*x^2 + a*c + (b*c + a*d)*x)/(((b*c*g^3 - a*d*g^3)*A*B + (b*c*g^3*log(e) - a*d*g^3*log(e))*B^2)*x^3 + (b*c*f^3 - a*d*f^3)*A*B + (b*c*f^3*log(e) - a*d*f^3*log(e))*B^2 + 3*((b*c*f*g^2 - a*d*f*g^2)*A*B + (b*c*f*g^2*log(e) - a*d*f*g^2*log(e))*B^2)*x^2 + 3*((b*c*f^2*g - a*d*f^2*g)*A*B + (b*c*f^2*g*log(e) - a*d*f^2*g*log(e))*B^2)*x + 2*((b*c*g^3 - a*d*g^3)*B^2*x^3 + 3*(b*c*f*g^2 - a*d*f*g^2)*B^2*x^2 + 3*(b*c*f^2*g - a*d*f^2*g)*B^2*x + (b*c*f^3 - a*d*f^3)*B^2)*log(b*x + a) - 2*((b*c*g^3 - a*d*g^3)*B^2*x^3 + 3*(b*c*f*g^2 - a*d*f*g^2)*B^2*x^2 + 3*(b*c*f^2*g - a*d*f^2*g)*B^2*x + (b*c*f^3 - a*d*f^3)*B^2)*log(d*x + c)) - integrate(1/2*(b*d*g*x^2 - b*c*f - (d*f - 3*c*g)*a + 2*(a*d*g - (d*f - c*g)*b)*x)/(((b*c*g^4 - a*d*g^4)*A*B + (b*c*g^4*log(e) - a*d*g^4*log(e))*B^2)*x^4 + 4*((b*c*f*g^3 - a*d*f*g^3)*A*B + (b*c*f*g^3*log(e) - a*d*f*g^3*log(e))*B^2)*x^3 + (b*c*f^4 - a*d*f^4)*A*B + (b*c*f^4*log(e) - a*d*f^4*log(e))*B^2 + 6*((b*c*f^2*g^2 - a*d*f^2*g^2)*A*B + (b*c*f^2*g^2*log(e) - a*d*f^2*g^2*log(e))*B^2)*x^2 + 4*((b*c*f^3*g - a*d*f^3*g)*A*B + (b*c*f^3*g*log(e) - a*d*f^3*g*log(e))*B^2)*x + 2*((b*c*g^4 - a*d*g^4)*B^2*x^4 + 4*(b*c*f*g^3 - a*d*f*g^3)*B^2*x^3 + 6*(b*c*f^2*g^2 - a*d*f^2*g^2)*B^2*x^2 + 4*(b*c*f^3*g - a*d*f^3*g)*B^2*x + (b*c*f^4 - a*d*f^4)*B^2)*log(b*x + a) - 2*((b*c*g^4 - a*d*g^4)*B^2*x^4 + 4*(b*c*f*g^3 - a*d*f*g^3)*B^2*x^3 + 6*(b*c*f^2*g^2 - a*d*f^2*g^2)*B^2*x^2 + 4*(b*c*f^3*g - a*d*f^3*g)*B^2*x + (b*c*f^4 - a*d*f^4)*B^2)*log(d*x + c)), x)","F",0
293,1,671,0,0.802244," ","integrate((h*x+g)^4*(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{1}{5} \, B h^{4} x^{5} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{5} \, A h^{4} x^{5} + B g h^{3} x^{4} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A g h^{3} x^{4} + 2 \, B g^{2} h^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + 2 \, A g^{2} h^{2} x^{3} + 2 \, B g^{3} h x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + 2 \, A g^{3} h x^{2} + B g^{4} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A g^{4} x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B g^{4}}{e} - \frac{2 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} B g^{3} h}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} B g^{2} h^{2}}{e} - \frac{{\left(\frac{6 \, a^{4} e n \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} e n \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} e n - a b^{2} d^{3} e n\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d e n - a^{2} b d^{3} e n\right)} x^{2} + 6 \, {\left(b^{3} c^{3} e n - a^{3} d^{3} e n\right)} x}{b^{3} d^{3}}\right)} B g h^{3}}{6 \, e} + \frac{{\left(\frac{12 \, a^{5} e n \log\left(b x + a\right)}{b^{5}} - \frac{12 \, c^{5} e n \log\left(d x + c\right)}{d^{5}} - \frac{3 \, {\left(b^{4} c d^{3} e n - a b^{3} d^{4} e n\right)} x^{4} - 4 \, {\left(b^{4} c^{2} d^{2} e n - a^{2} b^{2} d^{4} e n\right)} x^{3} + 6 \, {\left(b^{4} c^{3} d e n - a^{3} b d^{4} e n\right)} x^{2} - 12 \, {\left(b^{4} c^{4} e n - a^{4} d^{4} e n\right)} x}{b^{4} d^{4}}\right)} B h^{4}}{60 \, e}"," ",0,"1/5*B*h^4*x^5*log((b*x + a)^n*e/(d*x + c)^n) + 1/5*A*h^4*x^5 + B*g*h^3*x^4*log((b*x + a)^n*e/(d*x + c)^n) + A*g*h^3*x^4 + 2*B*g^2*h^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + 2*A*g^2*h^2*x^3 + 2*B*g^3*h*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 2*A*g^3*h*x^2 + B*g^4*x*log((b*x + a)^n*e/(d*x + c)^n) + A*g^4*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B*g^4/e - 2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*B*g^3*h/e + (2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*B*g^2*h^2/e - 1/6*(6*a^4*e*n*log(b*x + a)/b^4 - 6*c^4*e*n*log(d*x + c)/d^4 + (2*(b^3*c*d^2*e*n - a*b^2*d^3*e*n)*x^3 - 3*(b^3*c^2*d*e*n - a^2*b*d^3*e*n)*x^2 + 6*(b^3*c^3*e*n - a^3*d^3*e*n)*x)/(b^3*d^3))*B*g*h^3/e + 1/60*(12*a^5*e*n*log(b*x + a)/b^5 - 12*c^5*e*n*log(d*x + c)/d^5 - (3*(b^4*c*d^3*e*n - a*b^3*d^4*e*n)*x^4 - 4*(b^4*c^2*d^2*e*n - a^2*b^2*d^4*e*n)*x^3 + 6*(b^4*c^3*d*e*n - a^3*b*d^4*e*n)*x^2 - 12*(b^4*c^4*e*n - a^4*d^4*e*n)*x)/(b^4*d^4))*B*h^4/e","A",0
294,1,467,0,0.658551," ","integrate((h*x+g)^3*(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{1}{4} \, B h^{3} x^{4} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{4} \, A h^{3} x^{4} + B g h^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A g h^{2} x^{3} + \frac{3}{2} \, B g^{2} h x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{3}{2} \, A g^{2} h x^{2} + B g^{3} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A g^{3} x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B g^{3}}{e} - \frac{3 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} B g^{2} h}{2 \, e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} B g h^{2}}{2 \, e} - \frac{{\left(\frac{6 \, a^{4} e n \log\left(b x + a\right)}{b^{4}} - \frac{6 \, c^{4} e n \log\left(d x + c\right)}{d^{4}} + \frac{2 \, {\left(b^{3} c d^{2} e n - a b^{2} d^{3} e n\right)} x^{3} - 3 \, {\left(b^{3} c^{2} d e n - a^{2} b d^{3} e n\right)} x^{2} + 6 \, {\left(b^{3} c^{3} e n - a^{3} d^{3} e n\right)} x}{b^{3} d^{3}}\right)} B h^{3}}{24 \, e}"," ",0,"1/4*B*h^3*x^4*log((b*x + a)^n*e/(d*x + c)^n) + 1/4*A*h^3*x^4 + B*g*h^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + A*g*h^2*x^3 + 3/2*B*g^2*h*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 3/2*A*g^2*h*x^2 + B*g^3*x*log((b*x + a)^n*e/(d*x + c)^n) + A*g^3*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B*g^3/e - 3/2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*B*g^2*h/e + 1/2*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*B*g*h^2/e - 1/24*(6*a^4*e*n*log(b*x + a)/b^4 - 6*c^4*e*n*log(d*x + c)/d^4 + (2*(b^3*c*d^2*e*n - a*b^2*d^3*e*n)*x^3 - 3*(b^3*c^2*d*e*n - a^2*b*d^3*e*n)*x^2 + 6*(b^3*c^3*e*n - a^3*d^3*e*n)*x)/(b^3*d^3))*B*h^3/e","B",0
295,1,294,0,0.939749," ","integrate((h*x+g)^2*(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{1}{3} \, B h^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{3} \, A h^{2} x^{3} + B g h x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A g h x^{2} + B g^{2} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A g^{2} x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B g^{2}}{e} - \frac{{\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} B g h}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} B h^{2}}{6 \, e}"," ",0,"1/3*B*h^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + 1/3*A*h^2*x^3 + B*g*h*x^2*log((b*x + a)^n*e/(d*x + c)^n) + A*g*h*x^2 + B*g^2*x*log((b*x + a)^n*e/(d*x + c)^n) + A*g^2*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B*g^2/e - (a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*B*g*h/e + 1/6*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*B*h^2/e","A",0
296,1,154,0,0.624191," ","integrate((h*x+g)*(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""maxima"")","\frac{1}{2} \, B h x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{2} \, A h x^{2} + B g x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A g x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B g}{e} - \frac{{\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} B h}{2 \, e}"," ",0,"1/2*B*h*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 1/2*A*h*x^2 + B*g*x*log((b*x + a)^n*e/(d*x + c)^n) + A*g*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B*g/e - 1/2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*B*h/e","A",0
297,1,59,0,0.819758," ","integrate(A+B*log(e*(b*x+a)^n/((d*x+c)^n)),x, algorithm=""maxima"")","B x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A x + \frac{{\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} B}{e}"," ",0,"B*x*log((b*x + a)^n*e/(d*x + c)^n) + A*x + (a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*B/e","A",0
298,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(h*x+g),x, algorithm=""maxima"")","-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)}{h x + g}\,{d x} + \frac{A \log\left(h x + g\right)}{h}"," ",0,"-B*integrate(-(log((b*x + a)^n) - log((d*x + c)^n) + log(e))/(h*x + g), x) + A*log(h*x + g)/h","F",0
299,1,151,0,0.762122," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(h*x+g)^2,x, algorithm=""maxima"")","\frac{{\left(\frac{b e n \log\left(b x + a\right)}{b g h - a h^{2}} - \frac{d e n \log\left(d x + c\right)}{d g h - c h^{2}} - \frac{{\left(b c e n - a d e n\right)} \log\left(h x + g\right)}{{\left(d g h - c h^{2}\right)} a - {\left(d g^{2} - c g h\right)} b}\right)} B}{e} - \frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{h^{2} x + g h} - \frac{A}{h^{2} x + g h}"," ",0,"(b*e*n*log(b*x + a)/(b*g*h - a*h^2) - d*e*n*log(d*x + c)/(d*g*h - c*h^2) - (b*c*e*n - a*d*e*n)*log(h*x + g)/((d*g*h - c*h^2)*a - (d*g^2 - c*g*h)*b))*B/e - B*log((b*x + a)^n*e/(d*x + c)^n)/(h^2*x + g*h) - A/(h^2*x + g*h)","A",0
300,1,382,0,0.913789," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(h*x+g)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{b^{2} e n \log\left(b x + a\right)}{b^{2} g^{2} h - 2 \, a b g h^{2} + a^{2} h^{3}} - \frac{d^{2} e n \log\left(d x + c\right)}{d^{2} g^{2} h - 2 \, c d g h^{2} + c^{2} h^{3}} - \frac{{\left(2 \, a b d^{2} e g n - a^{2} d^{2} e h n - {\left(2 \, c d e g n - c^{2} e h n\right)} b^{2}\right)} \log\left(h x + g\right)}{{\left(d^{2} g^{2} h^{2} - 2 \, c d g h^{3} + c^{2} h^{4}\right)} a^{2} - 2 \, {\left(d^{2} g^{3} h - 2 \, c d g^{2} h^{2} + c^{2} g h^{3}\right)} a b + {\left(d^{2} g^{4} - 2 \, c d g^{3} h + c^{2} g^{2} h^{2}\right)} b^{2}} + \frac{b c e n - a d e n}{{\left(d g^{2} h - c g h^{2}\right)} a - {\left(d g^{3} - c g^{2} h\right)} b + {\left({\left(d g h^{2} - c h^{3}\right)} a - {\left(d g^{2} h - c g h^{2}\right)} b\right)} x}\right)} B}{2 \, e} - \frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{2 \, {\left(h^{3} x^{2} + 2 \, g h^{2} x + g^{2} h\right)}} - \frac{A}{2 \, {\left(h^{3} x^{2} + 2 \, g h^{2} x + g^{2} h\right)}}"," ",0,"1/2*(b^2*e*n*log(b*x + a)/(b^2*g^2*h - 2*a*b*g*h^2 + a^2*h^3) - d^2*e*n*log(d*x + c)/(d^2*g^2*h - 2*c*d*g*h^2 + c^2*h^3) - (2*a*b*d^2*e*g*n - a^2*d^2*e*h*n - (2*c*d*e*g*n - c^2*e*h*n)*b^2)*log(h*x + g)/((d^2*g^2*h^2 - 2*c*d*g*h^3 + c^2*h^4)*a^2 - 2*(d^2*g^3*h - 2*c*d*g^2*h^2 + c^2*g*h^3)*a*b + (d^2*g^4 - 2*c*d*g^3*h + c^2*g^2*h^2)*b^2) + (b*c*e*n - a*d*e*n)/((d*g^2*h - c*g*h^2)*a - (d*g^3 - c*g^2*h)*b + ((d*g*h^2 - c*h^3)*a - (d*g^2*h - c*g*h^2)*b)*x))*B/e - 1/2*B*log((b*x + a)^n*e/(d*x + c)^n)/(h^3*x^2 + 2*g*h^2*x + g^2*h) - 1/2*A/(h^3*x^2 + 2*g*h^2*x + g^2*h)","B",0
301,1,920,0,1.889171," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(h*x+g)^4,x, algorithm=""maxima"")","\frac{{\left(\frac{2 \, b^{3} e n \log\left(b x + a\right)}{b^{3} g^{3} h - 3 \, a b^{2} g^{2} h^{2} + 3 \, a^{2} b g h^{3} - a^{3} h^{4}} - \frac{2 \, d^{3} e n \log\left(d x + c\right)}{d^{3} g^{3} h - 3 \, c d^{2} g^{2} h^{2} + 3 \, c^{2} d g h^{3} - c^{3} h^{4}} + \frac{2 \, {\left(3 \, a b^{2} d^{3} e g^{2} n - 3 \, a^{2} b d^{3} e g h n + a^{3} d^{3} e h^{2} n - {\left(3 \, c d^{2} e g^{2} n - 3 \, c^{2} d e g h n + c^{3} e h^{2} n\right)} b^{3}\right)} \log\left(h x + g\right)}{{\left(d^{3} g^{3} h^{3} - 3 \, c d^{2} g^{2} h^{4} + 3 \, c^{2} d g h^{5} - c^{3} h^{6}\right)} a^{3} - 3 \, {\left(d^{3} g^{4} h^{2} - 3 \, c d^{2} g^{3} h^{3} + 3 \, c^{2} d g^{2} h^{4} - c^{3} g h^{5}\right)} a^{2} b + 3 \, {\left(d^{3} g^{5} h - 3 \, c d^{2} g^{4} h^{2} + 3 \, c^{2} d g^{3} h^{3} - c^{3} g^{2} h^{4}\right)} a b^{2} - {\left(d^{3} g^{6} - 3 \, c d^{2} g^{5} h + 3 \, c^{2} d g^{4} h^{2} - c^{3} g^{3} h^{3}\right)} b^{3}} - \frac{{\left(3 \, d^{2} e g h n - c d e h^{2} n\right)} a^{2} - {\left(5 \, d^{2} e g^{2} n - c^{2} e h^{2} n\right)} a b + {\left(5 \, c d e g^{2} n - 3 \, c^{2} e g h n\right)} b^{2} - 2 \, {\left(2 \, a b d^{2} e g h n - a^{2} d^{2} e h^{2} n - {\left(2 \, c d e g h n - c^{2} e h^{2} n\right)} b^{2}\right)} x}{{\left(d^{2} g^{4} h^{2} - 2 \, c d g^{3} h^{3} + c^{2} g^{2} h^{4}\right)} a^{2} - 2 \, {\left(d^{2} g^{5} h - 2 \, c d g^{4} h^{2} + c^{2} g^{3} h^{3}\right)} a b + {\left(d^{2} g^{6} - 2 \, c d g^{5} h + c^{2} g^{4} h^{2}\right)} b^{2} + {\left({\left(d^{2} g^{2} h^{4} - 2 \, c d g h^{5} + c^{2} h^{6}\right)} a^{2} - 2 \, {\left(d^{2} g^{3} h^{3} - 2 \, c d g^{2} h^{4} + c^{2} g h^{5}\right)} a b + {\left(d^{2} g^{4} h^{2} - 2 \, c d g^{3} h^{3} + c^{2} g^{2} h^{4}\right)} b^{2}\right)} x^{2} + 2 \, {\left({\left(d^{2} g^{3} h^{3} - 2 \, c d g^{2} h^{4} + c^{2} g h^{5}\right)} a^{2} - 2 \, {\left(d^{2} g^{4} h^{2} - 2 \, c d g^{3} h^{3} + c^{2} g^{2} h^{4}\right)} a b + {\left(d^{2} g^{5} h - 2 \, c d g^{4} h^{2} + c^{2} g^{3} h^{3}\right)} b^{2}\right)} x}\right)} B}{6 \, e} - \frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{3 \, {\left(h^{4} x^{3} + 3 \, g h^{3} x^{2} + 3 \, g^{2} h^{2} x + g^{3} h\right)}} - \frac{A}{3 \, {\left(h^{4} x^{3} + 3 \, g h^{3} x^{2} + 3 \, g^{2} h^{2} x + g^{3} h\right)}}"," ",0,"1/6*(2*b^3*e*n*log(b*x + a)/(b^3*g^3*h - 3*a*b^2*g^2*h^2 + 3*a^2*b*g*h^3 - a^3*h^4) - 2*d^3*e*n*log(d*x + c)/(d^3*g^3*h - 3*c*d^2*g^2*h^2 + 3*c^2*d*g*h^3 - c^3*h^4) + 2*(3*a*b^2*d^3*e*g^2*n - 3*a^2*b*d^3*e*g*h*n + a^3*d^3*e*h^2*n - (3*c*d^2*e*g^2*n - 3*c^2*d*e*g*h*n + c^3*e*h^2*n)*b^3)*log(h*x + g)/((d^3*g^3*h^3 - 3*c*d^2*g^2*h^4 + 3*c^2*d*g*h^5 - c^3*h^6)*a^3 - 3*(d^3*g^4*h^2 - 3*c*d^2*g^3*h^3 + 3*c^2*d*g^2*h^4 - c^3*g*h^5)*a^2*b + 3*(d^3*g^5*h - 3*c*d^2*g^4*h^2 + 3*c^2*d*g^3*h^3 - c^3*g^2*h^4)*a*b^2 - (d^3*g^6 - 3*c*d^2*g^5*h + 3*c^2*d*g^4*h^2 - c^3*g^3*h^3)*b^3) - ((3*d^2*e*g*h*n - c*d*e*h^2*n)*a^2 - (5*d^2*e*g^2*n - c^2*e*h^2*n)*a*b + (5*c*d*e*g^2*n - 3*c^2*e*g*h*n)*b^2 - 2*(2*a*b*d^2*e*g*h*n - a^2*d^2*e*h^2*n - (2*c*d*e*g*h*n - c^2*e*h^2*n)*b^2)*x)/((d^2*g^4*h^2 - 2*c*d*g^3*h^3 + c^2*g^2*h^4)*a^2 - 2*(d^2*g^5*h - 2*c*d*g^4*h^2 + c^2*g^3*h^3)*a*b + (d^2*g^6 - 2*c*d*g^5*h + c^2*g^4*h^2)*b^2 + ((d^2*g^2*h^4 - 2*c*d*g*h^5 + c^2*h^6)*a^2 - 2*(d^2*g^3*h^3 - 2*c*d*g^2*h^4 + c^2*g*h^5)*a*b + (d^2*g^4*h^2 - 2*c*d*g^3*h^3 + c^2*g^2*h^4)*b^2)*x^2 + 2*((d^2*g^3*h^3 - 2*c*d*g^2*h^4 + c^2*g*h^5)*a^2 - 2*(d^2*g^4*h^2 - 2*c*d*g^3*h^3 + c^2*g^2*h^4)*a*b + (d^2*g^5*h - 2*c*d*g^4*h^2 + c^2*g^3*h^3)*b^2)*x))*B/e - 1/3*B*log((b*x + a)^n*e/(d*x + c)^n)/(h^4*x^3 + 3*g*h^3*x^2 + 3*g^2*h^2*x + g^3*h) - 1/3*A/(h^4*x^3 + 3*g*h^3*x^2 + 3*g^2*h^2*x + g^3*h)","B",0
302,1,1912,0,2.969139," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(h*x+g)^5,x, algorithm=""maxima"")","\frac{{\left(\frac{6 \, b^{4} e n \log\left(b x + a\right)}{b^{4} g^{4} h - 4 \, a b^{3} g^{3} h^{2} + 6 \, a^{2} b^{2} g^{2} h^{3} - 4 \, a^{3} b g h^{4} + a^{4} h^{5}} - \frac{6 \, d^{4} e n \log\left(d x + c\right)}{d^{4} g^{4} h - 4 \, c d^{3} g^{3} h^{2} + 6 \, c^{2} d^{2} g^{2} h^{3} - 4 \, c^{3} d g h^{4} + c^{4} h^{5}} - \frac{6 \, {\left(4 \, a b^{3} d^{4} e g^{3} n - 6 \, a^{2} b^{2} d^{4} e g^{2} h n + 4 \, a^{3} b d^{4} e g h^{2} n - a^{4} d^{4} e h^{3} n - {\left(4 \, c d^{3} e g^{3} n - 6 \, c^{2} d^{2} e g^{2} h n + 4 \, c^{3} d e g h^{2} n - c^{4} e h^{3} n\right)} b^{4}\right)} \log\left(h x + g\right)}{{\left(d^{4} g^{4} h^{4} - 4 \, c d^{3} g^{3} h^{5} + 6 \, c^{2} d^{2} g^{2} h^{6} - 4 \, c^{3} d g h^{7} + c^{4} h^{8}\right)} a^{4} - 4 \, {\left(d^{4} g^{5} h^{3} - 4 \, c d^{3} g^{4} h^{4} + 6 \, c^{2} d^{2} g^{3} h^{5} - 4 \, c^{3} d g^{2} h^{6} + c^{4} g h^{7}\right)} a^{3} b + 6 \, {\left(d^{4} g^{6} h^{2} - 4 \, c d^{3} g^{5} h^{3} + 6 \, c^{2} d^{2} g^{4} h^{4} - 4 \, c^{3} d g^{3} h^{5} + c^{4} g^{2} h^{6}\right)} a^{2} b^{2} - 4 \, {\left(d^{4} g^{7} h - 4 \, c d^{3} g^{6} h^{2} + 6 \, c^{2} d^{2} g^{5} h^{3} - 4 \, c^{3} d g^{4} h^{4} + c^{4} g^{3} h^{5}\right)} a b^{3} + {\left(d^{4} g^{8} - 4 \, c d^{3} g^{7} h + 6 \, c^{2} d^{2} g^{6} h^{2} - 4 \, c^{3} d g^{5} h^{3} + c^{4} g^{4} h^{4}\right)} b^{4}} - \frac{{\left(11 \, d^{3} e g^{2} h^{2} n - 7 \, c d^{2} e g h^{3} n + 2 \, c^{2} d e h^{4} n\right)} a^{3} - {\left(31 \, d^{3} e g^{3} h n - 15 \, c d^{2} e g^{2} h^{2} n + 2 \, c^{3} e h^{4} n\right)} a^{2} b + {\left(26 \, d^{3} e g^{4} n - 15 \, c^{2} d e g^{2} h^{2} n + 7 \, c^{3} e g h^{3} n\right)} a b^{2} - {\left(26 \, c d^{2} e g^{4} n - 31 \, c^{2} d e g^{3} h n + 11 \, c^{3} e g^{2} h^{2} n\right)} b^{3} + 6 \, {\left(3 \, a b^{2} d^{3} e g^{2} h^{2} n - 3 \, a^{2} b d^{3} e g h^{3} n + a^{3} d^{3} e h^{4} n - {\left(3 \, c d^{2} e g^{2} h^{2} n - 3 \, c^{2} d e g h^{3} n + c^{3} e h^{4} n\right)} b^{3}\right)} x^{2} + 3 \, {\left({\left(5 \, d^{3} e g h^{3} n - c d^{2} e h^{4} n\right)} a^{3} - 3 \, {\left(5 \, d^{3} e g^{2} h^{2} n - c d^{2} e g h^{3} n\right)} a^{2} b + {\left(14 \, d^{3} e g^{3} h n - 3 \, c^{2} d e g h^{3} n + c^{3} e h^{4} n\right)} a b^{2} - {\left(14 \, c d^{2} e g^{3} h n - 15 \, c^{2} d e g^{2} h^{2} n + 5 \, c^{3} e g h^{3} n\right)} b^{3}\right)} x}{{\left(d^{3} g^{6} h^{3} - 3 \, c d^{2} g^{5} h^{4} + 3 \, c^{2} d g^{4} h^{5} - c^{3} g^{3} h^{6}\right)} a^{3} - 3 \, {\left(d^{3} g^{7} h^{2} - 3 \, c d^{2} g^{6} h^{3} + 3 \, c^{2} d g^{5} h^{4} - c^{3} g^{4} h^{5}\right)} a^{2} b + 3 \, {\left(d^{3} g^{8} h - 3 \, c d^{2} g^{7} h^{2} + 3 \, c^{2} d g^{6} h^{3} - c^{3} g^{5} h^{4}\right)} a b^{2} - {\left(d^{3} g^{9} - 3 \, c d^{2} g^{8} h + 3 \, c^{2} d g^{7} h^{2} - c^{3} g^{6} h^{3}\right)} b^{3} + {\left({\left(d^{3} g^{3} h^{6} - 3 \, c d^{2} g^{2} h^{7} + 3 \, c^{2} d g h^{8} - c^{3} h^{9}\right)} a^{3} - 3 \, {\left(d^{3} g^{4} h^{5} - 3 \, c d^{2} g^{3} h^{6} + 3 \, c^{2} d g^{2} h^{7} - c^{3} g h^{8}\right)} a^{2} b + 3 \, {\left(d^{3} g^{5} h^{4} - 3 \, c d^{2} g^{4} h^{5} + 3 \, c^{2} d g^{3} h^{6} - c^{3} g^{2} h^{7}\right)} a b^{2} - {\left(d^{3} g^{6} h^{3} - 3 \, c d^{2} g^{5} h^{4} + 3 \, c^{2} d g^{4} h^{5} - c^{3} g^{3} h^{6}\right)} b^{3}\right)} x^{3} + 3 \, {\left({\left(d^{3} g^{4} h^{5} - 3 \, c d^{2} g^{3} h^{6} + 3 \, c^{2} d g^{2} h^{7} - c^{3} g h^{8}\right)} a^{3} - 3 \, {\left(d^{3} g^{5} h^{4} - 3 \, c d^{2} g^{4} h^{5} + 3 \, c^{2} d g^{3} h^{6} - c^{3} g^{2} h^{7}\right)} a^{2} b + 3 \, {\left(d^{3} g^{6} h^{3} - 3 \, c d^{2} g^{5} h^{4} + 3 \, c^{2} d g^{4} h^{5} - c^{3} g^{3} h^{6}\right)} a b^{2} - {\left(d^{3} g^{7} h^{2} - 3 \, c d^{2} g^{6} h^{3} + 3 \, c^{2} d g^{5} h^{4} - c^{3} g^{4} h^{5}\right)} b^{3}\right)} x^{2} + 3 \, {\left({\left(d^{3} g^{5} h^{4} - 3 \, c d^{2} g^{4} h^{5} + 3 \, c^{2} d g^{3} h^{6} - c^{3} g^{2} h^{7}\right)} a^{3} - 3 \, {\left(d^{3} g^{6} h^{3} - 3 \, c d^{2} g^{5} h^{4} + 3 \, c^{2} d g^{4} h^{5} - c^{3} g^{3} h^{6}\right)} a^{2} b + 3 \, {\left(d^{3} g^{7} h^{2} - 3 \, c d^{2} g^{6} h^{3} + 3 \, c^{2} d g^{5} h^{4} - c^{3} g^{4} h^{5}\right)} a b^{2} - {\left(d^{3} g^{8} h - 3 \, c d^{2} g^{7} h^{2} + 3 \, c^{2} d g^{6} h^{3} - c^{3} g^{5} h^{4}\right)} b^{3}\right)} x}\right)} B}{24 \, e} - \frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{4 \, {\left(h^{5} x^{4} + 4 \, g h^{4} x^{3} + 6 \, g^{2} h^{3} x^{2} + 4 \, g^{3} h^{2} x + g^{4} h\right)}} - \frac{A}{4 \, {\left(h^{5} x^{4} + 4 \, g h^{4} x^{3} + 6 \, g^{2} h^{3} x^{2} + 4 \, g^{3} h^{2} x + g^{4} h\right)}}"," ",0,"1/24*(6*b^4*e*n*log(b*x + a)/(b^4*g^4*h - 4*a*b^3*g^3*h^2 + 6*a^2*b^2*g^2*h^3 - 4*a^3*b*g*h^4 + a^4*h^5) - 6*d^4*e*n*log(d*x + c)/(d^4*g^4*h - 4*c*d^3*g^3*h^2 + 6*c^2*d^2*g^2*h^3 - 4*c^3*d*g*h^4 + c^4*h^5) - 6*(4*a*b^3*d^4*e*g^3*n - 6*a^2*b^2*d^4*e*g^2*h*n + 4*a^3*b*d^4*e*g*h^2*n - a^4*d^4*e*h^3*n - (4*c*d^3*e*g^3*n - 6*c^2*d^2*e*g^2*h*n + 4*c^3*d*e*g*h^2*n - c^4*e*h^3*n)*b^4)*log(h*x + g)/((d^4*g^4*h^4 - 4*c*d^3*g^3*h^5 + 6*c^2*d^2*g^2*h^6 - 4*c^3*d*g*h^7 + c^4*h^8)*a^4 - 4*(d^4*g^5*h^3 - 4*c*d^3*g^4*h^4 + 6*c^2*d^2*g^3*h^5 - 4*c^3*d*g^2*h^6 + c^4*g*h^7)*a^3*b + 6*(d^4*g^6*h^2 - 4*c*d^3*g^5*h^3 + 6*c^2*d^2*g^4*h^4 - 4*c^3*d*g^3*h^5 + c^4*g^2*h^6)*a^2*b^2 - 4*(d^4*g^7*h - 4*c*d^3*g^6*h^2 + 6*c^2*d^2*g^5*h^3 - 4*c^3*d*g^4*h^4 + c^4*g^3*h^5)*a*b^3 + (d^4*g^8 - 4*c*d^3*g^7*h + 6*c^2*d^2*g^6*h^2 - 4*c^3*d*g^5*h^3 + c^4*g^4*h^4)*b^4) - ((11*d^3*e*g^2*h^2*n - 7*c*d^2*e*g*h^3*n + 2*c^2*d*e*h^4*n)*a^3 - (31*d^3*e*g^3*h*n - 15*c*d^2*e*g^2*h^2*n + 2*c^3*e*h^4*n)*a^2*b + (26*d^3*e*g^4*n - 15*c^2*d*e*g^2*h^2*n + 7*c^3*e*g*h^3*n)*a*b^2 - (26*c*d^2*e*g^4*n - 31*c^2*d*e*g^3*h*n + 11*c^3*e*g^2*h^2*n)*b^3 + 6*(3*a*b^2*d^3*e*g^2*h^2*n - 3*a^2*b*d^3*e*g*h^3*n + a^3*d^3*e*h^4*n - (3*c*d^2*e*g^2*h^2*n - 3*c^2*d*e*g*h^3*n + c^3*e*h^4*n)*b^3)*x^2 + 3*((5*d^3*e*g*h^3*n - c*d^2*e*h^4*n)*a^3 - 3*(5*d^3*e*g^2*h^2*n - c*d^2*e*g*h^3*n)*a^2*b + (14*d^3*e*g^3*h*n - 3*c^2*d*e*g*h^3*n + c^3*e*h^4*n)*a*b^2 - (14*c*d^2*e*g^3*h*n - 15*c^2*d*e*g^2*h^2*n + 5*c^3*e*g*h^3*n)*b^3)*x)/((d^3*g^6*h^3 - 3*c*d^2*g^5*h^4 + 3*c^2*d*g^4*h^5 - c^3*g^3*h^6)*a^3 - 3*(d^3*g^7*h^2 - 3*c*d^2*g^6*h^3 + 3*c^2*d*g^5*h^4 - c^3*g^4*h^5)*a^2*b + 3*(d^3*g^8*h - 3*c*d^2*g^7*h^2 + 3*c^2*d*g^6*h^3 - c^3*g^5*h^4)*a*b^2 - (d^3*g^9 - 3*c*d^2*g^8*h + 3*c^2*d*g^7*h^2 - c^3*g^6*h^3)*b^3 + ((d^3*g^3*h^6 - 3*c*d^2*g^2*h^7 + 3*c^2*d*g*h^8 - c^3*h^9)*a^3 - 3*(d^3*g^4*h^5 - 3*c*d^2*g^3*h^6 + 3*c^2*d*g^2*h^7 - c^3*g*h^8)*a^2*b + 3*(d^3*g^5*h^4 - 3*c*d^2*g^4*h^5 + 3*c^2*d*g^3*h^6 - c^3*g^2*h^7)*a*b^2 - (d^3*g^6*h^3 - 3*c*d^2*g^5*h^4 + 3*c^2*d*g^4*h^5 - c^3*g^3*h^6)*b^3)*x^3 + 3*((d^3*g^4*h^5 - 3*c*d^2*g^3*h^6 + 3*c^2*d*g^2*h^7 - c^3*g*h^8)*a^3 - 3*(d^3*g^5*h^4 - 3*c*d^2*g^4*h^5 + 3*c^2*d*g^3*h^6 - c^3*g^2*h^7)*a^2*b + 3*(d^3*g^6*h^3 - 3*c*d^2*g^5*h^4 + 3*c^2*d*g^4*h^5 - c^3*g^3*h^6)*a*b^2 - (d^3*g^7*h^2 - 3*c*d^2*g^6*h^3 + 3*c^2*d*g^5*h^4 - c^3*g^4*h^5)*b^3)*x^2 + 3*((d^3*g^5*h^4 - 3*c*d^2*g^4*h^5 + 3*c^2*d*g^3*h^6 - c^3*g^2*h^7)*a^3 - 3*(d^3*g^6*h^3 - 3*c*d^2*g^5*h^4 + 3*c^2*d*g^4*h^5 - c^3*g^3*h^6)*a^2*b + 3*(d^3*g^7*h^2 - 3*c*d^2*g^6*h^3 + 3*c^2*d*g^5*h^4 - c^3*g^4*h^5)*a*b^2 - (d^3*g^8*h - 3*c*d^2*g^7*h^2 + 3*c^2*d*g^6*h^3 - c^3*g^5*h^4)*b^3)*x))*B/e - 1/4*B*log((b*x + a)^n*e/(d*x + c)^n)/(h^5*x^4 + 4*g*h^4*x^3 + 6*g^2*h^3*x^2 + 4*g^3*h^2*x + g^4*h) - 1/4*A/(h^5*x^4 + 4*g*h^4*x^3 + 6*g^2*h^3*x^2 + 4*g^3*h^2*x + g^4*h)","B",0
303,1,1671,0,6.789389," ","integrate((h*x+g)^2*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","\frac{2}{3} \, A B h^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{3} \, A^{2} h^{2} x^{3} + 2 \, A B g h x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} g h x^{2} + 2 \, A B g^{2} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} g^{2} x + \frac{2 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A B g^{2}}{e} - \frac{2 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A B g h}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} A B h^{2}}{3 \, e} + \frac{{\left(2 \, a^{2} c d^{2} h^{2} n^{2} - {\left(6 \, c d^{2} g h n^{2} - c^{2} d h^{2} n^{2}\right)} a b - {\left(6 \, c d^{2} g^{2} n \log\left(e\right) + {\left(3 \, h^{2} n^{2} + 2 \, h^{2} n \log\left(e\right)\right)} c^{3} - 6 \, {\left(g h n^{2} + g h n \log\left(e\right)\right)} c^{2} d\right)} b^{2}\right)} B^{2} \log\left(d x + c\right)}{3 \, b^{2} d^{3}} + \frac{2 \, {\left(3 \, a b^{2} d^{3} g^{2} n^{2} - 3 \, a^{2} b d^{3} g h n^{2} + a^{3} d^{3} h^{2} n^{2} - {\left(3 \, c d^{2} g^{2} n^{2} - 3 \, c^{2} d g h n^{2} + c^{3} h^{2} n^{2}\right)} b^{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}}{3 \, b^{3} d^{3}} + \frac{B^{2} b^{3} d^{3} h^{2} x^{3} \log\left(e\right)^{2} + 2 \, {\left(3 \, c d^{2} g^{2} n^{2} - 3 \, c^{2} d g h n^{2} + c^{3} h^{2} n^{2}\right)} B^{2} b^{3} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(3 \, c d^{2} g^{2} n^{2} - 3 \, c^{2} d g h n^{2} + c^{3} h^{2} n^{2}\right)} B^{2} b^{3} \log\left(d x + c\right)^{2} + {\left(a b^{2} d^{3} h^{2} n \log\left(e\right) - {\left(c d^{2} h^{2} n \log\left(e\right) - 3 \, d^{3} g h \log\left(e\right)^{2}\right)} b^{3}\right)} B^{2} x^{2} - {\left(3 \, a b^{2} d^{3} g^{2} n^{2} - 3 \, a^{2} b d^{3} g h n^{2} + a^{3} d^{3} h^{2} n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + {\left({\left(h^{2} n^{2} - 2 \, h^{2} n \log\left(e\right)\right)} a^{2} b d^{3} - 2 \, {\left(c d^{2} h^{2} n^{2} - 3 \, d^{3} g h n \log\left(e\right)\right)} a b^{2} - {\left(6 \, c d^{2} g h n \log\left(e\right) - 3 \, d^{3} g^{2} \log\left(e\right)^{2} - {\left(h^{2} n^{2} + 2 \, h^{2} n \log\left(e\right)\right)} c^{2} d\right)} b^{3}\right)} B^{2} x - {\left({\left(3 \, h^{2} n^{2} - 2 \, h^{2} n \log\left(e\right)\right)} a^{3} d^{3} - {\left(c d^{2} h^{2} n^{2} + 6 \, {\left(g h n^{2} - g h n \log\left(e\right)\right)} d^{3}\right)} a^{2} b + 2 \, {\left(3 \, c d^{2} g h n^{2} - c^{2} d h^{2} n^{2} - 3 \, d^{3} g^{2} n \log\left(e\right)\right)} a b^{2}\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{3} d^{3} h^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} g h x^{2} + 3 \, B^{2} b^{3} d^{3} g^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{3} d^{3} h^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} g h x^{2} + 3 \, B^{2} b^{3} d^{3} g^{2} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(2 \, B^{2} b^{3} d^{3} h^{2} x^{3} \log\left(e\right) - 2 \, {\left(3 \, c d^{2} g^{2} n - 3 \, c^{2} d g h n + c^{3} h^{2} n\right)} B^{2} b^{3} \log\left(d x + c\right) + {\left(a b^{2} d^{3} h^{2} n - {\left(c d^{2} h^{2} n - 6 \, d^{3} g h \log\left(e\right)\right)} b^{3}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} d^{3} g h n - a^{2} b d^{3} h^{2} n - {\left(3 \, c d^{2} g h n - c^{2} d h^{2} n - 3 \, d^{3} g^{2} \log\left(e\right)\right)} b^{3}\right)} B^{2} x + 2 \, {\left(3 \, a b^{2} d^{3} g^{2} n - 3 \, a^{2} b d^{3} g h n + a^{3} d^{3} h^{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} h^{2} x^{3} \log\left(e\right) - 2 \, {\left(3 \, c d^{2} g^{2} n - 3 \, c^{2} d g h n + c^{3} h^{2} n\right)} B^{2} b^{3} \log\left(d x + c\right) + {\left(a b^{2} d^{3} h^{2} n - {\left(c d^{2} h^{2} n - 6 \, d^{3} g h \log\left(e\right)\right)} b^{3}\right)} B^{2} x^{2} + 2 \, {\left(3 \, a b^{2} d^{3} g h n - a^{2} b d^{3} h^{2} n - {\left(3 \, c d^{2} g h n - c^{2} d h^{2} n - 3 \, d^{3} g^{2} \log\left(e\right)\right)} b^{3}\right)} B^{2} x + 2 \, {\left(3 \, a b^{2} d^{3} g^{2} n - 3 \, a^{2} b d^{3} g h n + a^{3} d^{3} h^{2} n\right)} B^{2} \log\left(b x + a\right) + 2 \, {\left(B^{2} b^{3} d^{3} h^{2} x^{3} + 3 \, B^{2} b^{3} d^{3} g h x^{2} + 3 \, B^{2} b^{3} d^{3} g^{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^{3}}"," ",0,"2/3*A*B*h^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + 1/3*A^2*h^2*x^3 + 2*A*B*g*h*x^2*log((b*x + a)^n*e/(d*x + c)^n) + A^2*g*h*x^2 + 2*A*B*g^2*x*log((b*x + a)^n*e/(d*x + c)^n) + A^2*g^2*x + 2*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A*B*g^2/e - 2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A*B*g*h/e + 1/3*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*A*B*h^2/e + 1/3*(2*a^2*c*d^2*h^2*n^2 - (6*c*d^2*g*h*n^2 - c^2*d*h^2*n^2)*a*b - (6*c*d^2*g^2*n*log(e) + (3*h^2*n^2 + 2*h^2*n*log(e))*c^3 - 6*(g*h*n^2 + g*h*n*log(e))*c^2*d)*b^2)*B^2*log(d*x + c)/(b^2*d^3) + 2/3*(3*a*b^2*d^3*g^2*n^2 - 3*a^2*b*d^3*g*h*n^2 + a^3*d^3*h^2*n^2 - (3*c*d^2*g^2*n^2 - 3*c^2*d*g*h*n^2 + c^3*h^2*n^2)*b^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^3*d^3) + 1/3*(B^2*b^3*d^3*h^2*x^3*log(e)^2 + 2*(3*c*d^2*g^2*n^2 - 3*c^2*d*g*h*n^2 + c^3*h^2*n^2)*B^2*b^3*log(b*x + a)*log(d*x + c) - (3*c*d^2*g^2*n^2 - 3*c^2*d*g*h*n^2 + c^3*h^2*n^2)*B^2*b^3*log(d*x + c)^2 + (a*b^2*d^3*h^2*n*log(e) - (c*d^2*h^2*n*log(e) - 3*d^3*g*h*log(e)^2)*b^3)*B^2*x^2 - (3*a*b^2*d^3*g^2*n^2 - 3*a^2*b*d^3*g*h*n^2 + a^3*d^3*h^2*n^2)*B^2*log(b*x + a)^2 + ((h^2*n^2 - 2*h^2*n*log(e))*a^2*b*d^3 - 2*(c*d^2*h^2*n^2 - 3*d^3*g*h*n*log(e))*a*b^2 - (6*c*d^2*g*h*n*log(e) - 3*d^3*g^2*log(e)^2 - (h^2*n^2 + 2*h^2*n*log(e))*c^2*d)*b^3)*B^2*x - ((3*h^2*n^2 - 2*h^2*n*log(e))*a^3*d^3 - (c*d^2*h^2*n^2 + 6*(g*h*n^2 - g*h*n*log(e))*d^3)*a^2*b + 2*(3*c*d^2*g*h*n^2 - c^2*d*h^2*n^2 - 3*d^3*g^2*n*log(e))*a*b^2)*B^2*log(b*x + a) + (B^2*b^3*d^3*h^2*x^3 + 3*B^2*b^3*d^3*g*h*x^2 + 3*B^2*b^3*d^3*g^2*x)*log((b*x + a)^n)^2 + (B^2*b^3*d^3*h^2*x^3 + 3*B^2*b^3*d^3*g*h*x^2 + 3*B^2*b^3*d^3*g^2*x)*log((d*x + c)^n)^2 + (2*B^2*b^3*d^3*h^2*x^3*log(e) - 2*(3*c*d^2*g^2*n - 3*c^2*d*g*h*n + c^3*h^2*n)*B^2*b^3*log(d*x + c) + (a*b^2*d^3*h^2*n - (c*d^2*h^2*n - 6*d^3*g*h*log(e))*b^3)*B^2*x^2 + 2*(3*a*b^2*d^3*g*h*n - a^2*b*d^3*h^2*n - (3*c*d^2*g*h*n - c^2*d*h^2*n - 3*d^3*g^2*log(e))*b^3)*B^2*x + 2*(3*a*b^2*d^3*g^2*n - 3*a^2*b*d^3*g*h*n + a^3*d^3*h^2*n)*B^2*log(b*x + a))*log((b*x + a)^n) - (2*B^2*b^3*d^3*h^2*x^3*log(e) - 2*(3*c*d^2*g^2*n - 3*c^2*d*g*h*n + c^3*h^2*n)*B^2*b^3*log(d*x + c) + (a*b^2*d^3*h^2*n - (c*d^2*h^2*n - 6*d^3*g*h*log(e))*b^3)*B^2*x^2 + 2*(3*a*b^2*d^3*g*h*n - a^2*b*d^3*h^2*n - (3*c*d^2*g*h*n - c^2*d*h^2*n - 3*d^3*g^2*log(e))*b^3)*B^2*x + 2*(3*a*b^2*d^3*g^2*n - 3*a^2*b*d^3*g*h*n + a^3*d^3*h^2*n)*B^2*log(b*x + a) + 2*(B^2*b^3*d^3*h^2*x^3 + 3*B^2*b^3*d^3*g*h*x^2 + 3*B^2*b^3*d^3*g^2*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d^3)","B",0
304,1,903,0,6.534397," ","integrate((h*x+g)*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","A B h x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{2} \, A^{2} h x^{2} + 2 \, A B g x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} g x + \frac{2 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A B g}{e} - \frac{{\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A B h}{e} - \frac{{\left(a c d h n^{2} + {\left(2 \, c d g n \log\left(e\right) - {\left(h n^{2} + h n \log\left(e\right)\right)} c^{2}\right)} b\right)} B^{2} \log\left(d x + c\right)}{b d^{2}} + \frac{{\left(2 \, a b d^{2} g n^{2} - a^{2} d^{2} h n^{2} - {\left(2 \, c d g n^{2} - c^{2} h n^{2}\right)} b^{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^{2}} + \frac{B^{2} b^{2} d^{2} h x^{2} \log\left(e\right)^{2} + 2 \, {\left(2 \, c d g n^{2} - c^{2} h n^{2}\right)} B^{2} b^{2} \log\left(b x + a\right) \log\left(d x + c\right) - {\left(2 \, c d g n^{2} - c^{2} h n^{2}\right)} B^{2} b^{2} \log\left(d x + c\right)^{2} - {\left(2 \, a b d^{2} g n^{2} - a^{2} d^{2} h n^{2}\right)} B^{2} \log\left(b x + a\right)^{2} + 2 \, {\left(a b d^{2} h n \log\left(e\right) - {\left(c d h n \log\left(e\right) - d^{2} g \log\left(e\right)^{2}\right)} b^{2}\right)} B^{2} x + 2 \, {\left({\left(h n^{2} - h n \log\left(e\right)\right)} a^{2} d^{2} - {\left(c d h n^{2} - 2 \, d^{2} g n \log\left(e\right)\right)} a b\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{2} d^{2} h x^{2} + 2 \, B^{2} b^{2} d^{2} g x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{2} b^{2} d^{2} h x^{2} + 2 \, B^{2} b^{2} d^{2} g x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(B^{2} b^{2} d^{2} h x^{2} \log\left(e\right) - {\left(2 \, c d g n - c^{2} h n\right)} B^{2} b^{2} \log\left(d x + c\right) + {\left(a b d^{2} h n - {\left(c d h n - 2 \, d^{2} g \log\left(e\right)\right)} b^{2}\right)} B^{2} x + {\left(2 \, a b d^{2} g n - a^{2} d^{2} h 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} h x^{2} \log\left(e\right) - {\left(2 \, c d g n - c^{2} h n\right)} B^{2} b^{2} \log\left(d x + c\right) + {\left(a b d^{2} h n - {\left(c d h n - 2 \, d^{2} g \log\left(e\right)\right)} b^{2}\right)} B^{2} x + {\left(2 \, a b d^{2} g n - a^{2} d^{2} h n\right)} B^{2} \log\left(b x + a\right) + {\left(B^{2} b^{2} d^{2} h x^{2} + 2 \, B^{2} b^{2} d^{2} g 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^{2}}"," ",0,"A*B*h*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 1/2*A^2*h*x^2 + 2*A*B*g*x*log((b*x + a)^n*e/(d*x + c)^n) + A^2*g*x + 2*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A*B*g/e - (a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A*B*h/e - (a*c*d*h*n^2 + (2*c*d*g*n*log(e) - (h*n^2 + h*n*log(e))*c^2)*b)*B^2*log(d*x + c)/(b*d^2) + (2*a*b*d^2*g*n^2 - a^2*d^2*h*n^2 - (2*c*d*g*n^2 - c^2*h*n^2)*b^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) + 1/2*(B^2*b^2*d^2*h*x^2*log(e)^2 + 2*(2*c*d*g*n^2 - c^2*h*n^2)*B^2*b^2*log(b*x + a)*log(d*x + c) - (2*c*d*g*n^2 - c^2*h*n^2)*B^2*b^2*log(d*x + c)^2 - (2*a*b*d^2*g*n^2 - a^2*d^2*h*n^2)*B^2*log(b*x + a)^2 + 2*(a*b*d^2*h*n*log(e) - (c*d*h*n*log(e) - d^2*g*log(e)^2)*b^2)*B^2*x + 2*((h*n^2 - h*n*log(e))*a^2*d^2 - (c*d*h*n^2 - 2*d^2*g*n*log(e))*a*b)*B^2*log(b*x + a) + (B^2*b^2*d^2*h*x^2 + 2*B^2*b^2*d^2*g*x)*log((b*x + a)^n)^2 + (B^2*b^2*d^2*h*x^2 + 2*B^2*b^2*d^2*g*x)*log((d*x + c)^n)^2 + 2*(B^2*b^2*d^2*h*x^2*log(e) - (2*c*d*g*n - c^2*h*n)*B^2*b^2*log(d*x + c) + (a*b*d^2*h*n - (c*d*h*n - 2*d^2*g*log(e))*b^2)*B^2*x + (2*a*b*d^2*g*n - a^2*d^2*h*n)*B^2*log(b*x + a))*log((b*x + a)^n) - 2*(B^2*b^2*d^2*h*x^2*log(e) - (2*c*d*g*n - c^2*h*n)*B^2*b^2*log(d*x + c) + (a*b*d^2*h*n - (c*d*h*n - 2*d^2*g*log(e))*b^2)*B^2*x + (2*a*b*d^2*g*n - a^2*d^2*h*n)*B^2*log(b*x + a) + (B^2*b^2*d^2*h*x^2 + 2*B^2*b^2*d^2*g*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d^2)","B",0
305,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""maxima"")","2 \, A B x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2} x + B^{2} {\left(\frac{2 \, b c n^{2} \log\left(b x + a\right) \log\left(d x + c\right) - b c n^{2} \log\left(d x + c\right)^{2} + b d x \log\left({\left(b x + a\right)}^{n}\right)^{2} + b d x \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(a d n \log\left(b x + a\right) - b c n \log\left(d x + c\right) + b d x \log\left(e\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) - 2 \, {\left(a d n \log\left(b x + a\right) - b c n \log\left(d x + c\right) + b d x \log\left({\left(b x + a\right)}^{n}\right) + b d x \log\left(e\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b d} - \int -\frac{b^{2} d x^{2} \log\left(e\right)^{2} + a b c \log\left(e\right)^{2} - {\left({\left(2 \, n \log\left(e\right) - \log\left(e\right)^{2}\right)} b^{2} c - {\left(2 \, n \log\left(e\right) + \log\left(e\right)^{2}\right)} a b d\right)} x - 2 \, {\left(b^{2} c n^{2} x + 2 \, a b c n^{2} - a^{2} d n^{2}\right)} \log\left(b x + a\right)}{b^{2} d x^{2} + a b c + {\left(b^{2} c + a b d\right)} x}\,{d x}\right)} + \frac{2 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A B}{e}"," ",0,"2*A*B*x*log((b*x + a)^n*e/(d*x + c)^n) + A^2*x + B^2*((2*b*c*n^2*log(b*x + a)*log(d*x + c) - b*c*n^2*log(d*x + c)^2 + b*d*x*log((b*x + a)^n)^2 + b*d*x*log((d*x + c)^n)^2 + 2*(a*d*n*log(b*x + a) - b*c*n*log(d*x + c) + b*d*x*log(e))*log((b*x + a)^n) - 2*(a*d*n*log(b*x + a) - b*c*n*log(d*x + c) + b*d*x*log((b*x + a)^n) + b*d*x*log(e))*log((d*x + c)^n))/(b*d) - integrate(-(b^2*d*x^2*log(e)^2 + a*b*c*log(e)^2 - ((2*n*log(e) - log(e)^2)*b^2*c - (2*n*log(e) + log(e)^2)*a*b*d)*x - 2*(b^2*c*n^2*x + 2*a*b*c*n^2 - a^2*d*n^2)*log(b*x + a))/(b^2*d*x^2 + a*b*c + (b^2*c + a*b*d)*x), x)) + 2*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A*B/e","F",0
306,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(h*x+g),x, algorithm=""maxima"")","\frac{A^{2} \log\left(h x + g\right)}{h} + \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)}{h x + g}\,{d x}"," ",0,"A^2*log(h*x + 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))/(h*x + g), x)","F",0
307,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(h*x+g)^2,x, algorithm=""maxima"")","-B^{2} {\left(\frac{\log\left({\left(d x + c\right)}^{n}\right)^{2}}{h^{2} x + g h} + \int -\frac{d h x \log\left(e\right)^{2} + c h \log\left(e\right)^{2} + {\left(d h x + c h\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(d h x \log\left(e\right) + c h \log\left(e\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + 2 \, {\left(d g n + {\left(h n - h \log\left(e\right)\right)} d x - c h \log\left(e\right) - {\left(d h x + c h\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d h^{3} x^{3} + c g^{2} h + {\left(2 \, d g h^{2} + c h^{3}\right)} x^{2} + {\left(d g^{2} h + 2 \, c g h^{2}\right)} x}\,{d x}\right)} + \frac{2 \, {\left(\frac{b e n \log\left(b x + a\right)}{b g h - a h^{2}} - \frac{d e n \log\left(d x + c\right)}{d g h - c h^{2}} - \frac{{\left(b c e n - a d e n\right)} \log\left(h x + g\right)}{{\left(d g h - c h^{2}\right)} a - {\left(d g^{2} - c g h\right)} b}\right)} A B}{e} - \frac{2 \, A B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{h^{2} x + g h} - \frac{A^{2}}{h^{2} x + g h}"," ",0,"-B^2*(log((d*x + c)^n)^2/(h^2*x + g*h) + integrate(-(d*h*x*log(e)^2 + c*h*log(e)^2 + (d*h*x + c*h)*log((b*x + a)^n)^2 + 2*(d*h*x*log(e) + c*h*log(e))*log((b*x + a)^n) + 2*(d*g*n + (h*n - h*log(e))*d*x - c*h*log(e) - (d*h*x + c*h)*log((b*x + a)^n))*log((d*x + c)^n))/(d*h^3*x^3 + c*g^2*h + (2*d*g*h^2 + c*h^3)*x^2 + (d*g^2*h + 2*c*g*h^2)*x), x)) + 2*(b*e*n*log(b*x + a)/(b*g*h - a*h^2) - d*e*n*log(d*x + c)/(d*g*h - c*h^2) - (b*c*e*n - a*d*e*n)*log(h*x + g)/((d*g*h - c*h^2)*a - (d*g^2 - c*g*h)*b))*A*B/e - 2*A*B*log((b*x + a)^n*e/(d*x + c)^n)/(h^2*x + g*h) - A^2/(h^2*x + g*h)","F",0
308,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(h*x+g)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, B^{2} {\left(\frac{\log\left({\left(d x + c\right)}^{n}\right)^{2}}{h^{3} x^{2} + 2 \, g h^{2} x + g^{2} h} + 2 \, \int -\frac{d h x \log\left(e\right)^{2} + c h \log\left(e\right)^{2} + {\left(d h x + c h\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 2 \, {\left(d h x \log\left(e\right) + c h \log\left(e\right)\right)} \log\left({\left(b x + a\right)}^{n}\right) + {\left(d g n + {\left(h n - 2 \, h \log\left(e\right)\right)} d x - 2 \, c h \log\left(e\right) - 2 \, {\left(d h x + c h\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d h^{4} x^{4} + c g^{3} h + {\left(3 \, d g h^{3} + c h^{4}\right)} x^{3} + 3 \, {\left(d g^{2} h^{2} + c g h^{3}\right)} x^{2} + {\left(d g^{3} h + 3 \, c g^{2} h^{2}\right)} x}\,{d x}\right)} + \frac{{\left(\frac{b^{2} e n \log\left(b x + a\right)}{b^{2} g^{2} h - 2 \, a b g h^{2} + a^{2} h^{3}} - \frac{d^{2} e n \log\left(d x + c\right)}{d^{2} g^{2} h - 2 \, c d g h^{2} + c^{2} h^{3}} - \frac{{\left(2 \, a b d^{2} e g n - a^{2} d^{2} e h n - {\left(2 \, c d e g n - c^{2} e h n\right)} b^{2}\right)} \log\left(h x + g\right)}{{\left(d^{2} g^{2} h^{2} - 2 \, c d g h^{3} + c^{2} h^{4}\right)} a^{2} - 2 \, {\left(d^{2} g^{3} h - 2 \, c d g^{2} h^{2} + c^{2} g h^{3}\right)} a b + {\left(d^{2} g^{4} - 2 \, c d g^{3} h + c^{2} g^{2} h^{2}\right)} b^{2}} + \frac{b c e n - a d e n}{{\left(d g^{2} h - c g h^{2}\right)} a - {\left(d g^{3} - c g^{2} h\right)} b + {\left({\left(d g h^{2} - c h^{3}\right)} a - {\left(d g^{2} h - c g h^{2}\right)} b\right)} x}\right)} A B}{e} - \frac{A B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{h^{3} x^{2} + 2 \, g h^{2} x + g^{2} h} - \frac{A^{2}}{2 \, {\left(h^{3} x^{2} + 2 \, g h^{2} x + g^{2} h\right)}}"," ",0,"-1/2*B^2*(log((d*x + c)^n)^2/(h^3*x^2 + 2*g*h^2*x + g^2*h) + 2*integrate(-(d*h*x*log(e)^2 + c*h*log(e)^2 + (d*h*x + c*h)*log((b*x + a)^n)^2 + 2*(d*h*x*log(e) + c*h*log(e))*log((b*x + a)^n) + (d*g*n + (h*n - 2*h*log(e))*d*x - 2*c*h*log(e) - 2*(d*h*x + c*h)*log((b*x + a)^n))*log((d*x + c)^n))/(d*h^4*x^4 + c*g^3*h + (3*d*g*h^3 + c*h^4)*x^3 + 3*(d*g^2*h^2 + c*g*h^3)*x^2 + (d*g^3*h + 3*c*g^2*h^2)*x), x)) + (b^2*e*n*log(b*x + a)/(b^2*g^2*h - 2*a*b*g*h^2 + a^2*h^3) - d^2*e*n*log(d*x + c)/(d^2*g^2*h - 2*c*d*g*h^2 + c^2*h^3) - (2*a*b*d^2*e*g*n - a^2*d^2*e*h*n - (2*c*d*e*g*n - c^2*e*h*n)*b^2)*log(h*x + g)/((d^2*g^2*h^2 - 2*c*d*g*h^3 + c^2*h^4)*a^2 - 2*(d^2*g^3*h - 2*c*d*g^2*h^2 + c^2*g*h^3)*a*b + (d^2*g^4 - 2*c*d*g^3*h + c^2*g^2*h^2)*b^2) + (b*c*e*n - a*d*e*n)/((d*g^2*h - c*g*h^2)*a - (d*g^3 - c*g^2*h)*b + ((d*g*h^2 - c*h^3)*a - (d*g^2*h - c*g*h^2)*b)*x))*A*B/e - A*B*log((b*x + a)^n*e/(d*x + c)^n)/(h^3*x^2 + 2*g*h^2*x + g^2*h) - 1/2*A^2/(h^3*x^2 + 2*g*h^2*x + g^2*h)","F",0
309,0,0,0,0.000000," ","integrate((h*x+g)^2*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3,x, algorithm=""maxima"")","A^{2} B h^{2} x^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{3} \, A^{3} h^{2} x^{3} + 3 \, A^{2} B g h x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} g h x^{2} + 3 \, A^{2} B g^{2} x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} g^{2} x + \frac{3 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A^{2} B g^{2}}{e} - \frac{3 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A^{2} B g h}{e} + \frac{{\left(\frac{2 \, a^{3} e n \log\left(b x + a\right)}{b^{3}} - \frac{2 \, c^{3} e n \log\left(d x + c\right)}{d^{3}} - \frac{{\left(b^{2} c d e n - a b d^{2} e n\right)} x^{2} - 2 \, {\left(b^{2} c^{2} e n - a^{2} d^{2} e n\right)} x}{b^{2} d^{2}}\right)} A^{2} B h^{2}}{2 \, e} - \frac{2 \, {\left(B^{3} b^{3} d^{3} h^{2} x^{3} + 3 \, B^{3} b^{3} d^{3} g h x^{2} + 3 \, B^{3} b^{3} d^{3} g^{2} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{3} + 3 \, {\left(2 \, {\left(3 \, c d^{2} g^{2} n - 3 \, c^{2} d g h n + c^{3} h^{2} n\right)} B^{3} b^{3} \log\left(d x + c\right) - 2 \, {\left(3 \, a b^{2} d^{3} g^{2} n - 3 \, a^{2} b d^{3} g h n + a^{3} d^{3} h^{2} n\right)} B^{3} \log\left(b x + a\right) - 2 \, {\left(B^{3} b^{3} d^{3} h^{2} \log\left(e\right) + A B^{2} b^{3} d^{3} h^{2}\right)} x^{3} - {\left(6 \, A B^{2} b^{3} d^{3} g h + {\left(a b^{2} d^{3} h^{2} n - {\left(c d^{2} h^{2} n - 6 \, d^{3} g h \log\left(e\right)\right)} b^{3}\right)} B^{3}\right)} x^{2} - 2 \, {\left(3 \, A B^{2} b^{3} d^{3} g^{2} + {\left(3 \, a b^{2} d^{3} g h n - a^{2} b d^{3} h^{2} n - {\left(3 \, c d^{2} g h n - c^{2} d h^{2} n - 3 \, d^{3} g^{2} \log\left(e\right)\right)} b^{3}\right)} B^{3}\right)} x - 2 \, {\left(B^{3} b^{3} d^{3} h^{2} x^{3} + 3 \, B^{3} b^{3} d^{3} g h x^{2} + 3 \, B^{3} b^{3} d^{3} g^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{6 \, b^{3} d^{3}} - \int -\frac{B^{3} b^{3} c d^{2} g^{2} \log\left(e\right)^{3} + 3 \, A B^{2} b^{3} c d^{2} g^{2} \log\left(e\right)^{2} + {\left(B^{3} b^{3} d^{3} h^{2} \log\left(e\right)^{3} + 3 \, A B^{2} b^{3} d^{3} h^{2} \log\left(e\right)^{2}\right)} x^{3} + {\left(B^{3} b^{3} d^{3} h^{2} x^{3} + B^{3} b^{3} c d^{2} g^{2} + {\left(2 \, d^{3} g h + c d^{2} h^{2}\right)} B^{3} b^{3} x^{2} + {\left(d^{3} g^{2} + 2 \, c d^{2} g h\right)} B^{3} b^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + {\left(3 \, {\left(2 \, d^{3} g h \log\left(e\right)^{2} + c d^{2} h^{2} \log\left(e\right)^{2}\right)} A B^{2} b^{3} + {\left(2 \, d^{3} g h \log\left(e\right)^{3} + c d^{2} h^{2} \log\left(e\right)^{3}\right)} B^{3} b^{3}\right)} x^{2} + 3 \, {\left(B^{3} b^{3} c d^{2} g^{2} \log\left(e\right) + A B^{2} b^{3} c d^{2} g^{2} + {\left(B^{3} b^{3} d^{3} h^{2} \log\left(e\right) + A B^{2} b^{3} d^{3} h^{2}\right)} x^{3} + {\left({\left(2 \, d^{3} g h + c d^{2} h^{2}\right)} A B^{2} b^{3} + {\left(2 \, d^{3} g h \log\left(e\right) + c d^{2} h^{2} \log\left(e\right)\right)} B^{3} b^{3}\right)} x^{2} + {\left({\left(d^{3} g^{2} + 2 \, c d^{2} g h\right)} A B^{2} b^{3} + {\left(d^{3} g^{2} \log\left(e\right) + 2 \, c d^{2} g h \log\left(e\right)\right)} B^{3} b^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(3 \, {\left(d^{3} g^{2} \log\left(e\right)^{2} + 2 \, c d^{2} g h \log\left(e\right)^{2}\right)} A B^{2} b^{3} + {\left(d^{3} g^{2} \log\left(e\right)^{3} + 2 \, c d^{2} g h \log\left(e\right)^{3}\right)} B^{3} b^{3}\right)} x + 3 \, {\left(B^{3} b^{3} c d^{2} g^{2} \log\left(e\right)^{2} + 2 \, A B^{2} b^{3} c d^{2} g^{2} \log\left(e\right) + {\left(B^{3} b^{3} d^{3} h^{2} \log\left(e\right)^{2} + 2 \, A B^{2} b^{3} d^{3} h^{2} \log\left(e\right)\right)} x^{3} + {\left(2 \, {\left(2 \, d^{3} g h \log\left(e\right) + c d^{2} h^{2} \log\left(e\right)\right)} A B^{2} b^{3} + {\left(2 \, d^{3} g h \log\left(e\right)^{2} + c d^{2} h^{2} \log\left(e\right)^{2}\right)} B^{3} b^{3}\right)} x^{2} + {\left(2 \, {\left(d^{3} g^{2} \log\left(e\right) + 2 \, c d^{2} g h \log\left(e\right)\right)} A B^{2} b^{3} + {\left(d^{3} g^{2} \log\left(e\right)^{2} + 2 \, c d^{2} g h \log\left(e\right)^{2}\right)} B^{3} b^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - {\left(3 \, B^{3} b^{3} c d^{2} g^{2} \log\left(e\right)^{2} + 6 \, A B^{2} b^{3} c d^{2} g^{2} \log\left(e\right) - 2 \, {\left(3 \, c d^{2} g^{2} n^{2} - 3 \, c^{2} d g h n^{2} + c^{3} h^{2} n^{2}\right)} B^{3} b^{3} \log\left(d x + c\right) + 2 \, {\left(3 \, a b^{2} d^{3} g^{2} n^{2} - 3 \, a^{2} b d^{3} g h n^{2} + a^{3} d^{3} h^{2} n^{2}\right)} B^{3} \log\left(b x + a\right) + {\left(2 \, {\left(h^{2} n + 3 \, h^{2} \log\left(e\right)\right)} A B^{2} b^{3} d^{3} + {\left(2 \, h^{2} n \log\left(e\right) + 3 \, h^{2} \log\left(e\right)^{2}\right)} B^{3} b^{3} d^{3}\right)} x^{3} + {\left(6 \, {\left(c d^{2} h^{2} \log\left(e\right) + {\left(g h n + 2 \, g h \log\left(e\right)\right)} d^{3}\right)} A B^{2} b^{3} + {\left(a b^{2} d^{3} h^{2} n^{2} - {\left({\left(h^{2} n^{2} - 3 \, h^{2} \log\left(e\right)^{2}\right)} c d^{2} - 6 \, {\left(g h n \log\left(e\right) + g h \log\left(e\right)^{2}\right)} d^{3}\right)} b^{3}\right)} B^{3}\right)} x^{2} + 3 \, {\left(B^{3} b^{3} d^{3} h^{2} x^{3} + B^{3} b^{3} c d^{2} g^{2} + {\left(2 \, d^{3} g h + c d^{2} h^{2}\right)} B^{3} b^{3} x^{2} + {\left(d^{3} g^{2} + 2 \, c d^{2} g h\right)} B^{3} b^{3} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(6 \, {\left(2 \, c d^{2} g h \log\left(e\right) + {\left(g^{2} n + g^{2} \log\left(e\right)\right)} d^{3}\right)} A B^{2} b^{3} + {\left(6 \, a b^{2} d^{3} g h n^{2} - 2 \, a^{2} b d^{3} h^{2} n^{2} + {\left(2 \, c^{2} d h^{2} n^{2} - 6 \, {\left(g h n^{2} - g h \log\left(e\right)^{2}\right)} c d^{2} + 3 \, {\left(2 \, g^{2} n \log\left(e\right) + g^{2} \log\left(e\right)^{2}\right)} d^{3}\right)} b^{3}\right)} B^{3}\right)} x + 2 \, {\left(3 \, B^{3} b^{3} c d^{2} g^{2} \log\left(e\right) + 3 \, A B^{2} b^{3} c d^{2} g^{2} + {\left(3 \, A B^{2} b^{3} d^{3} h^{2} + {\left(h^{2} n + 3 \, h^{2} \log\left(e\right)\right)} B^{3} b^{3} d^{3}\right)} x^{3} + 3 \, {\left({\left(2 \, d^{3} g h + c d^{2} h^{2}\right)} A B^{2} b^{3} + {\left(c d^{2} h^{2} \log\left(e\right) + {\left(g h n + 2 \, g h \log\left(e\right)\right)} d^{3}\right)} B^{3} b^{3}\right)} x^{2} + 3 \, {\left({\left(d^{3} g^{2} + 2 \, c d^{2} g h\right)} A B^{2} b^{3} + {\left(2 \, c d^{2} g h \log\left(e\right) + {\left(g^{2} n + g^{2} \log\left(e\right)\right)} d^{3}\right)} B^{3} b^{3}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{3} d^{3} x + b^{3} c d^{2}}\,{d x}"," ",0,"A^2*B*h^2*x^3*log((b*x + a)^n*e/(d*x + c)^n) + 1/3*A^3*h^2*x^3 + 3*A^2*B*g*h*x^2*log((b*x + a)^n*e/(d*x + c)^n) + A^3*g*h*x^2 + 3*A^2*B*g^2*x*log((b*x + a)^n*e/(d*x + c)^n) + A^3*g^2*x + 3*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A^2*B*g^2/e - 3*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A^2*B*g*h/e + 1/2*(2*a^3*e*n*log(b*x + a)/b^3 - 2*c^3*e*n*log(d*x + c)/d^3 - ((b^2*c*d*e*n - a*b*d^2*e*n)*x^2 - 2*(b^2*c^2*e*n - a^2*d^2*e*n)*x)/(b^2*d^2))*A^2*B*h^2/e - 1/6*(2*(B^3*b^3*d^3*h^2*x^3 + 3*B^3*b^3*d^3*g*h*x^2 + 3*B^3*b^3*d^3*g^2*x)*log((d*x + c)^n)^3 + 3*(2*(3*c*d^2*g^2*n - 3*c^2*d*g*h*n + c^3*h^2*n)*B^3*b^3*log(d*x + c) - 2*(3*a*b^2*d^3*g^2*n - 3*a^2*b*d^3*g*h*n + a^3*d^3*h^2*n)*B^3*log(b*x + a) - 2*(B^3*b^3*d^3*h^2*log(e) + A*B^2*b^3*d^3*h^2)*x^3 - (6*A*B^2*b^3*d^3*g*h + (a*b^2*d^3*h^2*n - (c*d^2*h^2*n - 6*d^3*g*h*log(e))*b^3)*B^3)*x^2 - 2*(3*A*B^2*b^3*d^3*g^2 + (3*a*b^2*d^3*g*h*n - a^2*b*d^3*h^2*n - (3*c*d^2*g*h*n - c^2*d*h^2*n - 3*d^3*g^2*log(e))*b^3)*B^3)*x - 2*(B^3*b^3*d^3*h^2*x^3 + 3*B^3*b^3*d^3*g*h*x^2 + 3*B^3*b^3*d^3*g^2*x)*log((b*x + a)^n))*log((d*x + c)^n)^2)/(b^3*d^3) - integrate(-(B^3*b^3*c*d^2*g^2*log(e)^3 + 3*A*B^2*b^3*c*d^2*g^2*log(e)^2 + (B^3*b^3*d^3*h^2*log(e)^3 + 3*A*B^2*b^3*d^3*h^2*log(e)^2)*x^3 + (B^3*b^3*d^3*h^2*x^3 + B^3*b^3*c*d^2*g^2 + (2*d^3*g*h + c*d^2*h^2)*B^3*b^3*x^2 + (d^3*g^2 + 2*c*d^2*g*h)*B^3*b^3*x)*log((b*x + a)^n)^3 + (3*(2*d^3*g*h*log(e)^2 + c*d^2*h^2*log(e)^2)*A*B^2*b^3 + (2*d^3*g*h*log(e)^3 + c*d^2*h^2*log(e)^3)*B^3*b^3)*x^2 + 3*(B^3*b^3*c*d^2*g^2*log(e) + A*B^2*b^3*c*d^2*g^2 + (B^3*b^3*d^3*h^2*log(e) + A*B^2*b^3*d^3*h^2)*x^3 + ((2*d^3*g*h + c*d^2*h^2)*A*B^2*b^3 + (2*d^3*g*h*log(e) + c*d^2*h^2*log(e))*B^3*b^3)*x^2 + ((d^3*g^2 + 2*c*d^2*g*h)*A*B^2*b^3 + (d^3*g^2*log(e) + 2*c*d^2*g*h*log(e))*B^3*b^3)*x)*log((b*x + a)^n)^2 + (3*(d^3*g^2*log(e)^2 + 2*c*d^2*g*h*log(e)^2)*A*B^2*b^3 + (d^3*g^2*log(e)^3 + 2*c*d^2*g*h*log(e)^3)*B^3*b^3)*x + 3*(B^3*b^3*c*d^2*g^2*log(e)^2 + 2*A*B^2*b^3*c*d^2*g^2*log(e) + (B^3*b^3*d^3*h^2*log(e)^2 + 2*A*B^2*b^3*d^3*h^2*log(e))*x^3 + (2*(2*d^3*g*h*log(e) + c*d^2*h^2*log(e))*A*B^2*b^3 + (2*d^3*g*h*log(e)^2 + c*d^2*h^2*log(e)^2)*B^3*b^3)*x^2 + (2*(d^3*g^2*log(e) + 2*c*d^2*g*h*log(e))*A*B^2*b^3 + (d^3*g^2*log(e)^2 + 2*c*d^2*g*h*log(e)^2)*B^3*b^3)*x)*log((b*x + a)^n) - (3*B^3*b^3*c*d^2*g^2*log(e)^2 + 6*A*B^2*b^3*c*d^2*g^2*log(e) - 2*(3*c*d^2*g^2*n^2 - 3*c^2*d*g*h*n^2 + c^3*h^2*n^2)*B^3*b^3*log(d*x + c) + 2*(3*a*b^2*d^3*g^2*n^2 - 3*a^2*b*d^3*g*h*n^2 + a^3*d^3*h^2*n^2)*B^3*log(b*x + a) + (2*(h^2*n + 3*h^2*log(e))*A*B^2*b^3*d^3 + (2*h^2*n*log(e) + 3*h^2*log(e)^2)*B^3*b^3*d^3)*x^3 + (6*(c*d^2*h^2*log(e) + (g*h*n + 2*g*h*log(e))*d^3)*A*B^2*b^3 + (a*b^2*d^3*h^2*n^2 - ((h^2*n^2 - 3*h^2*log(e)^2)*c*d^2 - 6*(g*h*n*log(e) + g*h*log(e)^2)*d^3)*b^3)*B^3)*x^2 + 3*(B^3*b^3*d^3*h^2*x^3 + B^3*b^3*c*d^2*g^2 + (2*d^3*g*h + c*d^2*h^2)*B^3*b^3*x^2 + (d^3*g^2 + 2*c*d^2*g*h)*B^3*b^3*x)*log((b*x + a)^n)^2 + (6*(2*c*d^2*g*h*log(e) + (g^2*n + g^2*log(e))*d^3)*A*B^2*b^3 + (6*a*b^2*d^3*g*h*n^2 - 2*a^2*b*d^3*h^2*n^2 + (2*c^2*d*h^2*n^2 - 6*(g*h*n^2 - g*h*log(e)^2)*c*d^2 + 3*(2*g^2*n*log(e) + g^2*log(e)^2)*d^3)*b^3)*B^3)*x + 2*(3*B^3*b^3*c*d^2*g^2*log(e) + 3*A*B^2*b^3*c*d^2*g^2 + (3*A*B^2*b^3*d^3*h^2 + (h^2*n + 3*h^2*log(e))*B^3*b^3*d^3)*x^3 + 3*((2*d^3*g*h + c*d^2*h^2)*A*B^2*b^3 + (c*d^2*h^2*log(e) + (g*h*n + 2*g*h*log(e))*d^3)*B^3*b^3)*x^2 + 3*((d^3*g^2 + 2*c*d^2*g*h)*A*B^2*b^3 + (2*c*d^2*g*h*log(e) + (g^2*n + g^2*log(e))*d^3)*B^3*b^3)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^3*d^3*x + b^3*c*d^2), x)","F",0
310,0,0,0,0.000000," ","integrate((h*x+g)*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3,x, algorithm=""maxima"")","\frac{3}{2} \, A^{2} B h x^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + \frac{1}{2} \, A^{3} h x^{2} + 3 \, A^{2} B g x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} g x + \frac{3 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A^{2} B g}{e} - \frac{3 \, {\left(\frac{a^{2} e n \log\left(b x + a\right)}{b^{2}} - \frac{c^{2} e n \log\left(d x + c\right)}{d^{2}} + \frac{{\left(b c e n - a d e n\right)} x}{b d}\right)} A^{2} B h}{2 \, e} - \frac{{\left(B^{3} b^{2} d^{2} h x^{2} + 2 \, B^{3} b^{2} d^{2} g x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{3} + 3 \, {\left({\left(2 \, c d g n - c^{2} h n\right)} B^{3} b^{2} \log\left(d x + c\right) - {\left(2 \, a b d^{2} g n - a^{2} d^{2} h n\right)} B^{3} \log\left(b x + a\right) - {\left(B^{3} b^{2} d^{2} h \log\left(e\right) + A B^{2} b^{2} d^{2} h\right)} x^{2} - {\left(2 \, A B^{2} b^{2} d^{2} g + {\left(a b d^{2} h n - {\left(c d h n - 2 \, d^{2} g \log\left(e\right)\right)} b^{2}\right)} B^{3}\right)} x - {\left(B^{3} b^{2} d^{2} h x^{2} + 2 \, B^{3} b^{2} d^{2} g x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{2 \, b^{2} d^{2}} - \int -\frac{B^{3} b^{2} c d g \log\left(e\right)^{3} + 3 \, A B^{2} b^{2} c d g \log\left(e\right)^{2} + {\left(B^{3} b^{2} d^{2} h x^{2} + B^{3} b^{2} c d g + {\left(d^{2} g + c d h\right)} B^{3} b^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + {\left(B^{3} b^{2} d^{2} h \log\left(e\right)^{3} + 3 \, A B^{2} b^{2} d^{2} h \log\left(e\right)^{2}\right)} x^{2} + 3 \, {\left(B^{3} b^{2} c d g \log\left(e\right) + A B^{2} b^{2} c d g + {\left(B^{3} b^{2} d^{2} h \log\left(e\right) + A B^{2} b^{2} d^{2} h\right)} x^{2} + {\left({\left(d^{2} g + c d h\right)} A B^{2} b^{2} + {\left(d^{2} g \log\left(e\right) + c d h \log\left(e\right)\right)} B^{3} b^{2}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(3 \, {\left(d^{2} g \log\left(e\right)^{2} + c d h \log\left(e\right)^{2}\right)} A B^{2} b^{2} + {\left(d^{2} g \log\left(e\right)^{3} + c d h \log\left(e\right)^{3}\right)} B^{3} b^{2}\right)} x + 3 \, {\left(B^{3} b^{2} c d g \log\left(e\right)^{2} + 2 \, A B^{2} b^{2} c d g \log\left(e\right) + {\left(B^{3} b^{2} d^{2} h \log\left(e\right)^{2} + 2 \, A B^{2} b^{2} d^{2} h \log\left(e\right)\right)} x^{2} + {\left(2 \, {\left(d^{2} g \log\left(e\right) + c d h \log\left(e\right)\right)} A B^{2} b^{2} + {\left(d^{2} g \log\left(e\right)^{2} + c d h \log\left(e\right)^{2}\right)} B^{3} b^{2}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 3 \, {\left(B^{3} b^{2} c d g \log\left(e\right)^{2} + 2 \, A B^{2} b^{2} c d g \log\left(e\right) - {\left(2 \, c d g n^{2} - c^{2} h n^{2}\right)} B^{3} b^{2} \log\left(d x + c\right) + {\left(2 \, a b d^{2} g n^{2} - a^{2} d^{2} h n^{2}\right)} B^{3} \log\left(b x + a\right) + {\left({\left(h n + 2 \, h \log\left(e\right)\right)} A B^{2} b^{2} d^{2} + {\left(h n \log\left(e\right) + h \log\left(e\right)^{2}\right)} B^{3} b^{2} d^{2}\right)} x^{2} + {\left(B^{3} b^{2} d^{2} h x^{2} + B^{3} b^{2} c d g + {\left(d^{2} g + c d h\right)} B^{3} b^{2} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(2 \, {\left(c d h \log\left(e\right) + {\left(g n + g \log\left(e\right)\right)} d^{2}\right)} A B^{2} b^{2} + {\left(a b d^{2} h n^{2} - {\left({\left(h n^{2} - h \log\left(e\right)^{2}\right)} c d - {\left(2 \, g n \log\left(e\right) + g \log\left(e\right)^{2}\right)} d^{2}\right)} b^{2}\right)} B^{3}\right)} x + {\left(2 \, B^{3} b^{2} c d g \log\left(e\right) + 2 \, A B^{2} b^{2} c d g + {\left({\left(h n + 2 \, h \log\left(e\right)\right)} B^{3} b^{2} d^{2} + 2 \, A B^{2} b^{2} d^{2} h\right)} x^{2} + 2 \, {\left({\left(d^{2} g + c d h\right)} A B^{2} b^{2} + {\left(c d h \log\left(e\right) + {\left(g n + g \log\left(e\right)\right)} d^{2}\right)} B^{3} b^{2}\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b^{2} d^{2} x + b^{2} c d}\,{d x}"," ",0,"3/2*A^2*B*h*x^2*log((b*x + a)^n*e/(d*x + c)^n) + 1/2*A^3*h*x^2 + 3*A^2*B*g*x*log((b*x + a)^n*e/(d*x + c)^n) + A^3*g*x + 3*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A^2*B*g/e - 3/2*(a^2*e*n*log(b*x + a)/b^2 - c^2*e*n*log(d*x + c)/d^2 + (b*c*e*n - a*d*e*n)*x/(b*d))*A^2*B*h/e - 1/2*((B^3*b^2*d^2*h*x^2 + 2*B^3*b^2*d^2*g*x)*log((d*x + c)^n)^3 + 3*((2*c*d*g*n - c^2*h*n)*B^3*b^2*log(d*x + c) - (2*a*b*d^2*g*n - a^2*d^2*h*n)*B^3*log(b*x + a) - (B^3*b^2*d^2*h*log(e) + A*B^2*b^2*d^2*h)*x^2 - (2*A*B^2*b^2*d^2*g + (a*b*d^2*h*n - (c*d*h*n - 2*d^2*g*log(e))*b^2)*B^3)*x - (B^3*b^2*d^2*h*x^2 + 2*B^3*b^2*d^2*g*x)*log((b*x + a)^n))*log((d*x + c)^n)^2)/(b^2*d^2) - integrate(-(B^3*b^2*c*d*g*log(e)^3 + 3*A*B^2*b^2*c*d*g*log(e)^2 + (B^3*b^2*d^2*h*x^2 + B^3*b^2*c*d*g + (d^2*g + c*d*h)*B^3*b^2*x)*log((b*x + a)^n)^3 + (B^3*b^2*d^2*h*log(e)^3 + 3*A*B^2*b^2*d^2*h*log(e)^2)*x^2 + 3*(B^3*b^2*c*d*g*log(e) + A*B^2*b^2*c*d*g + (B^3*b^2*d^2*h*log(e) + A*B^2*b^2*d^2*h)*x^2 + ((d^2*g + c*d*h)*A*B^2*b^2 + (d^2*g*log(e) + c*d*h*log(e))*B^3*b^2)*x)*log((b*x + a)^n)^2 + (3*(d^2*g*log(e)^2 + c*d*h*log(e)^2)*A*B^2*b^2 + (d^2*g*log(e)^3 + c*d*h*log(e)^3)*B^3*b^2)*x + 3*(B^3*b^2*c*d*g*log(e)^2 + 2*A*B^2*b^2*c*d*g*log(e) + (B^3*b^2*d^2*h*log(e)^2 + 2*A*B^2*b^2*d^2*h*log(e))*x^2 + (2*(d^2*g*log(e) + c*d*h*log(e))*A*B^2*b^2 + (d^2*g*log(e)^2 + c*d*h*log(e)^2)*B^3*b^2)*x)*log((b*x + a)^n) - 3*(B^3*b^2*c*d*g*log(e)^2 + 2*A*B^2*b^2*c*d*g*log(e) - (2*c*d*g*n^2 - c^2*h*n^2)*B^3*b^2*log(d*x + c) + (2*a*b*d^2*g*n^2 - a^2*d^2*h*n^2)*B^3*log(b*x + a) + ((h*n + 2*h*log(e))*A*B^2*b^2*d^2 + (h*n*log(e) + h*log(e)^2)*B^3*b^2*d^2)*x^2 + (B^3*b^2*d^2*h*x^2 + B^3*b^2*c*d*g + (d^2*g + c*d*h)*B^3*b^2*x)*log((b*x + a)^n)^2 + (2*(c*d*h*log(e) + (g*n + g*log(e))*d^2)*A*B^2*b^2 + (a*b*d^2*h*n^2 - ((h*n^2 - h*log(e)^2)*c*d - (2*g*n*log(e) + g*log(e)^2)*d^2)*b^2)*B^3)*x + (2*B^3*b^2*c*d*g*log(e) + 2*A*B^2*b^2*c*d*g + ((h*n + 2*h*log(e))*B^3*b^2*d^2 + 2*A*B^2*b^2*d^2*h)*x^2 + 2*((d^2*g + c*d*h)*A*B^2*b^2 + (c*d*h*log(e) + (g*n + g*log(e))*d^2)*B^3*b^2)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b^2*d^2*x + b^2*c*d), x)","F",0
311,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3,x, algorithm=""maxima"")","3 \, A^{2} B x \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3} x + \frac{3 \, {\left(\frac{a e n \log\left(b x + a\right)}{b} - \frac{c e n \log\left(d x + c\right)}{d}\right)} A^{2} B}{e} - \frac{B^{3} b d x \log\left({\left(d x + c\right)}^{n}\right)^{3} - 3 \, {\left(B^{3} a d n \log\left(b x + a\right) - B^{3} b c n \log\left(d x + c\right) + B^{3} b d x \log\left({\left(b x + a\right)}^{n}\right) + {\left(B^{3} b d \log\left(e\right) + A B^{2} b d\right)} x\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2}}{b d} - \int -\frac{B^{3} b c \log\left(e\right)^{3} + 3 \, A B^{2} b c \log\left(e\right)^{2} + {\left(B^{3} b d x + B^{3} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + 3 \, {\left(B^{3} b c \log\left(e\right) + A B^{2} b c + {\left(B^{3} b d \log\left(e\right) + A B^{2} b d\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{3} b d \log\left(e\right)^{3} + 3 \, A B^{2} b d \log\left(e\right)^{2}\right)} x + 3 \, {\left(B^{3} b c \log\left(e\right)^{2} + 2 \, A B^{2} b c \log\left(e\right) + {\left(B^{3} b d \log\left(e\right)^{2} + 2 \, A B^{2} b d \log\left(e\right)\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 3 \, {\left(2 \, B^{3} a d n^{2} \log\left(b x + a\right) - 2 \, B^{3} b c n^{2} \log\left(d x + c\right) + B^{3} b c \log\left(e\right)^{2} + 2 \, A B^{2} b c \log\left(e\right) + {\left(B^{3} b d x + B^{3} b c\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left({\left(2 \, n \log\left(e\right) + \log\left(e\right)^{2}\right)} B^{3} b d + 2 \, A B^{2} b d {\left(n + \log\left(e\right)\right)}\right)} x + 2 \, {\left(B^{3} b c \log\left(e\right) + A B^{2} b c + {\left(B^{3} b d {\left(n + \log\left(e\right)\right)} + A B^{2} b d\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{b d x + b c}\,{d x}"," ",0,"3*A^2*B*x*log((b*x + a)^n*e/(d*x + c)^n) + A^3*x + 3*(a*e*n*log(b*x + a)/b - c*e*n*log(d*x + c)/d)*A^2*B/e - (B^3*b*d*x*log((d*x + c)^n)^3 - 3*(B^3*a*d*n*log(b*x + a) - B^3*b*c*n*log(d*x + c) + B^3*b*d*x*log((b*x + a)^n) + (B^3*b*d*log(e) + A*B^2*b*d)*x)*log((d*x + c)^n)^2)/(b*d) - integrate(-(B^3*b*c*log(e)^3 + 3*A*B^2*b*c*log(e)^2 + (B^3*b*d*x + B^3*b*c)*log((b*x + a)^n)^3 + 3*(B^3*b*c*log(e) + A*B^2*b*c + (B^3*b*d*log(e) + A*B^2*b*d)*x)*log((b*x + a)^n)^2 + (B^3*b*d*log(e)^3 + 3*A*B^2*b*d*log(e)^2)*x + 3*(B^3*b*c*log(e)^2 + 2*A*B^2*b*c*log(e) + (B^3*b*d*log(e)^2 + 2*A*B^2*b*d*log(e))*x)*log((b*x + a)^n) - 3*(2*B^3*a*d*n^2*log(b*x + a) - 2*B^3*b*c*n^2*log(d*x + c) + B^3*b*c*log(e)^2 + 2*A*B^2*b*c*log(e) + (B^3*b*d*x + B^3*b*c)*log((b*x + a)^n)^2 + ((2*n*log(e) + log(e)^2)*B^3*b*d + 2*A*B^2*b*d*(n + log(e)))*x + 2*(B^3*b*c*log(e) + A*B^2*b*c + (B^3*b*d*(n + log(e)) + A*B^2*b*d)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(b*d*x + b*c), x)","F",0
312,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(h*x+g),x, algorithm=""maxima"")","\frac{A^{3} \log\left(h x + g\right)}{h} - \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)}{h x + g}\,{d x}"," ",0,"A^3*log(h*x + 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))/(h*x + g), x)","F",0
313,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(h*x+g)^2,x, algorithm=""maxima"")","\frac{B^{3} \log\left({\left(d x + c\right)}^{n}\right)^{3}}{h^{2} x + g h} + \frac{3 \, {\left(\frac{b e n \log\left(b x + a\right)}{b g h - a h^{2}} - \frac{d e n \log\left(d x + c\right)}{d g h - c h^{2}} - \frac{{\left(b c e n - a d e n\right)} \log\left(h x + g\right)}{{\left(d g h - c h^{2}\right)} a - {\left(d g^{2} - c g h\right)} b}\right)} A^{2} B}{e} - \frac{3 \, A^{2} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{h^{2} x + g h} - \frac{A^{3}}{h^{2} x + g h} + \int \frac{B^{3} c h \log\left(e\right)^{3} + 3 \, A B^{2} c h \log\left(e\right)^{2} + {\left(B^{3} d h x + B^{3} c h\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + 3 \, {\left(B^{3} c h \log\left(e\right) + A B^{2} c h + {\left(B^{3} d h \log\left(e\right) + A B^{2} d h\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(A B^{2} c h - {\left(d g n - c h \log\left(e\right)\right)} B^{3} - {\left({\left(h n - h \log\left(e\right)\right)} B^{3} d - A B^{2} d h\right)} x + {\left(B^{3} d h x + B^{3} c h\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + {\left(B^{3} d h \log\left(e\right)^{3} + 3 \, A B^{2} d h \log\left(e\right)^{2}\right)} x + 3 \, {\left(B^{3} c h \log\left(e\right)^{2} + 2 \, A B^{2} c h \log\left(e\right) + {\left(B^{3} d h \log\left(e\right)^{2} + 2 \, A B^{2} d h \log\left(e\right)\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 3 \, {\left(B^{3} c h \log\left(e\right)^{2} + 2 \, A B^{2} c h \log\left(e\right) + {\left(B^{3} d h x + B^{3} c h\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{3} d h \log\left(e\right)^{2} + 2 \, A B^{2} d h \log\left(e\right)\right)} x + 2 \, {\left(B^{3} c h \log\left(e\right) + A B^{2} c h + {\left(B^{3} d h \log\left(e\right) + A B^{2} d h\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{d h^{3} x^{3} + c g^{2} h + {\left(2 \, d g h^{2} + c h^{3}\right)} x^{2} + {\left(d g^{2} h + 2 \, c g h^{2}\right)} x}\,{d x}"," ",0,"B^3*log((d*x + c)^n)^3/(h^2*x + g*h) + 3*(b*e*n*log(b*x + a)/(b*g*h - a*h^2) - d*e*n*log(d*x + c)/(d*g*h - c*h^2) - (b*c*e*n - a*d*e*n)*log(h*x + g)/((d*g*h - c*h^2)*a - (d*g^2 - c*g*h)*b))*A^2*B/e - 3*A^2*B*log((b*x + a)^n*e/(d*x + c)^n)/(h^2*x + g*h) - A^3/(h^2*x + g*h) + integrate((B^3*c*h*log(e)^3 + 3*A*B^2*c*h*log(e)^2 + (B^3*d*h*x + B^3*c*h)*log((b*x + a)^n)^3 + 3*(B^3*c*h*log(e) + A*B^2*c*h + (B^3*d*h*log(e) + A*B^2*d*h)*x)*log((b*x + a)^n)^2 + 3*(A*B^2*c*h - (d*g*n - c*h*log(e))*B^3 - ((h*n - h*log(e))*B^3*d - A*B^2*d*h)*x + (B^3*d*h*x + B^3*c*h)*log((b*x + a)^n))*log((d*x + c)^n)^2 + (B^3*d*h*log(e)^3 + 3*A*B^2*d*h*log(e)^2)*x + 3*(B^3*c*h*log(e)^2 + 2*A*B^2*c*h*log(e) + (B^3*d*h*log(e)^2 + 2*A*B^2*d*h*log(e))*x)*log((b*x + a)^n) - 3*(B^3*c*h*log(e)^2 + 2*A*B^2*c*h*log(e) + (B^3*d*h*x + B^3*c*h)*log((b*x + a)^n)^2 + (B^3*d*h*log(e)^2 + 2*A*B^2*d*h*log(e))*x + 2*(B^3*c*h*log(e) + A*B^2*c*h + (B^3*d*h*log(e) + A*B^2*d*h)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(d*h^3*x^3 + c*g^2*h + (2*d*g*h^2 + c*h^3)*x^2 + (d*g^2*h + 2*c*g*h^2)*x), x)","F",0
314,0,0,0,0.000000," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(h*x+g)^3,x, algorithm=""maxima"")","\frac{B^{3} \log\left({\left(d x + c\right)}^{n}\right)^{3}}{2 \, {\left(h^{3} x^{2} + 2 \, g h^{2} x + g^{2} h\right)}} + \frac{3 \, {\left(\frac{b^{2} e n \log\left(b x + a\right)}{b^{2} g^{2} h - 2 \, a b g h^{2} + a^{2} h^{3}} - \frac{d^{2} e n \log\left(d x + c\right)}{d^{2} g^{2} h - 2 \, c d g h^{2} + c^{2} h^{3}} - \frac{{\left(2 \, a b d^{2} e g n - a^{2} d^{2} e h n - {\left(2 \, c d e g n - c^{2} e h n\right)} b^{2}\right)} \log\left(h x + g\right)}{{\left(d^{2} g^{2} h^{2} - 2 \, c d g h^{3} + c^{2} h^{4}\right)} a^{2} - 2 \, {\left(d^{2} g^{3} h - 2 \, c d g^{2} h^{2} + c^{2} g h^{3}\right)} a b + {\left(d^{2} g^{4} - 2 \, c d g^{3} h + c^{2} g^{2} h^{2}\right)} b^{2}} + \frac{b c e n - a d e n}{{\left(d g^{2} h - c g h^{2}\right)} a - {\left(d g^{3} - c g^{2} h\right)} b + {\left({\left(d g h^{2} - c h^{3}\right)} a - {\left(d g^{2} h - c g h^{2}\right)} b\right)} x}\right)} A^{2} B}{2 \, e} - \frac{3 \, A^{2} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}{2 \, {\left(h^{3} x^{2} + 2 \, g h^{2} x + g^{2} h\right)}} - \frac{A^{3}}{2 \, {\left(h^{3} x^{2} + 2 \, g h^{2} x + g^{2} h\right)}} + \int \frac{2 \, B^{3} c h \log\left(e\right)^{3} + 6 \, A B^{2} c h \log\left(e\right)^{2} + 2 \, {\left(B^{3} d h x + B^{3} c h\right)} \log\left({\left(b x + a\right)}^{n}\right)^{3} + 6 \, {\left(B^{3} c h \log\left(e\right) + A B^{2} c h + {\left(B^{3} d h \log\left(e\right) + A B^{2} d h\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + 3 \, {\left(2 \, A B^{2} c h - {\left(d g n - 2 \, c h \log\left(e\right)\right)} B^{3} - {\left({\left(h n - 2 \, h \log\left(e\right)\right)} B^{3} d - 2 \, A B^{2} d h\right)} x + 2 \, {\left(B^{3} d h x + B^{3} c h\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)^{2} + 2 \, {\left(B^{3} d h \log\left(e\right)^{3} + 3 \, A B^{2} d h \log\left(e\right)^{2}\right)} x + 6 \, {\left(B^{3} c h \log\left(e\right)^{2} + 2 \, A B^{2} c h \log\left(e\right) + {\left(B^{3} d h \log\left(e\right)^{2} + 2 \, A B^{2} d h \log\left(e\right)\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right) - 6 \, {\left(B^{3} c h \log\left(e\right)^{2} + 2 \, A B^{2} c h \log\left(e\right) + {\left(B^{3} d h x + B^{3} c h\right)} \log\left({\left(b x + a\right)}^{n}\right)^{2} + {\left(B^{3} d h \log\left(e\right)^{2} + 2 \, A B^{2} d h \log\left(e\right)\right)} x + 2 \, {\left(B^{3} c h \log\left(e\right) + A B^{2} c h + {\left(B^{3} d h \log\left(e\right) + A B^{2} d h\right)} x\right)} \log\left({\left(b x + a\right)}^{n}\right)\right)} \log\left({\left(d x + c\right)}^{n}\right)}{2 \, {\left(d h^{4} x^{4} + c g^{3} h + {\left(3 \, d g h^{3} + c h^{4}\right)} x^{3} + 3 \, {\left(d g^{2} h^{2} + c g h^{3}\right)} x^{2} + {\left(d g^{3} h + 3 \, c g^{2} h^{2}\right)} x\right)}}\,{d x}"," ",0,"1/2*B^3*log((d*x + c)^n)^3/(h^3*x^2 + 2*g*h^2*x + g^2*h) + 3/2*(b^2*e*n*log(b*x + a)/(b^2*g^2*h - 2*a*b*g*h^2 + a^2*h^3) - d^2*e*n*log(d*x + c)/(d^2*g^2*h - 2*c*d*g*h^2 + c^2*h^3) - (2*a*b*d^2*e*g*n - a^2*d^2*e*h*n - (2*c*d*e*g*n - c^2*e*h*n)*b^2)*log(h*x + g)/((d^2*g^2*h^2 - 2*c*d*g*h^3 + c^2*h^4)*a^2 - 2*(d^2*g^3*h - 2*c*d*g^2*h^2 + c^2*g*h^3)*a*b + (d^2*g^4 - 2*c*d*g^3*h + c^2*g^2*h^2)*b^2) + (b*c*e*n - a*d*e*n)/((d*g^2*h - c*g*h^2)*a - (d*g^3 - c*g^2*h)*b + ((d*g*h^2 - c*h^3)*a - (d*g^2*h - c*g*h^2)*b)*x))*A^2*B/e - 3/2*A^2*B*log((b*x + a)^n*e/(d*x + c)^n)/(h^3*x^2 + 2*g*h^2*x + g^2*h) - 1/2*A^3/(h^3*x^2 + 2*g*h^2*x + g^2*h) + integrate(1/2*(2*B^3*c*h*log(e)^3 + 6*A*B^2*c*h*log(e)^2 + 2*(B^3*d*h*x + B^3*c*h)*log((b*x + a)^n)^3 + 6*(B^3*c*h*log(e) + A*B^2*c*h + (B^3*d*h*log(e) + A*B^2*d*h)*x)*log((b*x + a)^n)^2 + 3*(2*A*B^2*c*h - (d*g*n - 2*c*h*log(e))*B^3 - ((h*n - 2*h*log(e))*B^3*d - 2*A*B^2*d*h)*x + 2*(B^3*d*h*x + B^3*c*h)*log((b*x + a)^n))*log((d*x + c)^n)^2 + 2*(B^3*d*h*log(e)^3 + 3*A*B^2*d*h*log(e)^2)*x + 6*(B^3*c*h*log(e)^2 + 2*A*B^2*c*h*log(e) + (B^3*d*h*log(e)^2 + 2*A*B^2*d*h*log(e))*x)*log((b*x + a)^n) - 6*(B^3*c*h*log(e)^2 + 2*A*B^2*c*h*log(e) + (B^3*d*h*x + B^3*c*h)*log((b*x + a)^n)^2 + (B^3*d*h*log(e)^2 + 2*A*B^2*d*h*log(e))*x + 2*(B^3*c*h*log(e) + A*B^2*c*h + (B^3*d*h*log(e) + A*B^2*d*h)*x)*log((b*x + a)^n))*log((d*x + c)^n))/(d*h^4*x^4 + c*g^3*h + (3*d*g*h^3 + c*h^4)*x^3 + 3*(d*g^2*h^2 + c*g*h^3)*x^2 + (d*g^3*h + 3*c*g^2*h^2)*x), x)","F",0
