1,1,504,0,0.519603," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{24 \, A b^{5} d^{5} g^{3} i x^{5} + 6 \, {\left({\left(5 \, A - B\right)} b^{5} c d^{4} + {\left(15 \, A + B\right)} a b^{4} d^{5}\right)} g^{3} i x^{4} - 2 \, {\left(B b^{5} c^{2} d^{3} - 10 \, {\left(6 \, A - B\right)} a b^{4} c d^{4} - {\left(60 \, A + 11 \, B\right)} a^{2} b^{3} d^{5}\right)} g^{3} i x^{3} + 3 \, {\left(B b^{5} c^{3} d^{2} - 5 \, B a b^{4} c^{2} d^{3} + 5 \, {\left(12 \, A - B\right)} a^{2} b^{3} c d^{4} + {\left(20 \, A + 9 \, B\right)} a^{3} b^{2} d^{5}\right)} g^{3} i x^{2} - 6 \, {\left(B b^{5} c^{4} d - 5 \, B a b^{4} c^{3} d^{2} + 10 \, B a^{2} b^{3} c^{2} d^{3} - 5 \, {\left(4 \, A + B\right)} a^{3} b^{2} c d^{4} - B a^{4} b d^{5}\right)} g^{3} i x + 6 \, {\left(5 \, B a^{4} b c d^{4} - B a^{5} d^{5}\right)} g^{3} i \log\left(b x + a\right) + 6 \, {\left(B b^{5} c^{5} - 5 \, B a b^{4} c^{4} d + 10 \, B a^{2} b^{3} c^{3} d^{2} - 10 \, B a^{3} b^{2} c^{2} d^{3}\right)} g^{3} i \log\left(d x + c\right) + 6 \, {\left(4 \, B b^{5} d^{5} g^{3} i x^{5} + 20 \, B a^{3} b^{2} c d^{4} g^{3} i x + 5 \, {\left(B b^{5} c d^{4} + 3 \, B a b^{4} d^{5}\right)} g^{3} i x^{4} + 20 \, {\left(B a b^{4} c d^{4} + B a^{2} b^{3} d^{5}\right)} g^{3} i x^{3} + 10 \, {\left(3 \, B a^{2} b^{3} c d^{4} + B a^{3} b^{2} d^{5}\right)} g^{3} i x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{120 \, b^{2} d^{4}}"," ",0,"1/120*(24*A*b^5*d^5*g^3*i*x^5 + 6*((5*A - B)*b^5*c*d^4 + (15*A + B)*a*b^4*d^5)*g^3*i*x^4 - 2*(B*b^5*c^2*d^3 - 10*(6*A - B)*a*b^4*c*d^4 - (60*A + 11*B)*a^2*b^3*d^5)*g^3*i*x^3 + 3*(B*b^5*c^3*d^2 - 5*B*a*b^4*c^2*d^3 + 5*(12*A - B)*a^2*b^3*c*d^4 + (20*A + 9*B)*a^3*b^2*d^5)*g^3*i*x^2 - 6*(B*b^5*c^4*d - 5*B*a*b^4*c^3*d^2 + 10*B*a^2*b^3*c^2*d^3 - 5*(4*A + B)*a^3*b^2*c*d^4 - B*a^4*b*d^5)*g^3*i*x + 6*(5*B*a^4*b*c*d^4 - B*a^5*d^5)*g^3*i*log(b*x + a) + 6*(B*b^5*c^5 - 5*B*a*b^4*c^4*d + 10*B*a^2*b^3*c^3*d^2 - 10*B*a^3*b^2*c^2*d^3)*g^3*i*log(d*x + c) + 6*(4*B*b^5*d^5*g^3*i*x^5 + 20*B*a^3*b^2*c*d^4*g^3*i*x + 5*(B*b^5*c*d^4 + 3*B*a*b^4*d^5)*g^3*i*x^4 + 20*(B*a*b^4*c*d^4 + B*a^2*b^3*d^5)*g^3*i*x^3 + 10*(3*B*a^2*b^3*c*d^4 + B*a^3*b^2*d^5)*g^3*i*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^2*d^4)","B",0
2,1,370,0,0.472790," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{6 \, A b^{4} d^{4} g^{2} i x^{4} + 2 \, {\left({\left(4 \, A - B\right)} b^{4} c d^{3} + {\left(8 \, A + B\right)} a b^{3} d^{4}\right)} g^{2} i x^{3} - {\left(B b^{4} c^{2} d^{2} - 4 \, {\left(6 \, A - B\right)} a b^{3} c d^{3} - {\left(12 \, A + 5 \, B\right)} a^{2} b^{2} d^{4}\right)} g^{2} i x^{2} + 2 \, {\left(B b^{4} c^{3} d - 4 \, B a b^{3} c^{2} d^{2} + 2 \, {\left(6 \, A + B\right)} a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} g^{2} i x + 2 \, {\left(4 \, B a^{3} b c d^{3} - B a^{4} d^{4}\right)} g^{2} i \log\left(b x + a\right) - 2 \, {\left(B b^{4} c^{4} - 4 \, B a b^{3} c^{3} d + 6 \, B a^{2} b^{2} c^{2} d^{2}\right)} g^{2} i \log\left(d x + c\right) + 2 \, {\left(3 \, B b^{4} d^{4} g^{2} i x^{4} + 12 \, B a^{2} b^{2} c d^{3} g^{2} i x + 4 \, {\left(B b^{4} c d^{3} + 2 \, B a b^{3} d^{4}\right)} g^{2} i x^{3} + 6 \, {\left(2 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} g^{2} i x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{24 \, b^{2} d^{3}}"," ",0,"1/24*(6*A*b^4*d^4*g^2*i*x^4 + 2*((4*A - B)*b^4*c*d^3 + (8*A + B)*a*b^3*d^4)*g^2*i*x^3 - (B*b^4*c^2*d^2 - 4*(6*A - B)*a*b^3*c*d^3 - (12*A + 5*B)*a^2*b^2*d^4)*g^2*i*x^2 + 2*(B*b^4*c^3*d - 4*B*a*b^3*c^2*d^2 + 2*(6*A + B)*a^2*b^2*c*d^3 + B*a^3*b*d^4)*g^2*i*x + 2*(4*B*a^3*b*c*d^3 - B*a^4*d^4)*g^2*i*log(b*x + a) - 2*(B*b^4*c^4 - 4*B*a*b^3*c^3*d + 6*B*a^2*b^2*c^2*d^2)*g^2*i*log(d*x + c) + 2*(3*B*b^4*d^4*g^2*i*x^4 + 12*B*a^2*b^2*c*d^3*g^2*i*x + 4*(B*b^4*c*d^3 + 2*B*a*b^3*d^4)*g^2*i*x^3 + 6*(2*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*g^2*i*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^2*d^3)","B",0
3,1,226,0,0.473262," ","integrate((b*g*x+a*g)*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{2 \, A b^{3} d^{3} g i x^{3} + {\left({\left(3 \, A - B\right)} b^{3} c d^{2} + {\left(3 \, A + B\right)} a b^{2} d^{3}\right)} g i x^{2} - {\left(B b^{3} c^{2} d - 6 \, A a b^{2} c d^{2} - B a^{2} b d^{3}\right)} g i x + {\left(3 \, B a^{2} b c d^{2} - B a^{3} d^{3}\right)} g i \log\left(b x + a\right) + {\left(B b^{3} c^{3} - 3 \, B a b^{2} c^{2} d\right)} g i \log\left(d x + c\right) + {\left(2 \, B b^{3} d^{3} g i x^{3} + 6 \, B a b^{2} c d^{2} g i x + 3 \, {\left(B b^{3} c d^{2} + B a b^{2} d^{3}\right)} g i x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{6 \, b^{2} d^{2}}"," ",0,"1/6*(2*A*b^3*d^3*g*i*x^3 + ((3*A - B)*b^3*c*d^2 + (3*A + B)*a*b^2*d^3)*g*i*x^2 - (B*b^3*c^2*d - 6*A*a*b^2*c*d^2 - B*a^2*b*d^3)*g*i*x + (3*B*a^2*b*c*d^2 - B*a^3*d^3)*g*i*log(b*x + a) + (B*b^3*c^3 - 3*B*a*b^2*c^2*d)*g*i*log(d*x + c) + (2*B*b^3*d^3*g*i*x^3 + 6*B*a*b^2*c*d^2*g*i*x + 3*(B*b^3*c*d^2 + B*a*b^2*d^3)*g*i*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^2*d^2)","A",0
4,1,127,0,0.460369," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{A b^{2} d^{2} i x^{2} - B b^{2} c^{2} i \log\left(d x + c\right) + {\left({\left(2 \, A - B\right)} b^{2} c d + B a b d^{2}\right)} i x + {\left(2 \, B a b c d - B a^{2} d^{2}\right)} i \log\left(b x + a\right) + {\left(B b^{2} d^{2} i x^{2} + 2 \, B b^{2} c d i x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{2 \, b^{2} d}"," ",0,"1/2*(A*b^2*d^2*i*x^2 - B*b^2*c^2*i*log(d*x + c) + ((2*A - B)*b^2*c*d + B*a*b*d^2)*i*x + (2*B*a*b*c*d - B*a^2*d^2)*i*log(b*x + a) + (B*b^2*d^2*i*x^2 + 2*B*b^2*c*d*i*x)*log((b*e*x + a*e)/(d*x + c)))/(b^2*d)","A",0
5,0,0,0,0.444240," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d i x + A c i + {\left(B d i x + B c i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b g x + a g}, x\right)"," ",0,"integral((A*d*i*x + A*c*i + (B*d*i*x + B*c*i)*log((b*e*x + a*e)/(d*x + c)))/(b*g*x + a*g), x)","F",0
6,0,0,0,0.441789," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d i x + A c i + {\left(B d i x + B c i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A*d*i*x + A*c*i + (B*d*i*x + B*c*i)*log((b*e*x + a*e)/(d*x + c)))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
7,1,177,0,0.448469," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(2 \, A + B\right)} b^{2} c d - {\left(2 \, A + B\right)} a b d^{2}\right)} i x + {\left({\left(2 \, A + B\right)} b^{2} c^{2} - {\left(2 \, A + B\right)} a^{2} d^{2}\right)} i + 2 \, {\left(B b^{2} d^{2} i x^{2} + 2 \, B b^{2} c d i x + B b^{2} c^{2} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}\right)}}"," ",0,"-1/4*(2*((2*A + B)*b^2*c*d - (2*A + B)*a*b*d^2)*i*x + ((2*A + B)*b^2*c^2 - (2*A + B)*a^2*d^2)*i + 2*(B*b^2*d^2*i*x^2 + 2*B*b^2*c*d*i*x + B*b^2*c^2*i)*log((b*e*x + a*e)/(d*x + c)))/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3)","B",0
8,1,363,0,0.443341," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4,x, algorithm=""fricas"")","\frac{6 \, {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} i x^{2} - 3 \, {\left({\left(6 \, A + B\right)} b^{3} c^{2} d - 6 \, {\left(2 \, A + B\right)} a b^{2} c d^{2} + {\left(6 \, A + 5 \, B\right)} a^{2} b d^{3}\right)} i x - {\left(4 \, {\left(3 \, A + B\right)} b^{3} c^{3} - 9 \, {\left(2 \, A + B\right)} a b^{2} c^{2} d + {\left(6 \, A + 5 \, B\right)} a^{3} d^{3}\right)} i + 6 \, {\left(B b^{3} d^{3} i x^{3} + 3 \, B a b^{2} d^{3} i x^{2} - 3 \, {\left(B b^{3} c^{2} d - 2 \, B a b^{2} c d^{2}\right)} i x - {\left(2 \, B b^{3} c^{3} - 3 \, B a b^{2} c^{2} d\right)} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{36 \, {\left({\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}\right)}}"," ",0,"1/36*(6*(B*b^3*c*d^2 - B*a*b^2*d^3)*i*x^2 - 3*((6*A + B)*b^3*c^2*d - 6*(2*A + B)*a*b^2*c*d^2 + (6*A + 5*B)*a^2*b*d^3)*i*x - (4*(3*A + B)*b^3*c^3 - 9*(2*A + B)*a*b^2*c^2*d + (6*A + 5*B)*a^3*d^3)*i + 6*(B*b^3*d^3*i*x^3 + 3*B*a*b^2*d^3*i*x^2 - 3*(B*b^3*c^2*d - 2*B*a*b^2*c*d^2)*i*x - (2*B*b^3*c^3 - 3*B*a*b^2*c^2*d)*i)*log((b*e*x + a*e)/(d*x + c)))/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4)","B",0
9,1,602,0,0.437674," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^5,x, algorithm=""fricas"")","-\frac{12 \, {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} i x^{3} - 6 \, {\left(B b^{4} c^{2} d^{2} - 8 \, B a b^{3} c d^{3} + 7 \, B a^{2} b^{2} d^{4}\right)} i x^{2} + 4 \, {\left({\left(12 \, A + B\right)} b^{4} c^{3} d - 6 \, {\left(6 \, A + B\right)} a b^{3} c^{2} d^{2} + 18 \, {\left(2 \, A + B\right)} a^{2} b^{2} c d^{3} - {\left(12 \, A + 13 \, B\right)} a^{3} b d^{4}\right)} i x + {\left(9 \, {\left(4 \, A + B\right)} b^{4} c^{4} - 32 \, {\left(3 \, A + B\right)} a b^{3} c^{3} d + 36 \, {\left(2 \, A + B\right)} a^{2} b^{2} c^{2} d^{2} - {\left(12 \, A + 13 \, B\right)} a^{4} d^{4}\right)} i + 12 \, {\left(B b^{4} d^{4} i x^{4} + 4 \, B a b^{3} d^{4} i x^{3} + 6 \, B a^{2} b^{2} d^{4} i x^{2} + 4 \, {\left(B b^{4} c^{3} d - 3 \, B a b^{3} c^{2} d^{2} + 3 \, B a^{2} b^{2} c d^{3}\right)} i x + {\left(3 \, B b^{4} c^{4} - 8 \, B a b^{3} c^{3} d + 6 \, B a^{2} b^{2} c^{2} d^{2}\right)} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{144 \, {\left({\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}\right)}}"," ",0,"-1/144*(12*(B*b^4*c*d^3 - B*a*b^3*d^4)*i*x^3 - 6*(B*b^4*c^2*d^2 - 8*B*a*b^3*c*d^3 + 7*B*a^2*b^2*d^4)*i*x^2 + 4*((12*A + B)*b^4*c^3*d - 6*(6*A + B)*a*b^3*c^2*d^2 + 18*(2*A + B)*a^2*b^2*c*d^3 - (12*A + 13*B)*a^3*b*d^4)*i*x + (9*(4*A + B)*b^4*c^4 - 32*(3*A + B)*a*b^3*c^3*d + 36*(2*A + B)*a^2*b^2*c^2*d^2 - (12*A + 13*B)*a^4*d^4)*i + 12*(B*b^4*d^4*i*x^4 + 4*B*a*b^3*d^4*i*x^3 + 6*B*a^2*b^2*d^4*i*x^2 + 4*(B*b^4*c^3*d - 3*B*a*b^3*c^2*d^2 + 3*B*a^2*b^2*c*d^3)*i*x + (3*B*b^4*c^4 - 8*B*a*b^3*c^3*d + 6*B*a^2*b^2*c^2*d^2)*i)*log((b*e*x + a*e)/(d*x + c)))/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5)","B",0
10,1,724,0,0.688462," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{60 \, A b^{6} d^{6} g^{3} i^{2} x^{6} + 12 \, {\left({\left(12 \, A - B\right)} b^{6} c d^{5} + {\left(18 \, A + B\right)} a b^{5} d^{6}\right)} g^{3} i^{2} x^{5} + 3 \, {\left({\left(30 \, A - 7 \, B\right)} b^{6} c^{2} d^{4} + 6 \, {\left(30 \, A - B\right)} a b^{5} c d^{5} + {\left(90 \, A + 13 \, B\right)} a^{2} b^{4} d^{6}\right)} g^{3} i^{2} x^{4} - 2 \, {\left(B b^{6} c^{3} d^{3} - 3 \, {\left(60 \, A - 13 \, B\right)} a b^{5} c^{2} d^{4} - 3 \, {\left(120 \, A + 7 \, B\right)} a^{2} b^{4} c d^{5} - {\left(60 \, A + 19 \, B\right)} a^{3} b^{3} d^{6}\right)} g^{3} i^{2} x^{3} + 3 \, {\left(B b^{6} c^{4} d^{2} - 6 \, B a b^{5} c^{3} d^{3} + 30 \, {\left(6 \, A - B\right)} a^{2} b^{4} c^{2} d^{4} + 2 \, {\left(60 \, A + 17 \, B\right)} a^{3} b^{3} c d^{5} + B a^{4} b^{2} d^{6}\right)} g^{3} i^{2} x^{2} - 6 \, {\left(B b^{6} c^{5} d - 6 \, B a b^{5} c^{4} d^{2} + 15 \, B a^{2} b^{4} c^{3} d^{3} - 5 \, {\left(12 \, A + B\right)} a^{3} b^{3} c^{2} d^{4} - 6 \, B a^{4} b^{2} c d^{5} + B a^{5} b d^{6}\right)} g^{3} i^{2} x + 6 \, {\left(15 \, B a^{4} b^{2} c^{2} d^{4} - 6 \, B a^{5} b c d^{5} + B a^{6} d^{6}\right)} g^{3} i^{2} \log\left(b x + a\right) + 6 \, {\left(B b^{6} c^{6} - 6 \, B a b^{5} c^{5} d + 15 \, B a^{2} b^{4} c^{4} d^{2} - 20 \, B a^{3} b^{3} c^{3} d^{3}\right)} g^{3} i^{2} \log\left(d x + c\right) + 6 \, {\left(10 \, B b^{6} d^{6} g^{3} i^{2} x^{6} + 60 \, B a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} x + 12 \, {\left(2 \, B b^{6} c d^{5} + 3 \, B a b^{5} d^{6}\right)} g^{3} i^{2} x^{5} + 15 \, {\left(B b^{6} c^{2} d^{4} + 6 \, B a b^{5} c d^{5} + 3 \, B a^{2} b^{4} d^{6}\right)} g^{3} i^{2} x^{4} + 20 \, {\left(3 \, B a b^{5} c^{2} d^{4} + 6 \, B a^{2} b^{4} c d^{5} + B a^{3} b^{3} d^{6}\right)} g^{3} i^{2} x^{3} + 30 \, {\left(3 \, B a^{2} b^{4} c^{2} d^{4} + 2 \, B a^{3} b^{3} c d^{5}\right)} g^{3} i^{2} x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{360 \, b^{3} d^{4}}"," ",0,"1/360*(60*A*b^6*d^6*g^3*i^2*x^6 + 12*((12*A - B)*b^6*c*d^5 + (18*A + B)*a*b^5*d^6)*g^3*i^2*x^5 + 3*((30*A - 7*B)*b^6*c^2*d^4 + 6*(30*A - B)*a*b^5*c*d^5 + (90*A + 13*B)*a^2*b^4*d^6)*g^3*i^2*x^4 - 2*(B*b^6*c^3*d^3 - 3*(60*A - 13*B)*a*b^5*c^2*d^4 - 3*(120*A + 7*B)*a^2*b^4*c*d^5 - (60*A + 19*B)*a^3*b^3*d^6)*g^3*i^2*x^3 + 3*(B*b^6*c^4*d^2 - 6*B*a*b^5*c^3*d^3 + 30*(6*A - B)*a^2*b^4*c^2*d^4 + 2*(60*A + 17*B)*a^3*b^3*c*d^5 + B*a^4*b^2*d^6)*g^3*i^2*x^2 - 6*(B*b^6*c^5*d - 6*B*a*b^5*c^4*d^2 + 15*B*a^2*b^4*c^3*d^3 - 5*(12*A + B)*a^3*b^3*c^2*d^4 - 6*B*a^4*b^2*c*d^5 + B*a^5*b*d^6)*g^3*i^2*x + 6*(15*B*a^4*b^2*c^2*d^4 - 6*B*a^5*b*c*d^5 + B*a^6*d^6)*g^3*i^2*log(b*x + a) + 6*(B*b^6*c^6 - 6*B*a*b^5*c^5*d + 15*B*a^2*b^4*c^4*d^2 - 20*B*a^3*b^3*c^3*d^3)*g^3*i^2*log(d*x + c) + 6*(10*B*b^6*d^6*g^3*i^2*x^6 + 60*B*a^3*b^3*c^2*d^4*g^3*i^2*x + 12*(2*B*b^6*c*d^5 + 3*B*a*b^5*d^6)*g^3*i^2*x^5 + 15*(B*b^6*c^2*d^4 + 6*B*a*b^5*c*d^5 + 3*B*a^2*b^4*d^6)*g^3*i^2*x^4 + 20*(3*B*a*b^5*c^2*d^4 + 6*B*a^2*b^4*c*d^5 + B*a^3*b^3*d^6)*g^3*i^2*x^3 + 30*(3*B*a^2*b^4*c^2*d^4 + 2*B*a^3*b^3*c*d^5)*g^3*i^2*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^3*d^4)","A",0
11,1,534,0,0.520838," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{12 \, A b^{5} d^{5} g^{2} i^{2} x^{5} + 3 \, {\left({\left(10 \, A - B\right)} b^{5} c d^{4} + {\left(10 \, A + B\right)} a b^{4} d^{5}\right)} g^{2} i^{2} x^{4} + 2 \, {\left({\left(10 \, A - 3 \, B\right)} b^{5} c^{2} d^{3} + 40 \, A a b^{4} c d^{4} + {\left(10 \, A + 3 \, B\right)} a^{2} b^{3} d^{5}\right)} g^{2} i^{2} x^{3} - {\left(B b^{5} c^{3} d^{2} - 15 \, {\left(4 \, A - B\right)} a b^{4} c^{2} d^{3} - 15 \, {\left(4 \, A + B\right)} a^{2} b^{3} c d^{4} - B a^{3} b^{2} d^{5}\right)} g^{2} i^{2} x^{2} + 2 \, {\left(B b^{5} c^{4} d - 5 \, B a b^{4} c^{3} d^{2} + 30 \, A a^{2} b^{3} c^{2} d^{3} + 5 \, B a^{3} b^{2} c d^{4} - B a^{4} b d^{5}\right)} g^{2} i^{2} x + 2 \, {\left(10 \, B a^{3} b^{2} c^{2} d^{3} - 5 \, B a^{4} b c d^{4} + B a^{5} d^{5}\right)} g^{2} i^{2} \log\left(b x + a\right) - 2 \, {\left(B b^{5} c^{5} - 5 \, B a b^{4} c^{4} d + 10 \, B a^{2} b^{3} c^{3} d^{2}\right)} g^{2} i^{2} \log\left(d x + c\right) + 2 \, {\left(6 \, B b^{5} d^{5} g^{2} i^{2} x^{5} + 30 \, B a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} x + 15 \, {\left(B b^{5} c d^{4} + B a b^{4} d^{5}\right)} g^{2} i^{2} x^{4} + 10 \, {\left(B b^{5} c^{2} d^{3} + 4 \, B a b^{4} c d^{4} + B a^{2} b^{3} d^{5}\right)} g^{2} i^{2} x^{3} + 30 \, {\left(B a b^{4} c^{2} d^{3} + B a^{2} b^{3} c d^{4}\right)} g^{2} i^{2} x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{60 \, b^{3} d^{3}}"," ",0,"1/60*(12*A*b^5*d^5*g^2*i^2*x^5 + 3*((10*A - B)*b^5*c*d^4 + (10*A + B)*a*b^4*d^5)*g^2*i^2*x^4 + 2*((10*A - 3*B)*b^5*c^2*d^3 + 40*A*a*b^4*c*d^4 + (10*A + 3*B)*a^2*b^3*d^5)*g^2*i^2*x^3 - (B*b^5*c^3*d^2 - 15*(4*A - B)*a*b^4*c^2*d^3 - 15*(4*A + B)*a^2*b^3*c*d^4 - B*a^3*b^2*d^5)*g^2*i^2*x^2 + 2*(B*b^5*c^4*d - 5*B*a*b^4*c^3*d^2 + 30*A*a^2*b^3*c^2*d^3 + 5*B*a^3*b^2*c*d^4 - B*a^4*b*d^5)*g^2*i^2*x + 2*(10*B*a^3*b^2*c^2*d^3 - 5*B*a^4*b*c*d^4 + B*a^5*d^5)*g^2*i^2*log(b*x + a) - 2*(B*b^5*c^5 - 5*B*a*b^4*c^4*d + 10*B*a^2*b^3*c^3*d^2)*g^2*i^2*log(d*x + c) + 2*(6*B*b^5*d^5*g^2*i^2*x^5 + 30*B*a^2*b^3*c^2*d^3*g^2*i^2*x + 15*(B*b^5*c*d^4 + B*a*b^4*d^5)*g^2*i^2*x^4 + 10*(B*b^5*c^2*d^3 + 4*B*a*b^4*c*d^4 + B*a^2*b^3*d^5)*g^2*i^2*x^3 + 30*(B*a*b^4*c^2*d^3 + B*a^2*b^3*c*d^4)*g^2*i^2*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^3*d^3)","A",0
12,1,367,0,0.458511," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{6 \, A b^{4} d^{4} g i^{2} x^{4} + 2 \, {\left({\left(8 \, A - B\right)} b^{4} c d^{3} + {\left(4 \, A + B\right)} a b^{3} d^{4}\right)} g i^{2} x^{3} + {\left({\left(12 \, A - 5 \, B\right)} b^{4} c^{2} d^{2} + 4 \, {\left(6 \, A + B\right)} a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} g i^{2} x^{2} - 2 \, {\left(B b^{4} c^{3} d - 2 \, {\left(6 \, A - B\right)} a b^{3} c^{2} d^{2} - 4 \, B a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} g i^{2} x + 2 \, {\left(6 \, B a^{2} b^{2} c^{2} d^{2} - 4 \, B a^{3} b c d^{3} + B a^{4} d^{4}\right)} g i^{2} \log\left(b x + a\right) + 2 \, {\left(B b^{4} c^{4} - 4 \, B a b^{3} c^{3} d\right)} g i^{2} \log\left(d x + c\right) + 2 \, {\left(3 \, B b^{4} d^{4} g i^{2} x^{4} + 12 \, B a b^{3} c^{2} d^{2} g i^{2} x + 4 \, {\left(2 \, B b^{4} c d^{3} + B a b^{3} d^{4}\right)} g i^{2} x^{3} + 6 \, {\left(B b^{4} c^{2} d^{2} + 2 \, B a b^{3} c d^{3}\right)} g i^{2} x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{24 \, b^{3} d^{2}}"," ",0,"1/24*(6*A*b^4*d^4*g*i^2*x^4 + 2*((8*A - B)*b^4*c*d^3 + (4*A + B)*a*b^3*d^4)*g*i^2*x^3 + ((12*A - 5*B)*b^4*c^2*d^2 + 4*(6*A + B)*a*b^3*c*d^3 + B*a^2*b^2*d^4)*g*i^2*x^2 - 2*(B*b^4*c^3*d - 2*(6*A - B)*a*b^3*c^2*d^2 - 4*B*a^2*b^2*c*d^3 + B*a^3*b*d^4)*g*i^2*x + 2*(6*B*a^2*b^2*c^2*d^2 - 4*B*a^3*b*c*d^3 + B*a^4*d^4)*g*i^2*log(b*x + a) + 2*(B*b^4*c^4 - 4*B*a*b^3*c^3*d)*g*i^2*log(d*x + c) + 2*(3*B*b^4*d^4*g*i^2*x^4 + 12*B*a*b^3*c^2*d^2*g*i^2*x + 4*(2*B*b^4*c*d^3 + B*a*b^3*d^4)*g*i^2*x^3 + 6*(B*b^4*c^2*d^2 + 2*B*a*b^3*c*d^3)*g*i^2*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^3*d^2)","A",0
13,1,223,0,0.428138," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{2 \, A b^{3} d^{3} i^{2} x^{3} - 2 \, B b^{3} c^{3} i^{2} \log\left(d x + c\right) + {\left({\left(6 \, A - B\right)} b^{3} c d^{2} + B a b^{2} d^{3}\right)} i^{2} x^{2} + 2 \, {\left({\left(3 \, A - 2 \, B\right)} b^{3} c^{2} d + 3 \, B a b^{2} c d^{2} - B a^{2} b d^{3}\right)} i^{2} x + 2 \, {\left(3 \, B a b^{2} c^{2} d - 3 \, B a^{2} b c d^{2} + B a^{3} d^{3}\right)} i^{2} \log\left(b x + a\right) + 2 \, {\left(B b^{3} d^{3} i^{2} x^{3} + 3 \, B b^{3} c d^{2} i^{2} x^{2} + 3 \, B b^{3} c^{2} d i^{2} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{6 \, b^{3} d}"," ",0,"1/6*(2*A*b^3*d^3*i^2*x^3 - 2*B*b^3*c^3*i^2*log(d*x + c) + ((6*A - B)*b^3*c*d^2 + B*a*b^2*d^3)*i^2*x^2 + 2*((3*A - 2*B)*b^3*c^2*d + 3*B*a*b^2*c*d^2 - B*a^2*b*d^3)*i^2*x + 2*(3*B*a*b^2*c^2*d - 3*B*a^2*b*c*d^2 + B*a^3*d^3)*i^2*log(b*x + a) + 2*(B*b^3*d^3*i^2*x^3 + 3*B*b^3*c*d^2*i^2*x^2 + 3*B*b^3*c^2*d*i^2*x)*log((b*e*x + a*e)/(d*x + c)))/(b^3*d)","B",0
14,0,0,0,0.475885," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{2} i^{2} x^{2} + 2 \, A c d i^{2} x + A c^{2} i^{2} + {\left(B d^{2} i^{2} x^{2} + 2 \, B c d i^{2} x + B c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b g x + a g}, x\right)"," ",0,"integral((A*d^2*i^2*x^2 + 2*A*c*d*i^2*x + A*c^2*i^2 + (B*d^2*i^2*x^2 + 2*B*c*d*i^2*x + B*c^2*i^2)*log((b*e*x + a*e)/(d*x + c)))/(b*g*x + a*g), x)","F",0
15,0,0,0,0.466834," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{2} i^{2} x^{2} + 2 \, A c d i^{2} x + A c^{2} i^{2} + {\left(B d^{2} i^{2} x^{2} + 2 \, B c d i^{2} x + B c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A*d^2*i^2*x^2 + 2*A*c*d*i^2*x + A*c^2*i^2 + (B*d^2*i^2*x^2 + 2*B*c*d*i^2*x + B*c^2*i^2)*log((b*e*x + a*e)/(d*x + c)))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
16,0,0,0,0.432841," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{2} i^{2} x^{2} + 2 \, A c d i^{2} x + A c^{2} i^{2} + {\left(B d^{2} i^{2} x^{2} + 2 \, B c d i^{2} x + B c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{3} g^{3} x^{3} + 3 \, a b^{2} g^{3} x^{2} + 3 \, a^{2} b g^{3} x + a^{3} g^{3}}, x\right)"," ",0,"integral((A*d^2*i^2*x^2 + 2*A*c*d*i^2*x + A*c^2*i^2 + (B*d^2*i^2*x^2 + 2*B*c*d*i^2*x + B*c^2*i^2)*log((b*e*x + a*e)/(d*x + c)))/(b^3*g^3*x^3 + 3*a*b^2*g^3*x^2 + 3*a^2*b*g^3*x + a^3*g^3), x)","F",0
17,1,271,0,0.448571," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(3 \, A + B\right)} b^{3} c d^{2} - {\left(3 \, A + B\right)} a b^{2} d^{3}\right)} i^{2} x^{2} + 3 \, {\left({\left(3 \, A + B\right)} b^{3} c^{2} d - {\left(3 \, A + B\right)} a^{2} b d^{3}\right)} i^{2} x + {\left({\left(3 \, A + B\right)} b^{3} c^{3} - {\left(3 \, A + B\right)} a^{3} d^{3}\right)} i^{2} + 3 \, {\left(B b^{3} d^{3} i^{2} x^{3} + 3 \, B b^{3} c d^{2} i^{2} x^{2} + 3 \, B b^{3} c^{2} d i^{2} x + B b^{3} c^{3} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{9 \, {\left({\left(b^{7} c - a b^{6} d\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c - a^{2} b^{5} d\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c - a^{3} b^{4} d\right)} g^{4} x + {\left(a^{3} b^{4} c - a^{4} b^{3} d\right)} g^{4}\right)}}"," ",0,"-1/9*(3*((3*A + B)*b^3*c*d^2 - (3*A + B)*a*b^2*d^3)*i^2*x^2 + 3*((3*A + B)*b^3*c^2*d - (3*A + B)*a^2*b*d^3)*i^2*x + ((3*A + B)*b^3*c^3 - (3*A + B)*a^3*d^3)*i^2 + 3*(B*b^3*d^3*i^2*x^3 + 3*B*b^3*c*d^2*i^2*x^2 + 3*B*b^3*c^2*d*i^2*x + B*b^3*c^3*i^2)*log((b*e*x + a*e)/(d*x + c)))/((b^7*c - a*b^6*d)*g^4*x^3 + 3*(a*b^6*c - a^2*b^5*d)*g^4*x^2 + 3*(a^2*b^5*c - a^3*b^4*d)*g^4*x + (a^3*b^4*c - a^4*b^3*d)*g^4)","B",0
18,1,510,0,0.440150," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^5,x, algorithm=""fricas"")","\frac{12 \, {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} i^{2} x^{3} - 6 \, {\left({\left(12 \, A + B\right)} b^{4} c^{2} d^{2} - 8 \, {\left(3 \, A + B\right)} a b^{3} c d^{3} + {\left(12 \, A + 7 \, B\right)} a^{2} b^{2} d^{4}\right)} i^{2} x^{2} - 4 \, {\left({\left(24 \, A + 5 \, B\right)} b^{4} c^{3} d - 12 \, {\left(3 \, A + B\right)} a b^{3} c^{2} d^{2} + {\left(12 \, A + 7 \, B\right)} a^{3} b d^{4}\right)} i^{2} x - {\left(9 \, {\left(4 \, A + B\right)} b^{4} c^{4} - 16 \, {\left(3 \, A + B\right)} a b^{3} c^{3} d + {\left(12 \, A + 7 \, B\right)} a^{4} d^{4}\right)} i^{2} + 12 \, {\left(B b^{4} d^{4} i^{2} x^{4} + 4 \, B a b^{3} d^{4} i^{2} x^{3} - 6 \, {\left(B b^{4} c^{2} d^{2} - 2 \, B a b^{3} c d^{3}\right)} i^{2} x^{2} - 4 \, {\left(2 \, B b^{4} c^{3} d - 3 \, B a b^{3} c^{2} d^{2}\right)} i^{2} x - {\left(3 \, B b^{4} c^{4} - 4 \, B a b^{3} c^{3} d\right)} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{144 \, {\left({\left(b^{9} c^{2} - 2 \, a b^{8} c d + a^{2} b^{7} d^{2}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{2} - 2 \, a^{2} b^{7} c d + a^{3} b^{6} d^{2}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{2} - 2 \, a^{3} b^{6} c d + a^{4} b^{5} d^{2}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{2} - 2 \, a^{4} b^{5} c d + a^{5} b^{4} d^{2}\right)} g^{5} x + {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} g^{5}\right)}}"," ",0,"1/144*(12*(B*b^4*c*d^3 - B*a*b^3*d^4)*i^2*x^3 - 6*((12*A + B)*b^4*c^2*d^2 - 8*(3*A + B)*a*b^3*c*d^3 + (12*A + 7*B)*a^2*b^2*d^4)*i^2*x^2 - 4*((24*A + 5*B)*b^4*c^3*d - 12*(3*A + B)*a*b^3*c^2*d^2 + (12*A + 7*B)*a^3*b*d^4)*i^2*x - (9*(4*A + B)*b^4*c^4 - 16*(3*A + B)*a*b^3*c^3*d + (12*A + 7*B)*a^4*d^4)*i^2 + 12*(B*b^4*d^4*i^2*x^4 + 4*B*a*b^3*d^4*i^2*x^3 - 6*(B*b^4*c^2*d^2 - 2*B*a*b^3*c*d^3)*i^2*x^2 - 4*(2*B*b^4*c^3*d - 3*B*a*b^3*c^2*d^2)*i^2*x - (3*B*b^4*c^4 - 4*B*a*b^3*c^3*d)*i^2)*log((b*e*x + a*e)/(d*x + c)))/((b^9*c^2 - 2*a*b^8*c*d + a^2*b^7*d^2)*g^5*x^4 + 4*(a*b^8*c^2 - 2*a^2*b^7*c*d + a^3*b^6*d^2)*g^5*x^3 + 6*(a^2*b^7*c^2 - 2*a^3*b^6*c*d + a^4*b^5*d^2)*g^5*x^2 + 4*(a^3*b^6*c^2 - 2*a^4*b^5*c*d + a^5*b^4*d^2)*g^5*x + (a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*g^5)","B",0
19,1,807,0,0.482280," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^6,x, algorithm=""fricas"")","-\frac{60 \, {\left(B b^{5} c d^{4} - B a b^{4} d^{5}\right)} i^{2} x^{4} - 30 \, {\left(B b^{5} c^{2} d^{3} - 10 \, B a b^{4} c d^{4} + 9 \, B a^{2} b^{3} d^{5}\right)} i^{2} x^{3} + 10 \, {\left(2 \, {\left(30 \, A + B\right)} b^{5} c^{3} d^{2} - 15 \, {\left(12 \, A + B\right)} a b^{4} c^{2} d^{3} + 60 \, {\left(3 \, A + B\right)} a^{2} b^{3} c d^{4} - {\left(60 \, A + 47 \, B\right)} a^{3} b^{2} d^{5}\right)} i^{2} x^{2} + 5 \, {\left(9 \, {\left(20 \, A + 3 \, B\right)} b^{5} c^{4} d - 20 \, {\left(24 \, A + 5 \, B\right)} a b^{4} c^{3} d^{2} + 120 \, {\left(3 \, A + B\right)} a^{2} b^{3} c^{2} d^{3} - {\left(60 \, A + 47 \, B\right)} a^{4} b d^{5}\right)} i^{2} x + {\left(72 \, {\left(5 \, A + B\right)} b^{5} c^{5} - 225 \, {\left(4 \, A + B\right)} a b^{4} c^{4} d + 200 \, {\left(3 \, A + B\right)} a^{2} b^{3} c^{3} d^{2} - {\left(60 \, A + 47 \, B\right)} a^{5} d^{5}\right)} i^{2} + 60 \, {\left(B b^{5} d^{5} i^{2} x^{5} + 5 \, B a b^{4} d^{5} i^{2} x^{4} + 10 \, B a^{2} b^{3} d^{5} i^{2} x^{3} + 10 \, {\left(B b^{5} c^{3} d^{2} - 3 \, B a b^{4} c^{2} d^{3} + 3 \, B a^{2} b^{3} c d^{4}\right)} i^{2} x^{2} + 5 \, {\left(3 \, B b^{5} c^{4} d - 8 \, B a b^{4} c^{3} d^{2} + 6 \, B a^{2} b^{3} c^{2} d^{3}\right)} i^{2} x + {\left(6 \, B b^{5} c^{5} - 15 \, B a b^{4} c^{4} d + 10 \, B a^{2} b^{3} c^{3} d^{2}\right)} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{1800 \, {\left({\left(b^{11} c^{3} - 3 \, a b^{10} c^{2} d + 3 \, a^{2} b^{9} c d^{2} - a^{3} b^{8} d^{3}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{3} - 3 \, a^{2} b^{9} c^{2} d + 3 \, a^{3} b^{8} c d^{2} - a^{4} b^{7} d^{3}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{3} - 3 \, a^{3} b^{8} c^{2} d + 3 \, a^{4} b^{7} c d^{2} - a^{5} b^{6} d^{3}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{3} - 3 \, a^{4} b^{7} c^{2} d + 3 \, a^{5} b^{6} c d^{2} - a^{6} b^{5} d^{3}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{3} - 3 \, a^{5} b^{6} c^{2} d + 3 \, a^{6} b^{5} c d^{2} - a^{7} b^{4} d^{3}\right)} g^{6} x + {\left(a^{5} b^{6} c^{3} - 3 \, a^{6} b^{5} c^{2} d + 3 \, a^{7} b^{4} c d^{2} - a^{8} b^{3} d^{3}\right)} g^{6}\right)}}"," ",0,"-1/1800*(60*(B*b^5*c*d^4 - B*a*b^4*d^5)*i^2*x^4 - 30*(B*b^5*c^2*d^3 - 10*B*a*b^4*c*d^4 + 9*B*a^2*b^3*d^5)*i^2*x^3 + 10*(2*(30*A + B)*b^5*c^3*d^2 - 15*(12*A + B)*a*b^4*c^2*d^3 + 60*(3*A + B)*a^2*b^3*c*d^4 - (60*A + 47*B)*a^3*b^2*d^5)*i^2*x^2 + 5*(9*(20*A + 3*B)*b^5*c^4*d - 20*(24*A + 5*B)*a*b^4*c^3*d^2 + 120*(3*A + B)*a^2*b^3*c^2*d^3 - (60*A + 47*B)*a^4*b*d^5)*i^2*x + (72*(5*A + B)*b^5*c^5 - 225*(4*A + B)*a*b^4*c^4*d + 200*(3*A + B)*a^2*b^3*c^3*d^2 - (60*A + 47*B)*a^5*d^5)*i^2 + 60*(B*b^5*d^5*i^2*x^5 + 5*B*a*b^4*d^5*i^2*x^4 + 10*B*a^2*b^3*d^5*i^2*x^3 + 10*(B*b^5*c^3*d^2 - 3*B*a*b^4*c^2*d^3 + 3*B*a^2*b^3*c*d^4)*i^2*x^2 + 5*(3*B*b^5*c^4*d - 8*B*a*b^4*c^3*d^2 + 6*B*a^2*b^3*c^2*d^3)*i^2*x + (6*B*b^5*c^5 - 15*B*a*b^4*c^4*d + 10*B*a^2*b^3*c^3*d^2)*i^2)*log((b*e*x + a*e)/(d*x + c)))/((b^11*c^3 - 3*a*b^10*c^2*d + 3*a^2*b^9*c*d^2 - a^3*b^8*d^3)*g^6*x^5 + 5*(a*b^10*c^3 - 3*a^2*b^9*c^2*d + 3*a^3*b^8*c*d^2 - a^4*b^7*d^3)*g^6*x^4 + 10*(a^2*b^9*c^3 - 3*a^3*b^8*c^2*d + 3*a^4*b^7*c*d^2 - a^5*b^6*d^3)*g^6*x^3 + 10*(a^3*b^8*c^3 - 3*a^4*b^7*c^2*d + 3*a^5*b^6*c*d^2 - a^6*b^5*d^3)*g^6*x^2 + 5*(a^4*b^7*c^3 - 3*a^5*b^6*c^2*d + 3*a^6*b^5*c*d^2 - a^7*b^4*d^3)*g^6*x + (a^5*b^6*c^3 - 3*a^6*b^5*c^2*d + 3*a^7*b^4*c*d^2 - a^8*b^3*d^3)*g^6)","B",0
20,1,912,0,0.876920," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{120 \, A b^{7} d^{7} g^{3} i^{3} x^{7} + 20 \, {\left({\left(21 \, A - B\right)} b^{7} c d^{6} + {\left(21 \, A + B\right)} a b^{6} d^{7}\right)} g^{3} i^{3} x^{6} + 12 \, {\left({\left(42 \, A - 5 \, B\right)} b^{7} c^{2} d^{5} + 126 \, A a b^{6} c d^{6} + {\left(42 \, A + 5 \, B\right)} a^{2} b^{5} d^{7}\right)} g^{3} i^{3} x^{5} + 3 \, {\left({\left(70 \, A - 17 \, B\right)} b^{7} c^{3} d^{4} + 7 \, {\left(90 \, A - 7 \, B\right)} a b^{6} c^{2} d^{5} + 7 \, {\left(90 \, A + 7 \, B\right)} a^{2} b^{5} c d^{6} + {\left(70 \, A + 17 \, B\right)} a^{3} b^{4} d^{7}\right)} g^{3} i^{3} x^{4} - 2 \, {\left(B b^{7} c^{4} d^{3} - 14 \, {\left(30 \, A - 7 \, B\right)} a b^{6} c^{3} d^{4} - 1260 \, A a^{2} b^{5} c^{2} d^{5} - 14 \, {\left(30 \, A + 7 \, B\right)} a^{3} b^{4} c d^{6} - B a^{4} b^{3} d^{7}\right)} g^{3} i^{3} x^{3} + 3 \, {\left(B b^{7} c^{5} d^{2} - 7 \, B a b^{6} c^{4} d^{3} + 84 \, {\left(5 \, A - B\right)} a^{2} b^{5} c^{3} d^{4} + 84 \, {\left(5 \, A + B\right)} a^{3} b^{4} c^{2} d^{5} + 7 \, B a^{4} b^{3} c d^{6} - B a^{5} b^{2} d^{7}\right)} g^{3} i^{3} x^{2} - 6 \, {\left(B b^{7} c^{6} d - 7 \, B a b^{6} c^{5} d^{2} + 21 \, B a^{2} b^{5} c^{4} d^{3} - 140 \, A a^{3} b^{4} c^{3} d^{4} - 21 \, B a^{4} b^{3} c^{2} d^{5} + 7 \, B a^{5} b^{2} c d^{6} - B a^{6} b d^{7}\right)} g^{3} i^{3} x + 6 \, {\left(35 \, B a^{4} b^{3} c^{3} d^{4} - 21 \, B a^{5} b^{2} c^{2} d^{5} + 7 \, B a^{6} b c d^{6} - B a^{7} d^{7}\right)} g^{3} i^{3} \log\left(b x + a\right) + 6 \, {\left(B b^{7} c^{7} - 7 \, B a b^{6} c^{6} d + 21 \, B a^{2} b^{5} c^{5} d^{2} - 35 \, B a^{3} b^{4} c^{4} d^{3}\right)} g^{3} i^{3} \log\left(d x + c\right) + 6 \, {\left(20 \, B b^{7} d^{7} g^{3} i^{3} x^{7} + 140 \, B a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} x + 70 \, {\left(B b^{7} c d^{6} + B a b^{6} d^{7}\right)} g^{3} i^{3} x^{6} + 84 \, {\left(B b^{7} c^{2} d^{5} + 3 \, B a b^{6} c d^{6} + B a^{2} b^{5} d^{7}\right)} g^{3} i^{3} x^{5} + 35 \, {\left(B b^{7} c^{3} d^{4} + 9 \, B a b^{6} c^{2} d^{5} + 9 \, B a^{2} b^{5} c d^{6} + B a^{3} b^{4} d^{7}\right)} g^{3} i^{3} x^{4} + 140 \, {\left(B a b^{6} c^{3} d^{4} + 3 \, B a^{2} b^{5} c^{2} d^{5} + B a^{3} b^{4} c d^{6}\right)} g^{3} i^{3} x^{3} + 210 \, {\left(B a^{2} b^{5} c^{3} d^{4} + B a^{3} b^{4} c^{2} d^{5}\right)} g^{3} i^{3} x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{840 \, b^{4} d^{4}}"," ",0,"1/840*(120*A*b^7*d^7*g^3*i^3*x^7 + 20*((21*A - B)*b^7*c*d^6 + (21*A + B)*a*b^6*d^7)*g^3*i^3*x^6 + 12*((42*A - 5*B)*b^7*c^2*d^5 + 126*A*a*b^6*c*d^6 + (42*A + 5*B)*a^2*b^5*d^7)*g^3*i^3*x^5 + 3*((70*A - 17*B)*b^7*c^3*d^4 + 7*(90*A - 7*B)*a*b^6*c^2*d^5 + 7*(90*A + 7*B)*a^2*b^5*c*d^6 + (70*A + 17*B)*a^3*b^4*d^7)*g^3*i^3*x^4 - 2*(B*b^7*c^4*d^3 - 14*(30*A - 7*B)*a*b^6*c^3*d^4 - 1260*A*a^2*b^5*c^2*d^5 - 14*(30*A + 7*B)*a^3*b^4*c*d^6 - B*a^4*b^3*d^7)*g^3*i^3*x^3 + 3*(B*b^7*c^5*d^2 - 7*B*a*b^6*c^4*d^3 + 84*(5*A - B)*a^2*b^5*c^3*d^4 + 84*(5*A + B)*a^3*b^4*c^2*d^5 + 7*B*a^4*b^3*c*d^6 - B*a^5*b^2*d^7)*g^3*i^3*x^2 - 6*(B*b^7*c^6*d - 7*B*a*b^6*c^5*d^2 + 21*B*a^2*b^5*c^4*d^3 - 140*A*a^3*b^4*c^3*d^4 - 21*B*a^4*b^3*c^2*d^5 + 7*B*a^5*b^2*c*d^6 - B*a^6*b*d^7)*g^3*i^3*x + 6*(35*B*a^4*b^3*c^3*d^4 - 21*B*a^5*b^2*c^2*d^5 + 7*B*a^6*b*c*d^6 - B*a^7*d^7)*g^3*i^3*log(b*x + a) + 6*(B*b^7*c^7 - 7*B*a*b^6*c^6*d + 21*B*a^2*b^5*c^5*d^2 - 35*B*a^3*b^4*c^4*d^3)*g^3*i^3*log(d*x + c) + 6*(20*B*b^7*d^7*g^3*i^3*x^7 + 140*B*a^3*b^4*c^3*d^4*g^3*i^3*x + 70*(B*b^7*c*d^6 + B*a*b^6*d^7)*g^3*i^3*x^6 + 84*(B*b^7*c^2*d^5 + 3*B*a*b^6*c*d^6 + B*a^2*b^5*d^7)*g^3*i^3*x^5 + 35*(B*b^7*c^3*d^4 + 9*B*a*b^6*c^2*d^5 + 9*B*a^2*b^5*c*d^6 + B*a^3*b^4*d^7)*g^3*i^3*x^4 + 140*(B*a*b^6*c^3*d^4 + 3*B*a^2*b^5*c^2*d^5 + B*a^3*b^4*c*d^6)*g^3*i^3*x^3 + 210*(B*a^2*b^5*c^3*d^4 + B*a^3*b^4*c^2*d^5)*g^3*i^3*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^4*d^4)","B",0
21,1,722,0,0.638036," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{60 \, A b^{6} d^{6} g^{2} i^{3} x^{6} + 12 \, {\left({\left(18 \, A - B\right)} b^{6} c d^{5} + {\left(12 \, A + B\right)} a b^{5} d^{6}\right)} g^{2} i^{3} x^{5} + 3 \, {\left({\left(90 \, A - 13 \, B\right)} b^{6} c^{2} d^{4} + 6 \, {\left(30 \, A + B\right)} a b^{5} c d^{5} + {\left(30 \, A + 7 \, B\right)} a^{2} b^{4} d^{6}\right)} g^{2} i^{3} x^{4} + 2 \, {\left({\left(60 \, A - 19 \, B\right)} b^{6} c^{3} d^{3} + 3 \, {\left(120 \, A - 7 \, B\right)} a b^{5} c^{2} d^{4} + 3 \, {\left(60 \, A + 13 \, B\right)} a^{2} b^{4} c d^{5} + B a^{3} b^{3} d^{6}\right)} g^{2} i^{3} x^{3} - 3 \, {\left(B b^{6} c^{4} d^{2} - 2 \, {\left(60 \, A - 17 \, B\right)} a b^{5} c^{3} d^{3} - 30 \, {\left(6 \, A + B\right)} a^{2} b^{4} c^{2} d^{4} - 6 \, B a^{3} b^{3} c d^{5} + B a^{4} b^{2} d^{6}\right)} g^{2} i^{3} x^{2} + 6 \, {\left(B b^{6} c^{5} d - 6 \, B a b^{5} c^{4} d^{2} + 5 \, {\left(12 \, A - B\right)} a^{2} b^{4} c^{3} d^{3} + 15 \, B a^{3} b^{3} c^{2} d^{4} - 6 \, B a^{4} b^{2} c d^{5} + B a^{5} b d^{6}\right)} g^{2} i^{3} x + 6 \, {\left(20 \, B a^{3} b^{3} c^{3} d^{3} - 15 \, B a^{4} b^{2} c^{2} d^{4} + 6 \, B a^{5} b c d^{5} - B a^{6} d^{6}\right)} g^{2} i^{3} \log\left(b x + a\right) - 6 \, {\left(B b^{6} c^{6} - 6 \, B a b^{5} c^{5} d + 15 \, B a^{2} b^{4} c^{4} d^{2}\right)} g^{2} i^{3} \log\left(d x + c\right) + 6 \, {\left(10 \, B b^{6} d^{6} g^{2} i^{3} x^{6} + 60 \, B a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} x + 12 \, {\left(3 \, B b^{6} c d^{5} + 2 \, B a b^{5} d^{6}\right)} g^{2} i^{3} x^{5} + 15 \, {\left(3 \, B b^{6} c^{2} d^{4} + 6 \, B a b^{5} c d^{5} + B a^{2} b^{4} d^{6}\right)} g^{2} i^{3} x^{4} + 20 \, {\left(B b^{6} c^{3} d^{3} + 6 \, B a b^{5} c^{2} d^{4} + 3 \, B a^{2} b^{4} c d^{5}\right)} g^{2} i^{3} x^{3} + 30 \, {\left(2 \, B a b^{5} c^{3} d^{3} + 3 \, B a^{2} b^{4} c^{2} d^{4}\right)} g^{2} i^{3} x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{360 \, b^{4} d^{3}}"," ",0,"1/360*(60*A*b^6*d^6*g^2*i^3*x^6 + 12*((18*A - B)*b^6*c*d^5 + (12*A + B)*a*b^5*d^6)*g^2*i^3*x^5 + 3*((90*A - 13*B)*b^6*c^2*d^4 + 6*(30*A + B)*a*b^5*c*d^5 + (30*A + 7*B)*a^2*b^4*d^6)*g^2*i^3*x^4 + 2*((60*A - 19*B)*b^6*c^3*d^3 + 3*(120*A - 7*B)*a*b^5*c^2*d^4 + 3*(60*A + 13*B)*a^2*b^4*c*d^5 + B*a^3*b^3*d^6)*g^2*i^3*x^3 - 3*(B*b^6*c^4*d^2 - 2*(60*A - 17*B)*a*b^5*c^3*d^3 - 30*(6*A + B)*a^2*b^4*c^2*d^4 - 6*B*a^3*b^3*c*d^5 + B*a^4*b^2*d^6)*g^2*i^3*x^2 + 6*(B*b^6*c^5*d - 6*B*a*b^5*c^4*d^2 + 5*(12*A - B)*a^2*b^4*c^3*d^3 + 15*B*a^3*b^3*c^2*d^4 - 6*B*a^4*b^2*c*d^5 + B*a^5*b*d^6)*g^2*i^3*x + 6*(20*B*a^3*b^3*c^3*d^3 - 15*B*a^4*b^2*c^2*d^4 + 6*B*a^5*b*c*d^5 - B*a^6*d^6)*g^2*i^3*log(b*x + a) - 6*(B*b^6*c^6 - 6*B*a*b^5*c^5*d + 15*B*a^2*b^4*c^4*d^2)*g^2*i^3*log(d*x + c) + 6*(10*B*b^6*d^6*g^2*i^3*x^6 + 60*B*a^2*b^4*c^3*d^3*g^2*i^3*x + 12*(3*B*b^6*c*d^5 + 2*B*a*b^5*d^6)*g^2*i^3*x^5 + 15*(3*B*b^6*c^2*d^4 + 6*B*a*b^5*c*d^5 + B*a^2*b^4*d^6)*g^2*i^3*x^4 + 20*(B*b^6*c^3*d^3 + 6*B*a*b^5*c^2*d^4 + 3*B*a^2*b^4*c*d^5)*g^2*i^3*x^3 + 30*(2*B*a*b^5*c^3*d^3 + 3*B*a^2*b^4*c^2*d^4)*g^2*i^3*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^4*d^3)","B",0
22,1,502,0,0.602602," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{24 \, A b^{5} d^{5} g i^{3} x^{5} + 6 \, {\left({\left(15 \, A - B\right)} b^{5} c d^{4} + {\left(5 \, A + B\right)} a b^{4} d^{5}\right)} g i^{3} x^{4} + 2 \, {\left({\left(60 \, A - 11 \, B\right)} b^{5} c^{2} d^{3} + 10 \, {\left(6 \, A + B\right)} a b^{4} c d^{4} + B a^{2} b^{3} d^{5}\right)} g i^{3} x^{3} + 3 \, {\left({\left(20 \, A - 9 \, B\right)} b^{5} c^{3} d^{2} + 5 \, {\left(12 \, A + B\right)} a b^{4} c^{2} d^{3} + 5 \, B a^{2} b^{3} c d^{4} - B a^{3} b^{2} d^{5}\right)} g i^{3} x^{2} - 6 \, {\left(B b^{5} c^{4} d - 5 \, {\left(4 \, A - B\right)} a b^{4} c^{3} d^{2} - 10 \, B a^{2} b^{3} c^{2} d^{3} + 5 \, B a^{3} b^{2} c d^{4} - B a^{4} b d^{5}\right)} g i^{3} x + 6 \, {\left(10 \, B a^{2} b^{3} c^{3} d^{2} - 10 \, B a^{3} b^{2} c^{2} d^{3} + 5 \, B a^{4} b c d^{4} - B a^{5} d^{5}\right)} g i^{3} \log\left(b x + a\right) + 6 \, {\left(B b^{5} c^{5} - 5 \, B a b^{4} c^{4} d\right)} g i^{3} \log\left(d x + c\right) + 6 \, {\left(4 \, B b^{5} d^{5} g i^{3} x^{5} + 20 \, B a b^{4} c^{3} d^{2} g i^{3} x + 5 \, {\left(3 \, B b^{5} c d^{4} + B a b^{4} d^{5}\right)} g i^{3} x^{4} + 20 \, {\left(B b^{5} c^{2} d^{3} + B a b^{4} c d^{4}\right)} g i^{3} x^{3} + 10 \, {\left(B b^{5} c^{3} d^{2} + 3 \, B a b^{4} c^{2} d^{3}\right)} g i^{3} x^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{120 \, b^{4} d^{2}}"," ",0,"1/120*(24*A*b^5*d^5*g*i^3*x^5 + 6*((15*A - B)*b^5*c*d^4 + (5*A + B)*a*b^4*d^5)*g*i^3*x^4 + 2*((60*A - 11*B)*b^5*c^2*d^3 + 10*(6*A + B)*a*b^4*c*d^4 + B*a^2*b^3*d^5)*g*i^3*x^3 + 3*((20*A - 9*B)*b^5*c^3*d^2 + 5*(12*A + B)*a*b^4*c^2*d^3 + 5*B*a^2*b^3*c*d^4 - B*a^3*b^2*d^5)*g*i^3*x^2 - 6*(B*b^5*c^4*d - 5*(4*A - B)*a*b^4*c^3*d^2 - 10*B*a^2*b^3*c^2*d^3 + 5*B*a^3*b^2*c*d^4 - B*a^4*b*d^5)*g*i^3*x + 6*(10*B*a^2*b^3*c^3*d^2 - 10*B*a^3*b^2*c^2*d^3 + 5*B*a^4*b*c*d^4 - B*a^5*d^5)*g*i^3*log(b*x + a) + 6*(B*b^5*c^5 - 5*B*a*b^4*c^4*d)*g*i^3*log(d*x + c) + 6*(4*B*b^5*d^5*g*i^3*x^5 + 20*B*a*b^4*c^3*d^2*g*i^3*x + 5*(3*B*b^5*c*d^4 + B*a*b^4*d^5)*g*i^3*x^4 + 20*(B*b^5*c^2*d^3 + B*a*b^4*c*d^4)*g*i^3*x^3 + 10*(B*b^5*c^3*d^2 + 3*B*a*b^4*c^2*d^3)*g*i^3*x^2)*log((b*e*x + a*e)/(d*x + c)))/(b^4*d^2)","A",0
23,1,322,0,0.455442," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c))),x, algorithm=""fricas"")","\frac{6 \, A b^{4} d^{4} i^{3} x^{4} - 6 \, B b^{4} c^{4} i^{3} \log\left(d x + c\right) + 2 \, {\left({\left(12 \, A - B\right)} b^{4} c d^{3} + B a b^{3} d^{4}\right)} i^{3} x^{3} + 3 \, {\left(3 \, {\left(4 \, A - B\right)} b^{4} c^{2} d^{2} + 4 \, B a b^{3} c d^{3} - B a^{2} b^{2} d^{4}\right)} i^{3} x^{2} + 6 \, {\left({\left(4 \, A - 3 \, B\right)} b^{4} c^{3} d + 6 \, B a b^{3} c^{2} d^{2} - 4 \, B a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} i^{3} x + 6 \, {\left(4 \, B a b^{3} c^{3} d - 6 \, B a^{2} b^{2} c^{2} d^{2} + 4 \, B a^{3} b c d^{3} - B a^{4} d^{4}\right)} i^{3} \log\left(b x + a\right) + 6 \, {\left(B b^{4} d^{4} i^{3} x^{4} + 4 \, B b^{4} c d^{3} i^{3} x^{3} + 6 \, B b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B b^{4} c^{3} d i^{3} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{24 \, b^{4} d}"," ",0,"1/24*(6*A*b^4*d^4*i^3*x^4 - 6*B*b^4*c^4*i^3*log(d*x + c) + 2*((12*A - B)*b^4*c*d^3 + B*a*b^3*d^4)*i^3*x^3 + 3*(3*(4*A - B)*b^4*c^2*d^2 + 4*B*a*b^3*c*d^3 - B*a^2*b^2*d^4)*i^3*x^2 + 6*((4*A - 3*B)*b^4*c^3*d + 6*B*a*b^3*c^2*d^2 - 4*B*a^2*b^2*c*d^3 + B*a^3*b*d^4)*i^3*x + 6*(4*B*a*b^3*c^3*d - 6*B*a^2*b^2*c^2*d^2 + 4*B*a^3*b*c*d^3 - B*a^4*d^4)*i^3*log(b*x + a) + 6*(B*b^4*d^4*i^3*x^4 + 4*B*b^4*c*d^3*i^3*x^3 + 6*B*b^4*c^2*d^2*i^3*x^2 + 4*B*b^4*c^3*d*i^3*x)*log((b*e*x + a*e)/(d*x + c)))/(b^4*d)","B",0
24,0,0,0,0.418393," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{3} i^{3} x^{3} + 3 \, A c d^{2} i^{3} x^{2} + 3 \, A c^{2} d i^{3} x + A c^{3} i^{3} + {\left(B d^{3} i^{3} x^{3} + 3 \, B c d^{2} i^{3} x^{2} + 3 \, B c^{2} d i^{3} x + B c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b g x + a g}, x\right)"," ",0,"integral((A*d^3*i^3*x^3 + 3*A*c*d^2*i^3*x^2 + 3*A*c^2*d*i^3*x + A*c^3*i^3 + (B*d^3*i^3*x^3 + 3*B*c*d^2*i^3*x^2 + 3*B*c^2*d*i^3*x + B*c^3*i^3)*log((b*e*x + a*e)/(d*x + c)))/(b*g*x + a*g), x)","F",0
25,0,0,0,0.430936," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{3} i^{3} x^{3} + 3 \, A c d^{2} i^{3} x^{2} + 3 \, A c^{2} d i^{3} x + A c^{3} i^{3} + {\left(B d^{3} i^{3} x^{3} + 3 \, B c d^{2} i^{3} x^{2} + 3 \, B c^{2} d i^{3} x + B c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A*d^3*i^3*x^3 + 3*A*c*d^2*i^3*x^2 + 3*A*c^2*d*i^3*x + A*c^3*i^3 + (B*d^3*i^3*x^3 + 3*B*c*d^2*i^3*x^2 + 3*B*c^2*d*i^3*x + B*c^3*i^3)*log((b*e*x + a*e)/(d*x + c)))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
26,0,0,0,0.453051," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{3} i^{3} x^{3} + 3 \, A c d^{2} i^{3} x^{2} + 3 \, A c^{2} d i^{3} x + A c^{3} i^{3} + {\left(B d^{3} i^{3} x^{3} + 3 \, B c d^{2} i^{3} x^{2} + 3 \, B c^{2} d i^{3} x + B c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{3} g^{3} x^{3} + 3 \, a b^{2} g^{3} x^{2} + 3 \, a^{2} b g^{3} x + a^{3} g^{3}}, x\right)"," ",0,"integral((A*d^3*i^3*x^3 + 3*A*c*d^2*i^3*x^2 + 3*A*c^2*d*i^3*x + A*c^3*i^3 + (B*d^3*i^3*x^3 + 3*B*c*d^2*i^3*x^2 + 3*B*c^2*d*i^3*x + B*c^3*i^3)*log((b*e*x + a*e)/(d*x + c)))/(b^3*g^3*x^3 + 3*a*b^2*g^3*x^2 + 3*a^2*b*g^3*x + a^3*g^3), x)","F",0
27,0,0,0,0.452530," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{3} i^{3} x^{3} + 3 \, A c d^{2} i^{3} x^{2} + 3 \, A c^{2} d i^{3} x + A c^{3} i^{3} + {\left(B d^{3} i^{3} x^{3} + 3 \, B c d^{2} i^{3} x^{2} + 3 \, B c^{2} d i^{3} x + B c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{4} g^{4} x^{4} + 4 \, a b^{3} g^{4} x^{3} + 6 \, a^{2} b^{2} g^{4} x^{2} + 4 \, a^{3} b g^{4} x + a^{4} g^{4}}, x\right)"," ",0,"integral((A*d^3*i^3*x^3 + 3*A*c*d^2*i^3*x^2 + 3*A*c^2*d*i^3*x + A*c^3*i^3 + (B*d^3*i^3*x^3 + 3*B*c*d^2*i^3*x^2 + 3*B*c^2*d*i^3*x + B*c^3*i^3)*log((b*e*x + a*e)/(d*x + c)))/(b^4*g^4*x^4 + 4*a*b^3*g^4*x^3 + 6*a^2*b^2*g^4*x^2 + 4*a^3*b*g^4*x + a^4*g^4), x)","F",0
28,1,355,0,0.465757," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^5,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(4 \, A + B\right)} b^{4} c d^{3} - {\left(4 \, A + B\right)} a b^{3} d^{4}\right)} i^{3} x^{3} + 6 \, {\left({\left(4 \, A + B\right)} b^{4} c^{2} d^{2} - {\left(4 \, A + B\right)} a^{2} b^{2} d^{4}\right)} i^{3} x^{2} + 4 \, {\left({\left(4 \, A + B\right)} b^{4} c^{3} d - {\left(4 \, A + B\right)} a^{3} b d^{4}\right)} i^{3} x + {\left({\left(4 \, A + B\right)} b^{4} c^{4} - {\left(4 \, A + B\right)} a^{4} d^{4}\right)} i^{3} + 4 \, {\left(B b^{4} d^{4} i^{3} x^{4} + 4 \, B b^{4} c d^{3} i^{3} x^{3} + 6 \, B b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B b^{4} c^{3} d i^{3} x + B b^{4} c^{4} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{16 \, {\left({\left(b^{9} c - a b^{8} d\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c - a^{2} b^{7} d\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c - a^{3} b^{6} d\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c - a^{4} b^{5} d\right)} g^{5} x + {\left(a^{4} b^{5} c - a^{5} b^{4} d\right)} g^{5}\right)}}"," ",0,"-1/16*(4*((4*A + B)*b^4*c*d^3 - (4*A + B)*a*b^3*d^4)*i^3*x^3 + 6*((4*A + B)*b^4*c^2*d^2 - (4*A + B)*a^2*b^2*d^4)*i^3*x^2 + 4*((4*A + B)*b^4*c^3*d - (4*A + B)*a^3*b*d^4)*i^3*x + ((4*A + B)*b^4*c^4 - (4*A + B)*a^4*d^4)*i^3 + 4*(B*b^4*d^4*i^3*x^4 + 4*B*b^4*c*d^3*i^3*x^3 + 6*B*b^4*c^2*d^2*i^3*x^2 + 4*B*b^4*c^3*d*i^3*x + B*b^4*c^4*i^3)*log((b*e*x + a*e)/(d*x + c)))/((b^9*c - a*b^8*d)*g^5*x^4 + 4*(a*b^8*c - a^2*b^7*d)*g^5*x^3 + 6*(a^2*b^7*c - a^3*b^6*d)*g^5*x^2 + 4*(a^3*b^6*c - a^4*b^5*d)*g^5*x + (a^4*b^5*c - a^5*b^4*d)*g^5)","B",0
29,1,644,0,0.436417," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^6,x, algorithm=""fricas"")","\frac{20 \, {\left(B b^{5} c d^{4} - B a b^{4} d^{5}\right)} i^{3} x^{4} - 10 \, {\left({\left(20 \, A + B\right)} b^{5} c^{2} d^{3} - 10 \, {\left(4 \, A + B\right)} a b^{4} c d^{4} + {\left(20 \, A + 9 \, B\right)} a^{2} b^{3} d^{5}\right)} i^{3} x^{3} - 10 \, {\left(2 \, {\left(20 \, A + 3 \, B\right)} b^{5} c^{3} d^{2} - 15 \, {\left(4 \, A + B\right)} a b^{4} c^{2} d^{3} + {\left(20 \, A + 9 \, B\right)} a^{3} b^{2} d^{5}\right)} i^{3} x^{2} - 5 \, {\left({\left(60 \, A + 11 \, B\right)} b^{5} c^{4} d - 20 \, {\left(4 \, A + B\right)} a b^{4} c^{3} d^{2} + {\left(20 \, A + 9 \, B\right)} a^{4} b d^{5}\right)} i^{3} x - {\left(16 \, {\left(5 \, A + B\right)} b^{5} c^{5} - 25 \, {\left(4 \, A + B\right)} a b^{4} c^{4} d + {\left(20 \, A + 9 \, B\right)} a^{5} d^{5}\right)} i^{3} + 20 \, {\left(B b^{5} d^{5} i^{3} x^{5} + 5 \, B a b^{4} d^{5} i^{3} x^{4} - 10 \, {\left(B b^{5} c^{2} d^{3} - 2 \, B a b^{4} c d^{4}\right)} i^{3} x^{3} - 10 \, {\left(2 \, B b^{5} c^{3} d^{2} - 3 \, B a b^{4} c^{2} d^{3}\right)} i^{3} x^{2} - 5 \, {\left(3 \, B b^{5} c^{4} d - 4 \, B a b^{4} c^{3} d^{2}\right)} i^{3} x - {\left(4 \, B b^{5} c^{5} - 5 \, B a b^{4} c^{4} d\right)} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{400 \, {\left({\left(b^{11} c^{2} - 2 \, a b^{10} c d + a^{2} b^{9} d^{2}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{2} - 2 \, a^{2} b^{9} c d + a^{3} b^{8} d^{2}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{2} - 2 \, a^{3} b^{8} c d + a^{4} b^{7} d^{2}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{2} - 2 \, a^{4} b^{7} c d + a^{5} b^{6} d^{2}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{2} - 2 \, a^{5} b^{6} c d + a^{6} b^{5} d^{2}\right)} g^{6} x + {\left(a^{5} b^{6} c^{2} - 2 \, a^{6} b^{5} c d + a^{7} b^{4} d^{2}\right)} g^{6}\right)}}"," ",0,"1/400*(20*(B*b^5*c*d^4 - B*a*b^4*d^5)*i^3*x^4 - 10*((20*A + B)*b^5*c^2*d^3 - 10*(4*A + B)*a*b^4*c*d^4 + (20*A + 9*B)*a^2*b^3*d^5)*i^3*x^3 - 10*(2*(20*A + 3*B)*b^5*c^3*d^2 - 15*(4*A + B)*a*b^4*c^2*d^3 + (20*A + 9*B)*a^3*b^2*d^5)*i^3*x^2 - 5*((60*A + 11*B)*b^5*c^4*d - 20*(4*A + B)*a*b^4*c^3*d^2 + (20*A + 9*B)*a^4*b*d^5)*i^3*x - (16*(5*A + B)*b^5*c^5 - 25*(4*A + B)*a*b^4*c^4*d + (20*A + 9*B)*a^5*d^5)*i^3 + 20*(B*b^5*d^5*i^3*x^5 + 5*B*a*b^4*d^5*i^3*x^4 - 10*(B*b^5*c^2*d^3 - 2*B*a*b^4*c*d^4)*i^3*x^3 - 10*(2*B*b^5*c^3*d^2 - 3*B*a*b^4*c^2*d^3)*i^3*x^2 - 5*(3*B*b^5*c^4*d - 4*B*a*b^4*c^3*d^2)*i^3*x - (4*B*b^5*c^5 - 5*B*a*b^4*c^4*d)*i^3)*log((b*e*x + a*e)/(d*x + c)))/((b^11*c^2 - 2*a*b^10*c*d + a^2*b^9*d^2)*g^6*x^5 + 5*(a*b^10*c^2 - 2*a^2*b^9*c*d + a^3*b^8*d^2)*g^6*x^4 + 10*(a^2*b^9*c^2 - 2*a^3*b^8*c*d + a^4*b^7*d^2)*g^6*x^3 + 10*(a^3*b^8*c^2 - 2*a^4*b^7*c*d + a^5*b^6*d^2)*g^6*x^2 + 5*(a^4*b^7*c^2 - 2*a^5*b^6*c*d + a^6*b^5*d^2)*g^6*x + (a^5*b^6*c^2 - 2*a^6*b^5*c*d + a^7*b^4*d^2)*g^6)","B",0
30,1,991,0,0.482358," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^7,x, algorithm=""fricas"")","-\frac{60 \, {\left(B b^{6} c d^{5} - B a b^{5} d^{6}\right)} i^{3} x^{5} - 30 \, {\left(B b^{6} c^{2} d^{4} - 12 \, B a b^{5} c d^{5} + 11 \, B a^{2} b^{4} d^{6}\right)} i^{3} x^{4} + 20 \, {\left({\left(60 \, A + B\right)} b^{6} c^{3} d^{3} - 9 \, {\left(20 \, A + B\right)} a b^{5} c^{2} d^{4} + 45 \, {\left(4 \, A + B\right)} a^{2} b^{4} c d^{5} - {\left(60 \, A + 37 \, B\right)} a^{3} b^{3} d^{6}\right)} i^{3} x^{3} + 15 \, {\left({\left(180 \, A + 19 \, B\right)} b^{6} c^{4} d^{2} - 24 \, {\left(20 \, A + 3 \, B\right)} a b^{5} c^{3} d^{3} + 90 \, {\left(4 \, A + B\right)} a^{2} b^{4} c^{2} d^{4} - {\left(60 \, A + 37 \, B\right)} a^{4} b^{2} d^{6}\right)} i^{3} x^{2} + 6 \, {\left(4 \, {\left(90 \, A + 13 \, B\right)} b^{6} c^{5} d - 15 \, {\left(60 \, A + 11 \, B\right)} a b^{5} c^{4} d^{2} + 150 \, {\left(4 \, A + B\right)} a^{2} b^{4} c^{3} d^{3} - {\left(60 \, A + 37 \, B\right)} a^{5} b d^{6}\right)} i^{3} x + {\left(100 \, {\left(6 \, A + B\right)} b^{6} c^{6} - 288 \, {\left(5 \, A + B\right)} a b^{5} c^{5} d + 225 \, {\left(4 \, A + B\right)} a^{2} b^{4} c^{4} d^{2} - {\left(60 \, A + 37 \, B\right)} a^{6} d^{6}\right)} i^{3} + 60 \, {\left(B b^{6} d^{6} i^{3} x^{6} + 6 \, B a b^{5} d^{6} i^{3} x^{5} + 15 \, B a^{2} b^{4} d^{6} i^{3} x^{4} + 20 \, {\left(B b^{6} c^{3} d^{3} - 3 \, B a b^{5} c^{2} d^{4} + 3 \, B a^{2} b^{4} c d^{5}\right)} i^{3} x^{3} + 15 \, {\left(3 \, B b^{6} c^{4} d^{2} - 8 \, B a b^{5} c^{3} d^{3} + 6 \, B a^{2} b^{4} c^{2} d^{4}\right)} i^{3} x^{2} + 6 \, {\left(6 \, B b^{6} c^{5} d - 15 \, B a b^{5} c^{4} d^{2} + 10 \, B a^{2} b^{4} c^{3} d^{3}\right)} i^{3} x + {\left(10 \, B b^{6} c^{6} - 24 \, B a b^{5} c^{5} d + 15 \, B a^{2} b^{4} c^{4} d^{2}\right)} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{3600 \, {\left({\left(b^{13} c^{3} - 3 \, a b^{12} c^{2} d + 3 \, a^{2} b^{11} c d^{2} - a^{3} b^{10} d^{3}\right)} g^{7} x^{6} + 6 \, {\left(a b^{12} c^{3} - 3 \, a^{2} b^{11} c^{2} d + 3 \, a^{3} b^{10} c d^{2} - a^{4} b^{9} d^{3}\right)} g^{7} x^{5} + 15 \, {\left(a^{2} b^{11} c^{3} - 3 \, a^{3} b^{10} c^{2} d + 3 \, a^{4} b^{9} c d^{2} - a^{5} b^{8} d^{3}\right)} g^{7} x^{4} + 20 \, {\left(a^{3} b^{10} c^{3} - 3 \, a^{4} b^{9} c^{2} d + 3 \, a^{5} b^{8} c d^{2} - a^{6} b^{7} d^{3}\right)} g^{7} x^{3} + 15 \, {\left(a^{4} b^{9} c^{3} - 3 \, a^{5} b^{8} c^{2} d + 3 \, a^{6} b^{7} c d^{2} - a^{7} b^{6} d^{3}\right)} g^{7} x^{2} + 6 \, {\left(a^{5} b^{8} c^{3} - 3 \, a^{6} b^{7} c^{2} d + 3 \, a^{7} b^{6} c d^{2} - a^{8} b^{5} d^{3}\right)} g^{7} x + {\left(a^{6} b^{7} c^{3} - 3 \, a^{7} b^{6} c^{2} d + 3 \, a^{8} b^{5} c d^{2} - a^{9} b^{4} d^{3}\right)} g^{7}\right)}}"," ",0,"-1/3600*(60*(B*b^6*c*d^5 - B*a*b^5*d^6)*i^3*x^5 - 30*(B*b^6*c^2*d^4 - 12*B*a*b^5*c*d^5 + 11*B*a^2*b^4*d^6)*i^3*x^4 + 20*((60*A + B)*b^6*c^3*d^3 - 9*(20*A + B)*a*b^5*c^2*d^4 + 45*(4*A + B)*a^2*b^4*c*d^5 - (60*A + 37*B)*a^3*b^3*d^6)*i^3*x^3 + 15*((180*A + 19*B)*b^6*c^4*d^2 - 24*(20*A + 3*B)*a*b^5*c^3*d^3 + 90*(4*A + B)*a^2*b^4*c^2*d^4 - (60*A + 37*B)*a^4*b^2*d^6)*i^3*x^2 + 6*(4*(90*A + 13*B)*b^6*c^5*d - 15*(60*A + 11*B)*a*b^5*c^4*d^2 + 150*(4*A + B)*a^2*b^4*c^3*d^3 - (60*A + 37*B)*a^5*b*d^6)*i^3*x + (100*(6*A + B)*b^6*c^6 - 288*(5*A + B)*a*b^5*c^5*d + 225*(4*A + B)*a^2*b^4*c^4*d^2 - (60*A + 37*B)*a^6*d^6)*i^3 + 60*(B*b^6*d^6*i^3*x^6 + 6*B*a*b^5*d^6*i^3*x^5 + 15*B*a^2*b^4*d^6*i^3*x^4 + 20*(B*b^6*c^3*d^3 - 3*B*a*b^5*c^2*d^4 + 3*B*a^2*b^4*c*d^5)*i^3*x^3 + 15*(3*B*b^6*c^4*d^2 - 8*B*a*b^5*c^3*d^3 + 6*B*a^2*b^4*c^2*d^4)*i^3*x^2 + 6*(6*B*b^6*c^5*d - 15*B*a*b^5*c^4*d^2 + 10*B*a^2*b^4*c^3*d^3)*i^3*x + (10*B*b^6*c^6 - 24*B*a*b^5*c^5*d + 15*B*a^2*b^4*c^4*d^2)*i^3)*log((b*e*x + a*e)/(d*x + c)))/((b^13*c^3 - 3*a*b^12*c^2*d + 3*a^2*b^11*c*d^2 - a^3*b^10*d^3)*g^7*x^6 + 6*(a*b^12*c^3 - 3*a^2*b^11*c^2*d + 3*a^3*b^10*c*d^2 - a^4*b^9*d^3)*g^7*x^5 + 15*(a^2*b^11*c^3 - 3*a^3*b^10*c^2*d + 3*a^4*b^9*c*d^2 - a^5*b^8*d^3)*g^7*x^4 + 20*(a^3*b^10*c^3 - 3*a^4*b^9*c^2*d + 3*a^5*b^8*c*d^2 - a^6*b^7*d^3)*g^7*x^3 + 15*(a^4*b^9*c^3 - 3*a^5*b^8*c^2*d + 3*a^6*b^7*c*d^2 - a^7*b^6*d^3)*g^7*x^2 + 6*(a^5*b^8*c^3 - 3*a^6*b^7*c^2*d + 3*a^7*b^6*c*d^2 - a^8*b^5*d^3)*g^7*x + (a^6*b^7*c^3 - 3*a^7*b^6*c^2*d + 3*a^8*b^5*c*d^2 - a^9*b^4*d^3)*g^7)","B",0
31,0,0,0,0.427640," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{3} g^{3} x^{3} + 3 \, A a b^{2} g^{3} x^{2} + 3 \, A a^{2} b g^{3} x + A a^{3} g^{3} + {\left(B b^{3} g^{3} x^{3} + 3 \, B a b^{2} g^{3} x^{2} + 3 \, B a^{2} b g^{3} x + B a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d i x + c i}, x\right)"," ",0,"integral((A*b^3*g^3*x^3 + 3*A*a*b^2*g^3*x^2 + 3*A*a^2*b*g^3*x + A*a^3*g^3 + (B*b^3*g^3*x^3 + 3*B*a*b^2*g^3*x^2 + 3*B*a^2*b*g^3*x + B*a^3*g^3)*log((b*e*x + a*e)/(d*x + c)))/(d*i*x + c*i), x)","F",0
32,0,0,0,0.447556," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{2} g^{2} x^{2} + 2 \, A a b g^{2} x + A a^{2} g^{2} + {\left(B b^{2} g^{2} x^{2} + 2 \, B a b g^{2} x + B a^{2} g^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d i x + c i}, x\right)"," ",0,"integral((A*b^2*g^2*x^2 + 2*A*a*b*g^2*x + A*a^2*g^2 + (B*b^2*g^2*x^2 + 2*B*a*b*g^2*x + B*a^2*g^2)*log((b*e*x + a*e)/(d*x + c)))/(d*i*x + c*i), x)","F",0
33,0,0,0,0.421075," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b g x + A a g + {\left(B b g x + B a g\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d i x + c i}, x\right)"," ",0,"integral((A*b*g*x + A*a*g + (B*b*g*x + B*a*g)*log((b*e*x + a*e)/(d*x + c)))/(d*i*x + c*i), x)","F",0
34,0,0,0,0.418329," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \log\left(\frac{b e x + a e}{d x + c}\right) + A}{d i x + c i}, x\right)"," ",0,"integral((B*log((b*e*x + a*e)/(d*x + c)) + A)/(d*i*x + c*i), x)","F",0
35,1,60,0,0.446442," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)/(d*i*x+c*i),x, algorithm=""fricas"")","\frac{B \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, A \log\left(\frac{b e x + a e}{d x + c}\right)}{2 \, {\left(b c - a d\right)} g i}"," ",0,"1/2*(B*log((b*e*x + a*e)/(d*x + c))^2 + 2*A*log((b*e*x + a*e)/(d*x + c)))/((b*c - a*d)*g*i)","A",0
36,1,144,0,0.443699," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{2 \, {\left(A + B\right)} b c - 2 \, {\left(A + B\right)} a d + {\left(B b d x + B a d\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left({\left(A + B\right)} b d x + B b c + A a d\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{2 \, {\left({\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{2} i x + {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} g^{2} i\right)}}"," ",0,"-1/2*(2*(A + B)*b*c - 2*(A + B)*a*d + (B*b*d*x + B*a*d)*log((b*e*x + a*e)/(d*x + c))^2 + 2*((A + B)*b*d*x + B*b*c + A*a*d)*log((b*e*x + a*e)/(d*x + c)))/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^2*i*x + (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*g^2*i)","A",0
37,1,349,0,0.440754," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{{\left(2 \, A + B\right)} b^{2} c^{2} - 8 \, {\left(A + B\right)} a b c d + {\left(6 \, A + 7 \, B\right)} a^{2} d^{2} - 2 \, {\left(B b^{2} d^{2} x^{2} + 2 \, B a b d^{2} x + B a^{2} d^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 2 \, {\left({\left(2 \, A + 3 \, B\right)} b^{2} c d - {\left(2 \, A + 3 \, B\right)} a b d^{2}\right)} x - 2 \, {\left({\left(2 \, A + 3 \, B\right)} b^{2} d^{2} x^{2} - B b^{2} c^{2} + 4 \, B a b c d + 2 \, A a^{2} d^{2} + 2 \, {\left(B b^{2} c d + 2 \, {\left(A + B\right)} a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} g^{3} i x + {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} g^{3} i\right)}}"," ",0,"-1/4*((2*A + B)*b^2*c^2 - 8*(A + B)*a*b*c*d + (6*A + 7*B)*a^2*d^2 - 2*(B*b^2*d^2*x^2 + 2*B*a*b*d^2*x + B*a^2*d^2)*log((b*e*x + a*e)/(d*x + c))^2 - 2*((2*A + 3*B)*b^2*c*d - (2*A + 3*B)*a*b*d^2)*x - 2*((2*A + 3*B)*b^2*d^2*x^2 - B*b^2*c^2 + 4*B*a*b*c*d + 2*A*a^2*d^2 + 2*(B*b^2*c*d + 2*(A + B)*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^3*i*x^2 + 2*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*g^3*i*x + (a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*g^3*i)","A",0
38,1,611,0,0.473337," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, A + B\right)} b^{3} c^{3} - 27 \, {\left(2 \, A + B\right)} a b^{2} c^{2} d + 108 \, {\left(A + B\right)} a^{2} b c d^{2} - {\left(66 \, A + 85 \, B\right)} a^{3} d^{3} + 6 \, {\left({\left(6 \, A + 11 \, B\right)} b^{3} c d^{2} - {\left(6 \, A + 11 \, B\right)} a b^{2} d^{3}\right)} x^{2} + 18 \, {\left(B b^{3} d^{3} x^{3} + 3 \, B a b^{2} d^{3} x^{2} + 3 \, B a^{2} b d^{3} x + B a^{3} d^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 3 \, {\left({\left(6 \, A + 5 \, B\right)} b^{3} c^{2} d - 18 \, {\left(2 \, A + 3 \, B\right)} a b^{2} c d^{2} + {\left(30 \, A + 49 \, B\right)} a^{2} b d^{3}\right)} x + 6 \, {\left({\left(6 \, A + 11 \, B\right)} b^{3} d^{3} x^{3} + 2 \, B b^{3} c^{3} - 9 \, B a b^{2} c^{2} d + 18 \, B a^{2} b c d^{2} + 6 \, A a^{3} d^{3} + 3 \, {\left(2 \, B b^{3} c d^{2} + 3 \, {\left(2 \, A + 3 \, B\right)} a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(B b^{3} c^{2} d - 6 \, B a b^{2} c d^{2} - 6 \, {\left(A + B\right)} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{36 \, {\left({\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{6} c^{4} - 4 \, a^{2} b^{5} c^{3} d + 6 \, a^{3} b^{4} c^{2} d^{2} - 4 \, a^{4} b^{3} c d^{3} + a^{5} b^{2} d^{4}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}\right)} g^{4} i x + {\left(a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}\right)} g^{4} i\right)}}"," ",0,"-1/36*(4*(3*A + B)*b^3*c^3 - 27*(2*A + B)*a*b^2*c^2*d + 108*(A + B)*a^2*b*c*d^2 - (66*A + 85*B)*a^3*d^3 + 6*((6*A + 11*B)*b^3*c*d^2 - (6*A + 11*B)*a*b^2*d^3)*x^2 + 18*(B*b^3*d^3*x^3 + 3*B*a*b^2*d^3*x^2 + 3*B*a^2*b*d^3*x + B*a^3*d^3)*log((b*e*x + a*e)/(d*x + c))^2 - 3*((6*A + 5*B)*b^3*c^2*d - 18*(2*A + 3*B)*a*b^2*c*d^2 + (30*A + 49*B)*a^2*b*d^3)*x + 6*((6*A + 11*B)*b^3*d^3*x^3 + 2*B*b^3*c^3 - 9*B*a*b^2*c^2*d + 18*B*a^2*b*c*d^2 + 6*A*a^3*d^3 + 3*(2*B*b^3*c*d^2 + 3*(2*A + 3*B)*a*b^2*d^3)*x^2 - 3*(B*b^3*c^2*d - 6*B*a*b^2*c*d^2 - 6*(A + B)*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^4*i*x^3 + 3*(a*b^6*c^4 - 4*a^2*b^5*c^3*d + 6*a^3*b^4*c^2*d^2 - 4*a^4*b^3*c*d^3 + a^5*b^2*d^4)*g^4*i*x^2 + 3*(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 6*a^4*b^3*c^2*d^2 - 4*a^5*b^2*c*d^3 + a^6*b*d^4)*g^4*i*x + (a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4)*g^4*i)","A",0
39,0,0,0,0.490091," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{3} g^{3} x^{3} + 3 \, A a b^{2} g^{3} x^{2} + 3 \, A a^{2} b g^{3} x + A a^{3} g^{3} + {\left(B b^{3} g^{3} x^{3} + 3 \, B a b^{2} g^{3} x^{2} + 3 \, B a^{2} b g^{3} x + B a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A*b^3*g^3*x^3 + 3*A*a*b^2*g^3*x^2 + 3*A*a^2*b*g^3*x + A*a^3*g^3 + (B*b^3*g^3*x^3 + 3*B*a*b^2*g^3*x^2 + 3*B*a^2*b*g^3*x + B*a^3*g^3)*log((b*e*x + a*e)/(d*x + c)))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
40,0,0,0,0.469847," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{2} g^{2} x^{2} + 2 \, A a b g^{2} x + A a^{2} g^{2} + {\left(B b^{2} g^{2} x^{2} + 2 \, B a b g^{2} x + B a^{2} g^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A*b^2*g^2*x^2 + 2*A*a*b*g^2*x + A*a^2*g^2 + (B*b^2*g^2*x^2 + 2*B*a*b*g^2*x + B*a^2*g^2)*log((b*e*x + a*e)/(d*x + c)))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
41,0,0,0,0.477960," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b g x + A a g + {\left(B b g x + B a g\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A*b*g*x + A*a*g + (B*b*g*x + B*a*g)*log((b*e*x + a*e)/(d*x + c)))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
42,1,88,0,0.493426," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{{\left(A - B\right)} b c - {\left(A - B\right)} a d - {\left(B b d x + B a d\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{{\left(b c d^{2} - a d^{3}\right)} i^{2} x + {\left(b c^{2} d - a c d^{2}\right)} i^{2}}"," ",0,"-((A - B)*b*c - (A - B)*a*d - (B*b*d*x + B*a*d)*log((b*e*x + a*e)/(d*x + c)))/((b*c*d^2 - a*d^3)*i^2*x + (b*c^2*d - a*c*d^2)*i^2)","A",0
43,1,151,0,0.466805," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)/(d*i*x+c*i)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(A - B\right)} b c - 2 \, {\left(A - B\right)} a d + {\left(B b d x + B b c\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left({\left(A - B\right)} b d x + A b c - B a d\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{2 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} g i^{2} x + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} g i^{2}\right)}}"," ",0,"1/2*(2*(A - B)*b*c - 2*(A - B)*a*d + (B*b*d*x + B*b*c)*log((b*e*x + a*e)/(d*x + c))^2 + 2*((A - B)*b*d*x + A*b*c - B*a*d)*log((b*e*x + a*e)/(d*x + c)))/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g*i^2*x + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*g*i^2)","A",0
44,1,334,0,0.483914," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{{\left(A + B\right)} b^{2} c^{2} - 2 \, B a b c d - {\left(A - B\right)} a^{2} d^{2} + {\left(B b^{2} d^{2} x^{2} + B a b c d + {\left(B b^{2} c d + B a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A b^{2} c d - A a b d^{2}\right)} x + {\left(2 \, A b^{2} d^{2} x^{2} + B b^{2} c^{2} + 2 \, A a b c d - B a^{2} d^{2} + 2 \, {\left({\left(A + B\right)} b^{2} c d + {\left(A - B\right)} a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{{\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} g^{2} i^{2} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} g^{2} i^{2} x + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} g^{2} i^{2}}"," ",0,"-((A + B)*b^2*c^2 - 2*B*a*b*c*d - (A - B)*a^2*d^2 + (B*b^2*d^2*x^2 + B*a*b*c*d + (B*b^2*c*d + B*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*b^2*c*d - A*a*b*d^2)*x + (2*A*b^2*d^2*x^2 + B*b^2*c^2 + 2*A*a*b*c*d - B*a^2*d^2 + 2*((A + B)*b^2*c*d + (A - B)*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*g^2*i^2*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*g^2*i^2*x + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*g^2*i^2)","A",0
45,1,664,0,0.492076," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, A + B\right)} b^{3} c^{3} - 12 \, {\left(A + B\right)} a b^{2} c^{2} d + 3 \, {\left(2 \, A + 5 \, B\right)} a^{2} b c d^{2} + 4 \, {\left(A - B\right)} a^{3} d^{3} - 6 \, {\left({\left(2 \, A + B\right)} b^{3} c d^{2} - {\left(2 \, A + B\right)} a b^{2} d^{3}\right)} x^{2} - 6 \, {\left(B b^{3} d^{3} x^{3} + B a^{2} b c d^{2} + {\left(B b^{3} c d^{2} + 2 \, B a b^{2} d^{3}\right)} x^{2} + {\left(2 \, B a b^{2} c d^{2} + B a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 3 \, {\left({\left(2 \, A + 3 \, B\right)} b^{3} c^{2} d + 2 \, {\left(2 \, A - B\right)} a b^{2} c d^{2} - {\left(6 \, A + B\right)} a^{2} b d^{3}\right)} x - 2 \, {\left(3 \, {\left(2 \, A + B\right)} b^{3} d^{3} x^{3} - B b^{3} c^{3} + 6 \, B a b^{2} c^{2} d + 6 \, A a^{2} b c d^{2} - 2 \, B a^{3} d^{3} + 3 \, {\left({\left(2 \, A + 3 \, B\right)} b^{3} c d^{2} + 4 \, A a b^{2} d^{3}\right)} x^{2} + 3 \, {\left(B b^{3} c^{2} d + 4 \, {\left(A + B\right)} a b^{2} c d^{2} + 2 \, {\left(A - B\right)} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{6} c^{4} d - 4 \, a b^{5} c^{3} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} - 4 \, a^{3} b^{3} c d^{4} + a^{4} b^{2} d^{5}\right)} g^{3} i^{2} x^{3} + {\left(b^{6} c^{5} - 2 \, a b^{5} c^{4} d - 2 \, a^{2} b^{4} c^{3} d^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} - 7 \, a^{4} b^{2} c d^{4} + 2 \, a^{5} b d^{5}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{5} c^{5} - 7 \, a^{2} b^{4} c^{4} d + 8 \, a^{3} b^{3} c^{3} d^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} - 2 \, a^{5} b c d^{4} + a^{6} d^{5}\right)} g^{3} i^{2} x + {\left(a^{2} b^{4} c^{5} - 4 \, a^{3} b^{3} c^{4} d + 6 \, a^{4} b^{2} c^{3} d^{2} - 4 \, a^{5} b c^{2} d^{3} + a^{6} c d^{4}\right)} g^{3} i^{2}\right)}}"," ",0,"-1/4*((2*A + B)*b^3*c^3 - 12*(A + B)*a*b^2*c^2*d + 3*(2*A + 5*B)*a^2*b*c*d^2 + 4*(A - B)*a^3*d^3 - 6*((2*A + B)*b^3*c*d^2 - (2*A + B)*a*b^2*d^3)*x^2 - 6*(B*b^3*d^3*x^3 + B*a^2*b*c*d^2 + (B*b^3*c*d^2 + 2*B*a*b^2*d^3)*x^2 + (2*B*a*b^2*c*d^2 + B*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 3*((2*A + 3*B)*b^3*c^2*d + 2*(2*A - B)*a*b^2*c*d^2 - (6*A + B)*a^2*b*d^3)*x - 2*(3*(2*A + B)*b^3*d^3*x^3 - B*b^3*c^3 + 6*B*a*b^2*c^2*d + 6*A*a^2*b*c*d^2 - 2*B*a^3*d^3 + 3*((2*A + 3*B)*b^3*c*d^2 + 4*A*a*b^2*d^3)*x^2 + 3*(B*b^3*c^2*d + 4*(A + B)*a*b^2*c*d^2 + 2*(A - B)*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^6*c^4*d - 4*a*b^5*c^3*d^2 + 6*a^2*b^4*c^2*d^3 - 4*a^3*b^3*c*d^4 + a^4*b^2*d^5)*g^3*i^2*x^3 + (b^6*c^5 - 2*a*b^5*c^4*d - 2*a^2*b^4*c^3*d^2 + 8*a^3*b^3*c^2*d^3 - 7*a^4*b^2*c*d^4 + 2*a^5*b*d^5)*g^3*i^2*x^2 + (2*a*b^5*c^5 - 7*a^2*b^4*c^4*d + 8*a^3*b^3*c^3*d^2 - 2*a^4*b^2*c^2*d^3 - 2*a^5*b*c*d^4 + a^6*d^5)*g^3*i^2*x + (a^2*b^4*c^5 - 4*a^3*b^3*c^4*d + 6*a^4*b^2*c^3*d^2 - 4*a^5*b*c^2*d^3 + a^6*c*d^4)*g^3*i^2)","A",0
46,1,1019,0,0.523955," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{{\left(3 \, A + B\right)} b^{4} c^{4} - 9 \, {\left(2 \, A + B\right)} a b^{3} c^{3} d + 54 \, {\left(A + B\right)} a^{2} b^{2} c^{2} d^{2} - 5 \, {\left(6 \, A + 11 \, B\right)} a^{3} b c d^{3} - 9 \, {\left(A - B\right)} a^{4} d^{4} + 6 \, {\left({\left(6 \, A + 5 \, B\right)} b^{4} c d^{3} - {\left(6 \, A + 5 \, B\right)} a b^{3} d^{4}\right)} x^{3} + 3 \, {\left({\left(6 \, A + 11 \, B\right)} b^{4} c^{2} d^{2} + 8 \, {\left(3 \, A + B\right)} a b^{3} c d^{3} - {\left(30 \, A + 19 \, B\right)} a^{2} b^{2} d^{4}\right)} x^{2} + 18 \, {\left(B b^{4} d^{4} x^{4} + B a^{3} b c d^{3} + {\left(B b^{4} c d^{3} + 3 \, B a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, B a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - {\left({\left(6 \, A + 5 \, B\right)} b^{4} c^{3} d - 27 \, {\left(2 \, A + 3 \, B\right)} a b^{3} c^{2} d^{2} - 3 \, {\left(6 \, A - 19 \, B\right)} a^{2} b^{2} c d^{3} + {\left(66 \, A + 19 \, B\right)} a^{3} b d^{4}\right)} x + 3 \, {\left(2 \, {\left(6 \, A + 5 \, B\right)} b^{4} d^{4} x^{4} + B b^{4} c^{4} - 6 \, B a b^{3} c^{3} d + 18 \, B a^{2} b^{2} c^{2} d^{2} + 12 \, A a^{3} b c d^{3} - 3 \, B a^{4} d^{4} + 2 \, {\left({\left(6 \, A + 11 \, B\right)} b^{4} c d^{3} + 9 \, {\left(2 \, A + B\right)} a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(B b^{4} c^{2} d^{2} + 3 \, {\left(2 \, A + 3 \, B\right)} a b^{3} c d^{3} + 6 \, A a^{2} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(B b^{4} c^{3} d - 9 \, B a b^{3} c^{2} d^{2} - 18 \, {\left(A + B\right)} a^{2} b^{2} c d^{3} - 6 \, {\left(A - B\right)} a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{9 \, {\left({\left(b^{8} c^{5} d - 5 \, a b^{7} c^{4} d^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} - 10 \, a^{3} b^{5} c^{2} d^{4} + 5 \, a^{4} b^{4} c d^{5} - a^{5} b^{3} d^{6}\right)} g^{4} i^{2} x^{4} + {\left(b^{8} c^{6} - 2 \, a b^{7} c^{5} d - 5 \, a^{2} b^{6} c^{4} d^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} - 25 \, a^{4} b^{4} c^{2} d^{4} + 14 \, a^{5} b^{3} c d^{5} - 3 \, a^{6} b^{2} d^{6}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{7} c^{6} - 4 \, a^{2} b^{6} c^{5} d + 5 \, a^{3} b^{5} c^{4} d^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} + 4 \, a^{6} b^{2} c d^{5} - a^{7} b d^{6}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} - 14 \, a^{3} b^{5} c^{5} d + 25 \, a^{4} b^{4} c^{4} d^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} + 5 \, a^{6} b^{2} c^{2} d^{4} + 2 \, a^{7} b c d^{5} - a^{8} d^{6}\right)} g^{4} i^{2} x + {\left(a^{3} b^{5} c^{6} - 5 \, a^{4} b^{4} c^{5} d + 10 \, a^{5} b^{3} c^{4} d^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} + 5 \, a^{7} b c^{2} d^{4} - a^{8} c d^{5}\right)} g^{4} i^{2}\right)}}"," ",0,"-1/9*((3*A + B)*b^4*c^4 - 9*(2*A + B)*a*b^3*c^3*d + 54*(A + B)*a^2*b^2*c^2*d^2 - 5*(6*A + 11*B)*a^3*b*c*d^3 - 9*(A - B)*a^4*d^4 + 6*((6*A + 5*B)*b^4*c*d^3 - (6*A + 5*B)*a*b^3*d^4)*x^3 + 3*((6*A + 11*B)*b^4*c^2*d^2 + 8*(3*A + B)*a*b^3*c*d^3 - (30*A + 19*B)*a^2*b^2*d^4)*x^2 + 18*(B*b^4*d^4*x^4 + B*a^3*b*c*d^3 + (B*b^4*c*d^3 + 3*B*a*b^3*d^4)*x^3 + 3*(B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*x^2 + (3*B*a^2*b^2*c*d^3 + B*a^3*b*d^4)*x)*log((b*e*x + a*e)/(d*x + c))^2 - ((6*A + 5*B)*b^4*c^3*d - 27*(2*A + 3*B)*a*b^3*c^2*d^2 - 3*(6*A - 19*B)*a^2*b^2*c*d^3 + (66*A + 19*B)*a^3*b*d^4)*x + 3*(2*(6*A + 5*B)*b^4*d^4*x^4 + B*b^4*c^4 - 6*B*a*b^3*c^3*d + 18*B*a^2*b^2*c^2*d^2 + 12*A*a^3*b*c*d^3 - 3*B*a^4*d^4 + 2*((6*A + 11*B)*b^4*c*d^3 + 9*(2*A + B)*a*b^3*d^4)*x^3 + 6*(B*b^4*c^2*d^2 + 3*(2*A + 3*B)*a*b^3*c*d^3 + 6*A*a^2*b^2*d^4)*x^2 - 2*(B*b^4*c^3*d - 9*B*a*b^3*c^2*d^2 - 18*(A + B)*a^2*b^2*c*d^3 - 6*(A - B)*a^3*b*d^4)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^8*c^5*d - 5*a*b^7*c^4*d^2 + 10*a^2*b^6*c^3*d^3 - 10*a^3*b^5*c^2*d^4 + 5*a^4*b^4*c*d^5 - a^5*b^3*d^6)*g^4*i^2*x^4 + (b^8*c^6 - 2*a*b^7*c^5*d - 5*a^2*b^6*c^4*d^2 + 20*a^3*b^5*c^3*d^3 - 25*a^4*b^4*c^2*d^4 + 14*a^5*b^3*c*d^5 - 3*a^6*b^2*d^6)*g^4*i^2*x^3 + 3*(a*b^7*c^6 - 4*a^2*b^6*c^5*d + 5*a^3*b^5*c^4*d^2 - 5*a^5*b^3*c^2*d^4 + 4*a^6*b^2*c*d^5 - a^7*b*d^6)*g^4*i^2*x^2 + (3*a^2*b^6*c^6 - 14*a^3*b^5*c^5*d + 25*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 5*a^6*b^2*c^2*d^4 + 2*a^7*b*c*d^5 - a^8*d^6)*g^4*i^2*x + (a^3*b^5*c^6 - 5*a^4*b^4*c^5*d + 10*a^5*b^3*c^4*d^2 - 10*a^6*b^2*c^3*d^3 + 5*a^7*b*c^2*d^4 - a^8*c*d^5)*g^4*i^2)","B",0
47,0,0,0,0.430767," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{3} g^{3} x^{3} + 3 \, A a b^{2} g^{3} x^{2} + 3 \, A a^{2} b g^{3} x + A a^{3} g^{3} + {\left(B b^{3} g^{3} x^{3} + 3 \, B a b^{2} g^{3} x^{2} + 3 \, B a^{2} b g^{3} x + B a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{3} i^{3} x^{3} + 3 \, c d^{2} i^{3} x^{2} + 3 \, c^{2} d i^{3} x + c^{3} i^{3}}, x\right)"," ",0,"integral((A*b^3*g^3*x^3 + 3*A*a*b^2*g^3*x^2 + 3*A*a^2*b*g^3*x + A*a^3*g^3 + (B*b^3*g^3*x^3 + 3*B*a*b^2*g^3*x^2 + 3*B*a^2*b*g^3*x + B*a^3*g^3)*log((b*e*x + a*e)/(d*x + c)))/(d^3*i^3*x^3 + 3*c*d^2*i^3*x^2 + 3*c^2*d*i^3*x + c^3*i^3), x)","F",0
48,0,0,0,0.450019," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{2} g^{2} x^{2} + 2 \, A a b g^{2} x + A a^{2} g^{2} + {\left(B b^{2} g^{2} x^{2} + 2 \, B a b g^{2} x + B a^{2} g^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{3} i^{3} x^{3} + 3 \, c d^{2} i^{3} x^{2} + 3 \, c^{2} d i^{3} x + c^{3} i^{3}}, x\right)"," ",0,"integral((A*b^2*g^2*x^2 + 2*A*a*b*g^2*x + A*a^2*g^2 + (B*b^2*g^2*x^2 + 2*B*a*b*g^2*x + B*a^2*g^2)*log((b*e*x + a*e)/(d*x + c)))/(d^3*i^3*x^3 + 3*c*d^2*i^3*x^2 + 3*c^2*d*i^3*x + c^3*i^3), x)","F",0
49,1,185,0,0.435488," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(2 \, A - B\right)} b^{2} c d - {\left(2 \, A - B\right)} a b d^{2}\right)} g x + {\left({\left(2 \, A - B\right)} b^{2} c^{2} - {\left(2 \, A - B\right)} a^{2} d^{2}\right)} g - 2 \, {\left(B b^{2} d^{2} g x^{2} + 2 \, B a b d^{2} g x + B a^{2} d^{2} g\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}\right)}}"," ",0,"-1/4*(2*((2*A - B)*b^2*c*d - (2*A - B)*a*b*d^2)*g*x + ((2*A - B)*b^2*c^2 - (2*A - B)*a^2*d^2)*g - 2*(B*b^2*d^2*g*x^2 + 2*B*a*b*d^2*g*x + B*a^2*d^2*g)*log((b*e*x + a*e)/(d*x + c)))/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3)","B",0
50,1,221,0,0.472628," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, A - 3 \, B\right)} b^{2} c^{2} - 4 \, {\left(A - B\right)} a b c d + {\left(2 \, A - B\right)} a^{2} d^{2} - 2 \, {\left(B b^{2} c d - B a b d^{2}\right)} x - 2 \, {\left(B b^{2} d^{2} x^{2} + 2 \, B b^{2} c d x + 2 \, B a b c d - B a^{2} d^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} i^{3} x + {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} i^{3}\right)}}"," ",0,"-1/4*((2*A - 3*B)*b^2*c^2 - 4*(A - B)*a*b*c*d + (2*A - B)*a^2*d^2 - 2*(B*b^2*c*d - B*a*b*d^2)*x - 2*(B*b^2*d^2*x^2 + 2*B*b^2*c*d*x + 2*B*a*b*c*d - B*a^2*d^2)*log((b*e*x + a*e)/(d*x + c)))/((b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*i^3*x^2 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*i^3*x + (b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*i^3)","A",0
51,1,355,0,0.440357," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)/(d*i*x+c*i)^3,x, algorithm=""fricas"")","\frac{{\left(6 \, A - 7 \, B\right)} b^{2} c^{2} - 8 \, {\left(A - B\right)} a b c d + {\left(2 \, A - B\right)} a^{2} d^{2} + 2 \, {\left(B b^{2} d^{2} x^{2} + 2 \, B b^{2} c d x + B b^{2} c^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left({\left(2 \, A - 3 \, B\right)} b^{2} c d - {\left(2 \, A - 3 \, B\right)} a b d^{2}\right)} x + 2 \, {\left({\left(2 \, A - 3 \, B\right)} b^{2} d^{2} x^{2} + 2 \, A b^{2} c^{2} - 4 \, B a b c d + B a^{2} d^{2} + 2 \, {\left(2 \, {\left(A - B\right)} b^{2} c d - B a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} g i^{3} x^{2} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} g i^{3} x + {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} g i^{3}\right)}}"," ",0,"1/4*((6*A - 7*B)*b^2*c^2 - 8*(A - B)*a*b*c*d + (2*A - B)*a^2*d^2 + 2*(B*b^2*d^2*x^2 + 2*B*b^2*c*d*x + B*b^2*c^2)*log((b*e*x + a*e)/(d*x + c))^2 + 2*((2*A - 3*B)*b^2*c*d - (2*A - 3*B)*a*b*d^2)*x + 2*((2*A - 3*B)*b^2*d^2*x^2 + 2*A*b^2*c^2 - 4*B*a*b*c*d + B*a^2*d^2 + 2*(2*(A - B)*b^2*c*d - B*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*g*i^3*x^2 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*g*i^3*x + (b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*g*i^3)","A",0
52,1,672,0,0.455930," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(A + B\right)} b^{3} c^{3} + 3 \, {\left(2 \, A - 5 \, B\right)} a b^{2} c^{2} d - 12 \, {\left(A - B\right)} a^{2} b c d^{2} + {\left(2 \, A - B\right)} a^{3} d^{3} + 6 \, {\left({\left(2 \, A - B\right)} b^{3} c d^{2} - {\left(2 \, A - B\right)} a b^{2} d^{3}\right)} x^{2} + 6 \, {\left(B b^{3} d^{3} x^{3} + B a b^{2} c^{2} d + {\left(2 \, B b^{3} c d^{2} + B a b^{2} d^{3}\right)} x^{2} + {\left(B b^{3} c^{2} d + 2 \, B a b^{2} c d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 3 \, {\left({\left(6 \, A - B\right)} b^{3} c^{2} d - 2 \, {\left(2 \, A + B\right)} a b^{2} c d^{2} - {\left(2 \, A - 3 \, B\right)} a^{2} b d^{3}\right)} x + 2 \, {\left(3 \, {\left(2 \, A - B\right)} b^{3} d^{3} x^{3} + 2 \, B b^{3} c^{3} + 6 \, A a b^{2} c^{2} d - 6 \, B a^{2} b c d^{2} + B a^{3} d^{3} + 3 \, {\left(4 \, A b^{3} c d^{2} + {\left(2 \, A - 3 \, B\right)} a b^{2} d^{3}\right)} x^{2} + 3 \, {\left(2 \, {\left(A + B\right)} b^{3} c^{2} d + 4 \, {\left(A - B\right)} a b^{2} c d^{2} - B a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} g^{2} i^{3} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} g^{2} i^{3} x + {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4}\right)} g^{2} i^{3}\right)}}"," ",0,"-1/4*(4*(A + B)*b^3*c^3 + 3*(2*A - 5*B)*a*b^2*c^2*d - 12*(A - B)*a^2*b*c*d^2 + (2*A - B)*a^3*d^3 + 6*((2*A - B)*b^3*c*d^2 - (2*A - B)*a*b^2*d^3)*x^2 + 6*(B*b^3*d^3*x^3 + B*a*b^2*c^2*d + (2*B*b^3*c*d^2 + B*a*b^2*d^3)*x^2 + (B*b^3*c^2*d + 2*B*a*b^2*c*d^2)*x)*log((b*e*x + a*e)/(d*x + c))^2 + 3*((6*A - B)*b^3*c^2*d - 2*(2*A + B)*a*b^2*c*d^2 - (2*A - 3*B)*a^2*b*d^3)*x + 2*(3*(2*A - B)*b^3*d^3*x^3 + 2*B*b^3*c^3 + 6*A*a*b^2*c^2*d - 6*B*a^2*b*c*d^2 + B*a^3*d^3 + 3*(4*A*b^3*c*d^2 + (2*A - 3*B)*a*b^2*d^3)*x^2 + 3*(2*(A + B)*b^3*c^2*d + 4*(A - B)*a*b^2*c*d^2 - B*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*g^2*i^3*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*g^2*i^3*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*g^2*i^3*x + (a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4)*g^2*i^3)","A",0
53,1,1011,0,0.470658," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^3/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, A + B\right)} b^{4} c^{4} - 16 \, {\left(A + B\right)} a b^{3} c^{3} d + 30 \, B a^{2} b^{2} c^{2} d^{2} + 16 \, {\left(A - B\right)} a^{3} b c d^{3} - {\left(2 \, A - B\right)} a^{4} d^{4} - 24 \, {\left(A b^{4} c d^{3} - A a b^{3} d^{4}\right)} x^{3} - 12 \, {\left({\left(3 \, A + B\right)} b^{4} c^{2} d^{2} - 2 \, B a b^{3} c d^{3} - {\left(3 \, A - B\right)} a^{2} b^{2} d^{4}\right)} x^{2} - 12 \, {\left(B b^{4} d^{4} x^{4} + B a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(B b^{4} c d^{3} + B a b^{3} d^{4}\right)} x^{3} + {\left(B b^{4} c^{2} d^{2} + 4 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(B a b^{3} c^{2} d^{2} + B a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 4 \, {\left({\left(2 \, A + 3 \, B\right)} b^{4} c^{3} d + 3 \, {\left(4 \, A - B\right)} a b^{3} c^{2} d^{2} - 3 \, {\left(4 \, A + B\right)} a^{2} b^{2} c d^{3} - {\left(2 \, A - 3 \, B\right)} a^{3} b d^{4}\right)} x - 2 \, {\left(12 \, A b^{4} d^{4} x^{4} - B b^{4} c^{4} + 8 \, B a b^{3} c^{3} d + 12 \, A a^{2} b^{2} c^{2} d^{2} - 8 \, B a^{3} b c d^{3} + B a^{4} d^{4} + 12 \, {\left({\left(2 \, A + B\right)} b^{4} c d^{3} + {\left(2 \, A - B\right)} a b^{3} d^{4}\right)} x^{3} + 6 \, {\left({\left(2 \, A + 3 \, B\right)} b^{4} c^{2} d^{2} + 8 \, A a b^{3} c d^{3} + {\left(2 \, A - 3 \, B\right)} a^{2} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(B b^{4} c^{3} d + 6 \, {\left(A + B\right)} a b^{3} c^{2} d^{2} + 6 \, {\left(A - B\right)} a^{2} b^{2} c d^{3} - B a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} g^{3} i^{3} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} g^{3} i^{3} x + {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5}\right)} g^{3} i^{3}\right)}}"," ",0,"-1/4*((2*A + B)*b^4*c^4 - 16*(A + B)*a*b^3*c^3*d + 30*B*a^2*b^2*c^2*d^2 + 16*(A - B)*a^3*b*c*d^3 - (2*A - B)*a^4*d^4 - 24*(A*b^4*c*d^3 - A*a*b^3*d^4)*x^3 - 12*((3*A + B)*b^4*c^2*d^2 - 2*B*a*b^3*c*d^3 - (3*A - B)*a^2*b^2*d^4)*x^2 - 12*(B*b^4*d^4*x^4 + B*a^2*b^2*c^2*d^2 + 2*(B*b^4*c*d^3 + B*a*b^3*d^4)*x^3 + (B*b^4*c^2*d^2 + 4*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*x^2 + 2*(B*a*b^3*c^2*d^2 + B*a^2*b^2*c*d^3)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 4*((2*A + 3*B)*b^4*c^3*d + 3*(4*A - B)*a*b^3*c^2*d^2 - 3*(4*A + B)*a^2*b^2*c*d^3 - (2*A - 3*B)*a^3*b*d^4)*x - 2*(12*A*b^4*d^4*x^4 - B*b^4*c^4 + 8*B*a*b^3*c^3*d + 12*A*a^2*b^2*c^2*d^2 - 8*B*a^3*b*c*d^3 + B*a^4*d^4 + 12*((2*A + B)*b^4*c*d^3 + (2*A - B)*a*b^3*d^4)*x^3 + 6*((2*A + 3*B)*b^4*c^2*d^2 + 8*A*a*b^3*c*d^3 + (2*A - 3*B)*a^2*b^2*d^4)*x^2 + 4*(B*b^4*c^3*d + 6*(A + B)*a*b^3*c^2*d^2 + 6*(A - B)*a^2*b^2*c*d^3 - B*a^3*b*d^4)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*g^3*i^3*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*g^3*i^3*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*g^3*i^3*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*g^3*i^3*x + (a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5)*g^3*i^3)","B",0
54,1,1509,0,0.525233," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))/(b*g*x+a*g)^4/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, A + B\right)} b^{5} c^{5} - 45 \, {\left(2 \, A + B\right)} a b^{4} c^{4} d + 360 \, {\left(A + B\right)} a^{2} b^{3} c^{3} d^{2} - 10 \, {\left(12 \, A + 49 \, B\right)} a^{3} b^{2} c^{2} d^{3} - 180 \, {\left(A - B\right)} a^{4} b c d^{4} + 9 \, {\left(2 \, A - B\right)} a^{5} d^{5} + 120 \, {\left({\left(3 \, A + B\right)} b^{5} c d^{4} - {\left(3 \, A + B\right)} a b^{4} d^{5}\right)} x^{4} + 60 \, {\left(3 \, {\left(3 \, A + 2 \, B\right)} b^{5} c^{2} d^{3} + 2 \, {\left(3 \, A - 2 \, B\right)} a b^{4} c d^{4} - {\left(15 \, A + 2 \, B\right)} a^{2} b^{3} d^{5}\right)} x^{3} + 20 \, {\left({\left(6 \, A + 11 \, B\right)} b^{5} c^{3} d^{2} + 21 \, {\left(3 \, A + B\right)} a b^{4} c^{2} d^{3} - 3 \, {\left(12 \, A + 13 \, B\right)} a^{2} b^{3} c d^{4} - {\left(33 \, A - 7 \, B\right)} a^{3} b^{2} d^{5}\right)} x^{2} + 180 \, {\left(B b^{5} d^{5} x^{5} + B a^{3} b^{2} c^{2} d^{3} + {\left(2 \, B b^{5} c d^{4} + 3 \, B a b^{4} d^{5}\right)} x^{4} + {\left(B b^{5} c^{2} d^{3} + 6 \, B a b^{4} c d^{4} + 3 \, B a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, B a b^{4} c^{2} d^{3} + 6 \, B a^{2} b^{3} c d^{4} + B a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, B a^{2} b^{3} c^{2} d^{3} + 2 \, B a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 5 \, {\left({\left(6 \, A + 5 \, B\right)} b^{5} c^{4} d - 36 \, {\left(2 \, A + 3 \, B\right)} a b^{4} c^{3} d^{2} - 6 \, {\left(24 \, A - 13 \, B\right)} a^{2} b^{3} c^{2} d^{3} + 4 \, {\left(48 \, A + 13 \, B\right)} a^{3} b^{2} c d^{4} + 9 \, {\left(2 \, A - 3 \, B\right)} a^{4} b d^{5}\right)} x + 6 \, {\left(20 \, {\left(3 \, A + B\right)} b^{5} d^{5} x^{5} + 2 \, B b^{5} c^{5} - 15 \, B a b^{4} c^{4} d + 60 \, B a^{2} b^{3} c^{3} d^{2} + 60 \, A a^{3} b^{2} c^{2} d^{3} - 30 \, B a^{4} b c d^{4} + 3 \, B a^{5} d^{5} + 20 \, {\left({\left(6 \, A + 5 \, B\right)} b^{5} c d^{4} + 9 \, A a b^{4} d^{5}\right)} x^{4} + 10 \, {\left({\left(6 \, A + 11 \, B\right)} b^{5} c^{2} d^{3} + 18 \, {\left(2 \, A + B\right)} a b^{4} c d^{4} + 9 \, {\left(2 \, A - B\right)} a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(2 \, B b^{5} c^{3} d^{2} + 9 \, {\left(2 \, A + 3 \, B\right)} a b^{4} c^{2} d^{3} + 36 \, A a^{2} b^{3} c d^{4} + 3 \, {\left(2 \, A - 3 \, B\right)} a^{3} b^{2} d^{5}\right)} x^{2} - 5 \, {\left(B b^{5} c^{4} d - 12 \, B a b^{4} c^{3} d^{2} - 36 \, {\left(A + B\right)} a^{2} b^{3} c^{2} d^{3} - 24 \, {\left(A - B\right)} a^{3} b^{2} c d^{4} + 3 \, B a^{4} b d^{5}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{36 \, {\left({\left(b^{9} c^{6} d^{2} - 6 \, a b^{8} c^{5} d^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} - 20 \, a^{3} b^{6} c^{3} d^{5} + 15 \, a^{4} b^{5} c^{2} d^{6} - 6 \, a^{5} b^{4} c d^{7} + a^{6} b^{3} d^{8}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{9} c^{7} d - 9 \, a b^{8} c^{6} d^{2} + 12 \, a^{2} b^{7} c^{5} d^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} - 30 \, a^{4} b^{5} c^{3} d^{5} + 33 \, a^{5} b^{4} c^{2} d^{6} - 16 \, a^{6} b^{3} c d^{7} + 3 \, a^{7} b^{2} d^{8}\right)} g^{4} i^{3} x^{4} + {\left(b^{9} c^{8} - 18 \, a^{2} b^{7} c^{6} d^{2} + 52 \, a^{3} b^{6} c^{5} d^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} + 24 \, a^{5} b^{4} c^{3} d^{5} + 10 \, a^{6} b^{3} c^{2} d^{6} - 12 \, a^{7} b^{2} c d^{7} + 3 \, a^{8} b d^{8}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{8} c^{8} - 12 \, a^{2} b^{7} c^{7} d + 10 \, a^{3} b^{6} c^{6} d^{2} + 24 \, a^{4} b^{5} c^{5} d^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} + 52 \, a^{6} b^{3} c^{3} d^{5} - 18 \, a^{7} b^{2} c^{2} d^{6} + a^{9} d^{8}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} - 16 \, a^{3} b^{6} c^{7} d + 33 \, a^{4} b^{5} c^{6} d^{2} - 30 \, a^{5} b^{4} c^{5} d^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} + 12 \, a^{7} b^{2} c^{3} d^{5} - 9 \, a^{8} b c^{2} d^{6} + 2 \, a^{9} c d^{7}\right)} g^{4} i^{3} x + {\left(a^{3} b^{6} c^{8} - 6 \, a^{4} b^{5} c^{7} d + 15 \, a^{5} b^{4} c^{6} d^{2} - 20 \, a^{6} b^{3} c^{5} d^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} - 6 \, a^{8} b c^{3} d^{5} + a^{9} c^{2} d^{6}\right)} g^{4} i^{3}\right)}}"," ",0,"-1/36*(4*(3*A + B)*b^5*c^5 - 45*(2*A + B)*a*b^4*c^4*d + 360*(A + B)*a^2*b^3*c^3*d^2 - 10*(12*A + 49*B)*a^3*b^2*c^2*d^3 - 180*(A - B)*a^4*b*c*d^4 + 9*(2*A - B)*a^5*d^5 + 120*((3*A + B)*b^5*c*d^4 - (3*A + B)*a*b^4*d^5)*x^4 + 60*(3*(3*A + 2*B)*b^5*c^2*d^3 + 2*(3*A - 2*B)*a*b^4*c*d^4 - (15*A + 2*B)*a^2*b^3*d^5)*x^3 + 20*((6*A + 11*B)*b^5*c^3*d^2 + 21*(3*A + B)*a*b^4*c^2*d^3 - 3*(12*A + 13*B)*a^2*b^3*c*d^4 - (33*A - 7*B)*a^3*b^2*d^5)*x^2 + 180*(B*b^5*d^5*x^5 + B*a^3*b^2*c^2*d^3 + (2*B*b^5*c*d^4 + 3*B*a*b^4*d^5)*x^4 + (B*b^5*c^2*d^3 + 6*B*a*b^4*c*d^4 + 3*B*a^2*b^3*d^5)*x^3 + (3*B*a*b^4*c^2*d^3 + 6*B*a^2*b^3*c*d^4 + B*a^3*b^2*d^5)*x^2 + (3*B*a^2*b^3*c^2*d^3 + 2*B*a^3*b^2*c*d^4)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 5*((6*A + 5*B)*b^5*c^4*d - 36*(2*A + 3*B)*a*b^4*c^3*d^2 - 6*(24*A - 13*B)*a^2*b^3*c^2*d^3 + 4*(48*A + 13*B)*a^3*b^2*c*d^4 + 9*(2*A - 3*B)*a^4*b*d^5)*x + 6*(20*(3*A + B)*b^5*d^5*x^5 + 2*B*b^5*c^5 - 15*B*a*b^4*c^4*d + 60*B*a^2*b^3*c^3*d^2 + 60*A*a^3*b^2*c^2*d^3 - 30*B*a^4*b*c*d^4 + 3*B*a^5*d^5 + 20*((6*A + 5*B)*b^5*c*d^4 + 9*A*a*b^4*d^5)*x^4 + 10*((6*A + 11*B)*b^5*c^2*d^3 + 18*(2*A + B)*a*b^4*c*d^4 + 9*(2*A - B)*a^2*b^3*d^5)*x^3 + 10*(2*B*b^5*c^3*d^2 + 9*(2*A + 3*B)*a*b^4*c^2*d^3 + 36*A*a^2*b^3*c*d^4 + 3*(2*A - 3*B)*a^3*b^2*d^5)*x^2 - 5*(B*b^5*c^4*d - 12*B*a*b^4*c^3*d^2 - 36*(A + B)*a^2*b^3*c^2*d^3 - 24*(A - B)*a^3*b^2*c*d^4 + 3*B*a^4*b*d^5)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^9*c^6*d^2 - 6*a*b^8*c^5*d^3 + 15*a^2*b^7*c^4*d^4 - 20*a^3*b^6*c^3*d^5 + 15*a^4*b^5*c^2*d^6 - 6*a^5*b^4*c*d^7 + a^6*b^3*d^8)*g^4*i^3*x^5 + (2*b^9*c^7*d - 9*a*b^8*c^6*d^2 + 12*a^2*b^7*c^5*d^3 + 5*a^3*b^6*c^4*d^4 - 30*a^4*b^5*c^3*d^5 + 33*a^5*b^4*c^2*d^6 - 16*a^6*b^3*c*d^7 + 3*a^7*b^2*d^8)*g^4*i^3*x^4 + (b^9*c^8 - 18*a^2*b^7*c^6*d^2 + 52*a^3*b^6*c^5*d^3 - 60*a^4*b^5*c^4*d^4 + 24*a^5*b^4*c^3*d^5 + 10*a^6*b^3*c^2*d^6 - 12*a^7*b^2*c*d^7 + 3*a^8*b*d^8)*g^4*i^3*x^3 + (3*a*b^8*c^8 - 12*a^2*b^7*c^7*d + 10*a^3*b^6*c^6*d^2 + 24*a^4*b^5*c^5*d^3 - 60*a^5*b^4*c^4*d^4 + 52*a^6*b^3*c^3*d^5 - 18*a^7*b^2*c^2*d^6 + a^9*d^8)*g^4*i^3*x^2 + (3*a^2*b^7*c^8 - 16*a^3*b^6*c^7*d + 33*a^4*b^5*c^6*d^2 - 30*a^5*b^4*c^5*d^3 + 5*a^6*b^3*c^4*d^4 + 12*a^7*b^2*c^3*d^5 - 9*a^8*b*c^2*d^6 + 2*a^9*c*d^7)*g^4*i^3*x + (a^3*b^6*c^8 - 6*a^4*b^5*c^7*d + 15*a^5*b^4*c^6*d^2 - 20*a^6*b^3*c^5*d^3 + 15*a^7*b^2*c^4*d^4 - 6*a^8*b*c^3*d^5 + a^9*c^2*d^6)*g^4*i^3)","B",0
55,0,0,0,0.444125," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{3} d g^{3} i x^{4} + A^{2} a^{3} c g^{3} i + {\left(A^{2} b^{3} c + 3 \, A^{2} a b^{2} d\right)} g^{3} i x^{3} + 3 \, {\left(A^{2} a b^{2} c + A^{2} a^{2} b d\right)} g^{3} i x^{2} + {\left(3 \, A^{2} a^{2} b c + A^{2} a^{3} d\right)} g^{3} i x + {\left(B^{2} b^{3} d g^{3} i x^{4} + B^{2} a^{3} c g^{3} i + {\left(B^{2} b^{3} c + 3 \, B^{2} a b^{2} d\right)} g^{3} i x^{3} + 3 \, {\left(B^{2} a b^{2} c + B^{2} a^{2} b d\right)} g^{3} i x^{2} + {\left(3 \, B^{2} a^{2} b c + B^{2} a^{3} d\right)} g^{3} i x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{3} d g^{3} i x^{4} + A B a^{3} c g^{3} i + {\left(A B b^{3} c + 3 \, A B a b^{2} d\right)} g^{3} i x^{3} + 3 \, {\left(A B a b^{2} c + A B a^{2} b d\right)} g^{3} i x^{2} + {\left(3 \, A B a^{2} b c + A B a^{3} d\right)} g^{3} i x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b^3*d*g^3*i*x^4 + A^2*a^3*c*g^3*i + (A^2*b^3*c + 3*A^2*a*b^2*d)*g^3*i*x^3 + 3*(A^2*a*b^2*c + A^2*a^2*b*d)*g^3*i*x^2 + (3*A^2*a^2*b*c + A^2*a^3*d)*g^3*i*x + (B^2*b^3*d*g^3*i*x^4 + B^2*a^3*c*g^3*i + (B^2*b^3*c + 3*B^2*a*b^2*d)*g^3*i*x^3 + 3*(B^2*a*b^2*c + B^2*a^2*b*d)*g^3*i*x^2 + (3*B^2*a^2*b*c + B^2*a^3*d)*g^3*i*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^3*d*g^3*i*x^4 + A*B*a^3*c*g^3*i + (A*B*b^3*c + 3*A*B*a*b^2*d)*g^3*i*x^3 + 3*(A*B*a*b^2*c + A*B*a^2*b*d)*g^3*i*x^2 + (3*A*B*a^2*b*c + A*B*a^3*d)*g^3*i*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
56,0,0,0,0.440391," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{2} d g^{2} i x^{3} + A^{2} a^{2} c g^{2} i + {\left(A^{2} b^{2} c + 2 \, A^{2} a b d\right)} g^{2} i x^{2} + {\left(2 \, A^{2} a b c + A^{2} a^{2} d\right)} g^{2} i x + {\left(B^{2} b^{2} d g^{2} i x^{3} + B^{2} a^{2} c g^{2} i + {\left(B^{2} b^{2} c + 2 \, B^{2} a b d\right)} g^{2} i x^{2} + {\left(2 \, B^{2} a b c + B^{2} a^{2} d\right)} g^{2} i x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{2} d g^{2} i x^{3} + A B a^{2} c g^{2} i + {\left(A B b^{2} c + 2 \, A B a b d\right)} g^{2} i x^{2} + {\left(2 \, A B a b c + A B a^{2} d\right)} g^{2} i x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b^2*d*g^2*i*x^3 + A^2*a^2*c*g^2*i + (A^2*b^2*c + 2*A^2*a*b*d)*g^2*i*x^2 + (2*A^2*a*b*c + A^2*a^2*d)*g^2*i*x + (B^2*b^2*d*g^2*i*x^3 + B^2*a^2*c*g^2*i + (B^2*b^2*c + 2*B^2*a*b*d)*g^2*i*x^2 + (2*B^2*a*b*c + B^2*a^2*d)*g^2*i*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^2*d*g^2*i*x^3 + A*B*a^2*c*g^2*i + (A*B*b^2*c + 2*A*B*a*b*d)*g^2*i*x^2 + (2*A*B*a*b*c + A*B*a^2*d)*g^2*i*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
57,0,0,0,0.481744," ","integrate((b*g*x+a*g)*(d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b d g i x^{2} + A^{2} a c g i + {\left(A^{2} b c + A^{2} a d\right)} g i x + {\left(B^{2} b d g i x^{2} + B^{2} a c g i + {\left(B^{2} b c + B^{2} a d\right)} g i x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b d g i x^{2} + A B a c g i + {\left(A B b c + A B a d\right)} g i x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b*d*g*i*x^2 + A^2*a*c*g*i + (A^2*b*c + A^2*a*d)*g*i*x + (B^2*b*d*g*i*x^2 + B^2*a*c*g*i + (B^2*b*c + B^2*a*d)*g*i*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b*d*g*i*x^2 + A*B*a*c*g*i + (A*B*b*c + A*B*a*d)*g*i*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
58,0,0,0,0.444009," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} d i x + A^{2} c i + {\left(B^{2} d i x + B^{2} c i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d i x + A B c i\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*d*i*x + A^2*c*i + (B^2*d*i*x + B^2*c*i)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d*i*x + A*B*c*i)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
59,0,0,0,0.425861," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d i x + A^{2} c i + {\left(B^{2} d i x + B^{2} c i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d i x + A B c i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b g x + a g}, x\right)"," ",0,"integral((A^2*d*i*x + A^2*c*i + (B^2*d*i*x + B^2*c*i)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d*i*x + A*B*c*i)*log((b*e*x + a*e)/(d*x + c)))/(b*g*x + a*g), x)","F",0
60,0,0,0,0.421250," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d i x + A^{2} c i + {\left(B^{2} d i x + B^{2} c i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d i x + A B c i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A^2*d*i*x + A^2*c*i + (B^2*d*i*x + B^2*c*i)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d*i*x + A*B*c*i)*log((b*e*x + a*e)/(d*x + c)))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
61,1,289,0,0.451096," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} b^{2} c d - {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a b d^{2}\right)} i x + 2 \, {\left(B^{2} b^{2} d^{2} i x^{2} + 2 \, B^{2} b^{2} c d i x + B^{2} b^{2} c^{2} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + {\left({\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} b^{2} c^{2} - {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a^{2} d^{2}\right)} i + 2 \, {\left({\left(2 \, A B + B^{2}\right)} b^{2} d^{2} i x^{2} + 2 \, {\left(2 \, A B + B^{2}\right)} b^{2} c d i x + {\left(2 \, A B + B^{2}\right)} b^{2} c^{2} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}\right)}}"," ",0,"-1/4*(2*((2*A^2 + 2*A*B + B^2)*b^2*c*d - (2*A^2 + 2*A*B + B^2)*a*b*d^2)*i*x + 2*(B^2*b^2*d^2*i*x^2 + 2*B^2*b^2*c*d*i*x + B^2*b^2*c^2*i)*log((b*e*x + a*e)/(d*x + c))^2 + ((2*A^2 + 2*A*B + B^2)*b^2*c^2 - (2*A^2 + 2*A*B + B^2)*a^2*d^2)*i + 2*((2*A*B + B^2)*b^2*d^2*i*x^2 + 2*(2*A*B + B^2)*b^2*c*d*i*x + (2*A*B + B^2)*b^2*c^2*i)*log((b*e*x + a*e)/(d*x + c)))/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3)","B",0
62,1,601,0,0.517283," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4,x, algorithm=""fricas"")","\frac{6 \, {\left({\left(6 \, A B + 5 \, B^{2}\right)} b^{3} c d^{2} - {\left(6 \, A B + 5 \, B^{2}\right)} a b^{2} d^{3}\right)} i x^{2} - 3 \, {\left({\left(18 \, A^{2} + 6 \, A B - B^{2}\right)} b^{3} c^{2} d - 18 \, {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a b^{2} c d^{2} + {\left(18 \, A^{2} + 30 \, A B + 19 \, B^{2}\right)} a^{2} b d^{3}\right)} i x + 18 \, {\left(B^{2} b^{3} d^{3} i x^{3} + 3 \, B^{2} a b^{2} d^{3} i x^{2} - 3 \, {\left(B^{2} b^{3} c^{2} d - 2 \, B^{2} a b^{2} c d^{2}\right)} i x - {\left(2 \, B^{2} b^{3} c^{3} - 3 \, B^{2} a b^{2} c^{2} d\right)} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - {\left(4 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} b^{3} c^{3} - 27 \, {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a b^{2} c^{2} d + {\left(18 \, A^{2} + 30 \, A B + 19 \, B^{2}\right)} a^{3} d^{3}\right)} i + 6 \, {\left({\left(6 \, A B + 5 \, B^{2}\right)} b^{3} d^{3} i x^{3} + 3 \, {\left(2 \, B^{2} b^{3} c d^{2} + 3 \, {\left(2 \, A B + B^{2}\right)} a b^{2} d^{3}\right)} i x^{2} - 3 \, {\left({\left(6 \, A B + B^{2}\right)} b^{3} c^{2} d - 6 \, {\left(2 \, A B + B^{2}\right)} a b^{2} c d^{2}\right)} i x - {\left(4 \, {\left(3 \, A B + B^{2}\right)} b^{3} c^{3} - 9 \, {\left(2 \, A B + B^{2}\right)} a b^{2} c^{2} d\right)} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{108 \, {\left({\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}\right)}}"," ",0,"1/108*(6*((6*A*B + 5*B^2)*b^3*c*d^2 - (6*A*B + 5*B^2)*a*b^2*d^3)*i*x^2 - 3*((18*A^2 + 6*A*B - B^2)*b^3*c^2*d - 18*(2*A^2 + 2*A*B + B^2)*a*b^2*c*d^2 + (18*A^2 + 30*A*B + 19*B^2)*a^2*b*d^3)*i*x + 18*(B^2*b^3*d^3*i*x^3 + 3*B^2*a*b^2*d^3*i*x^2 - 3*(B^2*b^3*c^2*d - 2*B^2*a*b^2*c*d^2)*i*x - (2*B^2*b^3*c^3 - 3*B^2*a*b^2*c^2*d)*i)*log((b*e*x + a*e)/(d*x + c))^2 - (4*(9*A^2 + 6*A*B + 2*B^2)*b^3*c^3 - 27*(2*A^2 + 2*A*B + B^2)*a*b^2*c^2*d + (18*A^2 + 30*A*B + 19*B^2)*a^3*d^3)*i + 6*((6*A*B + 5*B^2)*b^3*d^3*i*x^3 + 3*(2*B^2*b^3*c*d^2 + 3*(2*A*B + B^2)*a*b^2*d^3)*i*x^2 - 3*((6*A*B + B^2)*b^3*c^2*d - 6*(2*A*B + B^2)*a*b^2*c*d^2)*i*x - (4*(3*A*B + B^2)*b^3*c^3 - 9*(2*A*B + B^2)*a*b^2*c^2*d)*i)*log((b*e*x + a*e)/(d*x + c)))/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4)","B",0
63,1,985,0,0.471412," ","integrate((d*i*x+c*i)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^5,x, algorithm=""fricas"")","-\frac{12 \, {\left({\left(12 \, A B + 13 \, B^{2}\right)} b^{4} c d^{3} - {\left(12 \, A B + 13 \, B^{2}\right)} a b^{3} d^{4}\right)} i x^{3} - 6 \, {\left({\left(12 \, A B + B^{2}\right)} b^{4} c^{2} d^{2} - 16 \, {\left(6 \, A B + 5 \, B^{2}\right)} a b^{3} c d^{3} + {\left(84 \, A B + 79 \, B^{2}\right)} a^{2} b^{2} d^{4}\right)} i x^{2} + 4 \, {\left({\left(72 \, A^{2} + 12 \, A B - 5 \, B^{2}\right)} b^{4} c^{3} d - 12 \, {\left(18 \, A^{2} + 6 \, A B - B^{2}\right)} a b^{3} c^{2} d^{2} + 108 \, {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a^{2} b^{2} c d^{3} - {\left(72 \, A^{2} + 156 \, A B + 115 \, B^{2}\right)} a^{3} b d^{4}\right)} i x + 72 \, {\left(B^{2} b^{4} d^{4} i x^{4} + 4 \, B^{2} a b^{3} d^{4} i x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} i x^{2} + 4 \, {\left(B^{2} b^{4} c^{3} d - 3 \, B^{2} a b^{3} c^{2} d^{2} + 3 \, B^{2} a^{2} b^{2} c d^{3}\right)} i x + {\left(3 \, B^{2} b^{4} c^{4} - 8 \, B^{2} a b^{3} c^{3} d + 6 \, B^{2} a^{2} b^{2} c^{2} d^{2}\right)} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + {\left(27 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} b^{4} c^{4} - 64 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a b^{3} c^{3} d + 216 \, {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a^{2} b^{2} c^{2} d^{2} - {\left(72 \, A^{2} + 156 \, A B + 115 \, B^{2}\right)} a^{4} d^{4}\right)} i + 12 \, {\left({\left(12 \, A B + 13 \, B^{2}\right)} b^{4} d^{4} i x^{4} + 4 \, {\left(3 \, B^{2} b^{4} c d^{3} + 2 \, {\left(6 \, A B + 5 \, B^{2}\right)} a b^{3} d^{4}\right)} i x^{3} - 6 \, {\left(B^{2} b^{4} c^{2} d^{2} - 8 \, B^{2} a b^{3} c d^{3} - 6 \, {\left(2 \, A B + B^{2}\right)} a^{2} b^{2} d^{4}\right)} i x^{2} + 4 \, {\left({\left(12 \, A B + B^{2}\right)} b^{4} c^{3} d - 6 \, {\left(6 \, A B + B^{2}\right)} a b^{3} c^{2} d^{2} + 18 \, {\left(2 \, A B + B^{2}\right)} a^{2} b^{2} c d^{3}\right)} i x + {\left(9 \, {\left(4 \, A B + B^{2}\right)} b^{4} c^{4} - 32 \, {\left(3 \, A B + B^{2}\right)} a b^{3} c^{3} d + 36 \, {\left(2 \, A B + B^{2}\right)} a^{2} b^{2} c^{2} d^{2}\right)} i\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{864 \, {\left({\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}\right)}}"," ",0,"-1/864*(12*((12*A*B + 13*B^2)*b^4*c*d^3 - (12*A*B + 13*B^2)*a*b^3*d^4)*i*x^3 - 6*((12*A*B + B^2)*b^4*c^2*d^2 - 16*(6*A*B + 5*B^2)*a*b^3*c*d^3 + (84*A*B + 79*B^2)*a^2*b^2*d^4)*i*x^2 + 4*((72*A^2 + 12*A*B - 5*B^2)*b^4*c^3*d - 12*(18*A^2 + 6*A*B - B^2)*a*b^3*c^2*d^2 + 108*(2*A^2 + 2*A*B + B^2)*a^2*b^2*c*d^3 - (72*A^2 + 156*A*B + 115*B^2)*a^3*b*d^4)*i*x + 72*(B^2*b^4*d^4*i*x^4 + 4*B^2*a*b^3*d^4*i*x^3 + 6*B^2*a^2*b^2*d^4*i*x^2 + 4*(B^2*b^4*c^3*d - 3*B^2*a*b^3*c^2*d^2 + 3*B^2*a^2*b^2*c*d^3)*i*x + (3*B^2*b^4*c^4 - 8*B^2*a*b^3*c^3*d + 6*B^2*a^2*b^2*c^2*d^2)*i)*log((b*e*x + a*e)/(d*x + c))^2 + (27*(8*A^2 + 4*A*B + B^2)*b^4*c^4 - 64*(9*A^2 + 6*A*B + 2*B^2)*a*b^3*c^3*d + 216*(2*A^2 + 2*A*B + B^2)*a^2*b^2*c^2*d^2 - (72*A^2 + 156*A*B + 115*B^2)*a^4*d^4)*i + 12*((12*A*B + 13*B^2)*b^4*d^4*i*x^4 + 4*(3*B^2*b^4*c*d^3 + 2*(6*A*B + 5*B^2)*a*b^3*d^4)*i*x^3 - 6*(B^2*b^4*c^2*d^2 - 8*B^2*a*b^3*c*d^3 - 6*(2*A*B + B^2)*a^2*b^2*d^4)*i*x^2 + 4*((12*A*B + B^2)*b^4*c^3*d - 6*(6*A*B + B^2)*a*b^3*c^2*d^2 + 18*(2*A*B + B^2)*a^2*b^2*c*d^3)*i*x + (9*(4*A*B + B^2)*b^4*c^4 - 32*(3*A*B + B^2)*a*b^3*c^3*d + 36*(2*A*B + B^2)*a^2*b^2*c^2*d^2)*i)*log((b*e*x + a*e)/(d*x + c)))/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5)","B",0
64,0,0,0,0.483758," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{3} d^{2} g^{3} i^{2} x^{5} + A^{2} a^{3} c^{2} g^{3} i^{2} + {\left(2 \, A^{2} b^{3} c d + 3 \, A^{2} a b^{2} d^{2}\right)} g^{3} i^{2} x^{4} + {\left(A^{2} b^{3} c^{2} + 6 \, A^{2} a b^{2} c d + 3 \, A^{2} a^{2} b d^{2}\right)} g^{3} i^{2} x^{3} + {\left(3 \, A^{2} a b^{2} c^{2} + 6 \, A^{2} a^{2} b c d + A^{2} a^{3} d^{2}\right)} g^{3} i^{2} x^{2} + {\left(3 \, A^{2} a^{2} b c^{2} + 2 \, A^{2} a^{3} c d\right)} g^{3} i^{2} x + {\left(B^{2} b^{3} d^{2} g^{3} i^{2} x^{5} + B^{2} a^{3} c^{2} g^{3} i^{2} + {\left(2 \, B^{2} b^{3} c d + 3 \, B^{2} a b^{2} d^{2}\right)} g^{3} i^{2} x^{4} + {\left(B^{2} b^{3} c^{2} + 6 \, B^{2} a b^{2} c d + 3 \, B^{2} a^{2} b d^{2}\right)} g^{3} i^{2} x^{3} + {\left(3 \, B^{2} a b^{2} c^{2} + 6 \, B^{2} a^{2} b c d + B^{2} a^{3} d^{2}\right)} g^{3} i^{2} x^{2} + {\left(3 \, B^{2} a^{2} b c^{2} + 2 \, B^{2} a^{3} c d\right)} g^{3} i^{2} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{3} d^{2} g^{3} i^{2} x^{5} + A B a^{3} c^{2} g^{3} i^{2} + {\left(2 \, A B b^{3} c d + 3 \, A B a b^{2} d^{2}\right)} g^{3} i^{2} x^{4} + {\left(A B b^{3} c^{2} + 6 \, A B a b^{2} c d + 3 \, A B a^{2} b d^{2}\right)} g^{3} i^{2} x^{3} + {\left(3 \, A B a b^{2} c^{2} + 6 \, A B a^{2} b c d + A B a^{3} d^{2}\right)} g^{3} i^{2} x^{2} + {\left(3 \, A B a^{2} b c^{2} + 2 \, A B a^{3} c d\right)} g^{3} i^{2} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b^3*d^2*g^3*i^2*x^5 + A^2*a^3*c^2*g^3*i^2 + (2*A^2*b^3*c*d + 3*A^2*a*b^2*d^2)*g^3*i^2*x^4 + (A^2*b^3*c^2 + 6*A^2*a*b^2*c*d + 3*A^2*a^2*b*d^2)*g^3*i^2*x^3 + (3*A^2*a*b^2*c^2 + 6*A^2*a^2*b*c*d + A^2*a^3*d^2)*g^3*i^2*x^2 + (3*A^2*a^2*b*c^2 + 2*A^2*a^3*c*d)*g^3*i^2*x + (B^2*b^3*d^2*g^3*i^2*x^5 + B^2*a^3*c^2*g^3*i^2 + (2*B^2*b^3*c*d + 3*B^2*a*b^2*d^2)*g^3*i^2*x^4 + (B^2*b^3*c^2 + 6*B^2*a*b^2*c*d + 3*B^2*a^2*b*d^2)*g^3*i^2*x^3 + (3*B^2*a*b^2*c^2 + 6*B^2*a^2*b*c*d + B^2*a^3*d^2)*g^3*i^2*x^2 + (3*B^2*a^2*b*c^2 + 2*B^2*a^3*c*d)*g^3*i^2*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^3*d^2*g^3*i^2*x^5 + A*B*a^3*c^2*g^3*i^2 + (2*A*B*b^3*c*d + 3*A*B*a*b^2*d^2)*g^3*i^2*x^4 + (A*B*b^3*c^2 + 6*A*B*a*b^2*c*d + 3*A*B*a^2*b*d^2)*g^3*i^2*x^3 + (3*A*B*a*b^2*c^2 + 6*A*B*a^2*b*c*d + A*B*a^3*d^2)*g^3*i^2*x^2 + (3*A*B*a^2*b*c^2 + 2*A*B*a^3*c*d)*g^3*i^2*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
65,0,0,0,0.451275," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{2} d^{2} g^{2} i^{2} x^{4} + A^{2} a^{2} c^{2} g^{2} i^{2} + 2 \, {\left(A^{2} b^{2} c d + A^{2} a b d^{2}\right)} g^{2} i^{2} x^{3} + {\left(A^{2} b^{2} c^{2} + 4 \, A^{2} a b c d + A^{2} a^{2} d^{2}\right)} g^{2} i^{2} x^{2} + 2 \, {\left(A^{2} a b c^{2} + A^{2} a^{2} c d\right)} g^{2} i^{2} x + {\left(B^{2} b^{2} d^{2} g^{2} i^{2} x^{4} + B^{2} a^{2} c^{2} g^{2} i^{2} + 2 \, {\left(B^{2} b^{2} c d + B^{2} a b d^{2}\right)} g^{2} i^{2} x^{3} + {\left(B^{2} b^{2} c^{2} + 4 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right)} g^{2} i^{2} x^{2} + 2 \, {\left(B^{2} a b c^{2} + B^{2} a^{2} c d\right)} g^{2} i^{2} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{2} d^{2} g^{2} i^{2} x^{4} + A B a^{2} c^{2} g^{2} i^{2} + 2 \, {\left(A B b^{2} c d + A B a b d^{2}\right)} g^{2} i^{2} x^{3} + {\left(A B b^{2} c^{2} + 4 \, A B a b c d + A B a^{2} d^{2}\right)} g^{2} i^{2} x^{2} + 2 \, {\left(A B a b c^{2} + A B a^{2} c d\right)} g^{2} i^{2} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b^2*d^2*g^2*i^2*x^4 + A^2*a^2*c^2*g^2*i^2 + 2*(A^2*b^2*c*d + A^2*a*b*d^2)*g^2*i^2*x^3 + (A^2*b^2*c^2 + 4*A^2*a*b*c*d + A^2*a^2*d^2)*g^2*i^2*x^2 + 2*(A^2*a*b*c^2 + A^2*a^2*c*d)*g^2*i^2*x + (B^2*b^2*d^2*g^2*i^2*x^4 + B^2*a^2*c^2*g^2*i^2 + 2*(B^2*b^2*c*d + B^2*a*b*d^2)*g^2*i^2*x^3 + (B^2*b^2*c^2 + 4*B^2*a*b*c*d + B^2*a^2*d^2)*g^2*i^2*x^2 + 2*(B^2*a*b*c^2 + B^2*a^2*c*d)*g^2*i^2*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^2*d^2*g^2*i^2*x^4 + A*B*a^2*c^2*g^2*i^2 + 2*(A*B*b^2*c*d + A*B*a*b*d^2)*g^2*i^2*x^3 + (A*B*b^2*c^2 + 4*A*B*a*b*c*d + A*B*a^2*d^2)*g^2*i^2*x^2 + 2*(A*B*a*b*c^2 + A*B*a^2*c*d)*g^2*i^2*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
66,0,0,0,0.474809," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b d^{2} g i^{2} x^{3} + A^{2} a c^{2} g i^{2} + {\left(2 \, A^{2} b c d + A^{2} a d^{2}\right)} g i^{2} x^{2} + {\left(A^{2} b c^{2} + 2 \, A^{2} a c d\right)} g i^{2} x + {\left(B^{2} b d^{2} g i^{2} x^{3} + B^{2} a c^{2} g i^{2} + {\left(2 \, B^{2} b c d + B^{2} a d^{2}\right)} g i^{2} x^{2} + {\left(B^{2} b c^{2} + 2 \, B^{2} a c d\right)} g i^{2} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b d^{2} g i^{2} x^{3} + A B a c^{2} g i^{2} + {\left(2 \, A B b c d + A B a d^{2}\right)} g i^{2} x^{2} + {\left(A B b c^{2} + 2 \, A B a c d\right)} g i^{2} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b*d^2*g*i^2*x^3 + A^2*a*c^2*g*i^2 + (2*A^2*b*c*d + A^2*a*d^2)*g*i^2*x^2 + (A^2*b*c^2 + 2*A^2*a*c*d)*g*i^2*x + (B^2*b*d^2*g*i^2*x^3 + B^2*a*c^2*g*i^2 + (2*B^2*b*c*d + B^2*a*d^2)*g*i^2*x^2 + (B^2*b*c^2 + 2*B^2*a*c*d)*g*i^2*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b*d^2*g*i^2*x^3 + A*B*a*c^2*g*i^2 + (2*A*B*b*c*d + A*B*a*d^2)*g*i^2*x^2 + (A*B*b*c^2 + 2*A*B*a*c*d)*g*i^2*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
67,0,0,0,0.439925," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left(B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*d^2*i^2*x^2 + 2*A^2*c*d*i^2*x + A^2*c^2*i^2 + (B^2*d^2*i^2*x^2 + 2*B^2*c*d*i^2*x + B^2*c^2*i^2)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d^2*i^2*x^2 + 2*A*B*c*d*i^2*x + A*B*c^2*i^2)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
68,0,0,0,0.431475," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left(B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b g x + a g}, x\right)"," ",0,"integral((A^2*d^2*i^2*x^2 + 2*A^2*c*d*i^2*x + A^2*c^2*i^2 + (B^2*d^2*i^2*x^2 + 2*B^2*c*d*i^2*x + B^2*c^2*i^2)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d^2*i^2*x^2 + 2*A*B*c*d*i^2*x + A*B*c^2*i^2)*log((b*e*x + a*e)/(d*x + c)))/(b*g*x + a*g), x)","F",0
69,0,0,0,0.456543," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left(B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A^2*d^2*i^2*x^2 + 2*A^2*c*d*i^2*x + A^2*c^2*i^2 + (B^2*d^2*i^2*x^2 + 2*B^2*c*d*i^2*x + B^2*c^2*i^2)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d^2*i^2*x^2 + 2*A*B*c*d*i^2*x + A*B*c^2*i^2)*log((b*e*x + a*e)/(d*x + c)))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
70,0,0,0,0.424512," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left(B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{3} g^{3} x^{3} + 3 \, a b^{2} g^{3} x^{2} + 3 \, a^{2} b g^{3} x + a^{3} g^{3}}, x\right)"," ",0,"integral((A^2*d^2*i^2*x^2 + 2*A^2*c*d*i^2*x + A^2*c^2*i^2 + (B^2*d^2*i^2*x^2 + 2*B^2*c*d*i^2*x + B^2*c^2*i^2)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d^2*i^2*x^2 + 2*A*B*c*d*i^2*x + A*B*c^2*i^2)*log((b*e*x + a*e)/(d*x + c)))/(b^3*g^3*x^3 + 3*a*b^2*g^3*x^2 + 3*a^2*b*g^3*x + a^3*g^3), x)","F",0
71,1,444,0,0.472341," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} b^{3} c d^{2} - {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a b^{2} d^{3}\right)} i^{2} x^{2} + 3 \, {\left({\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} b^{3} c^{2} d - {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a^{2} b d^{3}\right)} i^{2} x + {\left({\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} b^{3} c^{3} - {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a^{3} d^{3}\right)} i^{2} + 9 \, {\left(B^{2} b^{3} d^{3} i^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} x + B^{2} b^{3} c^{3} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 6 \, {\left({\left(3 \, A B + B^{2}\right)} b^{3} d^{3} i^{2} x^{3} + 3 \, {\left(3 \, A B + B^{2}\right)} b^{3} c d^{2} i^{2} x^{2} + 3 \, {\left(3 \, A B + B^{2}\right)} b^{3} c^{2} d i^{2} x + {\left(3 \, A B + B^{2}\right)} b^{3} c^{3} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{27 \, {\left({\left(b^{7} c - a b^{6} d\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c - a^{2} b^{5} d\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c - a^{3} b^{4} d\right)} g^{4} x + {\left(a^{3} b^{4} c - a^{4} b^{3} d\right)} g^{4}\right)}}"," ",0,"-1/27*(3*((9*A^2 + 6*A*B + 2*B^2)*b^3*c*d^2 - (9*A^2 + 6*A*B + 2*B^2)*a*b^2*d^3)*i^2*x^2 + 3*((9*A^2 + 6*A*B + 2*B^2)*b^3*c^2*d - (9*A^2 + 6*A*B + 2*B^2)*a^2*b*d^3)*i^2*x + ((9*A^2 + 6*A*B + 2*B^2)*b^3*c^3 - (9*A^2 + 6*A*B + 2*B^2)*a^3*d^3)*i^2 + 9*(B^2*b^3*d^3*i^2*x^3 + 3*B^2*b^3*c*d^2*i^2*x^2 + 3*B^2*b^3*c^2*d*i^2*x + B^2*b^3*c^3*i^2)*log((b*e*x + a*e)/(d*x + c))^2 + 6*((3*A*B + B^2)*b^3*d^3*i^2*x^3 + 3*(3*A*B + B^2)*b^3*c*d^2*i^2*x^2 + 3*(3*A*B + B^2)*b^3*c^2*d*i^2*x + (3*A*B + B^2)*b^3*c^3*i^2)*log((b*e*x + a*e)/(d*x + c)))/((b^7*c - a*b^6*d)*g^4*x^3 + 3*(a*b^6*c - a^2*b^5*d)*g^4*x^2 + 3*(a^2*b^5*c - a^3*b^4*d)*g^4*x + (a^3*b^4*c - a^4*b^3*d)*g^4)","B",0
72,1,837,0,0.501594," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^5,x, algorithm=""fricas"")","\frac{12 \, {\left({\left(12 \, A B + 7 \, B^{2}\right)} b^{4} c d^{3} - {\left(12 \, A B + 7 \, B^{2}\right)} a b^{3} d^{4}\right)} i^{2} x^{3} - 6 \, {\left({\left(72 \, A^{2} + 12 \, A B - 5 \, B^{2}\right)} b^{4} c^{2} d^{2} - 16 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a b^{3} c d^{3} + {\left(72 \, A^{2} + 84 \, A B + 37 \, B^{2}\right)} a^{2} b^{2} d^{4}\right)} i^{2} x^{2} - 4 \, {\left({\left(144 \, A^{2} + 60 \, A B + 11 \, B^{2}\right)} b^{4} c^{3} d - 24 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a b^{3} c^{2} d^{2} + {\left(72 \, A^{2} + 84 \, A B + 37 \, B^{2}\right)} a^{3} b d^{4}\right)} i^{2} x - {\left(27 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} b^{4} c^{4} - 32 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a b^{3} c^{3} d + {\left(72 \, A^{2} + 84 \, A B + 37 \, B^{2}\right)} a^{4} d^{4}\right)} i^{2} + 72 \, {\left(B^{2} b^{4} d^{4} i^{2} x^{4} + 4 \, B^{2} a b^{3} d^{4} i^{2} x^{3} - 6 \, {\left(B^{2} b^{4} c^{2} d^{2} - 2 \, B^{2} a b^{3} c d^{3}\right)} i^{2} x^{2} - 4 \, {\left(2 \, B^{2} b^{4} c^{3} d - 3 \, B^{2} a b^{3} c^{2} d^{2}\right)} i^{2} x - {\left(3 \, B^{2} b^{4} c^{4} - 4 \, B^{2} a b^{3} c^{3} d\right)} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 12 \, {\left({\left(12 \, A B + 7 \, B^{2}\right)} b^{4} d^{4} i^{2} x^{4} + 4 \, {\left(3 \, B^{2} b^{4} c d^{3} + 4 \, {\left(3 \, A B + B^{2}\right)} a b^{3} d^{4}\right)} i^{2} x^{3} - 6 \, {\left({\left(12 \, A B + B^{2}\right)} b^{4} c^{2} d^{2} - 8 \, {\left(3 \, A B + B^{2}\right)} a b^{3} c d^{3}\right)} i^{2} x^{2} - 4 \, {\left({\left(24 \, A B + 5 \, B^{2}\right)} b^{4} c^{3} d - 12 \, {\left(3 \, A B + B^{2}\right)} a b^{3} c^{2} d^{2}\right)} i^{2} x - {\left(9 \, {\left(4 \, A B + B^{2}\right)} b^{4} c^{4} - 16 \, {\left(3 \, A B + B^{2}\right)} a b^{3} c^{3} d\right)} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{864 \, {\left({\left(b^{9} c^{2} - 2 \, a b^{8} c d + a^{2} b^{7} d^{2}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{2} - 2 \, a^{2} b^{7} c d + a^{3} b^{6} d^{2}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{2} - 2 \, a^{3} b^{6} c d + a^{4} b^{5} d^{2}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{2} - 2 \, a^{4} b^{5} c d + a^{5} b^{4} d^{2}\right)} g^{5} x + {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} g^{5}\right)}}"," ",0,"1/864*(12*((12*A*B + 7*B^2)*b^4*c*d^3 - (12*A*B + 7*B^2)*a*b^3*d^4)*i^2*x^3 - 6*((72*A^2 + 12*A*B - 5*B^2)*b^4*c^2*d^2 - 16*(9*A^2 + 6*A*B + 2*B^2)*a*b^3*c*d^3 + (72*A^2 + 84*A*B + 37*B^2)*a^2*b^2*d^4)*i^2*x^2 - 4*((144*A^2 + 60*A*B + 11*B^2)*b^4*c^3*d - 24*(9*A^2 + 6*A*B + 2*B^2)*a*b^3*c^2*d^2 + (72*A^2 + 84*A*B + 37*B^2)*a^3*b*d^4)*i^2*x - (27*(8*A^2 + 4*A*B + B^2)*b^4*c^4 - 32*(9*A^2 + 6*A*B + 2*B^2)*a*b^3*c^3*d + (72*A^2 + 84*A*B + 37*B^2)*a^4*d^4)*i^2 + 72*(B^2*b^4*d^4*i^2*x^4 + 4*B^2*a*b^3*d^4*i^2*x^3 - 6*(B^2*b^4*c^2*d^2 - 2*B^2*a*b^3*c*d^3)*i^2*x^2 - 4*(2*B^2*b^4*c^3*d - 3*B^2*a*b^3*c^2*d^2)*i^2*x - (3*B^2*b^4*c^4 - 4*B^2*a*b^3*c^3*d)*i^2)*log((b*e*x + a*e)/(d*x + c))^2 + 12*((12*A*B + 7*B^2)*b^4*d^4*i^2*x^4 + 4*(3*B^2*b^4*c*d^3 + 4*(3*A*B + B^2)*a*b^3*d^4)*i^2*x^3 - 6*((12*A*B + B^2)*b^4*c^2*d^2 - 8*(3*A*B + B^2)*a*b^3*c*d^3)*i^2*x^2 - 4*((24*A*B + 5*B^2)*b^4*c^3*d - 12*(3*A*B + B^2)*a*b^3*c^2*d^2)*i^2*x - (9*(4*A*B + B^2)*b^4*c^4 - 16*(3*A*B + B^2)*a*b^3*c^3*d)*i^2)*log((b*e*x + a*e)/(d*x + c)))/((b^9*c^2 - 2*a*b^8*c*d + a^2*b^7*d^2)*g^5*x^4 + 4*(a*b^8*c^2 - 2*a^2*b^7*c*d + a^3*b^6*d^2)*g^5*x^3 + 6*(a^2*b^7*c^2 - 2*a^3*b^6*c*d + a^4*b^5*d^2)*g^5*x^2 + 4*(a^3*b^6*c^2 - 2*a^4*b^5*c*d + a^5*b^4*d^2)*g^5*x + (a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*g^5)","B",0
73,1,1323,0,0.464690," ","integrate((d*i*x+c*i)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^6,x, algorithm=""fricas"")","-\frac{60 \, {\left({\left(60 \, A B + 47 \, B^{2}\right)} b^{5} c d^{4} - {\left(60 \, A B + 47 \, B^{2}\right)} a b^{4} d^{5}\right)} i^{2} x^{4} - 30 \, {\left({\left(60 \, A B - 13 \, B^{2}\right)} b^{5} c^{2} d^{3} - 50 \, {\left(12 \, A B + 7 \, B^{2}\right)} a b^{4} c d^{4} + 3 \, {\left(180 \, A B + 121 \, B^{2}\right)} a^{2} b^{3} d^{5}\right)} i^{2} x^{3} + 10 \, {\left(2 \, {\left(900 \, A^{2} + 60 \, A B - 43 \, B^{2}\right)} b^{5} c^{3} d^{2} - 75 \, {\left(72 \, A^{2} + 12 \, A B - 5 \, B^{2}\right)} a b^{4} c^{2} d^{3} + 600 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a^{2} b^{3} c d^{4} - {\left(1800 \, A^{2} + 2820 \, A B + 1489 \, B^{2}\right)} a^{3} b^{2} d^{5}\right)} i^{2} x^{2} + 5 \, {\left(27 \, {\left(200 \, A^{2} + 60 \, A B + 7 \, B^{2}\right)} b^{5} c^{4} d - 100 \, {\left(144 \, A^{2} + 60 \, A B + 11 \, B^{2}\right)} a b^{4} c^{3} d^{2} + 1200 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a^{2} b^{3} c^{2} d^{3} - {\left(1800 \, A^{2} + 2820 \, A B + 1489 \, B^{2}\right)} a^{4} b d^{5}\right)} i^{2} x + {\left(432 \, {\left(25 \, A^{2} + 10 \, A B + 2 \, B^{2}\right)} b^{5} c^{5} - 3375 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a b^{4} c^{4} d + 2000 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} a^{2} b^{3} c^{3} d^{2} - {\left(1800 \, A^{2} + 2820 \, A B + 1489 \, B^{2}\right)} a^{5} d^{5}\right)} i^{2} + 1800 \, {\left(B^{2} b^{5} d^{5} i^{2} x^{5} + 5 \, B^{2} a b^{4} d^{5} i^{2} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} i^{2} x^{3} + 10 \, {\left(B^{2} b^{5} c^{3} d^{2} - 3 \, B^{2} a b^{4} c^{2} d^{3} + 3 \, B^{2} a^{2} b^{3} c d^{4}\right)} i^{2} x^{2} + 5 \, {\left(3 \, B^{2} b^{5} c^{4} d - 8 \, B^{2} a b^{4} c^{3} d^{2} + 6 \, B^{2} a^{2} b^{3} c^{2} d^{3}\right)} i^{2} x + {\left(6 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 10 \, B^{2} a^{2} b^{3} c^{3} d^{2}\right)} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 60 \, {\left({\left(60 \, A B + 47 \, B^{2}\right)} b^{5} d^{5} i^{2} x^{5} + 5 \, {\left(12 \, B^{2} b^{5} c d^{4} + 5 \, {\left(12 \, A B + 7 \, B^{2}\right)} a b^{4} d^{5}\right)} i^{2} x^{4} - 10 \, {\left(3 \, B^{2} b^{5} c^{2} d^{3} - 30 \, B^{2} a b^{4} c d^{4} - 20 \, {\left(3 \, A B + B^{2}\right)} a^{2} b^{3} d^{5}\right)} i^{2} x^{3} + 10 \, {\left(2 \, {\left(30 \, A B + B^{2}\right)} b^{5} c^{3} d^{2} - 15 \, {\left(12 \, A B + B^{2}\right)} a b^{4} c^{2} d^{3} + 60 \, {\left(3 \, A B + B^{2}\right)} a^{2} b^{3} c d^{4}\right)} i^{2} x^{2} + 5 \, {\left(9 \, {\left(20 \, A B + 3 \, B^{2}\right)} b^{5} c^{4} d - 20 \, {\left(24 \, A B + 5 \, B^{2}\right)} a b^{4} c^{3} d^{2} + 120 \, {\left(3 \, A B + B^{2}\right)} a^{2} b^{3} c^{2} d^{3}\right)} i^{2} x + {\left(72 \, {\left(5 \, A B + B^{2}\right)} b^{5} c^{5} - 225 \, {\left(4 \, A B + B^{2}\right)} a b^{4} c^{4} d + 200 \, {\left(3 \, A B + B^{2}\right)} a^{2} b^{3} c^{3} d^{2}\right)} i^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{54000 \, {\left({\left(b^{11} c^{3} - 3 \, a b^{10} c^{2} d + 3 \, a^{2} b^{9} c d^{2} - a^{3} b^{8} d^{3}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{3} - 3 \, a^{2} b^{9} c^{2} d + 3 \, a^{3} b^{8} c d^{2} - a^{4} b^{7} d^{3}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{3} - 3 \, a^{3} b^{8} c^{2} d + 3 \, a^{4} b^{7} c d^{2} - a^{5} b^{6} d^{3}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{3} - 3 \, a^{4} b^{7} c^{2} d + 3 \, a^{5} b^{6} c d^{2} - a^{6} b^{5} d^{3}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{3} - 3 \, a^{5} b^{6} c^{2} d + 3 \, a^{6} b^{5} c d^{2} - a^{7} b^{4} d^{3}\right)} g^{6} x + {\left(a^{5} b^{6} c^{3} - 3 \, a^{6} b^{5} c^{2} d + 3 \, a^{7} b^{4} c d^{2} - a^{8} b^{3} d^{3}\right)} g^{6}\right)}}"," ",0,"-1/54000*(60*((60*A*B + 47*B^2)*b^5*c*d^4 - (60*A*B + 47*B^2)*a*b^4*d^5)*i^2*x^4 - 30*((60*A*B - 13*B^2)*b^5*c^2*d^3 - 50*(12*A*B + 7*B^2)*a*b^4*c*d^4 + 3*(180*A*B + 121*B^2)*a^2*b^3*d^5)*i^2*x^3 + 10*(2*(900*A^2 + 60*A*B - 43*B^2)*b^5*c^3*d^2 - 75*(72*A^2 + 12*A*B - 5*B^2)*a*b^4*c^2*d^3 + 600*(9*A^2 + 6*A*B + 2*B^2)*a^2*b^3*c*d^4 - (1800*A^2 + 2820*A*B + 1489*B^2)*a^3*b^2*d^5)*i^2*x^2 + 5*(27*(200*A^2 + 60*A*B + 7*B^2)*b^5*c^4*d - 100*(144*A^2 + 60*A*B + 11*B^2)*a*b^4*c^3*d^2 + 1200*(9*A^2 + 6*A*B + 2*B^2)*a^2*b^3*c^2*d^3 - (1800*A^2 + 2820*A*B + 1489*B^2)*a^4*b*d^5)*i^2*x + (432*(25*A^2 + 10*A*B + 2*B^2)*b^5*c^5 - 3375*(8*A^2 + 4*A*B + B^2)*a*b^4*c^4*d + 2000*(9*A^2 + 6*A*B + 2*B^2)*a^2*b^3*c^3*d^2 - (1800*A^2 + 2820*A*B + 1489*B^2)*a^5*d^5)*i^2 + 1800*(B^2*b^5*d^5*i^2*x^5 + 5*B^2*a*b^4*d^5*i^2*x^4 + 10*B^2*a^2*b^3*d^5*i^2*x^3 + 10*(B^2*b^5*c^3*d^2 - 3*B^2*a*b^4*c^2*d^3 + 3*B^2*a^2*b^3*c*d^4)*i^2*x^2 + 5*(3*B^2*b^5*c^4*d - 8*B^2*a*b^4*c^3*d^2 + 6*B^2*a^2*b^3*c^2*d^3)*i^2*x + (6*B^2*b^5*c^5 - 15*B^2*a*b^4*c^4*d + 10*B^2*a^2*b^3*c^3*d^2)*i^2)*log((b*e*x + a*e)/(d*x + c))^2 + 60*((60*A*B + 47*B^2)*b^5*d^5*i^2*x^5 + 5*(12*B^2*b^5*c*d^4 + 5*(12*A*B + 7*B^2)*a*b^4*d^5)*i^2*x^4 - 10*(3*B^2*b^5*c^2*d^3 - 30*B^2*a*b^4*c*d^4 - 20*(3*A*B + B^2)*a^2*b^3*d^5)*i^2*x^3 + 10*(2*(30*A*B + B^2)*b^5*c^3*d^2 - 15*(12*A*B + B^2)*a*b^4*c^2*d^3 + 60*(3*A*B + B^2)*a^2*b^3*c*d^4)*i^2*x^2 + 5*(9*(20*A*B + 3*B^2)*b^5*c^4*d - 20*(24*A*B + 5*B^2)*a*b^4*c^3*d^2 + 120*(3*A*B + B^2)*a^2*b^3*c^2*d^3)*i^2*x + (72*(5*A*B + B^2)*b^5*c^5 - 225*(4*A*B + B^2)*a*b^4*c^4*d + 200*(3*A*B + B^2)*a^2*b^3*c^3*d^2)*i^2)*log((b*e*x + a*e)/(d*x + c)))/((b^11*c^3 - 3*a*b^10*c^2*d + 3*a^2*b^9*c*d^2 - a^3*b^8*d^3)*g^6*x^5 + 5*(a*b^10*c^3 - 3*a^2*b^9*c^2*d + 3*a^3*b^8*c*d^2 - a^4*b^7*d^3)*g^6*x^4 + 10*(a^2*b^9*c^3 - 3*a^3*b^8*c^2*d + 3*a^4*b^7*c*d^2 - a^5*b^6*d^3)*g^6*x^3 + 10*(a^3*b^8*c^3 - 3*a^4*b^7*c^2*d + 3*a^5*b^6*c*d^2 - a^6*b^5*d^3)*g^6*x^2 + 5*(a^4*b^7*c^3 - 3*a^5*b^6*c^2*d + 3*a^6*b^5*c*d^2 - a^7*b^4*d^3)*g^6*x + (a^5*b^6*c^3 - 3*a^6*b^5*c^2*d + 3*a^7*b^4*c*d^2 - a^8*b^3*d^3)*g^6)","B",0
74,0,0,0,0.490867," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{3} d^{3} g^{3} i^{3} x^{6} + A^{2} a^{3} c^{3} g^{3} i^{3} + 3 \, {\left(A^{2} b^{3} c d^{2} + A^{2} a b^{2} d^{3}\right)} g^{3} i^{3} x^{5} + 3 \, {\left(A^{2} b^{3} c^{2} d + 3 \, A^{2} a b^{2} c d^{2} + A^{2} a^{2} b d^{3}\right)} g^{3} i^{3} x^{4} + {\left(A^{2} b^{3} c^{3} + 9 \, A^{2} a b^{2} c^{2} d + 9 \, A^{2} a^{2} b c d^{2} + A^{2} a^{3} d^{3}\right)} g^{3} i^{3} x^{3} + 3 \, {\left(A^{2} a b^{2} c^{3} + 3 \, A^{2} a^{2} b c^{2} d + A^{2} a^{3} c d^{2}\right)} g^{3} i^{3} x^{2} + 3 \, {\left(A^{2} a^{2} b c^{3} + A^{2} a^{3} c^{2} d\right)} g^{3} i^{3} x + {\left(B^{2} b^{3} d^{3} g^{3} i^{3} x^{6} + B^{2} a^{3} c^{3} g^{3} i^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} + B^{2} a b^{2} d^{3}\right)} g^{3} i^{3} x^{5} + 3 \, {\left(B^{2} b^{3} c^{2} d + 3 \, B^{2} a b^{2} c d^{2} + B^{2} a^{2} b d^{3}\right)} g^{3} i^{3} x^{4} + {\left(B^{2} b^{3} c^{3} + 9 \, B^{2} a b^{2} c^{2} d + 9 \, B^{2} a^{2} b c d^{2} + B^{2} a^{3} d^{3}\right)} g^{3} i^{3} x^{3} + 3 \, {\left(B^{2} a b^{2} c^{3} + 3 \, B^{2} a^{2} b c^{2} d + B^{2} a^{3} c d^{2}\right)} g^{3} i^{3} x^{2} + 3 \, {\left(B^{2} a^{2} b c^{3} + B^{2} a^{3} c^{2} d\right)} g^{3} i^{3} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{3} d^{3} g^{3} i^{3} x^{6} + A B a^{3} c^{3} g^{3} i^{3} + 3 \, {\left(A B b^{3} c d^{2} + A B a b^{2} d^{3}\right)} g^{3} i^{3} x^{5} + 3 \, {\left(A B b^{3} c^{2} d + 3 \, A B a b^{2} c d^{2} + A B a^{2} b d^{3}\right)} g^{3} i^{3} x^{4} + {\left(A B b^{3} c^{3} + 9 \, A B a b^{2} c^{2} d + 9 \, A B a^{2} b c d^{2} + A B a^{3} d^{3}\right)} g^{3} i^{3} x^{3} + 3 \, {\left(A B a b^{2} c^{3} + 3 \, A B a^{2} b c^{2} d + A B a^{3} c d^{2}\right)} g^{3} i^{3} x^{2} + 3 \, {\left(A B a^{2} b c^{3} + A B a^{3} c^{2} d\right)} g^{3} i^{3} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b^3*d^3*g^3*i^3*x^6 + A^2*a^3*c^3*g^3*i^3 + 3*(A^2*b^3*c*d^2 + A^2*a*b^2*d^3)*g^3*i^3*x^5 + 3*(A^2*b^3*c^2*d + 3*A^2*a*b^2*c*d^2 + A^2*a^2*b*d^3)*g^3*i^3*x^4 + (A^2*b^3*c^3 + 9*A^2*a*b^2*c^2*d + 9*A^2*a^2*b*c*d^2 + A^2*a^3*d^3)*g^3*i^3*x^3 + 3*(A^2*a*b^2*c^3 + 3*A^2*a^2*b*c^2*d + A^2*a^3*c*d^2)*g^3*i^3*x^2 + 3*(A^2*a^2*b*c^3 + A^2*a^3*c^2*d)*g^3*i^3*x + (B^2*b^3*d^3*g^3*i^3*x^6 + B^2*a^3*c^3*g^3*i^3 + 3*(B^2*b^3*c*d^2 + B^2*a*b^2*d^3)*g^3*i^3*x^5 + 3*(B^2*b^3*c^2*d + 3*B^2*a*b^2*c*d^2 + B^2*a^2*b*d^3)*g^3*i^3*x^4 + (B^2*b^3*c^3 + 9*B^2*a*b^2*c^2*d + 9*B^2*a^2*b*c*d^2 + B^2*a^3*d^3)*g^3*i^3*x^3 + 3*(B^2*a*b^2*c^3 + 3*B^2*a^2*b*c^2*d + B^2*a^3*c*d^2)*g^3*i^3*x^2 + 3*(B^2*a^2*b*c^3 + B^2*a^3*c^2*d)*g^3*i^3*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^3*d^3*g^3*i^3*x^6 + A*B*a^3*c^3*g^3*i^3 + 3*(A*B*b^3*c*d^2 + A*B*a*b^2*d^3)*g^3*i^3*x^5 + 3*(A*B*b^3*c^2*d + 3*A*B*a*b^2*c*d^2 + A*B*a^2*b*d^3)*g^3*i^3*x^4 + (A*B*b^3*c^3 + 9*A*B*a*b^2*c^2*d + 9*A*B*a^2*b*c*d^2 + A*B*a^3*d^3)*g^3*i^3*x^3 + 3*(A*B*a*b^2*c^3 + 3*A*B*a^2*b*c^2*d + A*B*a^3*c*d^2)*g^3*i^3*x^2 + 3*(A*B*a^2*b*c^3 + A*B*a^3*c^2*d)*g^3*i^3*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
75,0,0,0,0.498882," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{2} d^{3} g^{2} i^{3} x^{5} + A^{2} a^{2} c^{3} g^{2} i^{3} + {\left(3 \, A^{2} b^{2} c d^{2} + 2 \, A^{2} a b d^{3}\right)} g^{2} i^{3} x^{4} + {\left(3 \, A^{2} b^{2} c^{2} d + 6 \, A^{2} a b c d^{2} + A^{2} a^{2} d^{3}\right)} g^{2} i^{3} x^{3} + {\left(A^{2} b^{2} c^{3} + 6 \, A^{2} a b c^{2} d + 3 \, A^{2} a^{2} c d^{2}\right)} g^{2} i^{3} x^{2} + {\left(2 \, A^{2} a b c^{3} + 3 \, A^{2} a^{2} c^{2} d\right)} g^{2} i^{3} x + {\left(B^{2} b^{2} d^{3} g^{2} i^{3} x^{5} + B^{2} a^{2} c^{3} g^{2} i^{3} + {\left(3 \, B^{2} b^{2} c d^{2} + 2 \, B^{2} a b d^{3}\right)} g^{2} i^{3} x^{4} + {\left(3 \, B^{2} b^{2} c^{2} d + 6 \, B^{2} a b c d^{2} + B^{2} a^{2} d^{3}\right)} g^{2} i^{3} x^{3} + {\left(B^{2} b^{2} c^{3} + 6 \, B^{2} a b c^{2} d + 3 \, B^{2} a^{2} c d^{2}\right)} g^{2} i^{3} x^{2} + {\left(2 \, B^{2} a b c^{3} + 3 \, B^{2} a^{2} c^{2} d\right)} g^{2} i^{3} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{2} d^{3} g^{2} i^{3} x^{5} + A B a^{2} c^{3} g^{2} i^{3} + {\left(3 \, A B b^{2} c d^{2} + 2 \, A B a b d^{3}\right)} g^{2} i^{3} x^{4} + {\left(3 \, A B b^{2} c^{2} d + 6 \, A B a b c d^{2} + A B a^{2} d^{3}\right)} g^{2} i^{3} x^{3} + {\left(A B b^{2} c^{3} + 6 \, A B a b c^{2} d + 3 \, A B a^{2} c d^{2}\right)} g^{2} i^{3} x^{2} + {\left(2 \, A B a b c^{3} + 3 \, A B a^{2} c^{2} d\right)} g^{2} i^{3} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b^2*d^3*g^2*i^3*x^5 + A^2*a^2*c^3*g^2*i^3 + (3*A^2*b^2*c*d^2 + 2*A^2*a*b*d^3)*g^2*i^3*x^4 + (3*A^2*b^2*c^2*d + 6*A^2*a*b*c*d^2 + A^2*a^2*d^3)*g^2*i^3*x^3 + (A^2*b^2*c^3 + 6*A^2*a*b*c^2*d + 3*A^2*a^2*c*d^2)*g^2*i^3*x^2 + (2*A^2*a*b*c^3 + 3*A^2*a^2*c^2*d)*g^2*i^3*x + (B^2*b^2*d^3*g^2*i^3*x^5 + B^2*a^2*c^3*g^2*i^3 + (3*B^2*b^2*c*d^2 + 2*B^2*a*b*d^3)*g^2*i^3*x^4 + (3*B^2*b^2*c^2*d + 6*B^2*a*b*c*d^2 + B^2*a^2*d^3)*g^2*i^3*x^3 + (B^2*b^2*c^3 + 6*B^2*a*b*c^2*d + 3*B^2*a^2*c*d^2)*g^2*i^3*x^2 + (2*B^2*a*b*c^3 + 3*B^2*a^2*c^2*d)*g^2*i^3*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^2*d^3*g^2*i^3*x^5 + A*B*a^2*c^3*g^2*i^3 + (3*A*B*b^2*c*d^2 + 2*A*B*a*b*d^3)*g^2*i^3*x^4 + (3*A*B*b^2*c^2*d + 6*A*B*a*b*c*d^2 + A*B*a^2*d^3)*g^2*i^3*x^3 + (A*B*b^2*c^3 + 6*A*B*a*b*c^2*d + 3*A*B*a^2*c*d^2)*g^2*i^3*x^2 + (2*A*B*a*b*c^3 + 3*A*B*a^2*c^2*d)*g^2*i^3*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
76,0,0,0,0.502903," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b d^{3} g i^{3} x^{4} + A^{2} a c^{3} g i^{3} + {\left(3 \, A^{2} b c d^{2} + A^{2} a d^{3}\right)} g i^{3} x^{3} + 3 \, {\left(A^{2} b c^{2} d + A^{2} a c d^{2}\right)} g i^{3} x^{2} + {\left(A^{2} b c^{3} + 3 \, A^{2} a c^{2} d\right)} g i^{3} x + {\left(B^{2} b d^{3} g i^{3} x^{4} + B^{2} a c^{3} g i^{3} + {\left(3 \, B^{2} b c d^{2} + B^{2} a d^{3}\right)} g i^{3} x^{3} + 3 \, {\left(B^{2} b c^{2} d + B^{2} a c d^{2}\right)} g i^{3} x^{2} + {\left(B^{2} b c^{3} + 3 \, B^{2} a c^{2} d\right)} g i^{3} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b d^{3} g i^{3} x^{4} + A B a c^{3} g i^{3} + {\left(3 \, A B b c d^{2} + A B a d^{3}\right)} g i^{3} x^{3} + 3 \, {\left(A B b c^{2} d + A B a c d^{2}\right)} g i^{3} x^{2} + {\left(A B b c^{3} + 3 \, A B a c^{2} d\right)} g i^{3} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*b*d^3*g*i^3*x^4 + A^2*a*c^3*g*i^3 + (3*A^2*b*c*d^2 + A^2*a*d^3)*g*i^3*x^3 + 3*(A^2*b*c^2*d + A^2*a*c*d^2)*g*i^3*x^2 + (A^2*b*c^3 + 3*A^2*a*c^2*d)*g*i^3*x + (B^2*b*d^3*g*i^3*x^4 + B^2*a*c^3*g*i^3 + (3*B^2*b*c*d^2 + B^2*a*d^3)*g*i^3*x^3 + 3*(B^2*b*c^2*d + B^2*a*c*d^2)*g*i^3*x^2 + (B^2*b*c^3 + 3*B^2*a*c^2*d)*g*i^3*x)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b*d^3*g*i^3*x^4 + A*B*a*c^3*g*i^3 + (3*A*B*b*c*d^2 + A*B*a*d^3)*g*i^3*x^3 + 3*(A*B*b*c^2*d + A*B*a*c*d^2)*g*i^3*x^2 + (A*B*b*c^3 + 3*A*B*a*c^2*d)*g*i^3*x)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
77,0,0,0,0.475919," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right), x\right)"," ",0,"integral(A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log((b*e*x + a*e)/(d*x + c)), x)","F",0
78,0,0,0,0.499264," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b g x + a g}, x\right)"," ",0,"integral((A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log((b*e*x + a*e)/(d*x + c)))/(b*g*x + a*g), x)","F",0
79,0,0,0,0.484542," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log((b*e*x + a*e)/(d*x + c)))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
80,0,0,0,0.479543," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{b^{3} g^{3} x^{3} + 3 \, a b^{2} g^{3} x^{2} + 3 \, a^{2} b g^{3} x + a^{3} g^{3}}, x\right)"," ",0,"integral((A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log((b*e*x + a*e)/(d*x + c)))/(b^3*g^3*x^3 + 3*a*b^2*g^3*x^2 + 3*a^2*b*g^3*x + a^3*g^3), x)","F",0
81,1,559,0,0.531187," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^5,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} b^{4} c d^{3} - {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a b^{3} d^{4}\right)} i^{3} x^{3} + 6 \, {\left({\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} b^{4} c^{2} d^{2} - {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a^{2} b^{2} d^{4}\right)} i^{3} x^{2} + 4 \, {\left({\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} b^{4} c^{3} d - {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a^{3} b d^{4}\right)} i^{3} x + {\left({\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} b^{4} c^{4} - {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a^{4} d^{4}\right)} i^{3} + 8 \, {\left(B^{2} b^{4} d^{4} i^{3} x^{4} + 4 \, B^{2} b^{4} c d^{3} i^{3} x^{3} + 6 \, B^{2} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B^{2} b^{4} c^{3} d i^{3} x + B^{2} b^{4} c^{4} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 4 \, {\left({\left(4 \, A B + B^{2}\right)} b^{4} d^{4} i^{3} x^{4} + 4 \, {\left(4 \, A B + B^{2}\right)} b^{4} c d^{3} i^{3} x^{3} + 6 \, {\left(4 \, A B + B^{2}\right)} b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, {\left(4 \, A B + B^{2}\right)} b^{4} c^{3} d i^{3} x + {\left(4 \, A B + B^{2}\right)} b^{4} c^{4} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{32 \, {\left({\left(b^{9} c - a b^{8} d\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c - a^{2} b^{7} d\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c - a^{3} b^{6} d\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c - a^{4} b^{5} d\right)} g^{5} x + {\left(a^{4} b^{5} c - a^{5} b^{4} d\right)} g^{5}\right)}}"," ",0,"-1/32*(4*((8*A^2 + 4*A*B + B^2)*b^4*c*d^3 - (8*A^2 + 4*A*B + B^2)*a*b^3*d^4)*i^3*x^3 + 6*((8*A^2 + 4*A*B + B^2)*b^4*c^2*d^2 - (8*A^2 + 4*A*B + B^2)*a^2*b^2*d^4)*i^3*x^2 + 4*((8*A^2 + 4*A*B + B^2)*b^4*c^3*d - (8*A^2 + 4*A*B + B^2)*a^3*b*d^4)*i^3*x + ((8*A^2 + 4*A*B + B^2)*b^4*c^4 - (8*A^2 + 4*A*B + B^2)*a^4*d^4)*i^3 + 8*(B^2*b^4*d^4*i^3*x^4 + 4*B^2*b^4*c*d^3*i^3*x^3 + 6*B^2*b^4*c^2*d^2*i^3*x^2 + 4*B^2*b^4*c^3*d*i^3*x + B^2*b^4*c^4*i^3)*log((b*e*x + a*e)/(d*x + c))^2 + 4*((4*A*B + B^2)*b^4*d^4*i^3*x^4 + 4*(4*A*B + B^2)*b^4*c*d^3*i^3*x^3 + 6*(4*A*B + B^2)*b^4*c^2*d^2*i^3*x^2 + 4*(4*A*B + B^2)*b^4*c^3*d*i^3*x + (4*A*B + B^2)*b^4*c^4*i^3)*log((b*e*x + a*e)/(d*x + c)))/((b^9*c - a*b^8*d)*g^5*x^4 + 4*(a*b^8*c - a^2*b^7*d)*g^5*x^3 + 6*(a^2*b^7*c - a^3*b^6*d)*g^5*x^2 + 4*(a^3*b^6*c - a^4*b^5*d)*g^5*x + (a^4*b^5*c - a^5*b^4*d)*g^5)","B",0
82,1,1045,0,0.509330," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^6,x, algorithm=""fricas"")","\frac{20 \, {\left({\left(20 \, A B + 9 \, B^{2}\right)} b^{5} c d^{4} - {\left(20 \, A B + 9 \, B^{2}\right)} a b^{4} d^{5}\right)} i^{3} x^{4} - 10 \, {\left({\left(200 \, A^{2} + 20 \, A B - 11 \, B^{2}\right)} b^{5} c^{2} d^{3} - 50 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a b^{4} c d^{4} + {\left(200 \, A^{2} + 180 \, A B + 61 \, B^{2}\right)} a^{2} b^{3} d^{5}\right)} i^{3} x^{3} - 10 \, {\left(2 \, {\left(200 \, A^{2} + 60 \, A B + 7 \, B^{2}\right)} b^{5} c^{3} d^{2} - 75 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a b^{4} c^{2} d^{3} + {\left(200 \, A^{2} + 180 \, A B + 61 \, B^{2}\right)} a^{3} b^{2} d^{5}\right)} i^{3} x^{2} - 5 \, {\left({\left(600 \, A^{2} + 220 \, A B + 39 \, B^{2}\right)} b^{5} c^{4} d - 100 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a b^{4} c^{3} d^{2} + {\left(200 \, A^{2} + 180 \, A B + 61 \, B^{2}\right)} a^{4} b d^{5}\right)} i^{3} x - {\left(32 \, {\left(25 \, A^{2} + 10 \, A B + 2 \, B^{2}\right)} b^{5} c^{5} - 125 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a b^{4} c^{4} d + {\left(200 \, A^{2} + 180 \, A B + 61 \, B^{2}\right)} a^{5} d^{5}\right)} i^{3} + 200 \, {\left(B^{2} b^{5} d^{5} i^{3} x^{5} + 5 \, B^{2} a b^{4} d^{5} i^{3} x^{4} - 10 \, {\left(B^{2} b^{5} c^{2} d^{3} - 2 \, B^{2} a b^{4} c d^{4}\right)} i^{3} x^{3} - 10 \, {\left(2 \, B^{2} b^{5} c^{3} d^{2} - 3 \, B^{2} a b^{4} c^{2} d^{3}\right)} i^{3} x^{2} - 5 \, {\left(3 \, B^{2} b^{5} c^{4} d - 4 \, B^{2} a b^{4} c^{3} d^{2}\right)} i^{3} x - {\left(4 \, B^{2} b^{5} c^{5} - 5 \, B^{2} a b^{4} c^{4} d\right)} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 20 \, {\left({\left(20 \, A B + 9 \, B^{2}\right)} b^{5} d^{5} i^{3} x^{5} + 5 \, {\left(4 \, B^{2} b^{5} c d^{4} + 5 \, {\left(4 \, A B + B^{2}\right)} a b^{4} d^{5}\right)} i^{3} x^{4} - 10 \, {\left({\left(20 \, A B + B^{2}\right)} b^{5} c^{2} d^{3} - 10 \, {\left(4 \, A B + B^{2}\right)} a b^{4} c d^{4}\right)} i^{3} x^{3} - 10 \, {\left(2 \, {\left(20 \, A B + 3 \, B^{2}\right)} b^{5} c^{3} d^{2} - 15 \, {\left(4 \, A B + B^{2}\right)} a b^{4} c^{2} d^{3}\right)} i^{3} x^{2} - 5 \, {\left({\left(60 \, A B + 11 \, B^{2}\right)} b^{5} c^{4} d - 20 \, {\left(4 \, A B + B^{2}\right)} a b^{4} c^{3} d^{2}\right)} i^{3} x - {\left(16 \, {\left(5 \, A B + B^{2}\right)} b^{5} c^{5} - 25 \, {\left(4 \, A B + B^{2}\right)} a b^{4} c^{4} d\right)} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4000 \, {\left({\left(b^{11} c^{2} - 2 \, a b^{10} c d + a^{2} b^{9} d^{2}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{2} - 2 \, a^{2} b^{9} c d + a^{3} b^{8} d^{2}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{2} - 2 \, a^{3} b^{8} c d + a^{4} b^{7} d^{2}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{2} - 2 \, a^{4} b^{7} c d + a^{5} b^{6} d^{2}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{2} - 2 \, a^{5} b^{6} c d + a^{6} b^{5} d^{2}\right)} g^{6} x + {\left(a^{5} b^{6} c^{2} - 2 \, a^{6} b^{5} c d + a^{7} b^{4} d^{2}\right)} g^{6}\right)}}"," ",0,"1/4000*(20*((20*A*B + 9*B^2)*b^5*c*d^4 - (20*A*B + 9*B^2)*a*b^4*d^5)*i^3*x^4 - 10*((200*A^2 + 20*A*B - 11*B^2)*b^5*c^2*d^3 - 50*(8*A^2 + 4*A*B + B^2)*a*b^4*c*d^4 + (200*A^2 + 180*A*B + 61*B^2)*a^2*b^3*d^5)*i^3*x^3 - 10*(2*(200*A^2 + 60*A*B + 7*B^2)*b^5*c^3*d^2 - 75*(8*A^2 + 4*A*B + B^2)*a*b^4*c^2*d^3 + (200*A^2 + 180*A*B + 61*B^2)*a^3*b^2*d^5)*i^3*x^2 - 5*((600*A^2 + 220*A*B + 39*B^2)*b^5*c^4*d - 100*(8*A^2 + 4*A*B + B^2)*a*b^4*c^3*d^2 + (200*A^2 + 180*A*B + 61*B^2)*a^4*b*d^5)*i^3*x - (32*(25*A^2 + 10*A*B + 2*B^2)*b^5*c^5 - 125*(8*A^2 + 4*A*B + B^2)*a*b^4*c^4*d + (200*A^2 + 180*A*B + 61*B^2)*a^5*d^5)*i^3 + 200*(B^2*b^5*d^5*i^3*x^5 + 5*B^2*a*b^4*d^5*i^3*x^4 - 10*(B^2*b^5*c^2*d^3 - 2*B^2*a*b^4*c*d^4)*i^3*x^3 - 10*(2*B^2*b^5*c^3*d^2 - 3*B^2*a*b^4*c^2*d^3)*i^3*x^2 - 5*(3*B^2*b^5*c^4*d - 4*B^2*a*b^4*c^3*d^2)*i^3*x - (4*B^2*b^5*c^5 - 5*B^2*a*b^4*c^4*d)*i^3)*log((b*e*x + a*e)/(d*x + c))^2 + 20*((20*A*B + 9*B^2)*b^5*d^5*i^3*x^5 + 5*(4*B^2*b^5*c*d^4 + 5*(4*A*B + B^2)*a*b^4*d^5)*i^3*x^4 - 10*((20*A*B + B^2)*b^5*c^2*d^3 - 10*(4*A*B + B^2)*a*b^4*c*d^4)*i^3*x^3 - 10*(2*(20*A*B + 3*B^2)*b^5*c^3*d^2 - 15*(4*A*B + B^2)*a*b^4*c^2*d^3)*i^3*x^2 - 5*((60*A*B + 11*B^2)*b^5*c^4*d - 20*(4*A*B + B^2)*a*b^4*c^3*d^2)*i^3*x - (16*(5*A*B + B^2)*b^5*c^5 - 25*(4*A*B + B^2)*a*b^4*c^4*d)*i^3)*log((b*e*x + a*e)/(d*x + c)))/((b^11*c^2 - 2*a*b^10*c*d + a^2*b^9*d^2)*g^6*x^5 + 5*(a*b^10*c^2 - 2*a^2*b^9*c*d + a^3*b^8*d^2)*g^6*x^4 + 10*(a^2*b^9*c^2 - 2*a^3*b^8*c*d + a^4*b^7*d^2)*g^6*x^3 + 10*(a^3*b^8*c^2 - 2*a^4*b^7*c*d + a^5*b^6*d^2)*g^6*x^2 + 5*(a^4*b^7*c^2 - 2*a^5*b^6*c*d + a^6*b^5*d^2)*g^6*x + (a^5*b^6*c^2 - 2*a^6*b^5*c*d + a^7*b^4*d^2)*g^6)","B",0
83,1,1610,0,0.540739," ","integrate((d*i*x+c*i)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^7,x, algorithm=""fricas"")","-\frac{60 \, {\left({\left(60 \, A B + 37 \, B^{2}\right)} b^{6} c d^{5} - {\left(60 \, A B + 37 \, B^{2}\right)} a b^{5} d^{6}\right)} i^{3} x^{5} - 30 \, {\left({\left(60 \, A B - 23 \, B^{2}\right)} b^{6} c^{2} d^{4} - 36 \, {\left(20 \, A B + 9 \, B^{2}\right)} a b^{5} c d^{5} + {\left(660 \, A B + 347 \, B^{2}\right)} a^{2} b^{4} d^{6}\right)} i^{3} x^{4} + 20 \, {\left({\left(1800 \, A^{2} + 60 \, A B - 53 \, B^{2}\right)} b^{6} c^{3} d^{3} - 27 \, {\left(200 \, A^{2} + 20 \, A B - 11 \, B^{2}\right)} a b^{5} c^{2} d^{4} + 675 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a^{2} b^{4} c d^{5} - {\left(1800 \, A^{2} + 2220 \, A B + 919 \, B^{2}\right)} a^{3} b^{3} d^{6}\right)} i^{3} x^{3} + 15 \, {\left({\left(5400 \, A^{2} + 1140 \, A B + 73 \, B^{2}\right)} b^{6} c^{4} d^{2} - 72 \, {\left(200 \, A^{2} + 60 \, A B + 7 \, B^{2}\right)} a b^{5} c^{3} d^{3} + 1350 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a^{2} b^{4} c^{2} d^{4} - {\left(1800 \, A^{2} + 2220 \, A B + 919 \, B^{2}\right)} a^{4} b^{2} d^{6}\right)} i^{3} x^{2} + 6 \, {\left(8 \, {\left(1350 \, A^{2} + 390 \, A B + 53 \, B^{2}\right)} b^{6} c^{5} d - 45 \, {\left(600 \, A^{2} + 220 \, A B + 39 \, B^{2}\right)} a b^{5} c^{4} d^{2} + 2250 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a^{2} b^{4} c^{3} d^{3} - {\left(1800 \, A^{2} + 2220 \, A B + 919 \, B^{2}\right)} a^{5} b d^{6}\right)} i^{3} x + {\left(1000 \, {\left(18 \, A^{2} + 6 \, A B + B^{2}\right)} b^{6} c^{6} - 1728 \, {\left(25 \, A^{2} + 10 \, A B + 2 \, B^{2}\right)} a b^{5} c^{5} d + 3375 \, {\left(8 \, A^{2} + 4 \, A B + B^{2}\right)} a^{2} b^{4} c^{4} d^{2} - {\left(1800 \, A^{2} + 2220 \, A B + 919 \, B^{2}\right)} a^{6} d^{6}\right)} i^{3} + 1800 \, {\left(B^{2} b^{6} d^{6} i^{3} x^{6} + 6 \, B^{2} a b^{5} d^{6} i^{3} x^{5} + 15 \, B^{2} a^{2} b^{4} d^{6} i^{3} x^{4} + 20 \, {\left(B^{2} b^{6} c^{3} d^{3} - 3 \, B^{2} a b^{5} c^{2} d^{4} + 3 \, B^{2} a^{2} b^{4} c d^{5}\right)} i^{3} x^{3} + 15 \, {\left(3 \, B^{2} b^{6} c^{4} d^{2} - 8 \, B^{2} a b^{5} c^{3} d^{3} + 6 \, B^{2} a^{2} b^{4} c^{2} d^{4}\right)} i^{3} x^{2} + 6 \, {\left(6 \, B^{2} b^{6} c^{5} d - 15 \, B^{2} a b^{5} c^{4} d^{2} + 10 \, B^{2} a^{2} b^{4} c^{3} d^{3}\right)} i^{3} x + {\left(10 \, B^{2} b^{6} c^{6} - 24 \, B^{2} a b^{5} c^{5} d + 15 \, B^{2} a^{2} b^{4} c^{4} d^{2}\right)} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 60 \, {\left({\left(60 \, A B + 37 \, B^{2}\right)} b^{6} d^{6} i^{3} x^{6} + 6 \, {\left(10 \, B^{2} b^{6} c d^{5} + 3 \, {\left(20 \, A B + 9 \, B^{2}\right)} a b^{5} d^{6}\right)} i^{3} x^{5} - 15 \, {\left(2 \, B^{2} b^{6} c^{2} d^{4} - 24 \, B^{2} a b^{5} c d^{5} - 15 \, {\left(4 \, A B + B^{2}\right)} a^{2} b^{4} d^{6}\right)} i^{3} x^{4} + 20 \, {\left({\left(60 \, A B + B^{2}\right)} b^{6} c^{3} d^{3} - 9 \, {\left(20 \, A B + B^{2}\right)} a b^{5} c^{2} d^{4} + 45 \, {\left(4 \, A B + B^{2}\right)} a^{2} b^{4} c d^{5}\right)} i^{3} x^{3} + 15 \, {\left({\left(180 \, A B + 19 \, B^{2}\right)} b^{6} c^{4} d^{2} - 24 \, {\left(20 \, A B + 3 \, B^{2}\right)} a b^{5} c^{3} d^{3} + 90 \, {\left(4 \, A B + B^{2}\right)} a^{2} b^{4} c^{2} d^{4}\right)} i^{3} x^{2} + 6 \, {\left(4 \, {\left(90 \, A B + 13 \, B^{2}\right)} b^{6} c^{5} d - 15 \, {\left(60 \, A B + 11 \, B^{2}\right)} a b^{5} c^{4} d^{2} + 150 \, {\left(4 \, A B + B^{2}\right)} a^{2} b^{4} c^{3} d^{3}\right)} i^{3} x + {\left(100 \, {\left(6 \, A B + B^{2}\right)} b^{6} c^{6} - 288 \, {\left(5 \, A B + B^{2}\right)} a b^{5} c^{5} d + 225 \, {\left(4 \, A B + B^{2}\right)} a^{2} b^{4} c^{4} d^{2}\right)} i^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{108000 \, {\left({\left(b^{13} c^{3} - 3 \, a b^{12} c^{2} d + 3 \, a^{2} b^{11} c d^{2} - a^{3} b^{10} d^{3}\right)} g^{7} x^{6} + 6 \, {\left(a b^{12} c^{3} - 3 \, a^{2} b^{11} c^{2} d + 3 \, a^{3} b^{10} c d^{2} - a^{4} b^{9} d^{3}\right)} g^{7} x^{5} + 15 \, {\left(a^{2} b^{11} c^{3} - 3 \, a^{3} b^{10} c^{2} d + 3 \, a^{4} b^{9} c d^{2} - a^{5} b^{8} d^{3}\right)} g^{7} x^{4} + 20 \, {\left(a^{3} b^{10} c^{3} - 3 \, a^{4} b^{9} c^{2} d + 3 \, a^{5} b^{8} c d^{2} - a^{6} b^{7} d^{3}\right)} g^{7} x^{3} + 15 \, {\left(a^{4} b^{9} c^{3} - 3 \, a^{5} b^{8} c^{2} d + 3 \, a^{6} b^{7} c d^{2} - a^{7} b^{6} d^{3}\right)} g^{7} x^{2} + 6 \, {\left(a^{5} b^{8} c^{3} - 3 \, a^{6} b^{7} c^{2} d + 3 \, a^{7} b^{6} c d^{2} - a^{8} b^{5} d^{3}\right)} g^{7} x + {\left(a^{6} b^{7} c^{3} - 3 \, a^{7} b^{6} c^{2} d + 3 \, a^{8} b^{5} c d^{2} - a^{9} b^{4} d^{3}\right)} g^{7}\right)}}"," ",0,"-1/108000*(60*((60*A*B + 37*B^2)*b^6*c*d^5 - (60*A*B + 37*B^2)*a*b^5*d^6)*i^3*x^5 - 30*((60*A*B - 23*B^2)*b^6*c^2*d^4 - 36*(20*A*B + 9*B^2)*a*b^5*c*d^5 + (660*A*B + 347*B^2)*a^2*b^4*d^6)*i^3*x^4 + 20*((1800*A^2 + 60*A*B - 53*B^2)*b^6*c^3*d^3 - 27*(200*A^2 + 20*A*B - 11*B^2)*a*b^5*c^2*d^4 + 675*(8*A^2 + 4*A*B + B^2)*a^2*b^4*c*d^5 - (1800*A^2 + 2220*A*B + 919*B^2)*a^3*b^3*d^6)*i^3*x^3 + 15*((5400*A^2 + 1140*A*B + 73*B^2)*b^6*c^4*d^2 - 72*(200*A^2 + 60*A*B + 7*B^2)*a*b^5*c^3*d^3 + 1350*(8*A^2 + 4*A*B + B^2)*a^2*b^4*c^2*d^4 - (1800*A^2 + 2220*A*B + 919*B^2)*a^4*b^2*d^6)*i^3*x^2 + 6*(8*(1350*A^2 + 390*A*B + 53*B^2)*b^6*c^5*d - 45*(600*A^2 + 220*A*B + 39*B^2)*a*b^5*c^4*d^2 + 2250*(8*A^2 + 4*A*B + B^2)*a^2*b^4*c^3*d^3 - (1800*A^2 + 2220*A*B + 919*B^2)*a^5*b*d^6)*i^3*x + (1000*(18*A^2 + 6*A*B + B^2)*b^6*c^6 - 1728*(25*A^2 + 10*A*B + 2*B^2)*a*b^5*c^5*d + 3375*(8*A^2 + 4*A*B + B^2)*a^2*b^4*c^4*d^2 - (1800*A^2 + 2220*A*B + 919*B^2)*a^6*d^6)*i^3 + 1800*(B^2*b^6*d^6*i^3*x^6 + 6*B^2*a*b^5*d^6*i^3*x^5 + 15*B^2*a^2*b^4*d^6*i^3*x^4 + 20*(B^2*b^6*c^3*d^3 - 3*B^2*a*b^5*c^2*d^4 + 3*B^2*a^2*b^4*c*d^5)*i^3*x^3 + 15*(3*B^2*b^6*c^4*d^2 - 8*B^2*a*b^5*c^3*d^3 + 6*B^2*a^2*b^4*c^2*d^4)*i^3*x^2 + 6*(6*B^2*b^6*c^5*d - 15*B^2*a*b^5*c^4*d^2 + 10*B^2*a^2*b^4*c^3*d^3)*i^3*x + (10*B^2*b^6*c^6 - 24*B^2*a*b^5*c^5*d + 15*B^2*a^2*b^4*c^4*d^2)*i^3)*log((b*e*x + a*e)/(d*x + c))^2 + 60*((60*A*B + 37*B^2)*b^6*d^6*i^3*x^6 + 6*(10*B^2*b^6*c*d^5 + 3*(20*A*B + 9*B^2)*a*b^5*d^6)*i^3*x^5 - 15*(2*B^2*b^6*c^2*d^4 - 24*B^2*a*b^5*c*d^5 - 15*(4*A*B + B^2)*a^2*b^4*d^6)*i^3*x^4 + 20*((60*A*B + B^2)*b^6*c^3*d^3 - 9*(20*A*B + B^2)*a*b^5*c^2*d^4 + 45*(4*A*B + B^2)*a^2*b^4*c*d^5)*i^3*x^3 + 15*((180*A*B + 19*B^2)*b^6*c^4*d^2 - 24*(20*A*B + 3*B^2)*a*b^5*c^3*d^3 + 90*(4*A*B + B^2)*a^2*b^4*c^2*d^4)*i^3*x^2 + 6*(4*(90*A*B + 13*B^2)*b^6*c^5*d - 15*(60*A*B + 11*B^2)*a*b^5*c^4*d^2 + 150*(4*A*B + B^2)*a^2*b^4*c^3*d^3)*i^3*x + (100*(6*A*B + B^2)*b^6*c^6 - 288*(5*A*B + B^2)*a*b^5*c^5*d + 225*(4*A*B + B^2)*a^2*b^4*c^4*d^2)*i^3)*log((b*e*x + a*e)/(d*x + c)))/((b^13*c^3 - 3*a*b^12*c^2*d + 3*a^2*b^11*c*d^2 - a^3*b^10*d^3)*g^7*x^6 + 6*(a*b^12*c^3 - 3*a^2*b^11*c^2*d + 3*a^3*b^10*c*d^2 - a^4*b^9*d^3)*g^7*x^5 + 15*(a^2*b^11*c^3 - 3*a^3*b^10*c^2*d + 3*a^4*b^9*c*d^2 - a^5*b^8*d^3)*g^7*x^4 + 20*(a^3*b^10*c^3 - 3*a^4*b^9*c^2*d + 3*a^5*b^8*c*d^2 - a^6*b^7*d^3)*g^7*x^3 + 15*(a^4*b^9*c^3 - 3*a^5*b^8*c^2*d + 3*a^6*b^7*c*d^2 - a^7*b^6*d^3)*g^7*x^2 + 6*(a^5*b^8*c^3 - 3*a^6*b^7*c^2*d + 3*a^7*b^6*c*d^2 - a^8*b^5*d^3)*g^7*x + (a^6*b^7*c^3 - 3*a^7*b^6*c^2*d + 3*a^8*b^5*c*d^2 - a^9*b^4*d^3)*g^7)","B",0
84,0,0,0,0.470379," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{3} g^{3} x^{3} + 3 \, A^{2} a b^{2} g^{3} x^{2} + 3 \, A^{2} a^{2} b g^{3} x + A^{2} a^{3} g^{3} + {\left(B^{2} b^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b g^{3} x + B^{2} a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{3} g^{3} x^{3} + 3 \, A B a b^{2} g^{3} x^{2} + 3 \, A B a^{2} b g^{3} x + A B a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d i x + c i}, x\right)"," ",0,"integral((A^2*b^3*g^3*x^3 + 3*A^2*a*b^2*g^3*x^2 + 3*A^2*a^2*b*g^3*x + A^2*a^3*g^3 + (B^2*b^3*g^3*x^3 + 3*B^2*a*b^2*g^3*x^2 + 3*B^2*a^2*b*g^3*x + B^2*a^3*g^3)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^3*g^3*x^3 + 3*A*B*a*b^2*g^3*x^2 + 3*A*B*a^2*b*g^3*x + A*B*a^3*g^3)*log((b*e*x + a*e)/(d*x + c)))/(d*i*x + c*i), x)","F",0
85,0,0,0,0.437764," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{2} g^{2} x^{2} + 2 \, A^{2} a b g^{2} x + A^{2} a^{2} g^{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(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{2} g^{2} x^{2} + 2 \, A B a b g^{2} x + A B a^{2} g^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d i x + c i}, x\right)"," ",0,"integral((A^2*b^2*g^2*x^2 + 2*A^2*a*b*g^2*x + A^2*a^2*g^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*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^2*g^2*x^2 + 2*A*B*a*b*g^2*x + A*B*a^2*g^2)*log((b*e*x + a*e)/(d*x + c)))/(d*i*x + c*i), x)","F",0
86,0,0,0,0.435456," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b g x + A^{2} a g + {\left(B^{2} b g x + B^{2} a g\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b g x + A B a g\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d i x + c i}, x\right)"," ",0,"integral((A^2*b*g*x + A^2*a*g + (B^2*b*g*x + B^2*a*g)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b*g*x + A*B*a*g)*log((b*e*x + a*e)/(d*x + c)))/(d*i*x + c*i), x)","F",0
87,0,0,0,0.440128," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B^{2} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, A B \log\left(\frac{b e x + a e}{d x + c}\right) + A^{2}}{d i x + c i}, x\right)"," ",0,"integral((B^2*log((b*e*x + a*e)/(d*x + c))^2 + 2*A*B*log((b*e*x + a*e)/(d*x + c)) + A^2)/(d*i*x + c*i), x)","F",0
88,1,87,0,0.414729," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)/(d*i*x+c*i),x, algorithm=""fricas"")","\frac{B^{2} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 3 \, A B \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 3 \, A^{2} \log\left(\frac{b e x + a e}{d x + c}\right)}{3 \, {\left(b c - a d\right)} g i}"," ",0,"1/3*(B^2*log((b*e*x + a*e)/(d*x + c))^3 + 3*A*B*log((b*e*x + a*e)/(d*x + c))^2 + 3*A^2*log((b*e*x + a*e)/(d*x + c)))/((b*c - a*d)*g*i)","B",0
89,1,231,0,0.473811," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{{\left(B^{2} b d x + B^{2} a d\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 3 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} b c - 3 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a d + 3 \, {\left(B^{2} b c + A B a d + {\left(A B + B^{2}\right)} b d x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 3 \, {\left(A^{2} a d + {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} b d x + 2 \, {\left(A B + B^{2}\right)} b c\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{3 \, {\left({\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{2} i x + {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} g^{2} i\right)}}"," ",0,"-1/3*((B^2*b*d*x + B^2*a*d)*log((b*e*x + a*e)/(d*x + c))^3 + 3*(A^2 + 2*A*B + 2*B^2)*b*c - 3*(A^2 + 2*A*B + 2*B^2)*a*d + 3*(B^2*b*c + A*B*a*d + (A*B + B^2)*b*d*x)*log((b*e*x + a*e)/(d*x + c))^2 + 3*(A^2*a*d + (A^2 + 2*A*B + 2*B^2)*b*d*x + 2*(A*B + B^2)*b*c)*log((b*e*x + a*e)/(d*x + c)))/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^2*i*x + (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*g^2*i)","A",0
90,1,540,0,0.437995," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} b^{2} c^{2} - 24 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a b c d + 3 \, {\left(6 \, A^{2} + 14 \, A B + 15 \, B^{2}\right)} a^{2} d^{2} - 4 \, {\left(B^{2} b^{2} d^{2} x^{2} + 2 \, B^{2} a b d^{2} x + B^{2} a^{2} d^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} - 6 \, {\left({\left(2 \, A B + 3 \, B^{2}\right)} b^{2} d^{2} x^{2} - B^{2} b^{2} c^{2} + 4 \, B^{2} a b c d + 2 \, A B a^{2} d^{2} + 2 \, {\left(B^{2} b^{2} c d + 2 \, {\left(A B + B^{2}\right)} a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 6 \, {\left({\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} b^{2} c d - {\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} a b d^{2}\right)} x - 6 \, {\left({\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} b^{2} d^{2} x^{2} + 2 \, A^{2} a^{2} d^{2} - {\left(2 \, A B + B^{2}\right)} b^{2} c^{2} + 8 \, {\left(A B + B^{2}\right)} a b c d + 2 \, {\left({\left(2 \, A B + 3 \, B^{2}\right)} b^{2} c d + 2 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{12 \, {\left({\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} g^{3} i x + {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} g^{3} i\right)}}"," ",0,"-1/12*(3*(2*A^2 + 2*A*B + B^2)*b^2*c^2 - 24*(A^2 + 2*A*B + 2*B^2)*a*b*c*d + 3*(6*A^2 + 14*A*B + 15*B^2)*a^2*d^2 - 4*(B^2*b^2*d^2*x^2 + 2*B^2*a*b*d^2*x + B^2*a^2*d^2)*log((b*e*x + a*e)/(d*x + c))^3 - 6*((2*A*B + 3*B^2)*b^2*d^2*x^2 - B^2*b^2*c^2 + 4*B^2*a*b*c*d + 2*A*B*a^2*d^2 + 2*(B^2*b^2*c*d + 2*(A*B + B^2)*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 6*((2*A^2 + 6*A*B + 7*B^2)*b^2*c*d - (2*A^2 + 6*A*B + 7*B^2)*a*b*d^2)*x - 6*((2*A^2 + 6*A*B + 7*B^2)*b^2*d^2*x^2 + 2*A^2*a^2*d^2 - (2*A*B + B^2)*b^2*c^2 + 8*(A*B + B^2)*a*b*c*d + 2*((2*A*B + 3*B^2)*b^2*c*d + 2*(A^2 + 2*A*B + 2*B^2)*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^3*i*x^2 + 2*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*g^3*i*x + (a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*g^3*i)","A",0
91,1,940,0,0.456418," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{4 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} b^{3} c^{3} - 81 \, {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a b^{2} c^{2} d + 324 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a^{2} b c d^{2} - {\left(198 \, A^{2} + 510 \, A B + 575 \, B^{2}\right)} a^{3} d^{3} + 36 \, {\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 + B^{2} a^{3} d^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 6 \, {\left({\left(18 \, A^{2} + 66 \, A B + 85 \, B^{2}\right)} b^{3} c d^{2} - {\left(18 \, A^{2} + 66 \, A B + 85 \, B^{2}\right)} a b^{2} d^{3}\right)} x^{2} + 18 \, {\left({\left(6 \, A B + 11 \, B^{2}\right)} b^{3} d^{3} x^{3} + 2 \, B^{2} b^{3} c^{3} - 9 \, B^{2} a b^{2} c^{2} d + 18 \, B^{2} a^{2} b c d^{2} + 6 \, A B a^{3} d^{3} + 3 \, {\left(2 \, B^{2} b^{3} c d^{2} + 3 \, {\left(2 \, A B + 3 \, B^{2}\right)} a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(B^{2} b^{3} c^{2} d - 6 \, B^{2} a b^{2} c d^{2} - 6 \, {\left(A B + B^{2}\right)} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 3 \, {\left({\left(18 \, A^{2} + 30 \, A B + 19 \, B^{2}\right)} b^{3} c^{2} d - 54 \, {\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} a b^{2} c d^{2} + {\left(90 \, A^{2} + 294 \, A B + 359 \, B^{2}\right)} a^{2} b d^{3}\right)} x + 6 \, {\left({\left(18 \, A^{2} + 66 \, A B + 85 \, B^{2}\right)} b^{3} d^{3} x^{3} + 18 \, A^{2} a^{3} d^{3} + 4 \, {\left(3 \, A B + B^{2}\right)} b^{3} c^{3} - 27 \, {\left(2 \, A B + B^{2}\right)} a b^{2} c^{2} d + 108 \, {\left(A B + B^{2}\right)} a^{2} b c d^{2} + 3 \, {\left(2 \, {\left(6 \, A B + 11 \, B^{2}\right)} b^{3} c d^{2} + 9 \, {\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} a b^{2} d^{3}\right)} x^{2} - 3 \, {\left({\left(6 \, A B + 5 \, B^{2}\right)} b^{3} c^{2} d - 18 \, {\left(2 \, A B + 3 \, B^{2}\right)} a b^{2} c d^{2} - 18 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{108 \, {\left({\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{6} c^{4} - 4 \, a^{2} b^{5} c^{3} d + 6 \, a^{3} b^{4} c^{2} d^{2} - 4 \, a^{4} b^{3} c d^{3} + a^{5} b^{2} d^{4}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}\right)} g^{4} i x + {\left(a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}\right)} g^{4} i\right)}}"," ",0,"-1/108*(4*(9*A^2 + 6*A*B + 2*B^2)*b^3*c^3 - 81*(2*A^2 + 2*A*B + B^2)*a*b^2*c^2*d + 324*(A^2 + 2*A*B + 2*B^2)*a^2*b*c*d^2 - (198*A^2 + 510*A*B + 575*B^2)*a^3*d^3 + 36*(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 + B^2*a^3*d^3)*log((b*e*x + a*e)/(d*x + c))^3 + 6*((18*A^2 + 66*A*B + 85*B^2)*b^3*c*d^2 - (18*A^2 + 66*A*B + 85*B^2)*a*b^2*d^3)*x^2 + 18*((6*A*B + 11*B^2)*b^3*d^3*x^3 + 2*B^2*b^3*c^3 - 9*B^2*a*b^2*c^2*d + 18*B^2*a^2*b*c*d^2 + 6*A*B*a^3*d^3 + 3*(2*B^2*b^3*c*d^2 + 3*(2*A*B + 3*B^2)*a*b^2*d^3)*x^2 - 3*(B^2*b^3*c^2*d - 6*B^2*a*b^2*c*d^2 - 6*(A*B + B^2)*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 3*((18*A^2 + 30*A*B + 19*B^2)*b^3*c^2*d - 54*(2*A^2 + 6*A*B + 7*B^2)*a*b^2*c*d^2 + (90*A^2 + 294*A*B + 359*B^2)*a^2*b*d^3)*x + 6*((18*A^2 + 66*A*B + 85*B^2)*b^3*d^3*x^3 + 18*A^2*a^3*d^3 + 4*(3*A*B + B^2)*b^3*c^3 - 27*(2*A*B + B^2)*a*b^2*c^2*d + 108*(A*B + B^2)*a^2*b*c*d^2 + 3*(2*(6*A*B + 11*B^2)*b^3*c*d^2 + 9*(2*A^2 + 6*A*B + 7*B^2)*a*b^2*d^3)*x^2 - 3*((6*A*B + 5*B^2)*b^3*c^2*d - 18*(2*A*B + 3*B^2)*a*b^2*c*d^2 - 18*(A^2 + 2*A*B + 2*B^2)*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^4*i*x^3 + 3*(a*b^6*c^4 - 4*a^2*b^5*c^3*d + 6*a^3*b^4*c^2*d^2 - 4*a^4*b^3*c*d^3 + a^5*b^2*d^4)*g^4*i*x^2 + 3*(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 6*a^4*b^3*c^2*d^2 - 4*a^5*b^2*c*d^3 + a^6*b*d^4)*g^4*i*x + (a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4)*g^4*i)","A",0
92,0,0,0,0.425737," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{3} g^{3} x^{3} + 3 \, A^{2} a b^{2} g^{3} x^{2} + 3 \, A^{2} a^{2} b g^{3} x + A^{2} a^{3} g^{3} + {\left(B^{2} b^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b g^{3} x + B^{2} a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{3} g^{3} x^{3} + 3 \, A B a b^{2} g^{3} x^{2} + 3 \, A B a^{2} b g^{3} x + A B a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A^2*b^3*g^3*x^3 + 3*A^2*a*b^2*g^3*x^2 + 3*A^2*a^2*b*g^3*x + A^2*a^3*g^3 + (B^2*b^3*g^3*x^3 + 3*B^2*a*b^2*g^3*x^2 + 3*B^2*a^2*b*g^3*x + B^2*a^3*g^3)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^3*g^3*x^3 + 3*A*B*a*b^2*g^3*x^2 + 3*A*B*a^2*b*g^3*x + A*B*a^3*g^3)*log((b*e*x + a*e)/(d*x + c)))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
93,0,0,0,0.505861," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{2} g^{2} x^{2} + 2 \, A^{2} a b g^{2} x + A^{2} a^{2} g^{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(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{2} g^{2} x^{2} + 2 \, A B a b g^{2} x + A B a^{2} g^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A^2*b^2*g^2*x^2 + 2*A^2*a*b*g^2*x + A^2*a^2*g^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*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^2*g^2*x^2 + 2*A*B*a*b*g^2*x + A*B*a^2*g^2)*log((b*e*x + a*e)/(d*x + c)))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
94,0,0,0,0.420977," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b g x + A^{2} a g + {\left(B^{2} b g x + B^{2} a g\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b g x + A B a g\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A^2*b*g*x + A^2*a*g + (B^2*b*g*x + B^2*a*g)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b*g*x + A*B*a*g)*log((b*e*x + a*e)/(d*x + c)))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
95,1,155,0,0.421335," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{{\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} b c - {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a d - {\left(B^{2} b d x + B^{2} a d\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 2 \, {\left({\left(A B - B^{2}\right)} b d x + {\left(A B - B^{2}\right)} a d\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{{\left(b c d^{2} - a d^{3}\right)} i^{2} x + {\left(b c^{2} d - a c d^{2}\right)} i^{2}}"," ",0,"-((A^2 - 2*A*B + 2*B^2)*b*c - (A^2 - 2*A*B + 2*B^2)*a*d - (B^2*b*d*x + B^2*a*d)*log((b*e*x + a*e)/(d*x + c))^2 - 2*((A*B - B^2)*b*d*x + (A*B - B^2)*a*d)*log((b*e*x + a*e)/(d*x + c)))/((b*c*d^2 - a*d^3)*i^2*x + (b*c^2*d - a*c*d^2)*i^2)","A",0
96,1,236,0,0.416450," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)/(d*i*x+c*i)^2,x, algorithm=""fricas"")","\frac{{\left(B^{2} b d x + B^{2} b c\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 3 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} b c - 3 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a d + 3 \, {\left(A B b c - B^{2} a d + {\left(A B - B^{2}\right)} b d x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 3 \, {\left(A^{2} b c + {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} b d x - 2 \, {\left(A B - B^{2}\right)} a d\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{3 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} g i^{2} x + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} g i^{2}\right)}}"," ",0,"1/3*((B^2*b*d*x + B^2*b*c)*log((b*e*x + a*e)/(d*x + c))^3 + 3*(A^2 - 2*A*B + 2*B^2)*b*c - 3*(A^2 - 2*A*B + 2*B^2)*a*d + 3*(A*B*b*c - B^2*a*d + (A*B - B^2)*b*d*x)*log((b*e*x + a*e)/(d*x + c))^2 + 3*(A^2*b*c + (A^2 - 2*A*B + 2*B^2)*b*d*x - 2*(A*B - B^2)*a*d)*log((b*e*x + a*e)/(d*x + c)))/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g*i^2*x + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*g*i^2)","A",0
97,1,515,0,0.448529," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","\frac{12 \, A B a b c d - 3 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} b^{2} c^{2} + 3 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{2} d^{2} - 2 \, {\left(B^{2} b^{2} d^{2} x^{2} + B^{2} a b c d + {\left(B^{2} b^{2} c d + B^{2} a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} - 3 \, {\left(2 \, A B b^{2} d^{2} x^{2} + B^{2} b^{2} c^{2} + 2 \, A B a b c d - B^{2} a^{2} d^{2} + 2 \, {\left({\left(A B + B^{2}\right)} b^{2} c d + {\left(A B - B^{2}\right)} a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 6 \, {\left({\left(A^{2} + 2 \, B^{2}\right)} b^{2} c d - {\left(A^{2} + 2 \, B^{2}\right)} a b d^{2}\right)} x - 6 \, {\left({\left(A^{2} + 2 \, B^{2}\right)} b^{2} d^{2} x^{2} + A^{2} a b c d + {\left(A B + B^{2}\right)} b^{2} c^{2} - {\left(A B - B^{2}\right)} a^{2} d^{2} + {\left({\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} b^{2} c d + {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{3 \, {\left({\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} g^{2} i^{2} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} g^{2} i^{2} x + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} g^{2} i^{2}\right)}}"," ",0,"1/3*(12*A*B*a*b*c*d - 3*(A^2 + 2*A*B + 2*B^2)*b^2*c^2 + 3*(A^2 - 2*A*B + 2*B^2)*a^2*d^2 - 2*(B^2*b^2*d^2*x^2 + B^2*a*b*c*d + (B^2*b^2*c*d + B^2*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c))^3 - 3*(2*A*B*b^2*d^2*x^2 + B^2*b^2*c^2 + 2*A*B*a*b*c*d - B^2*a^2*d^2 + 2*((A*B + B^2)*b^2*c*d + (A*B - B^2)*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 6*((A^2 + 2*B^2)*b^2*c*d - (A^2 + 2*B^2)*a*b*d^2)*x - 6*((A^2 + 2*B^2)*b^2*d^2*x^2 + A^2*a*b*c*d + (A*B + B^2)*b^2*c^2 - (A*B - B^2)*a^2*d^2 + ((A^2 + 2*A*B + 2*B^2)*b^2*c*d + (A^2 - 2*A*B + 2*B^2)*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*g^2*i^2*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*g^2*i^2*x + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*g^2*i^2)","A",0
98,1,1005,0,0.486299," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} b^{3} c^{3} - 12 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a b^{2} c^{2} d + 3 \, {\left(2 \, A^{2} + 10 \, A B + 5 \, B^{2}\right)} a^{2} b c d^{2} + 4 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{3} d^{3} - 4 \, {\left(B^{2} b^{3} d^{3} x^{3} + B^{2} a^{2} b c d^{2} + {\left(B^{2} b^{3} c d^{2} + 2 \, B^{2} a b^{2} d^{3}\right)} x^{2} + {\left(2 \, B^{2} a b^{2} c d^{2} + B^{2} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} - 6 \, {\left({\left(2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right)} b^{3} c d^{2} - {\left(2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right)} a b^{2} d^{3}\right)} x^{2} - 2 \, {\left(3 \, {\left(2 \, A B + B^{2}\right)} b^{3} d^{3} x^{3} - B^{2} b^{3} c^{3} + 6 \, B^{2} a b^{2} c^{2} d + 6 \, A B a^{2} b c d^{2} - 2 \, B^{2} a^{3} d^{3} + 3 \, {\left(4 \, A B a b^{2} d^{3} + {\left(2 \, A B + 3 \, B^{2}\right)} b^{3} c d^{2}\right)} x^{2} + 3 \, {\left(B^{2} b^{3} c^{2} d + 4 \, {\left(A B + B^{2}\right)} a b^{2} c d^{2} + 2 \, {\left(A B - B^{2}\right)} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 3 \, {\left({\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} b^{3} c^{2} d + 2 \, {\left(2 \, A^{2} - 2 \, A B + 3 \, B^{2}\right)} a b^{2} c d^{2} - {\left(6 \, A^{2} + 2 \, A B + 13 \, B^{2}\right)} a^{2} b d^{3}\right)} x - 2 \, {\left(3 \, {\left(2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right)} b^{3} d^{3} x^{3} + 6 \, A^{2} a^{2} b c d^{2} - {\left(2 \, A B + B^{2}\right)} b^{3} c^{3} + 12 \, {\left(A B + B^{2}\right)} a b^{2} c^{2} d - 4 \, {\left(A B - B^{2}\right)} a^{3} d^{3} + 3 \, {\left({\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} b^{3} c d^{2} + 4 \, {\left(A^{2} + 2 \, B^{2}\right)} a b^{2} d^{3}\right)} x^{2} + 3 \, {\left({\left(2 \, A B + 3 \, B^{2}\right)} b^{3} c^{2} d + 4 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a b^{2} c d^{2} + 2 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{6} c^{4} d - 4 \, a b^{5} c^{3} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} - 4 \, a^{3} b^{3} c d^{4} + a^{4} b^{2} d^{5}\right)} g^{3} i^{2} x^{3} + {\left(b^{6} c^{5} - 2 \, a b^{5} c^{4} d - 2 \, a^{2} b^{4} c^{3} d^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} - 7 \, a^{4} b^{2} c d^{4} + 2 \, a^{5} b d^{5}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{5} c^{5} - 7 \, a^{2} b^{4} c^{4} d + 8 \, a^{3} b^{3} c^{3} d^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} - 2 \, a^{5} b c d^{4} + a^{6} d^{5}\right)} g^{3} i^{2} x + {\left(a^{2} b^{4} c^{5} - 4 \, a^{3} b^{3} c^{4} d + 6 \, a^{4} b^{2} c^{3} d^{2} - 4 \, a^{5} b c^{2} d^{3} + a^{6} c d^{4}\right)} g^{3} i^{2}\right)}}"," ",0,"-1/4*((2*A^2 + 2*A*B + B^2)*b^3*c^3 - 12*(A^2 + 2*A*B + 2*B^2)*a*b^2*c^2*d + 3*(2*A^2 + 10*A*B + 5*B^2)*a^2*b*c*d^2 + 4*(A^2 - 2*A*B + 2*B^2)*a^3*d^3 - 4*(B^2*b^3*d^3*x^3 + B^2*a^2*b*c*d^2 + (B^2*b^3*c*d^2 + 2*B^2*a*b^2*d^3)*x^2 + (2*B^2*a*b^2*c*d^2 + B^2*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c))^3 - 6*((2*A^2 + 2*A*B + 5*B^2)*b^3*c*d^2 - (2*A^2 + 2*A*B + 5*B^2)*a*b^2*d^3)*x^2 - 2*(3*(2*A*B + B^2)*b^3*d^3*x^3 - B^2*b^3*c^3 + 6*B^2*a*b^2*c^2*d + 6*A*B*a^2*b*c*d^2 - 2*B^2*a^3*d^3 + 3*(4*A*B*a*b^2*d^3 + (2*A*B + 3*B^2)*b^3*c*d^2)*x^2 + 3*(B^2*b^3*c^2*d + 4*(A*B + B^2)*a*b^2*c*d^2 + 2*(A*B - B^2)*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 3*((2*A^2 + 6*A*B + 7*B^2)*b^3*c^2*d + 2*(2*A^2 - 2*A*B + 3*B^2)*a*b^2*c*d^2 - (6*A^2 + 2*A*B + 13*B^2)*a^2*b*d^3)*x - 2*(3*(2*A^2 + 2*A*B + 5*B^2)*b^3*d^3*x^3 + 6*A^2*a^2*b*c*d^2 - (2*A*B + B^2)*b^3*c^3 + 12*(A*B + B^2)*a*b^2*c^2*d - 4*(A*B - B^2)*a^3*d^3 + 3*((2*A^2 + 6*A*B + 7*B^2)*b^3*c*d^2 + 4*(A^2 + 2*B^2)*a*b^2*d^3)*x^2 + 3*((2*A*B + 3*B^2)*b^3*c^2*d + 4*(A^2 + 2*A*B + 2*B^2)*a*b^2*c*d^2 + 2*(A^2 - 2*A*B + 2*B^2)*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^6*c^4*d - 4*a*b^5*c^3*d^2 + 6*a^2*b^4*c^2*d^3 - 4*a^3*b^3*c*d^4 + a^4*b^2*d^5)*g^3*i^2*x^3 + (b^6*c^5 - 2*a*b^5*c^4*d - 2*a^2*b^4*c^3*d^2 + 8*a^3*b^3*c^2*d^3 - 7*a^4*b^2*c*d^4 + 2*a^5*b*d^5)*g^3*i^2*x^2 + (2*a*b^5*c^5 - 7*a^2*b^4*c^4*d + 8*a^3*b^3*c^3*d^2 - 2*a^4*b^2*c^2*d^3 - 2*a^5*b*c*d^4 + a^6*d^5)*g^3*i^2*x + (a^2*b^4*c^5 - 4*a^3*b^3*c^4*d + 6*a^4*b^2*c^3*d^2 - 4*a^5*b*c^2*d^3 + a^6*c*d^4)*g^3*i^2)","A",0
99,1,1534,0,0.536329," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{{\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} b^{4} c^{4} - 27 \, {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a b^{3} c^{3} d + 162 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a^{2} b^{2} c^{2} d^{2} - 5 \, {\left(18 \, A^{2} + 66 \, A B + 49 \, B^{2}\right)} a^{3} b c d^{3} - 27 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{4} d^{4} + 6 \, {\left({\left(18 \, A^{2} + 30 \, A B + 55 \, B^{2}\right)} b^{4} c d^{3} - {\left(18 \, A^{2} + 30 \, A B + 55 \, B^{2}\right)} a b^{3} d^{4}\right)} x^{3} + 36 \, {\left(B^{2} b^{4} d^{4} x^{4} + B^{2} a^{3} b c d^{3} + {\left(B^{2} b^{4} c d^{3} + 3 \, B^{2} a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, B^{2} a^{2} b^{2} c d^{3} + B^{2} a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 3 \, {\left({\left(18 \, A^{2} + 66 \, A B + 85 \, B^{2}\right)} b^{4} c^{2} d^{2} + 8 \, {\left(9 \, A^{2} + 6 \, A B + 20 \, B^{2}\right)} a b^{3} c d^{3} - {\left(90 \, A^{2} + 114 \, A B + 245 \, B^{2}\right)} a^{2} b^{2} d^{4}\right)} x^{2} + 9 \, {\left(2 \, {\left(6 \, A B + 5 \, B^{2}\right)} b^{4} d^{4} x^{4} + B^{2} b^{4} c^{4} - 6 \, B^{2} a b^{3} c^{3} d + 18 \, B^{2} a^{2} b^{2} c^{2} d^{2} + 12 \, A B a^{3} b c d^{3} - 3 \, B^{2} a^{4} d^{4} + 2 \, {\left({\left(6 \, A B + 11 \, B^{2}\right)} b^{4} c d^{3} + 9 \, {\left(2 \, A B + B^{2}\right)} a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} + 6 \, A B a^{2} b^{2} d^{4} + 3 \, {\left(2 \, A B + 3 \, B^{2}\right)} a b^{3} c d^{3}\right)} x^{2} - 2 \, {\left(B^{2} b^{4} c^{3} d - 9 \, B^{2} a b^{3} c^{2} d^{2} - 18 \, {\left(A B + B^{2}\right)} a^{2} b^{2} c d^{3} - 6 \, {\left(A B - B^{2}\right)} a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - {\left({\left(18 \, A^{2} + 30 \, A B + 19 \, B^{2}\right)} b^{4} c^{3} d - 81 \, {\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} a b^{3} c^{2} d^{2} - 3 \, {\left(18 \, A^{2} - 114 \, A B - 29 \, B^{2}\right)} a^{2} b^{2} c d^{3} + {\left(198 \, A^{2} + 114 \, A B + 461 \, B^{2}\right)} a^{3} b d^{4}\right)} x + 6 \, {\left({\left(18 \, A^{2} + 30 \, A B + 55 \, B^{2}\right)} b^{4} d^{4} x^{4} + 18 \, A^{2} a^{3} b c d^{3} + {\left(3 \, A B + B^{2}\right)} b^{4} c^{4} - 9 \, {\left(2 \, A B + B^{2}\right)} a b^{3} c^{3} d + 54 \, {\left(A B + B^{2}\right)} a^{2} b^{2} c^{2} d^{2} - 9 \, {\left(A B - B^{2}\right)} a^{4} d^{4} + {\left({\left(18 \, A^{2} + 66 \, A B + 85 \, B^{2}\right)} b^{4} c d^{3} + 27 \, {\left(2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right)} a b^{3} d^{4}\right)} x^{3} + 3 \, {\left({\left(6 \, A B + 11 \, B^{2}\right)} b^{4} c^{2} d^{2} + 9 \, {\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} a b^{3} c d^{3} + 18 \, {\left(A^{2} + 2 \, B^{2}\right)} a^{2} b^{2} d^{4}\right)} x^{2} - {\left({\left(6 \, A B + 5 \, B^{2}\right)} b^{4} c^{3} d - 27 \, {\left(2 \, A B + 3 \, B^{2}\right)} a b^{3} c^{2} d^{2} - 54 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a^{2} b^{2} c d^{3} - 18 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{27 \, {\left({\left(b^{8} c^{5} d - 5 \, a b^{7} c^{4} d^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} - 10 \, a^{3} b^{5} c^{2} d^{4} + 5 \, a^{4} b^{4} c d^{5} - a^{5} b^{3} d^{6}\right)} g^{4} i^{2} x^{4} + {\left(b^{8} c^{6} - 2 \, a b^{7} c^{5} d - 5 \, a^{2} b^{6} c^{4} d^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} - 25 \, a^{4} b^{4} c^{2} d^{4} + 14 \, a^{5} b^{3} c d^{5} - 3 \, a^{6} b^{2} d^{6}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{7} c^{6} - 4 \, a^{2} b^{6} c^{5} d + 5 \, a^{3} b^{5} c^{4} d^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} + 4 \, a^{6} b^{2} c d^{5} - a^{7} b d^{6}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} - 14 \, a^{3} b^{5} c^{5} d + 25 \, a^{4} b^{4} c^{4} d^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} + 5 \, a^{6} b^{2} c^{2} d^{4} + 2 \, a^{7} b c d^{5} - a^{8} d^{6}\right)} g^{4} i^{2} x + {\left(a^{3} b^{5} c^{6} - 5 \, a^{4} b^{4} c^{5} d + 10 \, a^{5} b^{3} c^{4} d^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} + 5 \, a^{7} b c^{2} d^{4} - a^{8} c d^{5}\right)} g^{4} i^{2}\right)}}"," ",0,"-1/27*((9*A^2 + 6*A*B + 2*B^2)*b^4*c^4 - 27*(2*A^2 + 2*A*B + B^2)*a*b^3*c^3*d + 162*(A^2 + 2*A*B + 2*B^2)*a^2*b^2*c^2*d^2 - 5*(18*A^2 + 66*A*B + 49*B^2)*a^3*b*c*d^3 - 27*(A^2 - 2*A*B + 2*B^2)*a^4*d^4 + 6*((18*A^2 + 30*A*B + 55*B^2)*b^4*c*d^3 - (18*A^2 + 30*A*B + 55*B^2)*a*b^3*d^4)*x^3 + 36*(B^2*b^4*d^4*x^4 + B^2*a^3*b*c*d^3 + (B^2*b^4*c*d^3 + 3*B^2*a*b^3*d^4)*x^3 + 3*(B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*x^2 + (3*B^2*a^2*b^2*c*d^3 + B^2*a^3*b*d^4)*x)*log((b*e*x + a*e)/(d*x + c))^3 + 3*((18*A^2 + 66*A*B + 85*B^2)*b^4*c^2*d^2 + 8*(9*A^2 + 6*A*B + 20*B^2)*a*b^3*c*d^3 - (90*A^2 + 114*A*B + 245*B^2)*a^2*b^2*d^4)*x^2 + 9*(2*(6*A*B + 5*B^2)*b^4*d^4*x^4 + B^2*b^4*c^4 - 6*B^2*a*b^3*c^3*d + 18*B^2*a^2*b^2*c^2*d^2 + 12*A*B*a^3*b*c*d^3 - 3*B^2*a^4*d^4 + 2*((6*A*B + 11*B^2)*b^4*c*d^3 + 9*(2*A*B + B^2)*a*b^3*d^4)*x^3 + 6*(B^2*b^4*c^2*d^2 + 6*A*B*a^2*b^2*d^4 + 3*(2*A*B + 3*B^2)*a*b^3*c*d^3)*x^2 - 2*(B^2*b^4*c^3*d - 9*B^2*a*b^3*c^2*d^2 - 18*(A*B + B^2)*a^2*b^2*c*d^3 - 6*(A*B - B^2)*a^3*b*d^4)*x)*log((b*e*x + a*e)/(d*x + c))^2 - ((18*A^2 + 30*A*B + 19*B^2)*b^4*c^3*d - 81*(2*A^2 + 6*A*B + 7*B^2)*a*b^3*c^2*d^2 - 3*(18*A^2 - 114*A*B - 29*B^2)*a^2*b^2*c*d^3 + (198*A^2 + 114*A*B + 461*B^2)*a^3*b*d^4)*x + 6*((18*A^2 + 30*A*B + 55*B^2)*b^4*d^4*x^4 + 18*A^2*a^3*b*c*d^3 + (3*A*B + B^2)*b^4*c^4 - 9*(2*A*B + B^2)*a*b^3*c^3*d + 54*(A*B + B^2)*a^2*b^2*c^2*d^2 - 9*(A*B - B^2)*a^4*d^4 + ((18*A^2 + 66*A*B + 85*B^2)*b^4*c*d^3 + 27*(2*A^2 + 2*A*B + 5*B^2)*a*b^3*d^4)*x^3 + 3*((6*A*B + 11*B^2)*b^4*c^2*d^2 + 9*(2*A^2 + 6*A*B + 7*B^2)*a*b^3*c*d^3 + 18*(A^2 + 2*B^2)*a^2*b^2*d^4)*x^2 - ((6*A*B + 5*B^2)*b^4*c^3*d - 27*(2*A*B + 3*B^2)*a*b^3*c^2*d^2 - 54*(A^2 + 2*A*B + 2*B^2)*a^2*b^2*c*d^3 - 18*(A^2 - 2*A*B + 2*B^2)*a^3*b*d^4)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^8*c^5*d - 5*a*b^7*c^4*d^2 + 10*a^2*b^6*c^3*d^3 - 10*a^3*b^5*c^2*d^4 + 5*a^4*b^4*c*d^5 - a^5*b^3*d^6)*g^4*i^2*x^4 + (b^8*c^6 - 2*a*b^7*c^5*d - 5*a^2*b^6*c^4*d^2 + 20*a^3*b^5*c^3*d^3 - 25*a^4*b^4*c^2*d^4 + 14*a^5*b^3*c*d^5 - 3*a^6*b^2*d^6)*g^4*i^2*x^3 + 3*(a*b^7*c^6 - 4*a^2*b^6*c^5*d + 5*a^3*b^5*c^4*d^2 - 5*a^5*b^3*c^2*d^4 + 4*a^6*b^2*c*d^5 - a^7*b*d^6)*g^4*i^2*x^2 + (3*a^2*b^6*c^6 - 14*a^3*b^5*c^5*d + 25*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 5*a^6*b^2*c^2*d^4 + 2*a^7*b*c*d^5 - a^8*d^6)*g^4*i^2*x + (a^3*b^5*c^6 - 5*a^4*b^4*c^5*d + 10*a^5*b^3*c^4*d^2 - 10*a^6*b^2*c^3*d^3 + 5*a^7*b*c^2*d^4 - a^8*c*d^5)*g^4*i^2)","B",0
100,0,0,0,0.421814," ","integrate((b*g*x+a*g)^3*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{3} g^{3} x^{3} + 3 \, A^{2} a b^{2} g^{3} x^{2} + 3 \, A^{2} a^{2} b g^{3} x + A^{2} a^{3} g^{3} + {\left(B^{2} b^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b g^{3} x + B^{2} a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{3} g^{3} x^{3} + 3 \, A B a b^{2} g^{3} x^{2} + 3 \, A B a^{2} b g^{3} x + A B a^{3} g^{3}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{3} i^{3} x^{3} + 3 \, c d^{2} i^{3} x^{2} + 3 \, c^{2} d i^{3} x + c^{3} i^{3}}, x\right)"," ",0,"integral((A^2*b^3*g^3*x^3 + 3*A^2*a*b^2*g^3*x^2 + 3*A^2*a^2*b*g^3*x + A^2*a^3*g^3 + (B^2*b^3*g^3*x^3 + 3*B^2*a*b^2*g^3*x^2 + 3*B^2*a^2*b*g^3*x + B^2*a^3*g^3)*log((b*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^3*g^3*x^3 + 3*A*B*a*b^2*g^3*x^2 + 3*A*B*a^2*b*g^3*x + A*B*a^3*g^3)*log((b*e*x + a*e)/(d*x + c)))/(d^3*i^3*x^3 + 3*c*d^2*i^3*x^2 + 3*c^2*d*i^3*x + c^3*i^3), x)","F",0
101,0,0,0,0.458735," ","integrate((b*g*x+a*g)^2*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{2} g^{2} x^{2} + 2 \, A^{2} a b g^{2} x + A^{2} a^{2} g^{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(\frac{b e x + a e}{d x + c}\right)^{2} + 2 \, {\left(A B b^{2} g^{2} x^{2} + 2 \, A B a b g^{2} x + A B a^{2} g^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{d^{3} i^{3} x^{3} + 3 \, c d^{2} i^{3} x^{2} + 3 \, c^{2} d i^{3} x + c^{3} i^{3}}, x\right)"," ",0,"integral((A^2*b^2*g^2*x^2 + 2*A^2*a*b*g^2*x + A^2*a^2*g^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*e*x + a*e)/(d*x + c))^2 + 2*(A*B*b^2*g^2*x^2 + 2*A*B*a*b*g^2*x + A*B*a^2*g^2)*log((b*e*x + a*e)/(d*x + c)))/(d^3*i^3*x^3 + 3*c*d^2*i^3*x^2 + 3*c^2*d*i^3*x + c^3*i^3), x)","F",0
102,1,295,0,0.439905," ","integrate((b*g*x+a*g)*(A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} b^{2} c d - {\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} a b d^{2}\right)} g 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(\frac{b e x + a e}{d x + c}\right)^{2} + {\left({\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} b^{2} c^{2} - {\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} a^{2} d^{2}\right)} g - 2 \, {\left({\left(2 \, A B - B^{2}\right)} b^{2} d^{2} g x^{2} + 2 \, {\left(2 \, A B - B^{2}\right)} a b d^{2} g x + {\left(2 \, A B - B^{2}\right)} a^{2} d^{2} g\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}\right)}}"," ",0,"-1/4*(2*((2*A^2 - 2*A*B + B^2)*b^2*c*d - (2*A^2 - 2*A*B + B^2)*a*b*d^2)*g*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*e*x + a*e)/(d*x + c))^2 + ((2*A^2 - 2*A*B + B^2)*b^2*c^2 - (2*A^2 - 2*A*B + B^2)*a^2*d^2)*g - 2*((2*A*B - B^2)*b^2*d^2*g*x^2 + 2*(2*A*B - B^2)*a*b*d^2*g*x + (2*A*B - B^2)*a^2*d^2*g)*log((b*e*x + a*e)/(d*x + c)))/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3)","B",0
103,1,373,0,0.460095," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} b^{2} c^{2} - 4 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a b c d + {\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} a^{2} d^{2} - 2 \, {\left(B^{2} b^{2} d^{2} x^{2} + 2 \, B^{2} b^{2} c d x + 2 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 2 \, {\left({\left(2 \, A B - 3 \, B^{2}\right)} b^{2} c d - {\left(2 \, A B - 3 \, B^{2}\right)} a b d^{2}\right)} x - 2 \, {\left({\left(2 \, A B - 3 \, B^{2}\right)} b^{2} d^{2} x^{2} + 4 \, {\left(A B - B^{2}\right)} a b c d - {\left(2 \, A B - B^{2}\right)} a^{2} d^{2} - 2 \, {\left(B^{2} a b d^{2} - 2 \, {\left(A B - B^{2}\right)} b^{2} c d\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} i^{3} x + {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} i^{3}\right)}}"," ",0,"-1/4*((2*A^2 - 6*A*B + 7*B^2)*b^2*c^2 - 4*(A^2 - 2*A*B + 2*B^2)*a*b*c*d + (2*A^2 - 2*A*B + B^2)*a^2*d^2 - 2*(B^2*b^2*d^2*x^2 + 2*B^2*b^2*c*d*x + 2*B^2*a*b*c*d - B^2*a^2*d^2)*log((b*e*x + a*e)/(d*x + c))^2 - 2*((2*A*B - 3*B^2)*b^2*c*d - (2*A*B - 3*B^2)*a*b*d^2)*x - 2*((2*A*B - 3*B^2)*b^2*d^2*x^2 + 4*(A*B - B^2)*a*b*c*d - (2*A*B - B^2)*a^2*d^2 - 2*(B^2*a*b*d^2 - 2*(A*B - B^2)*b^2*c*d)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*i^3*x^2 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*i^3*x + (b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*i^3)","A",0
104,1,545,0,0.449093," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)/(d*i*x+c*i)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(6 \, A^{2} - 14 \, A B + 15 \, B^{2}\right)} b^{2} c^{2} - 24 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a b c d + 3 \, {\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} a^{2} d^{2} + 4 \, {\left(B^{2} b^{2} d^{2} x^{2} + 2 \, B^{2} b^{2} c d x + B^{2} b^{2} c^{2}\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 6 \, {\left({\left(2 \, A B - 3 \, B^{2}\right)} b^{2} d^{2} x^{2} + 2 \, A B b^{2} c^{2} - 4 \, B^{2} a b c d + B^{2} a^{2} d^{2} - 2 \, {\left(B^{2} a b d^{2} - 2 \, {\left(A B - B^{2}\right)} b^{2} c d\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 6 \, {\left({\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} b^{2} c d - {\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} a b d^{2}\right)} x + 6 \, {\left({\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} b^{2} d^{2} x^{2} + 2 \, A^{2} b^{2} c^{2} - 8 \, {\left(A B - B^{2}\right)} a b c d + {\left(2 \, A B - B^{2}\right)} a^{2} d^{2} + 2 \, {\left(2 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} b^{2} c d - {\left(2 \, A B - 3 \, B^{2}\right)} a b d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{12 \, {\left({\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} g i^{3} x^{2} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} g i^{3} x + {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} g i^{3}\right)}}"," ",0,"1/12*(3*(6*A^2 - 14*A*B + 15*B^2)*b^2*c^2 - 24*(A^2 - 2*A*B + 2*B^2)*a*b*c*d + 3*(2*A^2 - 2*A*B + B^2)*a^2*d^2 + 4*(B^2*b^2*d^2*x^2 + 2*B^2*b^2*c*d*x + B^2*b^2*c^2)*log((b*e*x + a*e)/(d*x + c))^3 + 6*((2*A*B - 3*B^2)*b^2*d^2*x^2 + 2*A*B*b^2*c^2 - 4*B^2*a*b*c*d + B^2*a^2*d^2 - 2*(B^2*a*b*d^2 - 2*(A*B - B^2)*b^2*c*d)*x)*log((b*e*x + a*e)/(d*x + c))^2 + 6*((2*A^2 - 6*A*B + 7*B^2)*b^2*c*d - (2*A^2 - 6*A*B + 7*B^2)*a*b*d^2)*x + 6*((2*A^2 - 6*A*B + 7*B^2)*b^2*d^2*x^2 + 2*A^2*b^2*c^2 - 8*(A*B - B^2)*a*b*c*d + (2*A*B - B^2)*a^2*d^2 + 2*(2*(A^2 - 2*A*B + 2*B^2)*b^2*c*d - (2*A*B - 3*B^2)*a*b*d^2)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*g*i^3*x^2 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*g*i^3*x + (b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*g*i^3)","A",0
105,1,1008,0,0.469090," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} b^{3} c^{3} + 3 \, {\left(2 \, A^{2} - 10 \, A B + 5 \, B^{2}\right)} a b^{2} c^{2} d - 12 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{2} b c d^{2} + {\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} a^{3} d^{3} + 4 \, {\left(B^{2} b^{3} d^{3} x^{3} + B^{2} a b^{2} c^{2} d + {\left(2 \, B^{2} b^{3} c d^{2} + B^{2} a b^{2} d^{3}\right)} x^{2} + {\left(B^{2} b^{3} c^{2} d + 2 \, B^{2} a b^{2} c d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 6 \, {\left({\left(2 \, A^{2} - 2 \, A B + 5 \, B^{2}\right)} b^{3} c d^{2} - {\left(2 \, A^{2} - 2 \, A B + 5 \, B^{2}\right)} a b^{2} d^{3}\right)} x^{2} + 2 \, {\left(3 \, {\left(2 \, A B - B^{2}\right)} b^{3} d^{3} x^{3} + 2 \, B^{2} b^{3} c^{3} + 6 \, A B a b^{2} c^{2} d - 6 \, B^{2} a^{2} b c d^{2} + B^{2} a^{3} d^{3} + 3 \, {\left(4 \, A B b^{3} c d^{2} + {\left(2 \, A B - 3 \, B^{2}\right)} a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(B^{2} a^{2} b d^{3} - 2 \, {\left(A B + B^{2}\right)} b^{3} c^{2} d - 4 \, {\left(A B - B^{2}\right)} a b^{2} c d^{2}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} + 3 \, {\left({\left(6 \, A^{2} - 2 \, A B + 13 \, B^{2}\right)} b^{3} c^{2} d - 2 \, {\left(2 \, A^{2} + 2 \, A B + 3 \, B^{2}\right)} a b^{2} c d^{2} - {\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} a^{2} b d^{3}\right)} x + 2 \, {\left(3 \, {\left(2 \, A^{2} - 2 \, A B + 5 \, B^{2}\right)} b^{3} d^{3} x^{3} + 6 \, A^{2} a b^{2} c^{2} d + 4 \, {\left(A B + B^{2}\right)} b^{3} c^{3} - 12 \, {\left(A B - B^{2}\right)} a^{2} b c d^{2} + {\left(2 \, A B - B^{2}\right)} a^{3} d^{3} + 3 \, {\left(4 \, {\left(A^{2} + 2 \, B^{2}\right)} b^{3} c d^{2} + {\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} a b^{2} d^{3}\right)} x^{2} + 3 \, {\left(2 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} b^{3} c^{2} d + 4 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a b^{2} c d^{2} - {\left(2 \, A B - 3 \, B^{2}\right)} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} g^{2} i^{3} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} g^{2} i^{3} x + {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4}\right)} g^{2} i^{3}\right)}}"," ",0,"-1/4*(4*(A^2 + 2*A*B + 2*B^2)*b^3*c^3 + 3*(2*A^2 - 10*A*B + 5*B^2)*a*b^2*c^2*d - 12*(A^2 - 2*A*B + 2*B^2)*a^2*b*c*d^2 + (2*A^2 - 2*A*B + B^2)*a^3*d^3 + 4*(B^2*b^3*d^3*x^3 + B^2*a*b^2*c^2*d + (2*B^2*b^3*c*d^2 + B^2*a*b^2*d^3)*x^2 + (B^2*b^3*c^2*d + 2*B^2*a*b^2*c*d^2)*x)*log((b*e*x + a*e)/(d*x + c))^3 + 6*((2*A^2 - 2*A*B + 5*B^2)*b^3*c*d^2 - (2*A^2 - 2*A*B + 5*B^2)*a*b^2*d^3)*x^2 + 2*(3*(2*A*B - B^2)*b^3*d^3*x^3 + 2*B^2*b^3*c^3 + 6*A*B*a*b^2*c^2*d - 6*B^2*a^2*b*c*d^2 + B^2*a^3*d^3 + 3*(4*A*B*b^3*c*d^2 + (2*A*B - 3*B^2)*a*b^2*d^3)*x^2 - 3*(B^2*a^2*b*d^3 - 2*(A*B + B^2)*b^3*c^2*d - 4*(A*B - B^2)*a*b^2*c*d^2)*x)*log((b*e*x + a*e)/(d*x + c))^2 + 3*((6*A^2 - 2*A*B + 13*B^2)*b^3*c^2*d - 2*(2*A^2 + 2*A*B + 3*B^2)*a*b^2*c*d^2 - (2*A^2 - 6*A*B + 7*B^2)*a^2*b*d^3)*x + 2*(3*(2*A^2 - 2*A*B + 5*B^2)*b^3*d^3*x^3 + 6*A^2*a*b^2*c^2*d + 4*(A*B + B^2)*b^3*c^3 - 12*(A*B - B^2)*a^2*b*c*d^2 + (2*A*B - B^2)*a^3*d^3 + 3*(4*(A^2 + 2*B^2)*b^3*c*d^2 + (2*A^2 - 6*A*B + 7*B^2)*a*b^2*d^3)*x^2 + 3*(2*(A^2 + 2*A*B + 2*B^2)*b^3*c^2*d + 4*(A^2 - 2*A*B + 2*B^2)*a*b^2*c*d^2 - (2*A*B - 3*B^2)*a^2*b*d^3)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*g^2*i^3*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*g^2*i^3*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*g^2*i^3*x + (a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4)*g^2*i^3)","A",0
106,1,1517,0,0.486926," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^3/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{60 \, A B a^{2} b^{2} c^{2} d^{2} + {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} b^{4} c^{4} - 16 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a b^{3} c^{3} d + 16 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{3} b c d^{3} - {\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} a^{4} d^{4} - 12 \, {\left({\left(2 \, A^{2} + 5 \, B^{2}\right)} b^{4} c d^{3} - {\left(2 \, A^{2} + 5 \, B^{2}\right)} a b^{3} d^{4}\right)} x^{3} - 8 \, {\left(B^{2} b^{4} d^{4} x^{4} + B^{2} a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(B^{2} b^{4} c d^{3} + B^{2} a b^{3} d^{4}\right)} x^{3} + {\left(B^{2} b^{4} c^{2} d^{2} + 4 \, B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(B^{2} a b^{3} c^{2} d^{2} + B^{2} a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 6 \, {\left(8 \, A B a b^{3} c d^{3} - {\left(6 \, A^{2} + 4 \, A B + 15 \, B^{2}\right)} b^{4} c^{2} d^{2} + {\left(6 \, A^{2} - 4 \, A B + 15 \, B^{2}\right)} a^{2} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(12 \, A B b^{4} d^{4} x^{4} - B^{2} b^{4} c^{4} + 8 \, B^{2} a b^{3} c^{3} d + 12 \, A B a^{2} b^{2} c^{2} d^{2} - 8 \, B^{2} a^{3} b c d^{3} + B^{2} a^{4} d^{4} + 12 \, {\left({\left(2 \, A B + B^{2}\right)} b^{4} c d^{3} + {\left(2 \, A B - B^{2}\right)} a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(8 \, A B a b^{3} c d^{3} + {\left(2 \, A B + 3 \, B^{2}\right)} b^{4} c^{2} d^{2} + {\left(2 \, A B - 3 \, B^{2}\right)} a^{2} b^{2} d^{4}\right)} x^{2} + 4 \, {\left(B^{2} b^{4} c^{3} d - B^{2} a^{3} b d^{4} + 6 \, {\left(A B + B^{2}\right)} a b^{3} c^{2} d^{2} + 6 \, {\left(A B - B^{2}\right)} a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 4 \, {\left({\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} b^{4} c^{3} d + 6 \, {\left(2 \, A^{2} - A B + 4 \, B^{2}\right)} a b^{3} c^{2} d^{2} - 6 \, {\left(2 \, A^{2} + A B + 4 \, B^{2}\right)} a^{2} b^{2} c d^{3} - {\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} a^{3} b d^{4}\right)} x - 2 \, {\left(6 \, {\left(2 \, A^{2} + 5 \, B^{2}\right)} b^{4} d^{4} x^{4} + 12 \, A^{2} a^{2} b^{2} c^{2} d^{2} - {\left(2 \, A B + B^{2}\right)} b^{4} c^{4} + 16 \, {\left(A B + B^{2}\right)} a b^{3} c^{3} d - 16 \, {\left(A B - B^{2}\right)} a^{3} b c d^{3} + {\left(2 \, A B - B^{2}\right)} a^{4} d^{4} + 12 \, {\left({\left(2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right)} b^{4} c d^{3} + {\left(2 \, A^{2} - 2 \, A B + 5 \, B^{2}\right)} a b^{3} d^{4}\right)} x^{3} + 6 \, {\left({\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} b^{4} c^{2} d^{2} + 8 \, {\left(A^{2} + 2 \, B^{2}\right)} a b^{3} c d^{3} + {\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} a^{2} b^{2} d^{4}\right)} x^{2} + 4 \, {\left({\left(2 \, A B + 3 \, B^{2}\right)} b^{4} c^{3} d + 6 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a b^{3} c^{2} d^{2} + 6 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{2} b^{2} c d^{3} - {\left(2 \, A B - 3 \, B^{2}\right)} a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{4 \, {\left({\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} g^{3} i^{3} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} g^{3} i^{3} x + {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5}\right)} g^{3} i^{3}\right)}}"," ",0,"-1/4*(60*A*B*a^2*b^2*c^2*d^2 + (2*A^2 + 2*A*B + B^2)*b^4*c^4 - 16*(A^2 + 2*A*B + 2*B^2)*a*b^3*c^3*d + 16*(A^2 - 2*A*B + 2*B^2)*a^3*b*c*d^3 - (2*A^2 - 2*A*B + B^2)*a^4*d^4 - 12*((2*A^2 + 5*B^2)*b^4*c*d^3 - (2*A^2 + 5*B^2)*a*b^3*d^4)*x^3 - 8*(B^2*b^4*d^4*x^4 + B^2*a^2*b^2*c^2*d^2 + 2*(B^2*b^4*c*d^3 + B^2*a*b^3*d^4)*x^3 + (B^2*b^4*c^2*d^2 + 4*B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*x^2 + 2*(B^2*a*b^3*c^2*d^2 + B^2*a^2*b^2*c*d^3)*x)*log((b*e*x + a*e)/(d*x + c))^3 + 6*(8*A*B*a*b^3*c*d^3 - (6*A^2 + 4*A*B + 15*B^2)*b^4*c^2*d^2 + (6*A^2 - 4*A*B + 15*B^2)*a^2*b^2*d^4)*x^2 - 2*(12*A*B*b^4*d^4*x^4 - B^2*b^4*c^4 + 8*B^2*a*b^3*c^3*d + 12*A*B*a^2*b^2*c^2*d^2 - 8*B^2*a^3*b*c*d^3 + B^2*a^4*d^4 + 12*((2*A*B + B^2)*b^4*c*d^3 + (2*A*B - B^2)*a*b^3*d^4)*x^3 + 6*(8*A*B*a*b^3*c*d^3 + (2*A*B + 3*B^2)*b^4*c^2*d^2 + (2*A*B - 3*B^2)*a^2*b^2*d^4)*x^2 + 4*(B^2*b^4*c^3*d - B^2*a^3*b*d^4 + 6*(A*B + B^2)*a*b^3*c^2*d^2 + 6*(A*B - B^2)*a^2*b^2*c*d^3)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 4*((2*A^2 + 6*A*B + 7*B^2)*b^4*c^3*d + 6*(2*A^2 - A*B + 4*B^2)*a*b^3*c^2*d^2 - 6*(2*A^2 + A*B + 4*B^2)*a^2*b^2*c*d^3 - (2*A^2 - 6*A*B + 7*B^2)*a^3*b*d^4)*x - 2*(6*(2*A^2 + 5*B^2)*b^4*d^4*x^4 + 12*A^2*a^2*b^2*c^2*d^2 - (2*A*B + B^2)*b^4*c^4 + 16*(A*B + B^2)*a*b^3*c^3*d - 16*(A*B - B^2)*a^3*b*c*d^3 + (2*A*B - B^2)*a^4*d^4 + 12*((2*A^2 + 2*A*B + 5*B^2)*b^4*c*d^3 + (2*A^2 - 2*A*B + 5*B^2)*a*b^3*d^4)*x^3 + 6*((2*A^2 + 6*A*B + 7*B^2)*b^4*c^2*d^2 + 8*(A^2 + 2*B^2)*a*b^3*c*d^3 + (2*A^2 - 6*A*B + 7*B^2)*a^2*b^2*d^4)*x^2 + 4*((2*A*B + 3*B^2)*b^4*c^3*d + 6*(A^2 + 2*A*B + 2*B^2)*a*b^3*c^2*d^2 + 6*(A^2 - 2*A*B + 2*B^2)*a^2*b^2*c*d^3 - (2*A*B - 3*B^2)*a^3*b*d^4)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*g^3*i^3*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*g^3*i^3*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*g^3*i^3*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*g^3*i^3*x + (a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5)*g^3*i^3)","B",0
107,1,2257,0,0.581125," ","integrate((A+B*log(e*(b*x+a)/(d*x+c)))^2/(b*g*x+a*g)^4/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(9 \, A^{2} + 6 \, A B + 2 \, B^{2}\right)} b^{5} c^{5} - 135 \, {\left(2 \, A^{2} + 2 \, A B + B^{2}\right)} a b^{4} c^{4} d + 1080 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a^{2} b^{3} c^{3} d^{2} - 20 \, {\left(18 \, A^{2} + 147 \, A B + 49 \, B^{2}\right)} a^{3} b^{2} c^{2} d^{3} - 540 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{4} b c d^{4} + 27 \, {\left(2 \, A^{2} - 2 \, A B + B^{2}\right)} a^{5} d^{5} + 60 \, {\left({\left(18 \, A^{2} + 12 \, A B + 49 \, B^{2}\right)} b^{5} c d^{4} - {\left(18 \, A^{2} + 12 \, A B + 49 \, B^{2}\right)} a b^{4} d^{5}\right)} x^{4} + 30 \, {\left(3 \, {\left(18 \, A^{2} + 24 \, A B + 53 \, B^{2}\right)} b^{5} c^{2} d^{3} + 2 \, {\left(18 \, A^{2} - 24 \, A B + 37 \, B^{2}\right)} a b^{4} c d^{4} - {\left(90 \, A^{2} + 24 \, A B + 233 \, B^{2}\right)} a^{2} b^{3} d^{5}\right)} x^{3} + 360 \, {\left(B^{2} b^{5} d^{5} x^{5} + B^{2} a^{3} b^{2} c^{2} d^{3} + {\left(2 \, B^{2} b^{5} c d^{4} + 3 \, B^{2} a b^{4} d^{5}\right)} x^{4} + {\left(B^{2} b^{5} c^{2} d^{3} + 6 \, B^{2} a b^{4} c d^{4} + 3 \, B^{2} a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, B^{2} a b^{4} c^{2} d^{3} + 6 \, B^{2} a^{2} b^{3} c d^{4} + B^{2} a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 2 \, B^{2} a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{3} + 10 \, {\left(2 \, {\left(18 \, A^{2} + 66 \, A B + 85 \, B^{2}\right)} b^{5} c^{3} d^{2} + 3 \, {\left(126 \, A^{2} + 84 \, A B + 307 \, B^{2}\right)} a b^{4} c^{2} d^{3} - 12 \, {\left(18 \, A^{2} + 39 \, A B + 49 \, B^{2}\right)} a^{2} b^{3} c d^{4} - {\left(198 \, A^{2} - 84 \, A B + 503 \, B^{2}\right)} a^{3} b^{2} d^{5}\right)} x^{2} + 18 \, {\left(20 \, {\left(3 \, A B + B^{2}\right)} b^{5} d^{5} x^{5} + 2 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 60 \, B^{2} a^{2} b^{3} c^{3} d^{2} + 60 \, A B a^{3} b^{2} c^{2} d^{3} - 30 \, B^{2} a^{4} b c d^{4} + 3 \, B^{2} a^{5} d^{5} + 20 \, {\left(9 \, A B a b^{4} d^{5} + {\left(6 \, A B + 5 \, B^{2}\right)} b^{5} c d^{4}\right)} x^{4} + 10 \, {\left({\left(6 \, A B + 11 \, B^{2}\right)} b^{5} c^{2} d^{3} + 18 \, {\left(2 \, A B + B^{2}\right)} a b^{4} c d^{4} + 9 \, {\left(2 \, A B - B^{2}\right)} a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(2 \, B^{2} b^{5} c^{3} d^{2} + 36 \, A B a^{2} b^{3} c d^{4} + 9 \, {\left(2 \, A B + 3 \, B^{2}\right)} a b^{4} c^{2} d^{3} + 3 \, {\left(2 \, A B - 3 \, B^{2}\right)} a^{3} b^{2} d^{5}\right)} x^{2} - 5 \, {\left(B^{2} b^{5} c^{4} d - 12 \, B^{2} a b^{4} c^{3} d^{2} + 3 \, B^{2} a^{4} b d^{5} - 36 \, {\left(A B + B^{2}\right)} a^{2} b^{3} c^{2} d^{3} - 24 \, {\left(A B - B^{2}\right)} a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)^{2} - 5 \, {\left({\left(18 \, A^{2} + 30 \, A B + 19 \, B^{2}\right)} b^{5} c^{4} d - 108 \, {\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} a b^{4} c^{3} d^{2} - 12 \, {\left(36 \, A^{2} - 39 \, A B + 59 \, B^{2}\right)} a^{2} b^{3} c^{2} d^{3} + 8 \, {\left(72 \, A^{2} + 39 \, A B + 157 \, B^{2}\right)} a^{3} b^{2} c d^{4} + 27 \, {\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} a^{4} b d^{5}\right)} x + 6 \, {\left(10 \, {\left(18 \, A^{2} + 12 \, A B + 49 \, B^{2}\right)} b^{5} d^{5} x^{5} + 180 \, A^{2} a^{3} b^{2} c^{2} d^{3} + 4 \, {\left(3 \, A B + B^{2}\right)} b^{5} c^{5} - 45 \, {\left(2 \, A B + B^{2}\right)} a b^{4} c^{4} d + 360 \, {\left(A B + B^{2}\right)} a^{2} b^{3} c^{3} d^{2} - 180 \, {\left(A B - B^{2}\right)} a^{4} b c d^{4} + 9 \, {\left(2 \, A B - B^{2}\right)} a^{5} d^{5} + 10 \, {\left(2 \, {\left(18 \, A^{2} + 30 \, A B + 55 \, B^{2}\right)} b^{5} c d^{4} + 27 \, {\left(2 \, A^{2} + 5 \, B^{2}\right)} a b^{4} d^{5}\right)} x^{4} + 10 \, {\left({\left(18 \, A^{2} + 66 \, A B + 85 \, B^{2}\right)} b^{5} c^{2} d^{3} + 54 \, {\left(2 \, A^{2} + 2 \, A B + 5 \, B^{2}\right)} a b^{4} c d^{4} + 27 \, {\left(2 \, A^{2} - 2 \, A B + 5 \, B^{2}\right)} a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(2 \, {\left(6 \, A B + 11 \, B^{2}\right)} b^{5} c^{3} d^{2} + 27 \, {\left(2 \, A^{2} + 6 \, A B + 7 \, B^{2}\right)} a b^{4} c^{2} d^{3} + 108 \, {\left(A^{2} + 2 \, B^{2}\right)} a^{2} b^{3} c d^{4} + 9 \, {\left(2 \, A^{2} - 6 \, A B + 7 \, B^{2}\right)} a^{3} b^{2} d^{5}\right)} x^{2} - 5 \, {\left({\left(6 \, A B + 5 \, B^{2}\right)} b^{5} c^{4} d - 36 \, {\left(2 \, A B + 3 \, B^{2}\right)} a b^{4} c^{3} d^{2} - 108 \, {\left(A^{2} + 2 \, A B + 2 \, B^{2}\right)} a^{2} b^{3} c^{2} d^{3} - 72 \, {\left(A^{2} - 2 \, A B + 2 \, B^{2}\right)} a^{3} b^{2} c d^{4} + 9 \, {\left(2 \, A B - 3 \, B^{2}\right)} a^{4} b d^{5}\right)} x\right)} \log\left(\frac{b e x + a e}{d x + c}\right)}{108 \, {\left({\left(b^{9} c^{6} d^{2} - 6 \, a b^{8} c^{5} d^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} - 20 \, a^{3} b^{6} c^{3} d^{5} + 15 \, a^{4} b^{5} c^{2} d^{6} - 6 \, a^{5} b^{4} c d^{7} + a^{6} b^{3} d^{8}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{9} c^{7} d - 9 \, a b^{8} c^{6} d^{2} + 12 \, a^{2} b^{7} c^{5} d^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} - 30 \, a^{4} b^{5} c^{3} d^{5} + 33 \, a^{5} b^{4} c^{2} d^{6} - 16 \, a^{6} b^{3} c d^{7} + 3 \, a^{7} b^{2} d^{8}\right)} g^{4} i^{3} x^{4} + {\left(b^{9} c^{8} - 18 \, a^{2} b^{7} c^{6} d^{2} + 52 \, a^{3} b^{6} c^{5} d^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} + 24 \, a^{5} b^{4} c^{3} d^{5} + 10 \, a^{6} b^{3} c^{2} d^{6} - 12 \, a^{7} b^{2} c d^{7} + 3 \, a^{8} b d^{8}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{8} c^{8} - 12 \, a^{2} b^{7} c^{7} d + 10 \, a^{3} b^{6} c^{6} d^{2} + 24 \, a^{4} b^{5} c^{5} d^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} + 52 \, a^{6} b^{3} c^{3} d^{5} - 18 \, a^{7} b^{2} c^{2} d^{6} + a^{9} d^{8}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} - 16 \, a^{3} b^{6} c^{7} d + 33 \, a^{4} b^{5} c^{6} d^{2} - 30 \, a^{5} b^{4} c^{5} d^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} + 12 \, a^{7} b^{2} c^{3} d^{5} - 9 \, a^{8} b c^{2} d^{6} + 2 \, a^{9} c d^{7}\right)} g^{4} i^{3} x + {\left(a^{3} b^{6} c^{8} - 6 \, a^{4} b^{5} c^{7} d + 15 \, a^{5} b^{4} c^{6} d^{2} - 20 \, a^{6} b^{3} c^{5} d^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} - 6 \, a^{8} b c^{3} d^{5} + a^{9} c^{2} d^{6}\right)} g^{4} i^{3}\right)}}"," ",0,"-1/108*(4*(9*A^2 + 6*A*B + 2*B^2)*b^5*c^5 - 135*(2*A^2 + 2*A*B + B^2)*a*b^4*c^4*d + 1080*(A^2 + 2*A*B + 2*B^2)*a^2*b^3*c^3*d^2 - 20*(18*A^2 + 147*A*B + 49*B^2)*a^3*b^2*c^2*d^3 - 540*(A^2 - 2*A*B + 2*B^2)*a^4*b*c*d^4 + 27*(2*A^2 - 2*A*B + B^2)*a^5*d^5 + 60*((18*A^2 + 12*A*B + 49*B^2)*b^5*c*d^4 - (18*A^2 + 12*A*B + 49*B^2)*a*b^4*d^5)*x^4 + 30*(3*(18*A^2 + 24*A*B + 53*B^2)*b^5*c^2*d^3 + 2*(18*A^2 - 24*A*B + 37*B^2)*a*b^4*c*d^4 - (90*A^2 + 24*A*B + 233*B^2)*a^2*b^3*d^5)*x^3 + 360*(B^2*b^5*d^5*x^5 + B^2*a^3*b^2*c^2*d^3 + (2*B^2*b^5*c*d^4 + 3*B^2*a*b^4*d^5)*x^4 + (B^2*b^5*c^2*d^3 + 6*B^2*a*b^4*c*d^4 + 3*B^2*a^2*b^3*d^5)*x^3 + (3*B^2*a*b^4*c^2*d^3 + 6*B^2*a^2*b^3*c*d^4 + B^2*a^3*b^2*d^5)*x^2 + (3*B^2*a^2*b^3*c^2*d^3 + 2*B^2*a^3*b^2*c*d^4)*x)*log((b*e*x + a*e)/(d*x + c))^3 + 10*(2*(18*A^2 + 66*A*B + 85*B^2)*b^5*c^3*d^2 + 3*(126*A^2 + 84*A*B + 307*B^2)*a*b^4*c^2*d^3 - 12*(18*A^2 + 39*A*B + 49*B^2)*a^2*b^3*c*d^4 - (198*A^2 - 84*A*B + 503*B^2)*a^3*b^2*d^5)*x^2 + 18*(20*(3*A*B + B^2)*b^5*d^5*x^5 + 2*B^2*b^5*c^5 - 15*B^2*a*b^4*c^4*d + 60*B^2*a^2*b^3*c^3*d^2 + 60*A*B*a^3*b^2*c^2*d^3 - 30*B^2*a^4*b*c*d^4 + 3*B^2*a^5*d^5 + 20*(9*A*B*a*b^4*d^5 + (6*A*B + 5*B^2)*b^5*c*d^4)*x^4 + 10*((6*A*B + 11*B^2)*b^5*c^2*d^3 + 18*(2*A*B + B^2)*a*b^4*c*d^4 + 9*(2*A*B - B^2)*a^2*b^3*d^5)*x^3 + 10*(2*B^2*b^5*c^3*d^2 + 36*A*B*a^2*b^3*c*d^4 + 9*(2*A*B + 3*B^2)*a*b^4*c^2*d^3 + 3*(2*A*B - 3*B^2)*a^3*b^2*d^5)*x^2 - 5*(B^2*b^5*c^4*d - 12*B^2*a*b^4*c^3*d^2 + 3*B^2*a^4*b*d^5 - 36*(A*B + B^2)*a^2*b^3*c^2*d^3 - 24*(A*B - B^2)*a^3*b^2*c*d^4)*x)*log((b*e*x + a*e)/(d*x + c))^2 - 5*((18*A^2 + 30*A*B + 19*B^2)*b^5*c^4*d - 108*(2*A^2 + 6*A*B + 7*B^2)*a*b^4*c^3*d^2 - 12*(36*A^2 - 39*A*B + 59*B^2)*a^2*b^3*c^2*d^3 + 8*(72*A^2 + 39*A*B + 157*B^2)*a^3*b^2*c*d^4 + 27*(2*A^2 - 6*A*B + 7*B^2)*a^4*b*d^5)*x + 6*(10*(18*A^2 + 12*A*B + 49*B^2)*b^5*d^5*x^5 + 180*A^2*a^3*b^2*c^2*d^3 + 4*(3*A*B + B^2)*b^5*c^5 - 45*(2*A*B + B^2)*a*b^4*c^4*d + 360*(A*B + B^2)*a^2*b^3*c^3*d^2 - 180*(A*B - B^2)*a^4*b*c*d^4 + 9*(2*A*B - B^2)*a^5*d^5 + 10*(2*(18*A^2 + 30*A*B + 55*B^2)*b^5*c*d^4 + 27*(2*A^2 + 5*B^2)*a*b^4*d^5)*x^4 + 10*((18*A^2 + 66*A*B + 85*B^2)*b^5*c^2*d^3 + 54*(2*A^2 + 2*A*B + 5*B^2)*a*b^4*c*d^4 + 27*(2*A^2 - 2*A*B + 5*B^2)*a^2*b^3*d^5)*x^3 + 10*(2*(6*A*B + 11*B^2)*b^5*c^3*d^2 + 27*(2*A^2 + 6*A*B + 7*B^2)*a*b^4*c^2*d^3 + 108*(A^2 + 2*B^2)*a^2*b^3*c*d^4 + 9*(2*A^2 - 6*A*B + 7*B^2)*a^3*b^2*d^5)*x^2 - 5*((6*A*B + 5*B^2)*b^5*c^4*d - 36*(2*A*B + 3*B^2)*a*b^4*c^3*d^2 - 108*(A^2 + 2*A*B + 2*B^2)*a^2*b^3*c^2*d^3 - 72*(A^2 - 2*A*B + 2*B^2)*a^3*b^2*c*d^4 + 9*(2*A*B - 3*B^2)*a^4*b*d^5)*x)*log((b*e*x + a*e)/(d*x + c)))/((b^9*c^6*d^2 - 6*a*b^8*c^5*d^3 + 15*a^2*b^7*c^4*d^4 - 20*a^3*b^6*c^3*d^5 + 15*a^4*b^5*c^2*d^6 - 6*a^5*b^4*c*d^7 + a^6*b^3*d^8)*g^4*i^3*x^5 + (2*b^9*c^7*d - 9*a*b^8*c^6*d^2 + 12*a^2*b^7*c^5*d^3 + 5*a^3*b^6*c^4*d^4 - 30*a^4*b^5*c^3*d^5 + 33*a^5*b^4*c^2*d^6 - 16*a^6*b^3*c*d^7 + 3*a^7*b^2*d^8)*g^4*i^3*x^4 + (b^9*c^8 - 18*a^2*b^7*c^6*d^2 + 52*a^3*b^6*c^5*d^3 - 60*a^4*b^5*c^4*d^4 + 24*a^5*b^4*c^3*d^5 + 10*a^6*b^3*c^2*d^6 - 12*a^7*b^2*c*d^7 + 3*a^8*b*d^8)*g^4*i^3*x^3 + (3*a*b^8*c^8 - 12*a^2*b^7*c^7*d + 10*a^3*b^6*c^6*d^2 + 24*a^4*b^5*c^5*d^3 - 60*a^5*b^4*c^4*d^4 + 52*a^6*b^3*c^3*d^5 - 18*a^7*b^2*c^2*d^6 + a^9*d^8)*g^4*i^3*x^2 + (3*a^2*b^7*c^8 - 16*a^3*b^6*c^7*d + 33*a^4*b^5*c^6*d^2 - 30*a^5*b^4*c^5*d^3 + 5*a^6*b^3*c^4*d^4 + 12*a^7*b^2*c^3*d^5 - 9*a^8*b*c^2*d^6 + 2*a^9*c*d^7)*g^4*i^3*x + (a^3*b^6*c^8 - 6*a^4*b^5*c^7*d + 15*a^5*b^4*c^6*d^2 - 20*a^6*b^3*c^5*d^3 + 15*a^7*b^2*c^4*d^4 - 6*a^8*b*c^3*d^5 + a^9*c^2*d^6)*g^4*i^3)","B",0
108,1,720,0,0.590922," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{24 \, A b^{5} d^{5} g^{3} i x^{5} + 6 \, {\left(5 \, B a^{4} b c d^{4} - B a^{5} d^{5}\right)} g^{3} i n \log\left(b x + a\right) + 6 \, {\left(B b^{5} c^{5} - 5 \, B a b^{4} c^{4} d + 10 \, B a^{2} b^{3} c^{3} d^{2} - 10 \, B a^{3} b^{2} c^{2} d^{3}\right)} g^{3} i n \log\left(d x + c\right) - 6 \, {\left({\left(B b^{5} c d^{4} - B a b^{4} d^{5}\right)} g^{3} i n - 5 \, {\left(A b^{5} c d^{4} + 3 \, A a b^{4} d^{5}\right)} g^{3} i\right)} x^{4} - 2 \, {\left({\left(B b^{5} c^{2} d^{3} + 10 \, B a b^{4} c d^{4} - 11 \, B a^{2} b^{3} d^{5}\right)} g^{3} i n - 60 \, {\left(A a b^{4} c d^{4} + A a^{2} b^{3} d^{5}\right)} g^{3} i\right)} x^{3} + 3 \, {\left({\left(B b^{5} c^{3} d^{2} - 5 \, B a b^{4} c^{2} d^{3} - 5 \, B a^{2} b^{3} c d^{4} + 9 \, B a^{3} b^{2} d^{5}\right)} g^{3} i n + 20 \, {\left(3 \, A a^{2} b^{3} c d^{4} + A a^{3} b^{2} d^{5}\right)} g^{3} i\right)} x^{2} + 6 \, {\left(20 \, A a^{3} b^{2} c d^{4} g^{3} i - {\left(B b^{5} c^{4} d - 5 \, B a b^{4} c^{3} d^{2} + 10 \, B a^{2} b^{3} c^{2} d^{3} - 5 \, B a^{3} b^{2} c d^{4} - B a^{4} b d^{5}\right)} g^{3} i n\right)} x + 6 \, {\left(4 \, B b^{5} d^{5} g^{3} i x^{5} + 20 \, B a^{3} b^{2} c d^{4} g^{3} i x + 5 \, {\left(B b^{5} c d^{4} + 3 \, B a b^{4} d^{5}\right)} g^{3} i x^{4} + 20 \, {\left(B a b^{4} c d^{4} + B a^{2} b^{3} d^{5}\right)} g^{3} i x^{3} + 10 \, {\left(3 \, B a^{2} b^{3} c d^{4} + B a^{3} b^{2} d^{5}\right)} g^{3} i x^{2}\right)} \log\left(e\right) + 6 \, {\left(4 \, B b^{5} d^{5} g^{3} i n x^{5} + 20 \, B a^{3} b^{2} c d^{4} g^{3} i n x + 5 \, {\left(B b^{5} c d^{4} + 3 \, B a b^{4} d^{5}\right)} g^{3} i n x^{4} + 20 \, {\left(B a b^{4} c d^{4} + B a^{2} b^{3} d^{5}\right)} g^{3} i n x^{3} + 10 \, {\left(3 \, B a^{2} b^{3} c d^{4} + B a^{3} b^{2} d^{5}\right)} g^{3} i n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{120 \, b^{2} d^{4}}"," ",0,"1/120*(24*A*b^5*d^5*g^3*i*x^5 + 6*(5*B*a^4*b*c*d^4 - B*a^5*d^5)*g^3*i*n*log(b*x + a) + 6*(B*b^5*c^5 - 5*B*a*b^4*c^4*d + 10*B*a^2*b^3*c^3*d^2 - 10*B*a^3*b^2*c^2*d^3)*g^3*i*n*log(d*x + c) - 6*((B*b^5*c*d^4 - B*a*b^4*d^5)*g^3*i*n - 5*(A*b^5*c*d^4 + 3*A*a*b^4*d^5)*g^3*i)*x^4 - 2*((B*b^5*c^2*d^3 + 10*B*a*b^4*c*d^4 - 11*B*a^2*b^3*d^5)*g^3*i*n - 60*(A*a*b^4*c*d^4 + A*a^2*b^3*d^5)*g^3*i)*x^3 + 3*((B*b^5*c^3*d^2 - 5*B*a*b^4*c^2*d^3 - 5*B*a^2*b^3*c*d^4 + 9*B*a^3*b^2*d^5)*g^3*i*n + 20*(3*A*a^2*b^3*c*d^4 + A*a^3*b^2*d^5)*g^3*i)*x^2 + 6*(20*A*a^3*b^2*c*d^4*g^3*i - (B*b^5*c^4*d - 5*B*a*b^4*c^3*d^2 + 10*B*a^2*b^3*c^2*d^3 - 5*B*a^3*b^2*c*d^4 - B*a^4*b*d^5)*g^3*i*n)*x + 6*(4*B*b^5*d^5*g^3*i*x^5 + 20*B*a^3*b^2*c*d^4*g^3*i*x + 5*(B*b^5*c*d^4 + 3*B*a*b^4*d^5)*g^3*i*x^4 + 20*(B*a*b^4*c*d^4 + B*a^2*b^3*d^5)*g^3*i*x^3 + 10*(3*B*a^2*b^3*c*d^4 + B*a^3*b^2*d^5)*g^3*i*x^2)*log(e) + 6*(4*B*b^5*d^5*g^3*i*n*x^5 + 20*B*a^3*b^2*c*d^4*g^3*i*n*x + 5*(B*b^5*c*d^4 + 3*B*a*b^4*d^5)*g^3*i*n*x^4 + 20*(B*a*b^4*c*d^4 + B*a^2*b^3*d^5)*g^3*i*n*x^3 + 10*(3*B*a^2*b^3*c*d^4 + B*a^3*b^2*d^5)*g^3*i*n*x^2)*log((b*x + a)/(d*x + c)))/(b^2*d^4)","B",0
109,1,529,0,0.530250," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{6 \, A b^{4} d^{4} g^{2} i x^{4} + 2 \, {\left(4 \, B a^{3} b c d^{3} - B a^{4} d^{4}\right)} g^{2} i n \log\left(b x + a\right) - 2 \, {\left(B b^{4} c^{4} - 4 \, B a b^{3} c^{3} d + 6 \, B a^{2} b^{2} c^{2} d^{2}\right)} g^{2} i n \log\left(d x + c\right) - 2 \, {\left({\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} g^{2} i n - 4 \, {\left(A b^{4} c d^{3} + 2 \, A a b^{3} d^{4}\right)} g^{2} i\right)} x^{3} - {\left({\left(B b^{4} c^{2} d^{2} + 4 \, B a b^{3} c d^{3} - 5 \, B a^{2} b^{2} d^{4}\right)} g^{2} i n - 12 \, {\left(2 \, A a b^{3} c d^{3} + A a^{2} b^{2} d^{4}\right)} g^{2} i\right)} x^{2} + 2 \, {\left(12 \, A a^{2} b^{2} c d^{3} g^{2} i + {\left(B b^{4} c^{3} d - 4 \, B a b^{3} c^{2} d^{2} + 2 \, B a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} g^{2} i n\right)} x + 2 \, {\left(3 \, B b^{4} d^{4} g^{2} i x^{4} + 12 \, B a^{2} b^{2} c d^{3} g^{2} i x + 4 \, {\left(B b^{4} c d^{3} + 2 \, B a b^{3} d^{4}\right)} g^{2} i x^{3} + 6 \, {\left(2 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} g^{2} i x^{2}\right)} \log\left(e\right) + 2 \, {\left(3 \, B b^{4} d^{4} g^{2} i n x^{4} + 12 \, B a^{2} b^{2} c d^{3} g^{2} i n x + 4 \, {\left(B b^{4} c d^{3} + 2 \, B a b^{3} d^{4}\right)} g^{2} i n x^{3} + 6 \, {\left(2 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} g^{2} i n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{24 \, b^{2} d^{3}}"," ",0,"1/24*(6*A*b^4*d^4*g^2*i*x^4 + 2*(4*B*a^3*b*c*d^3 - B*a^4*d^4)*g^2*i*n*log(b*x + a) - 2*(B*b^4*c^4 - 4*B*a*b^3*c^3*d + 6*B*a^2*b^2*c^2*d^2)*g^2*i*n*log(d*x + c) - 2*((B*b^4*c*d^3 - B*a*b^3*d^4)*g^2*i*n - 4*(A*b^4*c*d^3 + 2*A*a*b^3*d^4)*g^2*i)*x^3 - ((B*b^4*c^2*d^2 + 4*B*a*b^3*c*d^3 - 5*B*a^2*b^2*d^4)*g^2*i*n - 12*(2*A*a*b^3*c*d^3 + A*a^2*b^2*d^4)*g^2*i)*x^2 + 2*(12*A*a^2*b^2*c*d^3*g^2*i + (B*b^4*c^3*d - 4*B*a*b^3*c^2*d^2 + 2*B*a^2*b^2*c*d^3 + B*a^3*b*d^4)*g^2*i*n)*x + 2*(3*B*b^4*d^4*g^2*i*x^4 + 12*B*a^2*b^2*c*d^3*g^2*i*x + 4*(B*b^4*c*d^3 + 2*B*a*b^3*d^4)*g^2*i*x^3 + 6*(2*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*g^2*i*x^2)*log(e) + 2*(3*B*b^4*d^4*g^2*i*n*x^4 + 12*B*a^2*b^2*c*d^3*g^2*i*n*x + 4*(B*b^4*c*d^3 + 2*B*a*b^3*d^4)*g^2*i*n*x^3 + 6*(2*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*g^2*i*n*x^2)*log((b*x + a)/(d*x + c)))/(b^2*d^3)","B",0
110,1,309,0,0.446065," ","integrate((b*g*x+a*g)*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{2 \, A b^{3} d^{3} g i x^{3} + {\left(3 \, B a^{2} b c d^{2} - B a^{3} d^{3}\right)} g i n \log\left(b x + a\right) + {\left(B b^{3} c^{3} - 3 \, B a b^{2} c^{2} d\right)} g i n \log\left(d x + c\right) - {\left({\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} g i n - 3 \, {\left(A b^{3} c d^{2} + A a b^{2} d^{3}\right)} g i\right)} x^{2} + {\left(6 \, A a b^{2} c d^{2} g i - {\left(B b^{3} c^{2} d - B a^{2} b d^{3}\right)} g i n\right)} x + {\left(2 \, B b^{3} d^{3} g i x^{3} + 6 \, B a b^{2} c d^{2} g i x + 3 \, {\left(B b^{3} c d^{2} + B a b^{2} d^{3}\right)} g i x^{2}\right)} \log\left(e\right) + {\left(2 \, B b^{3} d^{3} g i n x^{3} + 6 \, B a b^{2} c d^{2} g i n x + 3 \, {\left(B b^{3} c d^{2} + B a b^{2} d^{3}\right)} g i n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{6 \, b^{2} d^{2}}"," ",0,"1/6*(2*A*b^3*d^3*g*i*x^3 + (3*B*a^2*b*c*d^2 - B*a^3*d^3)*g*i*n*log(b*x + a) + (B*b^3*c^3 - 3*B*a*b^2*c^2*d)*g*i*n*log(d*x + c) - ((B*b^3*c*d^2 - B*a*b^2*d^3)*g*i*n - 3*(A*b^3*c*d^2 + A*a*b^2*d^3)*g*i)*x^2 + (6*A*a*b^2*c*d^2*g*i - (B*b^3*c^2*d - B*a^2*b*d^3)*g*i*n)*x + (2*B*b^3*d^3*g*i*x^3 + 6*B*a*b^2*c*d^2*g*i*x + 3*(B*b^3*c*d^2 + B*a*b^2*d^3)*g*i*x^2)*log(e) + (2*B*b^3*d^3*g*i*n*x^3 + 6*B*a*b^2*c*d^2*g*i*n*x + 3*(B*b^3*c*d^2 + B*a*b^2*d^3)*g*i*n*x^2)*log((b*x + a)/(d*x + c)))/(b^2*d^2)","B",0
111,1,162,0,0.472073," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{A b^{2} d^{2} i x^{2} - B b^{2} c^{2} i n \log\left(d x + c\right) + {\left(2 \, B a b c d - B a^{2} d^{2}\right)} i n \log\left(b x + a\right) + {\left(2 \, A b^{2} c d i - {\left(B b^{2} c d - B a b d^{2}\right)} i n\right)} x + {\left(B b^{2} d^{2} i x^{2} + 2 \, B b^{2} c d i x\right)} \log\left(e\right) + {\left(B b^{2} d^{2} i n x^{2} + 2 \, B b^{2} c d i n x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{2 \, b^{2} d}"," ",0,"1/2*(A*b^2*d^2*i*x^2 - B*b^2*c^2*i*n*log(d*x + c) + (2*B*a*b*c*d - B*a^2*d^2)*i*n*log(b*x + a) + (2*A*b^2*c*d*i - (B*b^2*c*d - B*a*b*d^2)*i*n)*x + (B*b^2*d^2*i*x^2 + 2*B*b^2*c*d*i*x)*log(e) + (B*b^2*d^2*i*n*x^2 + 2*B*b^2*c*d*i*n*x)*log((b*x + a)/(d*x + c)))/(b^2*d)","B",0
112,0,0,0,0.437508," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d i x + A c i + {\left(B d i x + B c i\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b g x + a g}, x\right)"," ",0,"integral((A*d*i*x + A*c*i + (B*d*i*x + B*c*i)*log(e*((b*x + a)/(d*x + c))^n))/(b*g*x + a*g), x)","F",0
113,0,0,0,0.473213," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d i x + A c i + {\left(B d i x + B c i\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A*d*i*x + A*c*i + (B*d*i*x + B*c*i)*log(e*((b*x + a)/(d*x + c))^n))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
114,1,250,0,0.461906," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3,x, algorithm=""fricas"")","-\frac{{\left(B b^{2} c^{2} - B a^{2} d^{2}\right)} i n + 2 \, {\left(A b^{2} c^{2} - A a^{2} d^{2}\right)} i + 2 \, {\left({\left(B b^{2} c d - B a b d^{2}\right)} i n + 2 \, {\left(A b^{2} c d - A a b d^{2}\right)} i\right)} x + 2 \, {\left(2 \, {\left(B b^{2} c d - B a b d^{2}\right)} i x + {\left(B b^{2} c^{2} - B a^{2} d^{2}\right)} i\right)} \log\left(e\right) + 2 \, {\left(B b^{2} d^{2} i n x^{2} + 2 \, B b^{2} c d i n x + B b^{2} c^{2} i n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}\right)}}"," ",0,"-1/4*((B*b^2*c^2 - B*a^2*d^2)*i*n + 2*(A*b^2*c^2 - A*a^2*d^2)*i + 2*((B*b^2*c*d - B*a*b*d^2)*i*n + 2*(A*b^2*c*d - A*a*b*d^2)*i)*x + 2*(2*(B*b^2*c*d - B*a*b*d^2)*i*x + (B*b^2*c^2 - B*a^2*d^2)*i)*log(e) + 2*(B*b^2*d^2*i*n*x^2 + 2*B*b^2*c*d*i*n*x + B*b^2*c^2*i*n)*log((b*x + a)/(d*x + c)))/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3)","B",0
115,1,478,0,0.454284," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4,x, algorithm=""fricas"")","\frac{6 \, {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} i n x^{2} - {\left(4 \, B b^{3} c^{3} - 9 \, B a b^{2} c^{2} d + 5 \, B a^{3} d^{3}\right)} i n - 6 \, {\left(2 \, A b^{3} c^{3} - 3 \, A a b^{2} c^{2} d + A a^{3} d^{3}\right)} i - 3 \, {\left({\left(B b^{3} c^{2} d - 6 \, B a b^{2} c d^{2} + 5 \, B a^{2} b d^{3}\right)} i n + 6 \, {\left(A b^{3} c^{2} d - 2 \, A a b^{2} c d^{2} + A a^{2} b d^{3}\right)} i\right)} x - 6 \, {\left(3 \, {\left(B b^{3} c^{2} d - 2 \, B a b^{2} c d^{2} + B a^{2} b d^{3}\right)} i x + {\left(2 \, B b^{3} c^{3} - 3 \, B a b^{2} c^{2} d + B a^{3} d^{3}\right)} i\right)} \log\left(e\right) + 6 \, {\left(B b^{3} d^{3} i n x^{3} + 3 \, B a b^{2} d^{3} i n x^{2} - 3 \, {\left(B b^{3} c^{2} d - 2 \, B a b^{2} c d^{2}\right)} i n x - {\left(2 \, B b^{3} c^{3} - 3 \, B a b^{2} c^{2} d\right)} i n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{36 \, {\left({\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}\right)}}"," ",0,"1/36*(6*(B*b^3*c*d^2 - B*a*b^2*d^3)*i*n*x^2 - (4*B*b^3*c^3 - 9*B*a*b^2*c^2*d + 5*B*a^3*d^3)*i*n - 6*(2*A*b^3*c^3 - 3*A*a*b^2*c^2*d + A*a^3*d^3)*i - 3*((B*b^3*c^2*d - 6*B*a*b^2*c*d^2 + 5*B*a^2*b*d^3)*i*n + 6*(A*b^3*c^2*d - 2*A*a*b^2*c*d^2 + A*a^2*b*d^3)*i)*x - 6*(3*(B*b^3*c^2*d - 2*B*a*b^2*c*d^2 + B*a^2*b*d^3)*i*x + (2*B*b^3*c^3 - 3*B*a*b^2*c^2*d + B*a^3*d^3)*i)*log(e) + 6*(B*b^3*d^3*i*n*x^3 + 3*B*a*b^2*d^3*i*n*x^2 - 3*(B*b^3*c^2*d - 2*B*a*b^2*c*d^2)*i*n*x - (2*B*b^3*c^3 - 3*B*a*b^2*c^2*d)*i*n)*log((b*x + a)/(d*x + c)))/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4)","B",0
116,1,773,0,0.461559," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^5,x, algorithm=""fricas"")","-\frac{12 \, {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} i n x^{3} - 6 \, {\left(B b^{4} c^{2} d^{2} - 8 \, B a b^{3} c d^{3} + 7 \, B a^{2} b^{2} d^{4}\right)} i n x^{2} + {\left(9 \, B b^{4} c^{4} - 32 \, B a b^{3} c^{3} d + 36 \, B a^{2} b^{2} c^{2} d^{2} - 13 \, B a^{4} d^{4}\right)} i n + 12 \, {\left(3 \, A b^{4} c^{4} - 8 \, A a b^{3} c^{3} d + 6 \, A a^{2} b^{2} c^{2} d^{2} - A a^{4} d^{4}\right)} i + 4 \, {\left({\left(B b^{4} c^{3} d - 6 \, B a b^{3} c^{2} d^{2} + 18 \, B a^{2} b^{2} c d^{3} - 13 \, B a^{3} b d^{4}\right)} i n + 12 \, {\left(A b^{4} c^{3} d - 3 \, A a b^{3} c^{2} d^{2} + 3 \, A a^{2} b^{2} c d^{3} - A a^{3} b d^{4}\right)} i\right)} x + 12 \, {\left(4 \, {\left(B b^{4} c^{3} d - 3 \, B a b^{3} c^{2} d^{2} + 3 \, B a^{2} b^{2} c d^{3} - B a^{3} b d^{4}\right)} i x + {\left(3 \, B b^{4} c^{4} - 8 \, B a b^{3} c^{3} d + 6 \, B a^{2} b^{2} c^{2} d^{2} - B a^{4} d^{4}\right)} i\right)} \log\left(e\right) + 12 \, {\left(B b^{4} d^{4} i n x^{4} + 4 \, B a b^{3} d^{4} i n x^{3} + 6 \, B a^{2} b^{2} d^{4} i n x^{2} + 4 \, {\left(B b^{4} c^{3} d - 3 \, B a b^{3} c^{2} d^{2} + 3 \, B a^{2} b^{2} c d^{3}\right)} i n x + {\left(3 \, B b^{4} c^{4} - 8 \, B a b^{3} c^{3} d + 6 \, B a^{2} b^{2} c^{2} d^{2}\right)} i n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{144 \, {\left({\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}\right)}}"," ",0,"-1/144*(12*(B*b^4*c*d^3 - B*a*b^3*d^4)*i*n*x^3 - 6*(B*b^4*c^2*d^2 - 8*B*a*b^3*c*d^3 + 7*B*a^2*b^2*d^4)*i*n*x^2 + (9*B*b^4*c^4 - 32*B*a*b^3*c^3*d + 36*B*a^2*b^2*c^2*d^2 - 13*B*a^4*d^4)*i*n + 12*(3*A*b^4*c^4 - 8*A*a*b^3*c^3*d + 6*A*a^2*b^2*c^2*d^2 - A*a^4*d^4)*i + 4*((B*b^4*c^3*d - 6*B*a*b^3*c^2*d^2 + 18*B*a^2*b^2*c*d^3 - 13*B*a^3*b*d^4)*i*n + 12*(A*b^4*c^3*d - 3*A*a*b^3*c^2*d^2 + 3*A*a^2*b^2*c*d^3 - A*a^3*b*d^4)*i)*x + 12*(4*(B*b^4*c^3*d - 3*B*a*b^3*c^2*d^2 + 3*B*a^2*b^2*c*d^3 - B*a^3*b*d^4)*i*x + (3*B*b^4*c^4 - 8*B*a*b^3*c^3*d + 6*B*a^2*b^2*c^2*d^2 - B*a^4*d^4)*i)*log(e) + 12*(B*b^4*d^4*i*n*x^4 + 4*B*a*b^3*d^4*i*n*x^3 + 6*B*a^2*b^2*d^4*i*n*x^2 + 4*(B*b^4*c^3*d - 3*B*a*b^3*c^2*d^2 + 3*B*a^2*b^2*c*d^3)*i*n*x + (3*B*b^4*c^4 - 8*B*a*b^3*c^3*d + 6*B*a^2*b^2*c^2*d^2)*i*n)*log((b*x + a)/(d*x + c)))/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5)","B",0
117,1,1074,0,0.844316," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{60 \, A b^{6} d^{6} g^{3} i^{2} x^{6} + 6 \, {\left(15 \, B a^{4} b^{2} c^{2} d^{4} - 6 \, B a^{5} b c d^{5} + B a^{6} d^{6}\right)} g^{3} i^{2} n \log\left(b x + a\right) + 6 \, {\left(B b^{6} c^{6} - 6 \, B a b^{5} c^{5} d + 15 \, B a^{2} b^{4} c^{4} d^{2} - 20 \, B a^{3} b^{3} c^{3} d^{3}\right)} g^{3} i^{2} n \log\left(d x + c\right) - 12 \, {\left({\left(B b^{6} c d^{5} - B a b^{5} d^{6}\right)} g^{3} i^{2} n - 6 \, {\left(2 \, A b^{6} c d^{5} + 3 \, A a b^{5} d^{6}\right)} g^{3} i^{2}\right)} x^{5} - 3 \, {\left({\left(7 \, B b^{6} c^{2} d^{4} + 6 \, B a b^{5} c d^{5} - 13 \, B a^{2} b^{4} d^{6}\right)} g^{3} i^{2} n - 30 \, {\left(A b^{6} c^{2} d^{4} + 6 \, A a b^{5} c d^{5} + 3 \, A a^{2} b^{4} d^{6}\right)} g^{3} i^{2}\right)} x^{4} - 2 \, {\left({\left(B b^{6} c^{3} d^{3} + 39 \, B a b^{5} c^{2} d^{4} - 21 \, B a^{2} b^{4} c d^{5} - 19 \, B a^{3} b^{3} d^{6}\right)} g^{3} i^{2} n - 60 \, {\left(3 \, A a b^{5} c^{2} d^{4} + 6 \, A a^{2} b^{4} c d^{5} + A a^{3} b^{3} d^{6}\right)} g^{3} i^{2}\right)} x^{3} + 3 \, {\left({\left(B b^{6} c^{4} d^{2} - 6 \, B a b^{5} c^{3} d^{3} - 30 \, B a^{2} b^{4} c^{2} d^{4} + 34 \, B a^{3} b^{3} c d^{5} + B a^{4} b^{2} d^{6}\right)} g^{3} i^{2} n + 60 \, {\left(3 \, A a^{2} b^{4} c^{2} d^{4} + 2 \, A a^{3} b^{3} c d^{5}\right)} g^{3} i^{2}\right)} x^{2} + 6 \, {\left(60 \, A a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} - {\left(B b^{6} c^{5} d - 6 \, B a b^{5} c^{4} d^{2} + 15 \, B a^{2} b^{4} c^{3} d^{3} - 5 \, B a^{3} b^{3} c^{2} d^{4} - 6 \, B a^{4} b^{2} c d^{5} + B a^{5} b d^{6}\right)} g^{3} i^{2} n\right)} x + 6 \, {\left(10 \, B b^{6} d^{6} g^{3} i^{2} x^{6} + 60 \, B a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} x + 12 \, {\left(2 \, B b^{6} c d^{5} + 3 \, B a b^{5} d^{6}\right)} g^{3} i^{2} x^{5} + 15 \, {\left(B b^{6} c^{2} d^{4} + 6 \, B a b^{5} c d^{5} + 3 \, B a^{2} b^{4} d^{6}\right)} g^{3} i^{2} x^{4} + 20 \, {\left(3 \, B a b^{5} c^{2} d^{4} + 6 \, B a^{2} b^{4} c d^{5} + B a^{3} b^{3} d^{6}\right)} g^{3} i^{2} x^{3} + 30 \, {\left(3 \, B a^{2} b^{4} c^{2} d^{4} + 2 \, B a^{3} b^{3} c d^{5}\right)} g^{3} i^{2} x^{2}\right)} \log\left(e\right) + 6 \, {\left(10 \, B b^{6} d^{6} g^{3} i^{2} n x^{6} + 60 \, B a^{3} b^{3} c^{2} d^{4} g^{3} i^{2} n x + 12 \, {\left(2 \, B b^{6} c d^{5} + 3 \, B a b^{5} d^{6}\right)} g^{3} i^{2} n x^{5} + 15 \, {\left(B b^{6} c^{2} d^{4} + 6 \, B a b^{5} c d^{5} + 3 \, B a^{2} b^{4} d^{6}\right)} g^{3} i^{2} n x^{4} + 20 \, {\left(3 \, B a b^{5} c^{2} d^{4} + 6 \, B a^{2} b^{4} c d^{5} + B a^{3} b^{3} d^{6}\right)} g^{3} i^{2} n x^{3} + 30 \, {\left(3 \, B a^{2} b^{4} c^{2} d^{4} + 2 \, B a^{3} b^{3} c d^{5}\right)} g^{3} i^{2} n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{360 \, b^{3} d^{4}}"," ",0,"1/360*(60*A*b^6*d^6*g^3*i^2*x^6 + 6*(15*B*a^4*b^2*c^2*d^4 - 6*B*a^5*b*c*d^5 + B*a^6*d^6)*g^3*i^2*n*log(b*x + a) + 6*(B*b^6*c^6 - 6*B*a*b^5*c^5*d + 15*B*a^2*b^4*c^4*d^2 - 20*B*a^3*b^3*c^3*d^3)*g^3*i^2*n*log(d*x + c) - 12*((B*b^6*c*d^5 - B*a*b^5*d^6)*g^3*i^2*n - 6*(2*A*b^6*c*d^5 + 3*A*a*b^5*d^6)*g^3*i^2)*x^5 - 3*((7*B*b^6*c^2*d^4 + 6*B*a*b^5*c*d^5 - 13*B*a^2*b^4*d^6)*g^3*i^2*n - 30*(A*b^6*c^2*d^4 + 6*A*a*b^5*c*d^5 + 3*A*a^2*b^4*d^6)*g^3*i^2)*x^4 - 2*((B*b^6*c^3*d^3 + 39*B*a*b^5*c^2*d^4 - 21*B*a^2*b^4*c*d^5 - 19*B*a^3*b^3*d^6)*g^3*i^2*n - 60*(3*A*a*b^5*c^2*d^4 + 6*A*a^2*b^4*c*d^5 + A*a^3*b^3*d^6)*g^3*i^2)*x^3 + 3*((B*b^6*c^4*d^2 - 6*B*a*b^5*c^3*d^3 - 30*B*a^2*b^4*c^2*d^4 + 34*B*a^3*b^3*c*d^5 + B*a^4*b^2*d^6)*g^3*i^2*n + 60*(3*A*a^2*b^4*c^2*d^4 + 2*A*a^3*b^3*c*d^5)*g^3*i^2)*x^2 + 6*(60*A*a^3*b^3*c^2*d^4*g^3*i^2 - (B*b^6*c^5*d - 6*B*a*b^5*c^4*d^2 + 15*B*a^2*b^4*c^3*d^3 - 5*B*a^3*b^3*c^2*d^4 - 6*B*a^4*b^2*c*d^5 + B*a^5*b*d^6)*g^3*i^2*n)*x + 6*(10*B*b^6*d^6*g^3*i^2*x^6 + 60*B*a^3*b^3*c^2*d^4*g^3*i^2*x + 12*(2*B*b^6*c*d^5 + 3*B*a*b^5*d^6)*g^3*i^2*x^5 + 15*(B*b^6*c^2*d^4 + 6*B*a*b^5*c*d^5 + 3*B*a^2*b^4*d^6)*g^3*i^2*x^4 + 20*(3*B*a*b^5*c^2*d^4 + 6*B*a^2*b^4*c*d^5 + B*a^3*b^3*d^6)*g^3*i^2*x^3 + 30*(3*B*a^2*b^4*c^2*d^4 + 2*B*a^3*b^3*c*d^5)*g^3*i^2*x^2)*log(e) + 6*(10*B*b^6*d^6*g^3*i^2*n*x^6 + 60*B*a^3*b^3*c^2*d^4*g^3*i^2*n*x + 12*(2*B*b^6*c*d^5 + 3*B*a*b^5*d^6)*g^3*i^2*n*x^5 + 15*(B*b^6*c^2*d^4 + 6*B*a*b^5*c*d^5 + 3*B*a^2*b^4*d^6)*g^3*i^2*n*x^4 + 20*(3*B*a*b^5*c^2*d^4 + 6*B*a^2*b^4*c*d^5 + B*a^3*b^3*d^6)*g^3*i^2*n*x^3 + 30*(3*B*a^2*b^4*c^2*d^4 + 2*B*a^3*b^3*c*d^5)*g^3*i^2*n*x^2)*log((b*x + a)/(d*x + c)))/(b^3*d^4)","B",0
118,1,774,0,0.599054," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{12 \, A b^{5} d^{5} g^{2} i^{2} x^{5} + 2 \, {\left(10 \, B a^{3} b^{2} c^{2} d^{3} - 5 \, B a^{4} b c d^{4} + B a^{5} d^{5}\right)} g^{2} i^{2} n \log\left(b x + a\right) - 2 \, {\left(B b^{5} c^{5} - 5 \, B a b^{4} c^{4} d + 10 \, B a^{2} b^{3} c^{3} d^{2}\right)} g^{2} i^{2} n \log\left(d x + c\right) - 3 \, {\left({\left(B b^{5} c d^{4} - B a b^{4} d^{5}\right)} g^{2} i^{2} n - 10 \, {\left(A b^{5} c d^{4} + A a b^{4} d^{5}\right)} g^{2} i^{2}\right)} x^{4} - 2 \, {\left(3 \, {\left(B b^{5} c^{2} d^{3} - B a^{2} b^{3} d^{5}\right)} g^{2} i^{2} n - 10 \, {\left(A b^{5} c^{2} d^{3} + 4 \, A a b^{4} c d^{4} + A a^{2} b^{3} d^{5}\right)} g^{2} i^{2}\right)} x^{3} - {\left({\left(B b^{5} c^{3} d^{2} + 15 \, B a b^{4} c^{2} d^{3} - 15 \, B a^{2} b^{3} c d^{4} - B a^{3} b^{2} d^{5}\right)} g^{2} i^{2} n - 60 \, {\left(A a b^{4} c^{2} d^{3} + A a^{2} b^{3} c d^{4}\right)} g^{2} i^{2}\right)} x^{2} + 2 \, {\left(30 \, A a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} + {\left(B b^{5} c^{4} d - 5 \, B a b^{4} c^{3} d^{2} + 5 \, B a^{3} b^{2} c d^{4} - B a^{4} b d^{5}\right)} g^{2} i^{2} n\right)} x + 2 \, {\left(6 \, B b^{5} d^{5} g^{2} i^{2} x^{5} + 30 \, B a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} x + 15 \, {\left(B b^{5} c d^{4} + B a b^{4} d^{5}\right)} g^{2} i^{2} x^{4} + 10 \, {\left(B b^{5} c^{2} d^{3} + 4 \, B a b^{4} c d^{4} + B a^{2} b^{3} d^{5}\right)} g^{2} i^{2} x^{3} + 30 \, {\left(B a b^{4} c^{2} d^{3} + B a^{2} b^{3} c d^{4}\right)} g^{2} i^{2} x^{2}\right)} \log\left(e\right) + 2 \, {\left(6 \, B b^{5} d^{5} g^{2} i^{2} n x^{5} + 30 \, B a^{2} b^{3} c^{2} d^{3} g^{2} i^{2} n x + 15 \, {\left(B b^{5} c d^{4} + B a b^{4} d^{5}\right)} g^{2} i^{2} n x^{4} + 10 \, {\left(B b^{5} c^{2} d^{3} + 4 \, B a b^{4} c d^{4} + B a^{2} b^{3} d^{5}\right)} g^{2} i^{2} n x^{3} + 30 \, {\left(B a b^{4} c^{2} d^{3} + B a^{2} b^{3} c d^{4}\right)} g^{2} i^{2} n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{60 \, b^{3} d^{3}}"," ",0,"1/60*(12*A*b^5*d^5*g^2*i^2*x^5 + 2*(10*B*a^3*b^2*c^2*d^3 - 5*B*a^4*b*c*d^4 + B*a^5*d^5)*g^2*i^2*n*log(b*x + a) - 2*(B*b^5*c^5 - 5*B*a*b^4*c^4*d + 10*B*a^2*b^3*c^3*d^2)*g^2*i^2*n*log(d*x + c) - 3*((B*b^5*c*d^4 - B*a*b^4*d^5)*g^2*i^2*n - 10*(A*b^5*c*d^4 + A*a*b^4*d^5)*g^2*i^2)*x^4 - 2*(3*(B*b^5*c^2*d^3 - B*a^2*b^3*d^5)*g^2*i^2*n - 10*(A*b^5*c^2*d^3 + 4*A*a*b^4*c*d^4 + A*a^2*b^3*d^5)*g^2*i^2)*x^3 - ((B*b^5*c^3*d^2 + 15*B*a*b^4*c^2*d^3 - 15*B*a^2*b^3*c*d^4 - B*a^3*b^2*d^5)*g^2*i^2*n - 60*(A*a*b^4*c^2*d^3 + A*a^2*b^3*c*d^4)*g^2*i^2)*x^2 + 2*(30*A*a^2*b^3*c^2*d^3*g^2*i^2 + (B*b^5*c^4*d - 5*B*a*b^4*c^3*d^2 + 5*B*a^3*b^2*c*d^4 - B*a^4*b*d^5)*g^2*i^2*n)*x + 2*(6*B*b^5*d^5*g^2*i^2*x^5 + 30*B*a^2*b^3*c^2*d^3*g^2*i^2*x + 15*(B*b^5*c*d^4 + B*a*b^4*d^5)*g^2*i^2*x^4 + 10*(B*b^5*c^2*d^3 + 4*B*a*b^4*c*d^4 + B*a^2*b^3*d^5)*g^2*i^2*x^3 + 30*(B*a*b^4*c^2*d^3 + B*a^2*b^3*c*d^4)*g^2*i^2*x^2)*log(e) + 2*(6*B*b^5*d^5*g^2*i^2*n*x^5 + 30*B*a^2*b^3*c^2*d^3*g^2*i^2*n*x + 15*(B*b^5*c*d^4 + B*a*b^4*d^5)*g^2*i^2*n*x^4 + 10*(B*b^5*c^2*d^3 + 4*B*a*b^4*c*d^4 + B*a^2*b^3*d^5)*g^2*i^2*n*x^3 + 30*(B*a*b^4*c^2*d^3 + B*a^2*b^3*c*d^4)*g^2*i^2*n*x^2)*log((b*x + a)/(d*x + c)))/(b^3*d^3)","B",0
119,1,530,0,0.533274," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{6 \, A b^{4} d^{4} g i^{2} x^{4} + 2 \, {\left(6 \, B a^{2} b^{2} c^{2} d^{2} - 4 \, B a^{3} b c d^{3} + B a^{4} d^{4}\right)} g i^{2} n \log\left(b x + a\right) + 2 \, {\left(B b^{4} c^{4} - 4 \, B a b^{3} c^{3} d\right)} g i^{2} n \log\left(d x + c\right) - 2 \, {\left({\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} g i^{2} n - 4 \, {\left(2 \, A b^{4} c d^{3} + A a b^{3} d^{4}\right)} g i^{2}\right)} x^{3} - {\left({\left(5 \, B b^{4} c^{2} d^{2} - 4 \, B a b^{3} c d^{3} - B a^{2} b^{2} d^{4}\right)} g i^{2} n - 12 \, {\left(A b^{4} c^{2} d^{2} + 2 \, A a b^{3} c d^{3}\right)} g i^{2}\right)} x^{2} + 2 \, {\left(12 \, A a b^{3} c^{2} d^{2} g i^{2} - {\left(B b^{4} c^{3} d + 2 \, B a b^{3} c^{2} d^{2} - 4 \, B a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} g i^{2} n\right)} x + 2 \, {\left(3 \, B b^{4} d^{4} g i^{2} x^{4} + 12 \, B a b^{3} c^{2} d^{2} g i^{2} x + 4 \, {\left(2 \, B b^{4} c d^{3} + B a b^{3} d^{4}\right)} g i^{2} x^{3} + 6 \, {\left(B b^{4} c^{2} d^{2} + 2 \, B a b^{3} c d^{3}\right)} g i^{2} x^{2}\right)} \log\left(e\right) + 2 \, {\left(3 \, B b^{4} d^{4} g i^{2} n x^{4} + 12 \, B a b^{3} c^{2} d^{2} g i^{2} n x + 4 \, {\left(2 \, B b^{4} c d^{3} + B a b^{3} d^{4}\right)} g i^{2} n x^{3} + 6 \, {\left(B b^{4} c^{2} d^{2} + 2 \, B a b^{3} c d^{3}\right)} g i^{2} n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{24 \, b^{3} d^{2}}"," ",0,"1/24*(6*A*b^4*d^4*g*i^2*x^4 + 2*(6*B*a^2*b^2*c^2*d^2 - 4*B*a^3*b*c*d^3 + B*a^4*d^4)*g*i^2*n*log(b*x + a) + 2*(B*b^4*c^4 - 4*B*a*b^3*c^3*d)*g*i^2*n*log(d*x + c) - 2*((B*b^4*c*d^3 - B*a*b^3*d^4)*g*i^2*n - 4*(2*A*b^4*c*d^3 + A*a*b^3*d^4)*g*i^2)*x^3 - ((5*B*b^4*c^2*d^2 - 4*B*a*b^3*c*d^3 - B*a^2*b^2*d^4)*g*i^2*n - 12*(A*b^4*c^2*d^2 + 2*A*a*b^3*c*d^3)*g*i^2)*x^2 + 2*(12*A*a*b^3*c^2*d^2*g*i^2 - (B*b^4*c^3*d + 2*B*a*b^3*c^2*d^2 - 4*B*a^2*b^2*c*d^3 + B*a^3*b*d^4)*g*i^2*n)*x + 2*(3*B*b^4*d^4*g*i^2*x^4 + 12*B*a*b^3*c^2*d^2*g*i^2*x + 4*(2*B*b^4*c*d^3 + B*a*b^3*d^4)*g*i^2*x^3 + 6*(B*b^4*c^2*d^2 + 2*B*a*b^3*c*d^3)*g*i^2*x^2)*log(e) + 2*(3*B*b^4*d^4*g*i^2*n*x^4 + 12*B*a*b^3*c^2*d^2*g*i^2*n*x + 4*(2*B*b^4*c*d^3 + B*a*b^3*d^4)*g*i^2*n*x^3 + 6*(B*b^4*c^2*d^2 + 2*B*a*b^3*c*d^3)*g*i^2*n*x^2)*log((b*x + a)/(d*x + c)))/(b^3*d^2)","B",0
120,1,297,0,0.495734," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{2 \, A b^{3} d^{3} i^{2} x^{3} - 2 \, B b^{3} c^{3} i^{2} n \log\left(d x + c\right) + 2 \, {\left(3 \, B a b^{2} c^{2} d - 3 \, B a^{2} b c d^{2} + B a^{3} d^{3}\right)} i^{2} n \log\left(b x + a\right) + {\left(6 \, A b^{3} c d^{2} i^{2} - {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} i^{2} n\right)} x^{2} + 2 \, {\left(3 \, A b^{3} c^{2} d i^{2} - {\left(2 \, B b^{3} c^{2} d - 3 \, B a b^{2} c d^{2} + B a^{2} b d^{3}\right)} i^{2} n\right)} x + 2 \, {\left(B b^{3} d^{3} i^{2} x^{3} + 3 \, B b^{3} c d^{2} i^{2} x^{2} + 3 \, B b^{3} c^{2} d i^{2} x\right)} \log\left(e\right) + 2 \, {\left(B b^{3} d^{3} i^{2} n x^{3} + 3 \, B b^{3} c d^{2} i^{2} n x^{2} + 3 \, B b^{3} c^{2} d i^{2} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{6 \, b^{3} d}"," ",0,"1/6*(2*A*b^3*d^3*i^2*x^3 - 2*B*b^3*c^3*i^2*n*log(d*x + c) + 2*(3*B*a*b^2*c^2*d - 3*B*a^2*b*c*d^2 + B*a^3*d^3)*i^2*n*log(b*x + a) + (6*A*b^3*c*d^2*i^2 - (B*b^3*c*d^2 - B*a*b^2*d^3)*i^2*n)*x^2 + 2*(3*A*b^3*c^2*d*i^2 - (2*B*b^3*c^2*d - 3*B*a*b^2*c*d^2 + B*a^2*b*d^3)*i^2*n)*x + 2*(B*b^3*d^3*i^2*x^3 + 3*B*b^3*c*d^2*i^2*x^2 + 3*B*b^3*c^2*d*i^2*x)*log(e) + 2*(B*b^3*d^3*i^2*n*x^3 + 3*B*b^3*c*d^2*i^2*n*x^2 + 3*B*b^3*c^2*d*i^2*n*x)*log((b*x + a)/(d*x + c)))/(b^3*d)","B",0
121,0,0,0,0.488125," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{2} i^{2} x^{2} + 2 \, A c d i^{2} x + A c^{2} i^{2} + {\left(B d^{2} i^{2} x^{2} + 2 \, B c d i^{2} x + B c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b g x + a g}, x\right)"," ",0,"integral((A*d^2*i^2*x^2 + 2*A*c*d*i^2*x + A*c^2*i^2 + (B*d^2*i^2*x^2 + 2*B*c*d*i^2*x + B*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n))/(b*g*x + a*g), x)","F",0
122,0,0,0,0.425475," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{2} i^{2} x^{2} + 2 \, A c d i^{2} x + A c^{2} i^{2} + {\left(B d^{2} i^{2} x^{2} + 2 \, B c d i^{2} x + B c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A*d^2*i^2*x^2 + 2*A*c*d*i^2*x + A*c^2*i^2 + (B*d^2*i^2*x^2 + 2*B*c*d*i^2*x + B*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
123,0,0,0,0.435565," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{2} i^{2} x^{2} + 2 \, A c d i^{2} x + A c^{2} i^{2} + {\left(B d^{2} i^{2} x^{2} + 2 \, B c d i^{2} x + B c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{3} g^{3} x^{3} + 3 \, a b^{2} g^{3} x^{2} + 3 \, a^{2} b g^{3} x + a^{3} g^{3}}, x\right)"," ",0,"integral((A*d^2*i^2*x^2 + 2*A*c*d*i^2*x + A*c^2*i^2 + (B*d^2*i^2*x^2 + 2*B*c*d*i^2*x + B*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n))/(b^3*g^3*x^3 + 3*a*b^2*g^3*x^2 + 3*a^2*b*g^3*x + a^3*g^3), x)","F",0
124,1,409,0,0.437401," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4,x, algorithm=""fricas"")","-\frac{{\left(B b^{3} c^{3} - B a^{3} d^{3}\right)} i^{2} n + 3 \, {\left(A b^{3} c^{3} - A a^{3} d^{3}\right)} i^{2} + 3 \, {\left({\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} i^{2} n + 3 \, {\left(A b^{3} c d^{2} - A a b^{2} d^{3}\right)} i^{2}\right)} x^{2} + 3 \, {\left({\left(B b^{3} c^{2} d - B a^{2} b d^{3}\right)} i^{2} n + 3 \, {\left(A b^{3} c^{2} d - A a^{2} b d^{3}\right)} i^{2}\right)} x + 3 \, {\left(3 \, {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} i^{2} x^{2} + 3 \, {\left(B b^{3} c^{2} d - B a^{2} b d^{3}\right)} i^{2} x + {\left(B b^{3} c^{3} - B a^{3} d^{3}\right)} i^{2}\right)} \log\left(e\right) + 3 \, {\left(B b^{3} d^{3} i^{2} n x^{3} + 3 \, B b^{3} c d^{2} i^{2} n x^{2} + 3 \, B b^{3} c^{2} d i^{2} n x + B b^{3} c^{3} i^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{9 \, {\left({\left(b^{7} c - a b^{6} d\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c - a^{2} b^{5} d\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c - a^{3} b^{4} d\right)} g^{4} x + {\left(a^{3} b^{4} c - a^{4} b^{3} d\right)} g^{4}\right)}}"," ",0,"-1/9*((B*b^3*c^3 - B*a^3*d^3)*i^2*n + 3*(A*b^3*c^3 - A*a^3*d^3)*i^2 + 3*((B*b^3*c*d^2 - B*a*b^2*d^3)*i^2*n + 3*(A*b^3*c*d^2 - A*a*b^2*d^3)*i^2)*x^2 + 3*((B*b^3*c^2*d - B*a^2*b*d^3)*i^2*n + 3*(A*b^3*c^2*d - A*a^2*b*d^3)*i^2)*x + 3*(3*(B*b^3*c*d^2 - B*a*b^2*d^3)*i^2*x^2 + 3*(B*b^3*c^2*d - B*a^2*b*d^3)*i^2*x + (B*b^3*c^3 - B*a^3*d^3)*i^2)*log(e) + 3*(B*b^3*d^3*i^2*n*x^3 + 3*B*b^3*c*d^2*i^2*n*x^2 + 3*B*b^3*c^2*d*i^2*n*x + B*b^3*c^3*i^2*n)*log((b*x + a)/(d*x + c)))/((b^7*c - a*b^6*d)*g^4*x^3 + 3*(a*b^6*c - a^2*b^5*d)*g^4*x^2 + 3*(a^2*b^5*c - a^3*b^4*d)*g^4*x + (a^3*b^4*c - a^4*b^3*d)*g^4)","B",0
125,1,710,0,0.467446," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^5,x, algorithm=""fricas"")","\frac{12 \, {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} i^{2} n x^{3} - {\left(9 \, B b^{4} c^{4} - 16 \, B a b^{3} c^{3} d + 7 \, B a^{4} d^{4}\right)} i^{2} n - 12 \, {\left(3 \, A b^{4} c^{4} - 4 \, A a b^{3} c^{3} d + A a^{4} d^{4}\right)} i^{2} - 6 \, {\left({\left(B b^{4} c^{2} d^{2} - 8 \, B a b^{3} c d^{3} + 7 \, B a^{2} b^{2} d^{4}\right)} i^{2} n + 12 \, {\left(A b^{4} c^{2} d^{2} - 2 \, A a b^{3} c d^{3} + A a^{2} b^{2} d^{4}\right)} i^{2}\right)} x^{2} - 4 \, {\left({\left(5 \, B b^{4} c^{3} d - 12 \, B a b^{3} c^{2} d^{2} + 7 \, B a^{3} b d^{4}\right)} i^{2} n + 12 \, {\left(2 \, A b^{4} c^{3} d - 3 \, A a b^{3} c^{2} d^{2} + A a^{3} b d^{4}\right)} i^{2}\right)} x - 12 \, {\left(6 \, {\left(B b^{4} c^{2} d^{2} - 2 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} i^{2} x^{2} + 4 \, {\left(2 \, B b^{4} c^{3} d - 3 \, B a b^{3} c^{2} d^{2} + B a^{3} b d^{4}\right)} i^{2} x + {\left(3 \, B b^{4} c^{4} - 4 \, B a b^{3} c^{3} d + B a^{4} d^{4}\right)} i^{2}\right)} \log\left(e\right) + 12 \, {\left(B b^{4} d^{4} i^{2} n x^{4} + 4 \, B a b^{3} d^{4} i^{2} n x^{3} - 6 \, {\left(B b^{4} c^{2} d^{2} - 2 \, B a b^{3} c d^{3}\right)} i^{2} n x^{2} - 4 \, {\left(2 \, B b^{4} c^{3} d - 3 \, B a b^{3} c^{2} d^{2}\right)} i^{2} n x - {\left(3 \, B b^{4} c^{4} - 4 \, B a b^{3} c^{3} d\right)} i^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{144 \, {\left({\left(b^{9} c^{2} - 2 \, a b^{8} c d + a^{2} b^{7} d^{2}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{2} - 2 \, a^{2} b^{7} c d + a^{3} b^{6} d^{2}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{2} - 2 \, a^{3} b^{6} c d + a^{4} b^{5} d^{2}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{2} - 2 \, a^{4} b^{5} c d + a^{5} b^{4} d^{2}\right)} g^{5} x + {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} g^{5}\right)}}"," ",0,"1/144*(12*(B*b^4*c*d^3 - B*a*b^3*d^4)*i^2*n*x^3 - (9*B*b^4*c^4 - 16*B*a*b^3*c^3*d + 7*B*a^4*d^4)*i^2*n - 12*(3*A*b^4*c^4 - 4*A*a*b^3*c^3*d + A*a^4*d^4)*i^2 - 6*((B*b^4*c^2*d^2 - 8*B*a*b^3*c*d^3 + 7*B*a^2*b^2*d^4)*i^2*n + 12*(A*b^4*c^2*d^2 - 2*A*a*b^3*c*d^3 + A*a^2*b^2*d^4)*i^2)*x^2 - 4*((5*B*b^4*c^3*d - 12*B*a*b^3*c^2*d^2 + 7*B*a^3*b*d^4)*i^2*n + 12*(2*A*b^4*c^3*d - 3*A*a*b^3*c^2*d^2 + A*a^3*b*d^4)*i^2)*x - 12*(6*(B*b^4*c^2*d^2 - 2*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*i^2*x^2 + 4*(2*B*b^4*c^3*d - 3*B*a*b^3*c^2*d^2 + B*a^3*b*d^4)*i^2*x + (3*B*b^4*c^4 - 4*B*a*b^3*c^3*d + B*a^4*d^4)*i^2)*log(e) + 12*(B*b^4*d^4*i^2*n*x^4 + 4*B*a*b^3*d^4*i^2*n*x^3 - 6*(B*b^4*c^2*d^2 - 2*B*a*b^3*c*d^3)*i^2*n*x^2 - 4*(2*B*b^4*c^3*d - 3*B*a*b^3*c^2*d^2)*i^2*n*x - (3*B*b^4*c^4 - 4*B*a*b^3*c^3*d)*i^2*n)*log((b*x + a)/(d*x + c)))/((b^9*c^2 - 2*a*b^8*c*d + a^2*b^7*d^2)*g^5*x^4 + 4*(a*b^8*c^2 - 2*a^2*b^7*c*d + a^3*b^6*d^2)*g^5*x^3 + 6*(a^2*b^7*c^2 - 2*a^3*b^6*c*d + a^4*b^5*d^2)*g^5*x^2 + 4*(a^3*b^6*c^2 - 2*a^4*b^5*c*d + a^5*b^4*d^2)*g^5*x + (a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*g^5)","B",0
126,1,1087,0,0.518925," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^6,x, algorithm=""fricas"")","-\frac{60 \, {\left(B b^{5} c d^{4} - B a b^{4} d^{5}\right)} i^{2} n x^{4} - 30 \, {\left(B b^{5} c^{2} d^{3} - 10 \, B a b^{4} c d^{4} + 9 \, B a^{2} b^{3} d^{5}\right)} i^{2} n x^{3} + {\left(72 \, B b^{5} c^{5} - 225 \, B a b^{4} c^{4} d + 200 \, B a^{2} b^{3} c^{3} d^{2} - 47 \, B a^{5} d^{5}\right)} i^{2} n + 60 \, {\left(6 \, A b^{5} c^{5} - 15 \, A a b^{4} c^{4} d + 10 \, A a^{2} b^{3} c^{3} d^{2} - A a^{5} d^{5}\right)} i^{2} + 10 \, {\left({\left(2 \, B b^{5} c^{3} d^{2} - 15 \, B a b^{4} c^{2} d^{3} + 60 \, B a^{2} b^{3} c d^{4} - 47 \, B a^{3} b^{2} d^{5}\right)} i^{2} n + 60 \, {\left(A b^{5} c^{3} d^{2} - 3 \, A a b^{4} c^{2} d^{3} + 3 \, A a^{2} b^{3} c d^{4} - A a^{3} b^{2} d^{5}\right)} i^{2}\right)} x^{2} + 5 \, {\left({\left(27 \, B b^{5} c^{4} d - 100 \, B a b^{4} c^{3} d^{2} + 120 \, B a^{2} b^{3} c^{2} d^{3} - 47 \, B a^{4} b d^{5}\right)} i^{2} n + 60 \, {\left(3 \, A b^{5} c^{4} d - 8 \, A a b^{4} c^{3} d^{2} + 6 \, A a^{2} b^{3} c^{2} d^{3} - A a^{4} b d^{5}\right)} i^{2}\right)} x + 60 \, {\left(10 \, {\left(B b^{5} c^{3} d^{2} - 3 \, B a b^{4} c^{2} d^{3} + 3 \, B a^{2} b^{3} c d^{4} - B a^{3} b^{2} d^{5}\right)} i^{2} x^{2} + 5 \, {\left(3 \, B b^{5} c^{4} d - 8 \, B a b^{4} c^{3} d^{2} + 6 \, B a^{2} b^{3} c^{2} d^{3} - B a^{4} b d^{5}\right)} i^{2} x + {\left(6 \, B b^{5} c^{5} - 15 \, B a b^{4} c^{4} d + 10 \, B a^{2} b^{3} c^{3} d^{2} - B a^{5} d^{5}\right)} i^{2}\right)} \log\left(e\right) + 60 \, {\left(B b^{5} d^{5} i^{2} n x^{5} + 5 \, B a b^{4} d^{5} i^{2} n x^{4} + 10 \, B a^{2} b^{3} d^{5} i^{2} n x^{3} + 10 \, {\left(B b^{5} c^{3} d^{2} - 3 \, B a b^{4} c^{2} d^{3} + 3 \, B a^{2} b^{3} c d^{4}\right)} i^{2} n x^{2} + 5 \, {\left(3 \, B b^{5} c^{4} d - 8 \, B a b^{4} c^{3} d^{2} + 6 \, B a^{2} b^{3} c^{2} d^{3}\right)} i^{2} n x + {\left(6 \, B b^{5} c^{5} - 15 \, B a b^{4} c^{4} d + 10 \, B a^{2} b^{3} c^{3} d^{2}\right)} i^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{1800 \, {\left({\left(b^{11} c^{3} - 3 \, a b^{10} c^{2} d + 3 \, a^{2} b^{9} c d^{2} - a^{3} b^{8} d^{3}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{3} - 3 \, a^{2} b^{9} c^{2} d + 3 \, a^{3} b^{8} c d^{2} - a^{4} b^{7} d^{3}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{3} - 3 \, a^{3} b^{8} c^{2} d + 3 \, a^{4} b^{7} c d^{2} - a^{5} b^{6} d^{3}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{3} - 3 \, a^{4} b^{7} c^{2} d + 3 \, a^{5} b^{6} c d^{2} - a^{6} b^{5} d^{3}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{3} - 3 \, a^{5} b^{6} c^{2} d + 3 \, a^{6} b^{5} c d^{2} - a^{7} b^{4} d^{3}\right)} g^{6} x + {\left(a^{5} b^{6} c^{3} - 3 \, a^{6} b^{5} c^{2} d + 3 \, a^{7} b^{4} c d^{2} - a^{8} b^{3} d^{3}\right)} g^{6}\right)}}"," ",0,"-1/1800*(60*(B*b^5*c*d^4 - B*a*b^4*d^5)*i^2*n*x^4 - 30*(B*b^5*c^2*d^3 - 10*B*a*b^4*c*d^4 + 9*B*a^2*b^3*d^5)*i^2*n*x^3 + (72*B*b^5*c^5 - 225*B*a*b^4*c^4*d + 200*B*a^2*b^3*c^3*d^2 - 47*B*a^5*d^5)*i^2*n + 60*(6*A*b^5*c^5 - 15*A*a*b^4*c^4*d + 10*A*a^2*b^3*c^3*d^2 - A*a^5*d^5)*i^2 + 10*((2*B*b^5*c^3*d^2 - 15*B*a*b^4*c^2*d^3 + 60*B*a^2*b^3*c*d^4 - 47*B*a^3*b^2*d^5)*i^2*n + 60*(A*b^5*c^3*d^2 - 3*A*a*b^4*c^2*d^3 + 3*A*a^2*b^3*c*d^4 - A*a^3*b^2*d^5)*i^2)*x^2 + 5*((27*B*b^5*c^4*d - 100*B*a*b^4*c^3*d^2 + 120*B*a^2*b^3*c^2*d^3 - 47*B*a^4*b*d^5)*i^2*n + 60*(3*A*b^5*c^4*d - 8*A*a*b^4*c^3*d^2 + 6*A*a^2*b^3*c^2*d^3 - A*a^4*b*d^5)*i^2)*x + 60*(10*(B*b^5*c^3*d^2 - 3*B*a*b^4*c^2*d^3 + 3*B*a^2*b^3*c*d^4 - B*a^3*b^2*d^5)*i^2*x^2 + 5*(3*B*b^5*c^4*d - 8*B*a*b^4*c^3*d^2 + 6*B*a^2*b^3*c^2*d^3 - B*a^4*b*d^5)*i^2*x + (6*B*b^5*c^5 - 15*B*a*b^4*c^4*d + 10*B*a^2*b^3*c^3*d^2 - B*a^5*d^5)*i^2)*log(e) + 60*(B*b^5*d^5*i^2*n*x^5 + 5*B*a*b^4*d^5*i^2*n*x^4 + 10*B*a^2*b^3*d^5*i^2*n*x^3 + 10*(B*b^5*c^3*d^2 - 3*B*a*b^4*c^2*d^3 + 3*B*a^2*b^3*c*d^4)*i^2*n*x^2 + 5*(3*B*b^5*c^4*d - 8*B*a*b^4*c^3*d^2 + 6*B*a^2*b^3*c^2*d^3)*i^2*n*x + (6*B*b^5*c^5 - 15*B*a*b^4*c^4*d + 10*B*a^2*b^3*c^3*d^2)*i^2*n)*log((b*x + a)/(d*x + c)))/((b^11*c^3 - 3*a*b^10*c^2*d + 3*a^2*b^9*c*d^2 - a^3*b^8*d^3)*g^6*x^5 + 5*(a*b^10*c^3 - 3*a^2*b^9*c^2*d + 3*a^3*b^8*c*d^2 - a^4*b^7*d^3)*g^6*x^4 + 10*(a^2*b^9*c^3 - 3*a^3*b^8*c^2*d + 3*a^4*b^7*c*d^2 - a^5*b^6*d^3)*g^6*x^3 + 10*(a^3*b^8*c^3 - 3*a^4*b^7*c^2*d + 3*a^5*b^6*c*d^2 - a^6*b^5*d^3)*g^6*x^2 + 5*(a^4*b^7*c^3 - 3*a^5*b^6*c^2*d + 3*a^6*b^5*c*d^2 - a^7*b^4*d^3)*g^6*x + (a^5*b^6*c^3 - 3*a^6*b^5*c^2*d + 3*a^7*b^4*c*d^2 - a^8*b^3*d^3)*g^6)","B",0
127,1,1336,0,1.250357," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{120 \, A b^{7} d^{7} g^{3} i^{3} x^{7} + 6 \, {\left(35 \, B a^{4} b^{3} c^{3} d^{4} - 21 \, B a^{5} b^{2} c^{2} d^{5} + 7 \, B a^{6} b c d^{6} - B a^{7} d^{7}\right)} g^{3} i^{3} n \log\left(b x + a\right) + 6 \, {\left(B b^{7} c^{7} - 7 \, B a b^{6} c^{6} d + 21 \, B a^{2} b^{5} c^{5} d^{2} - 35 \, B a^{3} b^{4} c^{4} d^{3}\right)} g^{3} i^{3} n \log\left(d x + c\right) - 20 \, {\left({\left(B b^{7} c d^{6} - B a b^{6} d^{7}\right)} g^{3} i^{3} n - 21 \, {\left(A b^{7} c d^{6} + A a b^{6} d^{7}\right)} g^{3} i^{3}\right)} x^{6} - 12 \, {\left(5 \, {\left(B b^{7} c^{2} d^{5} - B a^{2} b^{5} d^{7}\right)} g^{3} i^{3} n - 42 \, {\left(A b^{7} c^{2} d^{5} + 3 \, A a b^{6} c d^{6} + A a^{2} b^{5} d^{7}\right)} g^{3} i^{3}\right)} x^{5} - 3 \, {\left({\left(17 \, B b^{7} c^{3} d^{4} + 49 \, B a b^{6} c^{2} d^{5} - 49 \, B a^{2} b^{5} c d^{6} - 17 \, B a^{3} b^{4} d^{7}\right)} g^{3} i^{3} n - 70 \, {\left(A b^{7} c^{3} d^{4} + 9 \, A a b^{6} c^{2} d^{5} + 9 \, A a^{2} b^{5} c d^{6} + A a^{3} b^{4} d^{7}\right)} g^{3} i^{3}\right)} x^{4} - 2 \, {\left({\left(B b^{7} c^{4} d^{3} + 98 \, B a b^{6} c^{3} d^{4} - 98 \, B a^{3} b^{4} c d^{6} - B a^{4} b^{3} d^{7}\right)} g^{3} i^{3} n - 420 \, {\left(A a b^{6} c^{3} d^{4} + 3 \, A a^{2} b^{5} c^{2} d^{5} + A a^{3} b^{4} c d^{6}\right)} g^{3} i^{3}\right)} x^{3} + 3 \, {\left({\left(B b^{7} c^{5} d^{2} - 7 \, B a b^{6} c^{4} d^{3} - 84 \, B a^{2} b^{5} c^{3} d^{4} + 84 \, B a^{3} b^{4} c^{2} d^{5} + 7 \, B a^{4} b^{3} c d^{6} - B a^{5} b^{2} d^{7}\right)} g^{3} i^{3} n + 420 \, {\left(A a^{2} b^{5} c^{3} d^{4} + A a^{3} b^{4} c^{2} d^{5}\right)} g^{3} i^{3}\right)} x^{2} + 6 \, {\left(140 \, A a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} - {\left(B b^{7} c^{6} d - 7 \, B a b^{6} c^{5} d^{2} + 21 \, B a^{2} b^{5} c^{4} d^{3} - 21 \, B a^{4} b^{3} c^{2} d^{5} + 7 \, B a^{5} b^{2} c d^{6} - B a^{6} b d^{7}\right)} g^{3} i^{3} n\right)} x + 6 \, {\left(20 \, B b^{7} d^{7} g^{3} i^{3} x^{7} + 140 \, B a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} x + 70 \, {\left(B b^{7} c d^{6} + B a b^{6} d^{7}\right)} g^{3} i^{3} x^{6} + 84 \, {\left(B b^{7} c^{2} d^{5} + 3 \, B a b^{6} c d^{6} + B a^{2} b^{5} d^{7}\right)} g^{3} i^{3} x^{5} + 35 \, {\left(B b^{7} c^{3} d^{4} + 9 \, B a b^{6} c^{2} d^{5} + 9 \, B a^{2} b^{5} c d^{6} + B a^{3} b^{4} d^{7}\right)} g^{3} i^{3} x^{4} + 140 \, {\left(B a b^{6} c^{3} d^{4} + 3 \, B a^{2} b^{5} c^{2} d^{5} + B a^{3} b^{4} c d^{6}\right)} g^{3} i^{3} x^{3} + 210 \, {\left(B a^{2} b^{5} c^{3} d^{4} + B a^{3} b^{4} c^{2} d^{5}\right)} g^{3} i^{3} x^{2}\right)} \log\left(e\right) + 6 \, {\left(20 \, B b^{7} d^{7} g^{3} i^{3} n x^{7} + 140 \, B a^{3} b^{4} c^{3} d^{4} g^{3} i^{3} n x + 70 \, {\left(B b^{7} c d^{6} + B a b^{6} d^{7}\right)} g^{3} i^{3} n x^{6} + 84 \, {\left(B b^{7} c^{2} d^{5} + 3 \, B a b^{6} c d^{6} + B a^{2} b^{5} d^{7}\right)} g^{3} i^{3} n x^{5} + 35 \, {\left(B b^{7} c^{3} d^{4} + 9 \, B a b^{6} c^{2} d^{5} + 9 \, B a^{2} b^{5} c d^{6} + B a^{3} b^{4} d^{7}\right)} g^{3} i^{3} n x^{4} + 140 \, {\left(B a b^{6} c^{3} d^{4} + 3 \, B a^{2} b^{5} c^{2} d^{5} + B a^{3} b^{4} c d^{6}\right)} g^{3} i^{3} n x^{3} + 210 \, {\left(B a^{2} b^{5} c^{3} d^{4} + B a^{3} b^{4} c^{2} d^{5}\right)} g^{3} i^{3} n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{840 \, b^{4} d^{4}}"," ",0,"1/840*(120*A*b^7*d^7*g^3*i^3*x^7 + 6*(35*B*a^4*b^3*c^3*d^4 - 21*B*a^5*b^2*c^2*d^5 + 7*B*a^6*b*c*d^6 - B*a^7*d^7)*g^3*i^3*n*log(b*x + a) + 6*(B*b^7*c^7 - 7*B*a*b^6*c^6*d + 21*B*a^2*b^5*c^5*d^2 - 35*B*a^3*b^4*c^4*d^3)*g^3*i^3*n*log(d*x + c) - 20*((B*b^7*c*d^6 - B*a*b^6*d^7)*g^3*i^3*n - 21*(A*b^7*c*d^6 + A*a*b^6*d^7)*g^3*i^3)*x^6 - 12*(5*(B*b^7*c^2*d^5 - B*a^2*b^5*d^7)*g^3*i^3*n - 42*(A*b^7*c^2*d^5 + 3*A*a*b^6*c*d^6 + A*a^2*b^5*d^7)*g^3*i^3)*x^5 - 3*((17*B*b^7*c^3*d^4 + 49*B*a*b^6*c^2*d^5 - 49*B*a^2*b^5*c*d^6 - 17*B*a^3*b^4*d^7)*g^3*i^3*n - 70*(A*b^7*c^3*d^4 + 9*A*a*b^6*c^2*d^5 + 9*A*a^2*b^5*c*d^6 + A*a^3*b^4*d^7)*g^3*i^3)*x^4 - 2*((B*b^7*c^4*d^3 + 98*B*a*b^6*c^3*d^4 - 98*B*a^3*b^4*c*d^6 - B*a^4*b^3*d^7)*g^3*i^3*n - 420*(A*a*b^6*c^3*d^4 + 3*A*a^2*b^5*c^2*d^5 + A*a^3*b^4*c*d^6)*g^3*i^3)*x^3 + 3*((B*b^7*c^5*d^2 - 7*B*a*b^6*c^4*d^3 - 84*B*a^2*b^5*c^3*d^4 + 84*B*a^3*b^4*c^2*d^5 + 7*B*a^4*b^3*c*d^6 - B*a^5*b^2*d^7)*g^3*i^3*n + 420*(A*a^2*b^5*c^3*d^4 + A*a^3*b^4*c^2*d^5)*g^3*i^3)*x^2 + 6*(140*A*a^3*b^4*c^3*d^4*g^3*i^3 - (B*b^7*c^6*d - 7*B*a*b^6*c^5*d^2 + 21*B*a^2*b^5*c^4*d^3 - 21*B*a^4*b^3*c^2*d^5 + 7*B*a^5*b^2*c*d^6 - B*a^6*b*d^7)*g^3*i^3*n)*x + 6*(20*B*b^7*d^7*g^3*i^3*x^7 + 140*B*a^3*b^4*c^3*d^4*g^3*i^3*x + 70*(B*b^7*c*d^6 + B*a*b^6*d^7)*g^3*i^3*x^6 + 84*(B*b^7*c^2*d^5 + 3*B*a*b^6*c*d^6 + B*a^2*b^5*d^7)*g^3*i^3*x^5 + 35*(B*b^7*c^3*d^4 + 9*B*a*b^6*c^2*d^5 + 9*B*a^2*b^5*c*d^6 + B*a^3*b^4*d^7)*g^3*i^3*x^4 + 140*(B*a*b^6*c^3*d^4 + 3*B*a^2*b^5*c^2*d^5 + B*a^3*b^4*c*d^6)*g^3*i^3*x^3 + 210*(B*a^2*b^5*c^3*d^4 + B*a^3*b^4*c^2*d^5)*g^3*i^3*x^2)*log(e) + 6*(20*B*b^7*d^7*g^3*i^3*n*x^7 + 140*B*a^3*b^4*c^3*d^4*g^3*i^3*n*x + 70*(B*b^7*c*d^6 + B*a*b^6*d^7)*g^3*i^3*n*x^6 + 84*(B*b^7*c^2*d^5 + 3*B*a*b^6*c*d^6 + B*a^2*b^5*d^7)*g^3*i^3*n*x^5 + 35*(B*b^7*c^3*d^4 + 9*B*a*b^6*c^2*d^5 + 9*B*a^2*b^5*c*d^6 + B*a^3*b^4*d^7)*g^3*i^3*n*x^4 + 140*(B*a*b^6*c^3*d^4 + 3*B*a^2*b^5*c^2*d^5 + B*a^3*b^4*c*d^6)*g^3*i^3*n*x^3 + 210*(B*a^2*b^5*c^3*d^4 + B*a^3*b^4*c^2*d^5)*g^3*i^3*n*x^2)*log((b*x + a)/(d*x + c)))/(b^4*d^4)","B",0
128,1,1075,0,0.876298," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{60 \, A b^{6} d^{6} g^{2} i^{3} x^{6} + 6 \, {\left(20 \, B a^{3} b^{3} c^{3} d^{3} - 15 \, B a^{4} b^{2} c^{2} d^{4} + 6 \, B a^{5} b c d^{5} - B a^{6} d^{6}\right)} g^{2} i^{3} n \log\left(b x + a\right) - 6 \, {\left(B b^{6} c^{6} - 6 \, B a b^{5} c^{5} d + 15 \, B a^{2} b^{4} c^{4} d^{2}\right)} g^{2} i^{3} n \log\left(d x + c\right) - 12 \, {\left({\left(B b^{6} c d^{5} - B a b^{5} d^{6}\right)} g^{2} i^{3} n - 6 \, {\left(3 \, A b^{6} c d^{5} + 2 \, A a b^{5} d^{6}\right)} g^{2} i^{3}\right)} x^{5} - 3 \, {\left({\left(13 \, B b^{6} c^{2} d^{4} - 6 \, B a b^{5} c d^{5} - 7 \, B a^{2} b^{4} d^{6}\right)} g^{2} i^{3} n - 30 \, {\left(3 \, A b^{6} c^{2} d^{4} + 6 \, A a b^{5} c d^{5} + A a^{2} b^{4} d^{6}\right)} g^{2} i^{3}\right)} x^{4} - 2 \, {\left({\left(19 \, B b^{6} c^{3} d^{3} + 21 \, B a b^{5} c^{2} d^{4} - 39 \, B a^{2} b^{4} c d^{5} - B a^{3} b^{3} d^{6}\right)} g^{2} i^{3} n - 60 \, {\left(A b^{6} c^{3} d^{3} + 6 \, A a b^{5} c^{2} d^{4} + 3 \, A a^{2} b^{4} c d^{5}\right)} g^{2} i^{3}\right)} x^{3} - 3 \, {\left({\left(B b^{6} c^{4} d^{2} + 34 \, B a b^{5} c^{3} d^{3} - 30 \, B a^{2} b^{4} c^{2} d^{4} - 6 \, B a^{3} b^{3} c d^{5} + B a^{4} b^{2} d^{6}\right)} g^{2} i^{3} n - 60 \, {\left(2 \, A a b^{5} c^{3} d^{3} + 3 \, A a^{2} b^{4} c^{2} d^{4}\right)} g^{2} i^{3}\right)} x^{2} + 6 \, {\left(60 \, A a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} + {\left(B b^{6} c^{5} d - 6 \, B a b^{5} c^{4} d^{2} - 5 \, B a^{2} b^{4} c^{3} d^{3} + 15 \, B a^{3} b^{3} c^{2} d^{4} - 6 \, B a^{4} b^{2} c d^{5} + B a^{5} b d^{6}\right)} g^{2} i^{3} n\right)} x + 6 \, {\left(10 \, B b^{6} d^{6} g^{2} i^{3} x^{6} + 60 \, B a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} x + 12 \, {\left(3 \, B b^{6} c d^{5} + 2 \, B a b^{5} d^{6}\right)} g^{2} i^{3} x^{5} + 15 \, {\left(3 \, B b^{6} c^{2} d^{4} + 6 \, B a b^{5} c d^{5} + B a^{2} b^{4} d^{6}\right)} g^{2} i^{3} x^{4} + 20 \, {\left(B b^{6} c^{3} d^{3} + 6 \, B a b^{5} c^{2} d^{4} + 3 \, B a^{2} b^{4} c d^{5}\right)} g^{2} i^{3} x^{3} + 30 \, {\left(2 \, B a b^{5} c^{3} d^{3} + 3 \, B a^{2} b^{4} c^{2} d^{4}\right)} g^{2} i^{3} x^{2}\right)} \log\left(e\right) + 6 \, {\left(10 \, B b^{6} d^{6} g^{2} i^{3} n x^{6} + 60 \, B a^{2} b^{4} c^{3} d^{3} g^{2} i^{3} n x + 12 \, {\left(3 \, B b^{6} c d^{5} + 2 \, B a b^{5} d^{6}\right)} g^{2} i^{3} n x^{5} + 15 \, {\left(3 \, B b^{6} c^{2} d^{4} + 6 \, B a b^{5} c d^{5} + B a^{2} b^{4} d^{6}\right)} g^{2} i^{3} n x^{4} + 20 \, {\left(B b^{6} c^{3} d^{3} + 6 \, B a b^{5} c^{2} d^{4} + 3 \, B a^{2} b^{4} c d^{5}\right)} g^{2} i^{3} n x^{3} + 30 \, {\left(2 \, B a b^{5} c^{3} d^{3} + 3 \, B a^{2} b^{4} c^{2} d^{4}\right)} g^{2} i^{3} n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{360 \, b^{4} d^{3}}"," ",0,"1/360*(60*A*b^6*d^6*g^2*i^3*x^6 + 6*(20*B*a^3*b^3*c^3*d^3 - 15*B*a^4*b^2*c^2*d^4 + 6*B*a^5*b*c*d^5 - B*a^6*d^6)*g^2*i^3*n*log(b*x + a) - 6*(B*b^6*c^6 - 6*B*a*b^5*c^5*d + 15*B*a^2*b^4*c^4*d^2)*g^2*i^3*n*log(d*x + c) - 12*((B*b^6*c*d^5 - B*a*b^5*d^6)*g^2*i^3*n - 6*(3*A*b^6*c*d^5 + 2*A*a*b^5*d^6)*g^2*i^3)*x^5 - 3*((13*B*b^6*c^2*d^4 - 6*B*a*b^5*c*d^5 - 7*B*a^2*b^4*d^6)*g^2*i^3*n - 30*(3*A*b^6*c^2*d^4 + 6*A*a*b^5*c*d^5 + A*a^2*b^4*d^6)*g^2*i^3)*x^4 - 2*((19*B*b^6*c^3*d^3 + 21*B*a*b^5*c^2*d^4 - 39*B*a^2*b^4*c*d^5 - B*a^3*b^3*d^6)*g^2*i^3*n - 60*(A*b^6*c^3*d^3 + 6*A*a*b^5*c^2*d^4 + 3*A*a^2*b^4*c*d^5)*g^2*i^3)*x^3 - 3*((B*b^6*c^4*d^2 + 34*B*a*b^5*c^3*d^3 - 30*B*a^2*b^4*c^2*d^4 - 6*B*a^3*b^3*c*d^5 + B*a^4*b^2*d^6)*g^2*i^3*n - 60*(2*A*a*b^5*c^3*d^3 + 3*A*a^2*b^4*c^2*d^4)*g^2*i^3)*x^2 + 6*(60*A*a^2*b^4*c^3*d^3*g^2*i^3 + (B*b^6*c^5*d - 6*B*a*b^5*c^4*d^2 - 5*B*a^2*b^4*c^3*d^3 + 15*B*a^3*b^3*c^2*d^4 - 6*B*a^4*b^2*c*d^5 + B*a^5*b*d^6)*g^2*i^3*n)*x + 6*(10*B*b^6*d^6*g^2*i^3*x^6 + 60*B*a^2*b^4*c^3*d^3*g^2*i^3*x + 12*(3*B*b^6*c*d^5 + 2*B*a*b^5*d^6)*g^2*i^3*x^5 + 15*(3*B*b^6*c^2*d^4 + 6*B*a*b^5*c*d^5 + B*a^2*b^4*d^6)*g^2*i^3*x^4 + 20*(B*b^6*c^3*d^3 + 6*B*a*b^5*c^2*d^4 + 3*B*a^2*b^4*c*d^5)*g^2*i^3*x^3 + 30*(2*B*a*b^5*c^3*d^3 + 3*B*a^2*b^4*c^2*d^4)*g^2*i^3*x^2)*log(e) + 6*(10*B*b^6*d^6*g^2*i^3*n*x^6 + 60*B*a^2*b^4*c^3*d^3*g^2*i^3*n*x + 12*(3*B*b^6*c*d^5 + 2*B*a*b^5*d^6)*g^2*i^3*n*x^5 + 15*(3*B*b^6*c^2*d^4 + 6*B*a*b^5*c*d^5 + B*a^2*b^4*d^6)*g^2*i^3*n*x^4 + 20*(B*b^6*c^3*d^3 + 6*B*a*b^5*c^2*d^4 + 3*B*a^2*b^4*c*d^5)*g^2*i^3*n*x^3 + 30*(2*B*a*b^5*c^3*d^3 + 3*B*a^2*b^4*c^2*d^4)*g^2*i^3*n*x^2)*log((b*x + a)/(d*x + c)))/(b^4*d^3)","B",0
129,1,721,0,0.573050," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{24 \, A b^{5} d^{5} g i^{3} x^{5} + 6 \, {\left(10 \, B a^{2} b^{3} c^{3} d^{2} - 10 \, B a^{3} b^{2} c^{2} d^{3} + 5 \, B a^{4} b c d^{4} - B a^{5} d^{5}\right)} g i^{3} n \log\left(b x + a\right) + 6 \, {\left(B b^{5} c^{5} - 5 \, B a b^{4} c^{4} d\right)} g i^{3} n \log\left(d x + c\right) - 6 \, {\left({\left(B b^{5} c d^{4} - B a b^{4} d^{5}\right)} g i^{3} n - 5 \, {\left(3 \, A b^{5} c d^{4} + A a b^{4} d^{5}\right)} g i^{3}\right)} x^{4} - 2 \, {\left({\left(11 \, B b^{5} c^{2} d^{3} - 10 \, B a b^{4} c d^{4} - B a^{2} b^{3} d^{5}\right)} g i^{3} n - 60 \, {\left(A b^{5} c^{2} d^{3} + A a b^{4} c d^{4}\right)} g i^{3}\right)} x^{3} - 3 \, {\left({\left(9 \, B b^{5} c^{3} d^{2} - 5 \, B a b^{4} c^{2} d^{3} - 5 \, B a^{2} b^{3} c d^{4} + B a^{3} b^{2} d^{5}\right)} g i^{3} n - 20 \, {\left(A b^{5} c^{3} d^{2} + 3 \, A a b^{4} c^{2} d^{3}\right)} g i^{3}\right)} x^{2} + 6 \, {\left(20 \, A a b^{4} c^{3} d^{2} g i^{3} - {\left(B b^{5} c^{4} d + 5 \, B a b^{4} c^{3} d^{2} - 10 \, B a^{2} b^{3} c^{2} d^{3} + 5 \, B a^{3} b^{2} c d^{4} - B a^{4} b d^{5}\right)} g i^{3} n\right)} x + 6 \, {\left(4 \, B b^{5} d^{5} g i^{3} x^{5} + 20 \, B a b^{4} c^{3} d^{2} g i^{3} x + 5 \, {\left(3 \, B b^{5} c d^{4} + B a b^{4} d^{5}\right)} g i^{3} x^{4} + 20 \, {\left(B b^{5} c^{2} d^{3} + B a b^{4} c d^{4}\right)} g i^{3} x^{3} + 10 \, {\left(B b^{5} c^{3} d^{2} + 3 \, B a b^{4} c^{2} d^{3}\right)} g i^{3} x^{2}\right)} \log\left(e\right) + 6 \, {\left(4 \, B b^{5} d^{5} g i^{3} n x^{5} + 20 \, B a b^{4} c^{3} d^{2} g i^{3} n x + 5 \, {\left(3 \, B b^{5} c d^{4} + B a b^{4} d^{5}\right)} g i^{3} n x^{4} + 20 \, {\left(B b^{5} c^{2} d^{3} + B a b^{4} c d^{4}\right)} g i^{3} n x^{3} + 10 \, {\left(B b^{5} c^{3} d^{2} + 3 \, B a b^{4} c^{2} d^{3}\right)} g i^{3} n x^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)}{120 \, b^{4} d^{2}}"," ",0,"1/120*(24*A*b^5*d^5*g*i^3*x^5 + 6*(10*B*a^2*b^3*c^3*d^2 - 10*B*a^3*b^2*c^2*d^3 + 5*B*a^4*b*c*d^4 - B*a^5*d^5)*g*i^3*n*log(b*x + a) + 6*(B*b^5*c^5 - 5*B*a*b^4*c^4*d)*g*i^3*n*log(d*x + c) - 6*((B*b^5*c*d^4 - B*a*b^4*d^5)*g*i^3*n - 5*(3*A*b^5*c*d^4 + A*a*b^4*d^5)*g*i^3)*x^4 - 2*((11*B*b^5*c^2*d^3 - 10*B*a*b^4*c*d^4 - B*a^2*b^3*d^5)*g*i^3*n - 60*(A*b^5*c^2*d^3 + A*a*b^4*c*d^4)*g*i^3)*x^3 - 3*((9*B*b^5*c^3*d^2 - 5*B*a*b^4*c^2*d^3 - 5*B*a^2*b^3*c*d^4 + B*a^3*b^2*d^5)*g*i^3*n - 20*(A*b^5*c^3*d^2 + 3*A*a*b^4*c^2*d^3)*g*i^3)*x^2 + 6*(20*A*a*b^4*c^3*d^2*g*i^3 - (B*b^5*c^4*d + 5*B*a*b^4*c^3*d^2 - 10*B*a^2*b^3*c^2*d^3 + 5*B*a^3*b^2*c*d^4 - B*a^4*b*d^5)*g*i^3*n)*x + 6*(4*B*b^5*d^5*g*i^3*x^5 + 20*B*a*b^4*c^3*d^2*g*i^3*x + 5*(3*B*b^5*c*d^4 + B*a*b^4*d^5)*g*i^3*x^4 + 20*(B*b^5*c^2*d^3 + B*a*b^4*c*d^4)*g*i^3*x^3 + 10*(B*b^5*c^3*d^2 + 3*B*a*b^4*c^2*d^3)*g*i^3*x^2)*log(e) + 6*(4*B*b^5*d^5*g*i^3*n*x^5 + 20*B*a*b^4*c^3*d^2*g*i^3*n*x + 5*(3*B*b^5*c*d^4 + B*a*b^4*d^5)*g*i^3*n*x^4 + 20*(B*b^5*c^2*d^3 + B*a*b^4*c*d^4)*g*i^3*n*x^3 + 10*(B*b^5*c^3*d^2 + 3*B*a*b^4*c^2*d^3)*g*i^3*n*x^2)*log((b*x + a)/(d*x + c)))/(b^4*d^2)","B",0
130,1,429,0,0.488514," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{6 \, A b^{4} d^{4} i^{3} x^{4} - 6 \, B b^{4} c^{4} i^{3} n \log\left(d x + c\right) + 6 \, {\left(4 \, B a b^{3} c^{3} d - 6 \, B a^{2} b^{2} c^{2} d^{2} + 4 \, B a^{3} b c d^{3} - B a^{4} d^{4}\right)} i^{3} n \log\left(b x + a\right) + 2 \, {\left(12 \, A b^{4} c d^{3} i^{3} - {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} i^{3} n\right)} x^{3} + 3 \, {\left(12 \, A b^{4} c^{2} d^{2} i^{3} - {\left(3 \, B b^{4} c^{2} d^{2} - 4 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} i^{3} n\right)} x^{2} + 6 \, {\left(4 \, A b^{4} c^{3} d i^{3} - {\left(3 \, B b^{4} c^{3} d - 6 \, B a b^{3} c^{2} d^{2} + 4 \, B a^{2} b^{2} c d^{3} - B a^{3} b d^{4}\right)} i^{3} n\right)} x + 6 \, {\left(B b^{4} d^{4} i^{3} x^{4} + 4 \, B b^{4} c d^{3} i^{3} x^{3} + 6 \, B b^{4} c^{2} d^{2} i^{3} x^{2} + 4 \, B b^{4} c^{3} d i^{3} x\right)} \log\left(e\right) + 6 \, {\left(B b^{4} d^{4} i^{3} n x^{4} + 4 \, B b^{4} c d^{3} i^{3} n x^{3} + 6 \, B b^{4} c^{2} d^{2} i^{3} n x^{2} + 4 \, B b^{4} c^{3} d i^{3} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{24 \, b^{4} d}"," ",0,"1/24*(6*A*b^4*d^4*i^3*x^4 - 6*B*b^4*c^4*i^3*n*log(d*x + c) + 6*(4*B*a*b^3*c^3*d - 6*B*a^2*b^2*c^2*d^2 + 4*B*a^3*b*c*d^3 - B*a^4*d^4)*i^3*n*log(b*x + a) + 2*(12*A*b^4*c*d^3*i^3 - (B*b^4*c*d^3 - B*a*b^3*d^4)*i^3*n)*x^3 + 3*(12*A*b^4*c^2*d^2*i^3 - (3*B*b^4*c^2*d^2 - 4*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*i^3*n)*x^2 + 6*(4*A*b^4*c^3*d*i^3 - (3*B*b^4*c^3*d - 6*B*a*b^3*c^2*d^2 + 4*B*a^2*b^2*c*d^3 - B*a^3*b*d^4)*i^3*n)*x + 6*(B*b^4*d^4*i^3*x^4 + 4*B*b^4*c*d^3*i^3*x^3 + 6*B*b^4*c^2*d^2*i^3*x^2 + 4*B*b^4*c^3*d*i^3*x)*log(e) + 6*(B*b^4*d^4*i^3*n*x^4 + 4*B*b^4*c*d^3*i^3*n*x^3 + 6*B*b^4*c^2*d^2*i^3*n*x^2 + 4*B*b^4*c^3*d*i^3*n*x)*log((b*x + a)/(d*x + c)))/(b^4*d)","B",0
131,0,0,0,0.429008," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{3} i^{3} x^{3} + 3 \, A c d^{2} i^{3} x^{2} + 3 \, A c^{2} d i^{3} x + A c^{3} i^{3} + {\left(B d^{3} i^{3} x^{3} + 3 \, B c d^{2} i^{3} x^{2} + 3 \, B c^{2} d i^{3} x + B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b g x + a g}, x\right)"," ",0,"integral((A*d^3*i^3*x^3 + 3*A*c*d^2*i^3*x^2 + 3*A*c^2*d*i^3*x + A*c^3*i^3 + (B*d^3*i^3*x^3 + 3*B*c*d^2*i^3*x^2 + 3*B*c^2*d*i^3*x + B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n))/(b*g*x + a*g), x)","F",0
132,0,0,0,0.446247," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{3} i^{3} x^{3} + 3 \, A c d^{2} i^{3} x^{2} + 3 \, A c^{2} d i^{3} x + A c^{3} i^{3} + {\left(B d^{3} i^{3} x^{3} + 3 \, B c d^{2} i^{3} x^{2} + 3 \, B c^{2} d i^{3} x + B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A*d^3*i^3*x^3 + 3*A*c*d^2*i^3*x^2 + 3*A*c^2*d*i^3*x + A*c^3*i^3 + (B*d^3*i^3*x^3 + 3*B*c*d^2*i^3*x^2 + 3*B*c^2*d*i^3*x + B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
133,0,0,0,0.458106," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{3} i^{3} x^{3} + 3 \, A c d^{2} i^{3} x^{2} + 3 \, A c^{2} d i^{3} x + A c^{3} i^{3} + {\left(B d^{3} i^{3} x^{3} + 3 \, B c d^{2} i^{3} x^{2} + 3 \, B c^{2} d i^{3} x + B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{3} g^{3} x^{3} + 3 \, a b^{2} g^{3} x^{2} + 3 \, a^{2} b g^{3} x + a^{3} g^{3}}, x\right)"," ",0,"integral((A*d^3*i^3*x^3 + 3*A*c*d^2*i^3*x^2 + 3*A*c^2*d*i^3*x + A*c^3*i^3 + (B*d^3*i^3*x^3 + 3*B*c*d^2*i^3*x^2 + 3*B*c^2*d*i^3*x + B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n))/(b^3*g^3*x^3 + 3*a*b^2*g^3*x^2 + 3*a^2*b*g^3*x + a^3*g^3), x)","F",0
134,0,0,0,0.446545," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A d^{3} i^{3} x^{3} + 3 \, A c d^{2} i^{3} x^{2} + 3 \, A c^{2} d i^{3} x + A c^{3} i^{3} + {\left(B d^{3} i^{3} x^{3} + 3 \, B c d^{2} i^{3} x^{2} + 3 \, B c^{2} d i^{3} x + B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{4} g^{4} x^{4} + 4 \, a b^{3} g^{4} x^{3} + 6 \, a^{2} b^{2} g^{4} x^{2} + 4 \, a^{3} b g^{4} x + a^{4} g^{4}}, x\right)"," ",0,"integral((A*d^3*i^3*x^3 + 3*A*c*d^2*i^3*x^2 + 3*A*c^2*d*i^3*x + A*c^3*i^3 + (B*d^3*i^3*x^3 + 3*B*c*d^2*i^3*x^2 + 3*B*c^2*d*i^3*x + B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n))/(b^4*g^4*x^4 + 4*a*b^3*g^4*x^3 + 6*a^2*b^2*g^4*x^2 + 4*a^3*b*g^4*x + a^4*g^4), x)","F",0
135,0,0,0,0.449214," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{3} g^{3} x^{3} + 3 \, A a b^{2} g^{3} x^{2} + 3 \, A a^{2} b g^{3} x + A a^{3} g^{3} + {\left(B b^{3} g^{3} x^{3} + 3 \, B a b^{2} g^{3} x^{2} + 3 \, B a^{2} b g^{3} x + B a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d i x + c i}, x\right)"," ",0,"integral((A*b^3*g^3*x^3 + 3*A*a*b^2*g^3*x^2 + 3*A*a^2*b*g^3*x + A*a^3*g^3 + (B*b^3*g^3*x^3 + 3*B*a*b^2*g^3*x^2 + 3*B*a^2*b*g^3*x + B*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n))/(d*i*x + c*i), x)","F",0
136,0,0,0,0.432098," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{2} g^{2} x^{2} + 2 \, A a b g^{2} x + A a^{2} g^{2} + {\left(B b^{2} g^{2} x^{2} + 2 \, B a b g^{2} x + B a^{2} g^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d i x + c i}, x\right)"," ",0,"integral((A*b^2*g^2*x^2 + 2*A*a*b*g^2*x + A*a^2*g^2 + (B*b^2*g^2*x^2 + 2*B*a*b*g^2*x + B*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n))/(d*i*x + c*i), x)","F",0
137,0,0,0,0.421092," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b g x + A a g + {\left(B b g x + B a g\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d i x + c i}, x\right)"," ",0,"integral((A*b*g*x + A*a*g + (B*b*g*x + B*a*g)*log(e*((b*x + a)/(d*x + c))^n))/(d*i*x + c*i), x)","F",0
138,0,0,0,0.409303," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A}{d i x + c i}, x\right)"," ",0,"integral((B*log(e*((b*x + a)/(d*x + c))^n) + A)/(d*i*x + c*i), x)","F",0
139,1,74,0,0.415506," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)/(d*i*x+c*i),x, algorithm=""fricas"")","\frac{B n \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, B \log\left(e\right) \log\left(\frac{b x + a}{d x + c}\right) + 2 \, A \log\left(\frac{b x + a}{d x + c}\right)}{2 \, {\left(b c - a d\right)} g i}"," ",0,"1/2*(B*n*log((b*x + a)/(d*x + c))^2 + 2*B*log(e)*log((b*x + a)/(d*x + c)) + 2*A*log((b*x + a)/(d*x + c)))/((b*c - a*d)*g*i)","A",0
140,1,194,0,0.433925," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{2 \, A b c - 2 \, A a d + {\left(B b d n x + B a d n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(B b c - B a d\right)} n + 2 \, {\left(B b c - B a d + {\left(B b d x + B a d\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left(B b c n + A a d + {\left(B b d n + A b d\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{2 \, {\left({\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{2} i x + {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} g^{2} i\right)}}"," ",0,"-1/2*(2*A*b*c - 2*A*a*d + (B*b*d*n*x + B*a*d*n)*log((b*x + a)/(d*x + c))^2 + 2*(B*b*c - B*a*d)*n + 2*(B*b*c - B*a*d + (B*b*d*x + B*a*d)*log((b*x + a)/(d*x + c)))*log(e) + 2*(B*b*c*n + A*a*d + (B*b*d*n + A*b*d)*x)*log((b*x + a)/(d*x + c)))/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^2*i*x + (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*g^2*i)","A",0
141,1,483,0,0.450629," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{2 \, A b^{2} c^{2} - 8 \, A a b c d + 6 \, A a^{2} d^{2} - 2 \, {\left(B b^{2} d^{2} n x^{2} + 2 \, B a b d^{2} n x + B a^{2} d^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B b^{2} c^{2} - 8 \, B a b c d + 7 \, B a^{2} d^{2}\right)} n - 2 \, {\left(2 \, A b^{2} c d - 2 \, A a b d^{2} + 3 \, {\left(B b^{2} c d - B a b d^{2}\right)} n\right)} x + 2 \, {\left(B b^{2} c^{2} - 4 \, B a b c d + 3 \, B a^{2} d^{2} - 2 \, {\left(B b^{2} c d - B a b d^{2}\right)} x - 2 \, {\left(B b^{2} d^{2} x^{2} + 2 \, B a b d^{2} x + B a^{2} d^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) - 2 \, {\left(2 \, A a^{2} d^{2} + {\left(3 \, B b^{2} d^{2} n + 2 \, A b^{2} d^{2}\right)} x^{2} - {\left(B b^{2} c^{2} - 4 \, B a b c d\right)} n + 2 \, {\left(2 \, A a b d^{2} + {\left(B b^{2} c d + 2 \, B a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} g^{3} i x + {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} g^{3} i\right)}}"," ",0,"-1/4*(2*A*b^2*c^2 - 8*A*a*b*c*d + 6*A*a^2*d^2 - 2*(B*b^2*d^2*n*x^2 + 2*B*a*b*d^2*n*x + B*a^2*d^2*n)*log((b*x + a)/(d*x + c))^2 + (B*b^2*c^2 - 8*B*a*b*c*d + 7*B*a^2*d^2)*n - 2*(2*A*b^2*c*d - 2*A*a*b*d^2 + 3*(B*b^2*c*d - B*a*b*d^2)*n)*x + 2*(B*b^2*c^2 - 4*B*a*b*c*d + 3*B*a^2*d^2 - 2*(B*b^2*c*d - B*a*b*d^2)*x - 2*(B*b^2*d^2*x^2 + 2*B*a*b*d^2*x + B*a^2*d^2)*log((b*x + a)/(d*x + c)))*log(e) - 2*(2*A*a^2*d^2 + (3*B*b^2*d^2*n + 2*A*b^2*d^2)*x^2 - (B*b^2*c^2 - 4*B*a*b*c*d)*n + 2*(2*A*a*b*d^2 + (B*b^2*c*d + 2*B*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^3*i*x^2 + 2*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*g^3*i*x + (a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*g^3*i)","A",0
142,1,859,0,0.466172," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{12 \, A b^{3} c^{3} - 54 \, A a b^{2} c^{2} d + 108 \, A a^{2} b c d^{2} - 66 \, A a^{3} d^{3} + 6 \, {\left(6 \, A b^{3} c d^{2} - 6 \, A a b^{2} d^{3} + 11 \, {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} n\right)} x^{2} + 18 \, {\left(B b^{3} d^{3} n x^{3} + 3 \, B a b^{2} d^{3} n x^{2} + 3 \, B a^{2} b d^{3} n x + B a^{3} d^{3} n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(4 \, B b^{3} c^{3} - 27 \, B a b^{2} c^{2} d + 108 \, B a^{2} b c d^{2} - 85 \, B a^{3} d^{3}\right)} n - 3 \, {\left(6 \, A b^{3} c^{2} d - 36 \, A a b^{2} c d^{2} + 30 \, A a^{2} b d^{3} + {\left(5 \, B b^{3} c^{2} d - 54 \, B a b^{2} c d^{2} + 49 \, B a^{2} b d^{3}\right)} n\right)} x + 6 \, {\left(2 \, B b^{3} c^{3} - 9 \, B a b^{2} c^{2} d + 18 \, B a^{2} b c d^{2} - 11 \, B a^{3} d^{3} + 6 \, {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(B b^{3} c^{2} d - 6 \, B a b^{2} c d^{2} + 5 \, B a^{2} b d^{3}\right)} x + 6 \, {\left(B b^{3} d^{3} x^{3} + 3 \, B a b^{2} d^{3} x^{2} + 3 \, B a^{2} b d^{3} x + B a^{3} d^{3}\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left(6 \, A a^{3} d^{3} + {\left(11 \, B b^{3} d^{3} n + 6 \, A b^{3} d^{3}\right)} x^{3} + 3 \, {\left(6 \, A a b^{2} d^{3} + {\left(2 \, B b^{3} c d^{2} + 9 \, B a b^{2} d^{3}\right)} n\right)} x^{2} + {\left(2 \, B b^{3} c^{3} - 9 \, B a b^{2} c^{2} d + 18 \, B a^{2} b c d^{2}\right)} n + 3 \, {\left(6 \, A a^{2} b d^{3} - {\left(B b^{3} c^{2} d - 6 \, B a b^{2} c d^{2} - 6 \, B a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{36 \, {\left({\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{6} c^{4} - 4 \, a^{2} b^{5} c^{3} d + 6 \, a^{3} b^{4} c^{2} d^{2} - 4 \, a^{4} b^{3} c d^{3} + a^{5} b^{2} d^{4}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}\right)} g^{4} i x + {\left(a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}\right)} g^{4} i\right)}}"," ",0,"-1/36*(12*A*b^3*c^3 - 54*A*a*b^2*c^2*d + 108*A*a^2*b*c*d^2 - 66*A*a^3*d^3 + 6*(6*A*b^3*c*d^2 - 6*A*a*b^2*d^3 + 11*(B*b^3*c*d^2 - B*a*b^2*d^3)*n)*x^2 + 18*(B*b^3*d^3*n*x^3 + 3*B*a*b^2*d^3*n*x^2 + 3*B*a^2*b*d^3*n*x + B*a^3*d^3*n)*log((b*x + a)/(d*x + c))^2 + (4*B*b^3*c^3 - 27*B*a*b^2*c^2*d + 108*B*a^2*b*c*d^2 - 85*B*a^3*d^3)*n - 3*(6*A*b^3*c^2*d - 36*A*a*b^2*c*d^2 + 30*A*a^2*b*d^3 + (5*B*b^3*c^2*d - 54*B*a*b^2*c*d^2 + 49*B*a^2*b*d^3)*n)*x + 6*(2*B*b^3*c^3 - 9*B*a*b^2*c^2*d + 18*B*a^2*b*c*d^2 - 11*B*a^3*d^3 + 6*(B*b^3*c*d^2 - B*a*b^2*d^3)*x^2 - 3*(B*b^3*c^2*d - 6*B*a*b^2*c*d^2 + 5*B*a^2*b*d^3)*x + 6*(B*b^3*d^3*x^3 + 3*B*a*b^2*d^3*x^2 + 3*B*a^2*b*d^3*x + B*a^3*d^3)*log((b*x + a)/(d*x + c)))*log(e) + 6*(6*A*a^3*d^3 + (11*B*b^3*d^3*n + 6*A*b^3*d^3)*x^3 + 3*(6*A*a*b^2*d^3 + (2*B*b^3*c*d^2 + 9*B*a*b^2*d^3)*n)*x^2 + (2*B*b^3*c^3 - 9*B*a*b^2*c^2*d + 18*B*a^2*b*c*d^2)*n + 3*(6*A*a^2*b*d^3 - (B*b^3*c^2*d - 6*B*a*b^2*c*d^2 - 6*B*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^4*i*x^3 + 3*(a*b^6*c^4 - 4*a^2*b^5*c^3*d + 6*a^3*b^4*c^2*d^2 - 4*a^4*b^3*c*d^3 + a^5*b^2*d^4)*g^4*i*x^2 + 3*(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 6*a^4*b^3*c^2*d^2 - 4*a^5*b^2*c*d^3 + a^6*b*d^4)*g^4*i*x + (a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4)*g^4*i)","B",0
143,0,0,0,0.443173," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{3} g^{3} x^{3} + 3 \, A a b^{2} g^{3} x^{2} + 3 \, A a^{2} b g^{3} x + A a^{3} g^{3} + {\left(B b^{3} g^{3} x^{3} + 3 \, B a b^{2} g^{3} x^{2} + 3 \, B a^{2} b g^{3} x + B a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A*b^3*g^3*x^3 + 3*A*a*b^2*g^3*x^2 + 3*A*a^2*b*g^3*x + A*a^3*g^3 + (B*b^3*g^3*x^3 + 3*B*a*b^2*g^3*x^2 + 3*B*a^2*b*g^3*x + B*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
144,0,0,0,0.481056," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{2} g^{2} x^{2} + 2 \, A a b g^{2} x + A a^{2} g^{2} + {\left(B b^{2} g^{2} x^{2} + 2 \, B a b g^{2} x + B a^{2} g^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A*b^2*g^2*x^2 + 2*A*a*b*g^2*x + A*a^2*g^2 + (B*b^2*g^2*x^2 + 2*B*a*b*g^2*x + B*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
145,0,0,0,0.435288," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b g x + A a g + {\left(B b g x + B a g\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A*b*g*x + A*a*g + (B*b*g*x + B*a*g)*log(e*((b*x + a)/(d*x + c))^n))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
146,1,105,0,0.439622," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{A b c - A a d - {\left(B b c - B a d\right)} n + {\left(B b c - B a d\right)} \log\left(e\right) - {\left(B b d n x + B a d n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{{\left(b c d^{2} - a d^{3}\right)} i^{2} x + {\left(b c^{2} d - a c d^{2}\right)} i^{2}}"," ",0,"-(A*b*c - A*a*d - (B*b*c - B*a*d)*n + (B*b*c - B*a*d)*log(e) - (B*b*d*n*x + B*a*d*n)*log((b*x + a)/(d*x + c)))/((b*c*d^2 - a*d^3)*i^2*x + (b*c^2*d - a*c*d^2)*i^2)","A",0
147,1,196,0,0.449784," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)/(d*i*x+c*i)^2,x, algorithm=""fricas"")","\frac{2 \, A b c - 2 \, A a d + {\left(B b d n x + B b c n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 2 \, {\left(B b c - B a d\right)} n + 2 \, {\left(B b c - B a d + {\left(B b d x + B b c\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) - 2 \, {\left(B a d n - A b c + {\left(B b d n - A b d\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{2 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} g i^{2} x + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} g i^{2}\right)}}"," ",0,"1/2*(2*A*b*c - 2*A*a*d + (B*b*d*n*x + B*b*c*n)*log((b*x + a)/(d*x + c))^2 - 2*(B*b*c - B*a*d)*n + 2*(B*b*c - B*a*d + (B*b*d*x + B*b*c)*log((b*x + a)/(d*x + c)))*log(e) - 2*(B*a*d*n - A*b*c + (B*b*d*n - A*b*d)*x)*log((b*x + a)/(d*x + c)))/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g*i^2*x + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*g*i^2)","A",0
148,1,450,0,0.447544," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{A b^{2} c^{2} - A a^{2} d^{2} + {\left(B b^{2} d^{2} n x^{2} + B a b c d n + {\left(B b^{2} c d + B a b d^{2}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B b^{2} c^{2} - 2 \, B a b c d + B a^{2} d^{2}\right)} n + 2 \, {\left(A b^{2} c d - A a b d^{2}\right)} x + {\left(B b^{2} c^{2} - B a^{2} d^{2} + 2 \, {\left(B b^{2} c d - B a b d^{2}\right)} x + 2 \, {\left(B b^{2} d^{2} x^{2} + B a b c d + {\left(B b^{2} c d + B a b d^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + {\left(2 \, A b^{2} d^{2} x^{2} + 2 \, A a b c d + {\left(B b^{2} c^{2} - B a^{2} d^{2}\right)} n + 2 \, {\left(A b^{2} c d + A a b d^{2} + {\left(B b^{2} c d - B a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{{\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} g^{2} i^{2} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} g^{2} i^{2} x + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} g^{2} i^{2}}"," ",0,"-(A*b^2*c^2 - A*a^2*d^2 + (B*b^2*d^2*n*x^2 + B*a*b*c*d*n + (B*b^2*c*d + B*a*b*d^2)*n*x)*log((b*x + a)/(d*x + c))^2 + (B*b^2*c^2 - 2*B*a*b*c*d + B*a^2*d^2)*n + 2*(A*b^2*c*d - A*a*b*d^2)*x + (B*b^2*c^2 - B*a^2*d^2 + 2*(B*b^2*c*d - B*a*b*d^2)*x + 2*(B*b^2*d^2*x^2 + B*a*b*c*d + (B*b^2*c*d + B*a*b*d^2)*x)*log((b*x + a)/(d*x + c)))*log(e) + (2*A*b^2*d^2*x^2 + 2*A*a*b*c*d + (B*b^2*c^2 - B*a^2*d^2)*n + 2*(A*b^2*c*d + A*a*b*d^2 + (B*b^2*c*d - B*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))/((b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*g^2*i^2*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*g^2*i^2*x + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*g^2*i^2)","A",0
149,1,946,0,0.485925," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{2 \, A b^{3} c^{3} - 12 \, A a b^{2} c^{2} d + 6 \, A a^{2} b c d^{2} + 4 \, A a^{3} d^{3} - 6 \, {\left(2 \, A b^{3} c d^{2} - 2 \, A a b^{2} d^{3} + {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} n\right)} x^{2} - 6 \, {\left(B b^{3} d^{3} n x^{3} + B a^{2} b c d^{2} n + {\left(B b^{3} c d^{2} + 2 \, B a b^{2} d^{3}\right)} n x^{2} + {\left(2 \, B a b^{2} c d^{2} + B a^{2} b d^{3}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B b^{3} c^{3} - 12 \, B a b^{2} c^{2} d + 15 \, B a^{2} b c d^{2} - 4 \, B a^{3} d^{3}\right)} n - 3 \, {\left(2 \, A b^{3} c^{2} d + 4 \, A a b^{2} c d^{2} - 6 \, A a^{2} b d^{3} + {\left(3 \, B b^{3} c^{2} d - 2 \, B a b^{2} c d^{2} - B a^{2} b d^{3}\right)} n\right)} x + 2 \, {\left(B b^{3} c^{3} - 6 \, B a b^{2} c^{2} d + 3 \, B a^{2} b c d^{2} + 2 \, B a^{3} d^{3} - 6 \, {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(B b^{3} c^{2} d + 2 \, B a b^{2} c d^{2} - 3 \, B a^{2} b d^{3}\right)} x - 6 \, {\left(B b^{3} d^{3} x^{3} + B a^{2} b c d^{2} + {\left(B b^{3} c d^{2} + 2 \, B a b^{2} d^{3}\right)} x^{2} + {\left(2 \, B a b^{2} c d^{2} + B a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) - 2 \, {\left(6 \, A a^{2} b c d^{2} + 3 \, {\left(B b^{3} d^{3} n + 2 \, A b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, B b^{3} c d^{2} n + 2 \, A b^{3} c d^{2} + 4 \, A a b^{2} d^{3}\right)} x^{2} - {\left(B b^{3} c^{3} - 6 \, B a b^{2} c^{2} d + 2 \, B a^{3} d^{3}\right)} n + 3 \, {\left(4 \, A a b^{2} c d^{2} + 2 \, A a^{2} b d^{3} + {\left(B b^{3} c^{2} d + 4 \, B a b^{2} c d^{2} - 2 \, B a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{6} c^{4} d - 4 \, a b^{5} c^{3} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} - 4 \, a^{3} b^{3} c d^{4} + a^{4} b^{2} d^{5}\right)} g^{3} i^{2} x^{3} + {\left(b^{6} c^{5} - 2 \, a b^{5} c^{4} d - 2 \, a^{2} b^{4} c^{3} d^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} - 7 \, a^{4} b^{2} c d^{4} + 2 \, a^{5} b d^{5}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{5} c^{5} - 7 \, a^{2} b^{4} c^{4} d + 8 \, a^{3} b^{3} c^{3} d^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} - 2 \, a^{5} b c d^{4} + a^{6} d^{5}\right)} g^{3} i^{2} x + {\left(a^{2} b^{4} c^{5} - 4 \, a^{3} b^{3} c^{4} d + 6 \, a^{4} b^{2} c^{3} d^{2} - 4 \, a^{5} b c^{2} d^{3} + a^{6} c d^{4}\right)} g^{3} i^{2}\right)}}"," ",0,"-1/4*(2*A*b^3*c^3 - 12*A*a*b^2*c^2*d + 6*A*a^2*b*c*d^2 + 4*A*a^3*d^3 - 6*(2*A*b^3*c*d^2 - 2*A*a*b^2*d^3 + (B*b^3*c*d^2 - B*a*b^2*d^3)*n)*x^2 - 6*(B*b^3*d^3*n*x^3 + B*a^2*b*c*d^2*n + (B*b^3*c*d^2 + 2*B*a*b^2*d^3)*n*x^2 + (2*B*a*b^2*c*d^2 + B*a^2*b*d^3)*n*x)*log((b*x + a)/(d*x + c))^2 + (B*b^3*c^3 - 12*B*a*b^2*c^2*d + 15*B*a^2*b*c*d^2 - 4*B*a^3*d^3)*n - 3*(2*A*b^3*c^2*d + 4*A*a*b^2*c*d^2 - 6*A*a^2*b*d^3 + (3*B*b^3*c^2*d - 2*B*a*b^2*c*d^2 - B*a^2*b*d^3)*n)*x + 2*(B*b^3*c^3 - 6*B*a*b^2*c^2*d + 3*B*a^2*b*c*d^2 + 2*B*a^3*d^3 - 6*(B*b^3*c*d^2 - B*a*b^2*d^3)*x^2 - 3*(B*b^3*c^2*d + 2*B*a*b^2*c*d^2 - 3*B*a^2*b*d^3)*x - 6*(B*b^3*d^3*x^3 + B*a^2*b*c*d^2 + (B*b^3*c*d^2 + 2*B*a*b^2*d^3)*x^2 + (2*B*a*b^2*c*d^2 + B*a^2*b*d^3)*x)*log((b*x + a)/(d*x + c)))*log(e) - 2*(6*A*a^2*b*c*d^2 + 3*(B*b^3*d^3*n + 2*A*b^3*d^3)*x^3 + 3*(3*B*b^3*c*d^2*n + 2*A*b^3*c*d^2 + 4*A*a*b^2*d^3)*x^2 - (B*b^3*c^3 - 6*B*a*b^2*c^2*d + 2*B*a^3*d^3)*n + 3*(4*A*a*b^2*c*d^2 + 2*A*a^2*b*d^3 + (B*b^3*c^2*d + 4*B*a*b^2*c*d^2 - 2*B*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))/((b^6*c^4*d - 4*a*b^5*c^3*d^2 + 6*a^2*b^4*c^2*d^3 - 4*a^3*b^3*c*d^4 + a^4*b^2*d^5)*g^3*i^2*x^3 + (b^6*c^5 - 2*a*b^5*c^4*d - 2*a^2*b^4*c^3*d^2 + 8*a^3*b^3*c^2*d^3 - 7*a^4*b^2*c*d^4 + 2*a^5*b*d^5)*g^3*i^2*x^2 + (2*a*b^5*c^5 - 7*a^2*b^4*c^4*d + 8*a^3*b^3*c^3*d^2 - 2*a^4*b^2*c^2*d^3 - 2*a^5*b*c*d^4 + a^6*d^5)*g^3*i^2*x + (a^2*b^4*c^5 - 4*a^3*b^3*c^4*d + 6*a^4*b^2*c^3*d^2 - 4*a^5*b*c^2*d^3 + a^6*c*d^4)*g^3*i^2)","B",0
150,1,1458,0,0.541962," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{3 \, A b^{4} c^{4} - 18 \, A a b^{3} c^{3} d + 54 \, A a^{2} b^{2} c^{2} d^{2} - 30 \, A a^{3} b c d^{3} - 9 \, A a^{4} d^{4} + 6 \, {\left(6 \, A b^{4} c d^{3} - 6 \, A a b^{3} d^{4} + 5 \, {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} n\right)} x^{3} + 3 \, {\left(6 \, A b^{4} c^{2} d^{2} + 24 \, A a b^{3} c d^{3} - 30 \, A a^{2} b^{2} d^{4} + {\left(11 \, B b^{4} c^{2} d^{2} + 8 \, B a b^{3} c d^{3} - 19 \, B a^{2} b^{2} d^{4}\right)} n\right)} x^{2} + 18 \, {\left(B b^{4} d^{4} n x^{4} + B a^{3} b c d^{3} n + {\left(B b^{4} c d^{3} + 3 \, B a b^{3} d^{4}\right)} n x^{3} + 3 \, {\left(B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} n x^{2} + {\left(3 \, B a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B b^{4} c^{4} - 9 \, B a b^{3} c^{3} d + 54 \, B a^{2} b^{2} c^{2} d^{2} - 55 \, B a^{3} b c d^{3} + 9 \, B a^{4} d^{4}\right)} n - {\left(6 \, A b^{4} c^{3} d - 54 \, A a b^{3} c^{2} d^{2} - 18 \, A a^{2} b^{2} c d^{3} + 66 \, A a^{3} b d^{4} + {\left(5 \, B b^{4} c^{3} d - 81 \, B a b^{3} c^{2} d^{2} + 57 \, B a^{2} b^{2} c d^{3} + 19 \, B a^{3} b d^{4}\right)} n\right)} x + 3 \, {\left(B b^{4} c^{4} - 6 \, B a b^{3} c^{3} d + 18 \, B a^{2} b^{2} c^{2} d^{2} - 10 \, B a^{3} b c d^{3} - 3 \, B a^{4} d^{4} + 12 \, {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(B b^{4} c^{2} d^{2} + 4 \, B a b^{3} c d^{3} - 5 \, B a^{2} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(B b^{4} c^{3} d - 9 \, B a b^{3} c^{2} d^{2} - 3 \, B a^{2} b^{2} c d^{3} + 11 \, B a^{3} b d^{4}\right)} x + 12 \, {\left(B b^{4} d^{4} x^{4} + B a^{3} b c d^{3} + {\left(B b^{4} c d^{3} + 3 \, B a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, B a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 3 \, {\left(12 \, A a^{3} b c d^{3} + 2 \, {\left(5 \, B b^{4} d^{4} n + 6 \, A b^{4} d^{4}\right)} x^{4} + 2 \, {\left(6 \, A b^{4} c d^{3} + 18 \, A a b^{3} d^{4} + {\left(11 \, B b^{4} c d^{3} + 9 \, B a b^{3} d^{4}\right)} n\right)} x^{3} + 6 \, {\left(6 \, A a b^{3} c d^{3} + 6 \, A a^{2} b^{2} d^{4} + {\left(B b^{4} c^{2} d^{2} + 9 \, B a b^{3} c d^{3}\right)} n\right)} x^{2} + {\left(B b^{4} c^{4} - 6 \, B a b^{3} c^{3} d + 18 \, B a^{2} b^{2} c^{2} d^{2} - 3 \, B a^{4} d^{4}\right)} n + 2 \, {\left(18 \, A a^{2} b^{2} c d^{3} + 6 \, A a^{3} b d^{4} - {\left(B b^{4} c^{3} d - 9 \, B a b^{3} c^{2} d^{2} - 18 \, B a^{2} b^{2} c d^{3} + 6 \, B a^{3} b d^{4}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{9 \, {\left({\left(b^{8} c^{5} d - 5 \, a b^{7} c^{4} d^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} - 10 \, a^{3} b^{5} c^{2} d^{4} + 5 \, a^{4} b^{4} c d^{5} - a^{5} b^{3} d^{6}\right)} g^{4} i^{2} x^{4} + {\left(b^{8} c^{6} - 2 \, a b^{7} c^{5} d - 5 \, a^{2} b^{6} c^{4} d^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} - 25 \, a^{4} b^{4} c^{2} d^{4} + 14 \, a^{5} b^{3} c d^{5} - 3 \, a^{6} b^{2} d^{6}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{7} c^{6} - 4 \, a^{2} b^{6} c^{5} d + 5 \, a^{3} b^{5} c^{4} d^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} + 4 \, a^{6} b^{2} c d^{5} - a^{7} b d^{6}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} - 14 \, a^{3} b^{5} c^{5} d + 25 \, a^{4} b^{4} c^{4} d^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} + 5 \, a^{6} b^{2} c^{2} d^{4} + 2 \, a^{7} b c d^{5} - a^{8} d^{6}\right)} g^{4} i^{2} x + {\left(a^{3} b^{5} c^{6} - 5 \, a^{4} b^{4} c^{5} d + 10 \, a^{5} b^{3} c^{4} d^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} + 5 \, a^{7} b c^{2} d^{4} - a^{8} c d^{5}\right)} g^{4} i^{2}\right)}}"," ",0,"-1/9*(3*A*b^4*c^4 - 18*A*a*b^3*c^3*d + 54*A*a^2*b^2*c^2*d^2 - 30*A*a^3*b*c*d^3 - 9*A*a^4*d^4 + 6*(6*A*b^4*c*d^3 - 6*A*a*b^3*d^4 + 5*(B*b^4*c*d^3 - B*a*b^3*d^4)*n)*x^3 + 3*(6*A*b^4*c^2*d^2 + 24*A*a*b^3*c*d^3 - 30*A*a^2*b^2*d^4 + (11*B*b^4*c^2*d^2 + 8*B*a*b^3*c*d^3 - 19*B*a^2*b^2*d^4)*n)*x^2 + 18*(B*b^4*d^4*n*x^4 + B*a^3*b*c*d^3*n + (B*b^4*c*d^3 + 3*B*a*b^3*d^4)*n*x^3 + 3*(B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*n*x^2 + (3*B*a^2*b^2*c*d^3 + B*a^3*b*d^4)*n*x)*log((b*x + a)/(d*x + c))^2 + (B*b^4*c^4 - 9*B*a*b^3*c^3*d + 54*B*a^2*b^2*c^2*d^2 - 55*B*a^3*b*c*d^3 + 9*B*a^4*d^4)*n - (6*A*b^4*c^3*d - 54*A*a*b^3*c^2*d^2 - 18*A*a^2*b^2*c*d^3 + 66*A*a^3*b*d^4 + (5*B*b^4*c^3*d - 81*B*a*b^3*c^2*d^2 + 57*B*a^2*b^2*c*d^3 + 19*B*a^3*b*d^4)*n)*x + 3*(B*b^4*c^4 - 6*B*a*b^3*c^3*d + 18*B*a^2*b^2*c^2*d^2 - 10*B*a^3*b*c*d^3 - 3*B*a^4*d^4 + 12*(B*b^4*c*d^3 - B*a*b^3*d^4)*x^3 + 6*(B*b^4*c^2*d^2 + 4*B*a*b^3*c*d^3 - 5*B*a^2*b^2*d^4)*x^2 - 2*(B*b^4*c^3*d - 9*B*a*b^3*c^2*d^2 - 3*B*a^2*b^2*c*d^3 + 11*B*a^3*b*d^4)*x + 12*(B*b^4*d^4*x^4 + B*a^3*b*c*d^3 + (B*b^4*c*d^3 + 3*B*a*b^3*d^4)*x^3 + 3*(B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*x^2 + (3*B*a^2*b^2*c*d^3 + B*a^3*b*d^4)*x)*log((b*x + a)/(d*x + c)))*log(e) + 3*(12*A*a^3*b*c*d^3 + 2*(5*B*b^4*d^4*n + 6*A*b^4*d^4)*x^4 + 2*(6*A*b^4*c*d^3 + 18*A*a*b^3*d^4 + (11*B*b^4*c*d^3 + 9*B*a*b^3*d^4)*n)*x^3 + 6*(6*A*a*b^3*c*d^3 + 6*A*a^2*b^2*d^4 + (B*b^4*c^2*d^2 + 9*B*a*b^3*c*d^3)*n)*x^2 + (B*b^4*c^4 - 6*B*a*b^3*c^3*d + 18*B*a^2*b^2*c^2*d^2 - 3*B*a^4*d^4)*n + 2*(18*A*a^2*b^2*c*d^3 + 6*A*a^3*b*d^4 - (B*b^4*c^3*d - 9*B*a*b^3*c^2*d^2 - 18*B*a^2*b^2*c*d^3 + 6*B*a^3*b*d^4)*n)*x)*log((b*x + a)/(d*x + c)))/((b^8*c^5*d - 5*a*b^7*c^4*d^2 + 10*a^2*b^6*c^3*d^3 - 10*a^3*b^5*c^2*d^4 + 5*a^4*b^4*c*d^5 - a^5*b^3*d^6)*g^4*i^2*x^4 + (b^8*c^6 - 2*a*b^7*c^5*d - 5*a^2*b^6*c^4*d^2 + 20*a^3*b^5*c^3*d^3 - 25*a^4*b^4*c^2*d^4 + 14*a^5*b^3*c*d^5 - 3*a^6*b^2*d^6)*g^4*i^2*x^3 + 3*(a*b^7*c^6 - 4*a^2*b^6*c^5*d + 5*a^3*b^5*c^4*d^2 - 5*a^5*b^3*c^2*d^4 + 4*a^6*b^2*c*d^5 - a^7*b*d^6)*g^4*i^2*x^2 + (3*a^2*b^6*c^6 - 14*a^3*b^5*c^5*d + 25*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 5*a^6*b^2*c^2*d^4 + 2*a^7*b*c*d^5 - a^8*d^6)*g^4*i^2*x + (a^3*b^5*c^6 - 5*a^4*b^4*c^5*d + 10*a^5*b^3*c^4*d^2 - 10*a^6*b^2*c^3*d^3 + 5*a^7*b*c^2*d^4 - a^8*c*d^5)*g^4*i^2)","B",0
151,0,0,0,0.429044," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{3} g^{3} x^{3} + 3 \, A a b^{2} g^{3} x^{2} + 3 \, A a^{2} b g^{3} x + A a^{3} g^{3} + {\left(B b^{3} g^{3} x^{3} + 3 \, B a b^{2} g^{3} x^{2} + 3 \, B a^{2} b g^{3} x + B a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{3} i^{3} x^{3} + 3 \, c d^{2} i^{3} x^{2} + 3 \, c^{2} d i^{3} x + c^{3} i^{3}}, x\right)"," ",0,"integral((A*b^3*g^3*x^3 + 3*A*a*b^2*g^3*x^2 + 3*A*a^2*b*g^3*x + A*a^3*g^3 + (B*b^3*g^3*x^3 + 3*B*a*b^2*g^3*x^2 + 3*B*a^2*b*g^3*x + B*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n))/(d^3*i^3*x^3 + 3*c*d^2*i^3*x^2 + 3*c^2*d*i^3*x + c^3*i^3), x)","F",0
152,0,0,0,0.426848," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A b^{2} g^{2} x^{2} + 2 \, A a b g^{2} x + A a^{2} g^{2} + {\left(B b^{2} g^{2} x^{2} + 2 \, B a b g^{2} x + B a^{2} g^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{3} i^{3} x^{3} + 3 \, c d^{2} i^{3} x^{2} + 3 \, c^{2} d i^{3} x + c^{3} i^{3}}, x\right)"," ",0,"integral((A*b^2*g^2*x^2 + 2*A*a*b*g^2*x + A*a^2*g^2 + (B*b^2*g^2*x^2 + 2*B*a*b*g^2*x + B*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n))/(d^3*i^3*x^3 + 3*c*d^2*i^3*x^2 + 3*c^2*d*i^3*x + c^3*i^3), x)","F",0
153,1,250,0,0.470630," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^3,x, algorithm=""fricas"")","\frac{{\left(B b^{2} c^{2} - B a^{2} d^{2}\right)} g n - 2 \, {\left(A b^{2} c^{2} - A a^{2} d^{2}\right)} g + 2 \, {\left({\left(B b^{2} c d - B a b d^{2}\right)} g n - 2 \, {\left(A b^{2} c d - A a b d^{2}\right)} g\right)} x - 2 \, {\left(2 \, {\left(B b^{2} c d - B a b d^{2}\right)} g x + {\left(B b^{2} c^{2} - B a^{2} d^{2}\right)} g\right)} \log\left(e\right) + 2 \, {\left(B b^{2} d^{2} g n x^{2} + 2 \, B a b d^{2} g n x + B a^{2} d^{2} g n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}\right)}}"," ",0,"1/4*((B*b^2*c^2 - B*a^2*d^2)*g*n - 2*(A*b^2*c^2 - A*a^2*d^2)*g + 2*((B*b^2*c*d - B*a*b*d^2)*g*n - 2*(A*b^2*c*d - A*a*b*d^2)*g)*x - 2*(2*(B*b^2*c*d - B*a*b*d^2)*g*x + (B*b^2*c^2 - B*a^2*d^2)*g)*log(e) + 2*(B*b^2*d^2*g*n*x^2 + 2*B*a*b*d^2*g*n*x + B*a^2*d^2*g*n)*log((b*x + a)/(d*x + c)))/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3)","B",0
154,1,266,0,0.435033," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{2 \, A b^{2} c^{2} - 4 \, A a b c d + 2 \, A a^{2} d^{2} - 2 \, {\left(B b^{2} c d - B a b d^{2}\right)} n x - {\left(3 \, B b^{2} c^{2} - 4 \, B a b c d + B a^{2} d^{2}\right)} n + 2 \, {\left(B b^{2} c^{2} - 2 \, B a b c d + B a^{2} d^{2}\right)} \log\left(e\right) - 2 \, {\left(B b^{2} d^{2} n x^{2} + 2 \, B b^{2} c d n x + {\left(2 \, B a b c d - B a^{2} d^{2}\right)} n\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} i^{3} x + {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} i^{3}\right)}}"," ",0,"-1/4*(2*A*b^2*c^2 - 4*A*a*b*c*d + 2*A*a^2*d^2 - 2*(B*b^2*c*d - B*a*b*d^2)*n*x - (3*B*b^2*c^2 - 4*B*a*b*c*d + B*a^2*d^2)*n + 2*(B*b^2*c^2 - 2*B*a*b*c*d + B*a^2*d^2)*log(e) - 2*(B*b^2*d^2*n*x^2 + 2*B*b^2*c*d*n*x + (2*B*a*b*c*d - B*a^2*d^2)*n)*log((b*x + a)/(d*x + c)))/((b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*i^3*x^2 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*i^3*x + (b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*i^3)","A",0
155,1,487,0,0.452714," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)/(d*i*x+c*i)^3,x, algorithm=""fricas"")","\frac{6 \, A b^{2} c^{2} - 8 \, A a b c d + 2 \, A a^{2} d^{2} + 2 \, {\left(B b^{2} d^{2} n x^{2} + 2 \, B b^{2} c d n x + B b^{2} c^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - {\left(7 \, B b^{2} c^{2} - 8 \, B a b c d + B a^{2} d^{2}\right)} n + 2 \, {\left(2 \, A b^{2} c d - 2 \, A a b d^{2} - 3 \, {\left(B b^{2} c d - B a b d^{2}\right)} n\right)} x + 2 \, {\left(3 \, B b^{2} c^{2} - 4 \, B a b c d + B a^{2} d^{2} + 2 \, {\left(B b^{2} c d - B a b d^{2}\right)} x + 2 \, {\left(B b^{2} d^{2} x^{2} + 2 \, B b^{2} c d x + B b^{2} c^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left(2 \, A b^{2} c^{2} - {\left(3 \, B b^{2} d^{2} n - 2 \, A b^{2} d^{2}\right)} x^{2} - {\left(4 \, B a b c d - B a^{2} d^{2}\right)} n + 2 \, {\left(2 \, A b^{2} c d - {\left(2 \, B b^{2} c d + B a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} g i^{3} x^{2} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} g i^{3} x + {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} g i^{3}\right)}}"," ",0,"1/4*(6*A*b^2*c^2 - 8*A*a*b*c*d + 2*A*a^2*d^2 + 2*(B*b^2*d^2*n*x^2 + 2*B*b^2*c*d*n*x + B*b^2*c^2*n)*log((b*x + a)/(d*x + c))^2 - (7*B*b^2*c^2 - 8*B*a*b*c*d + B*a^2*d^2)*n + 2*(2*A*b^2*c*d - 2*A*a*b*d^2 - 3*(B*b^2*c*d - B*a*b*d^2)*n)*x + 2*(3*B*b^2*c^2 - 4*B*a*b*c*d + B*a^2*d^2 + 2*(B*b^2*c*d - B*a*b*d^2)*x + 2*(B*b^2*d^2*x^2 + 2*B*b^2*c*d*x + B*b^2*c^2)*log((b*x + a)/(d*x + c)))*log(e) + 2*(2*A*b^2*c^2 - (3*B*b^2*d^2*n - 2*A*b^2*d^2)*x^2 - (4*B*a*b*c*d - B*a^2*d^2)*n + 2*(2*A*b^2*c*d - (2*B*b^2*c*d + B*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))/((b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*g*i^3*x^2 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*g*i^3*x + (b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*g*i^3)","A",0
156,1,949,0,0.473073," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{4 \, A b^{3} c^{3} + 6 \, A a b^{2} c^{2} d - 12 \, A a^{2} b c d^{2} + 2 \, A a^{3} d^{3} + 6 \, {\left(2 \, A b^{3} c d^{2} - 2 \, A a b^{2} d^{3} - {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} n\right)} x^{2} + 6 \, {\left(B b^{3} d^{3} n x^{3} + B a b^{2} c^{2} d n + {\left(2 \, B b^{3} c d^{2} + B a b^{2} d^{3}\right)} n x^{2} + {\left(B b^{3} c^{2} d + 2 \, B a b^{2} c d^{2}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(4 \, B b^{3} c^{3} - 15 \, B a b^{2} c^{2} d + 12 \, B a^{2} b c d^{2} - B a^{3} d^{3}\right)} n + 3 \, {\left(6 \, A b^{3} c^{2} d - 4 \, A a b^{2} c d^{2} - 2 \, A a^{2} b d^{3} - {\left(B b^{3} c^{2} d + 2 \, B a b^{2} c d^{2} - 3 \, B a^{2} b d^{3}\right)} n\right)} x + 2 \, {\left(2 \, B b^{3} c^{3} + 3 \, B a b^{2} c^{2} d - 6 \, B a^{2} b c d^{2} + B a^{3} d^{3} + 6 \, {\left(B b^{3} c d^{2} - B a b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, B b^{3} c^{2} d - 2 \, B a b^{2} c d^{2} - B a^{2} b d^{3}\right)} x + 6 \, {\left(B b^{3} d^{3} x^{3} + B a b^{2} c^{2} d + {\left(2 \, B b^{3} c d^{2} + B a b^{2} d^{3}\right)} x^{2} + {\left(B b^{3} c^{2} d + 2 \, B a b^{2} c d^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left(6 \, A a b^{2} c^{2} d - 3 \, {\left(B b^{3} d^{3} n - 2 \, A b^{3} d^{3}\right)} x^{3} - 3 \, {\left(3 \, B a b^{2} d^{3} n - 4 \, A b^{3} c d^{2} - 2 \, A a b^{2} d^{3}\right)} x^{2} + {\left(2 \, B b^{3} c^{3} - 6 \, B a^{2} b c d^{2} + B a^{3} d^{3}\right)} n + 3 \, {\left(2 \, A b^{3} c^{2} d + 4 \, A a b^{2} c d^{2} + {\left(2 \, B b^{3} c^{2} d - 4 \, B a b^{2} c d^{2} - B a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} g^{2} i^{3} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} g^{2} i^{3} x + {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4}\right)} g^{2} i^{3}\right)}}"," ",0,"-1/4*(4*A*b^3*c^3 + 6*A*a*b^2*c^2*d - 12*A*a^2*b*c*d^2 + 2*A*a^3*d^3 + 6*(2*A*b^3*c*d^2 - 2*A*a*b^2*d^3 - (B*b^3*c*d^2 - B*a*b^2*d^3)*n)*x^2 + 6*(B*b^3*d^3*n*x^3 + B*a*b^2*c^2*d*n + (2*B*b^3*c*d^2 + B*a*b^2*d^3)*n*x^2 + (B*b^3*c^2*d + 2*B*a*b^2*c*d^2)*n*x)*log((b*x + a)/(d*x + c))^2 + (4*B*b^3*c^3 - 15*B*a*b^2*c^2*d + 12*B*a^2*b*c*d^2 - B*a^3*d^3)*n + 3*(6*A*b^3*c^2*d - 4*A*a*b^2*c*d^2 - 2*A*a^2*b*d^3 - (B*b^3*c^2*d + 2*B*a*b^2*c*d^2 - 3*B*a^2*b*d^3)*n)*x + 2*(2*B*b^3*c^3 + 3*B*a*b^2*c^2*d - 6*B*a^2*b*c*d^2 + B*a^3*d^3 + 6*(B*b^3*c*d^2 - B*a*b^2*d^3)*x^2 + 3*(3*B*b^3*c^2*d - 2*B*a*b^2*c*d^2 - B*a^2*b*d^3)*x + 6*(B*b^3*d^3*x^3 + B*a*b^2*c^2*d + (2*B*b^3*c*d^2 + B*a*b^2*d^3)*x^2 + (B*b^3*c^2*d + 2*B*a*b^2*c*d^2)*x)*log((b*x + a)/(d*x + c)))*log(e) + 2*(6*A*a*b^2*c^2*d - 3*(B*b^3*d^3*n - 2*A*b^3*d^3)*x^3 - 3*(3*B*a*b^2*d^3*n - 4*A*b^3*c*d^2 - 2*A*a*b^2*d^3)*x^2 + (2*B*b^3*c^3 - 6*B*a^2*b*c*d^2 + B*a^3*d^3)*n + 3*(2*A*b^3*c^2*d + 4*A*a*b^2*c*d^2 + (2*B*b^3*c^2*d - 4*B*a*b^2*c*d^2 - B*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))/((b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*g^2*i^3*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*g^2*i^3*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*g^2*i^3*x + (a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4)*g^2*i^3)","B",0
157,1,1416,0,0.525464," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^3/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{2 \, A b^{4} c^{4} - 16 \, A a b^{3} c^{3} d + 16 \, A a^{3} b c d^{3} - 2 \, A a^{4} d^{4} - 24 \, {\left(A b^{4} c d^{3} - A a b^{3} d^{4}\right)} x^{3} - 12 \, {\left(3 \, A b^{4} c^{2} d^{2} - 3 \, A a^{2} b^{2} d^{4} + {\left(B b^{4} c^{2} d^{2} - 2 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} n\right)} x^{2} - 12 \, {\left(B b^{4} d^{4} n x^{4} + B a^{2} b^{2} c^{2} d^{2} n + 2 \, {\left(B b^{4} c d^{3} + B a b^{3} d^{4}\right)} n x^{3} + {\left(B b^{4} c^{2} d^{2} + 4 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} n x^{2} + 2 \, {\left(B a b^{3} c^{2} d^{2} + B a^{2} b^{2} c d^{3}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B b^{4} c^{4} - 16 \, B a b^{3} c^{3} d + 30 \, B a^{2} b^{2} c^{2} d^{2} - 16 \, B a^{3} b c d^{3} + B a^{4} d^{4}\right)} n - 4 \, {\left(2 \, A b^{4} c^{3} d + 12 \, A a b^{3} c^{2} d^{2} - 12 \, A a^{2} b^{2} c d^{3} - 2 \, A a^{3} b d^{4} + 3 \, {\left(B b^{4} c^{3} d - B a b^{3} c^{2} d^{2} - B a^{2} b^{2} c d^{3} + B a^{3} b d^{4}\right)} n\right)} x + 2 \, {\left(B b^{4} c^{4} - 8 \, B a b^{3} c^{3} d + 8 \, B a^{3} b c d^{3} - B a^{4} d^{4} - 12 \, {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} x^{3} - 18 \, {\left(B b^{4} c^{2} d^{2} - B a^{2} b^{2} d^{4}\right)} x^{2} - 4 \, {\left(B b^{4} c^{3} d + 6 \, B a b^{3} c^{2} d^{2} - 6 \, B a^{2} b^{2} c d^{3} - B a^{3} b d^{4}\right)} x - 12 \, {\left(B b^{4} d^{4} x^{4} + B a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(B b^{4} c d^{3} + B a b^{3} d^{4}\right)} x^{3} + {\left(B b^{4} c^{2} d^{2} + 4 \, B a b^{3} c d^{3} + B a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(B a b^{3} c^{2} d^{2} + B a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) - 2 \, {\left(12 \, A b^{4} d^{4} x^{4} + 12 \, A a^{2} b^{2} c^{2} d^{2} + 12 \, {\left(2 \, A b^{4} c d^{3} + 2 \, A a b^{3} d^{4} + {\left(B b^{4} c d^{3} - B a b^{3} d^{4}\right)} n\right)} x^{3} + 6 \, {\left(2 \, A b^{4} c^{2} d^{2} + 8 \, A a b^{3} c d^{3} + 2 \, A a^{2} b^{2} d^{4} + 3 \, {\left(B b^{4} c^{2} d^{2} - B a^{2} b^{2} d^{4}\right)} n\right)} x^{2} - {\left(B b^{4} c^{4} - 8 \, B a b^{3} c^{3} d + 8 \, B a^{3} b c d^{3} - B a^{4} d^{4}\right)} n + 4 \, {\left(6 \, A a b^{3} c^{2} d^{2} + 6 \, A a^{2} b^{2} c d^{3} + {\left(B b^{4} c^{3} d + 6 \, B a b^{3} c^{2} d^{2} - 6 \, B a^{2} b^{2} c d^{3} - B a^{3} b d^{4}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} g^{3} i^{3} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} g^{3} i^{3} x + {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5}\right)} g^{3} i^{3}\right)}}"," ",0,"-1/4*(2*A*b^4*c^4 - 16*A*a*b^3*c^3*d + 16*A*a^3*b*c*d^3 - 2*A*a^4*d^4 - 24*(A*b^4*c*d^3 - A*a*b^3*d^4)*x^3 - 12*(3*A*b^4*c^2*d^2 - 3*A*a^2*b^2*d^4 + (B*b^4*c^2*d^2 - 2*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*n)*x^2 - 12*(B*b^4*d^4*n*x^4 + B*a^2*b^2*c^2*d^2*n + 2*(B*b^4*c*d^3 + B*a*b^3*d^4)*n*x^3 + (B*b^4*c^2*d^2 + 4*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*n*x^2 + 2*(B*a*b^3*c^2*d^2 + B*a^2*b^2*c*d^3)*n*x)*log((b*x + a)/(d*x + c))^2 + (B*b^4*c^4 - 16*B*a*b^3*c^3*d + 30*B*a^2*b^2*c^2*d^2 - 16*B*a^3*b*c*d^3 + B*a^4*d^4)*n - 4*(2*A*b^4*c^3*d + 12*A*a*b^3*c^2*d^2 - 12*A*a^2*b^2*c*d^3 - 2*A*a^3*b*d^4 + 3*(B*b^4*c^3*d - B*a*b^3*c^2*d^2 - B*a^2*b^2*c*d^3 + B*a^3*b*d^4)*n)*x + 2*(B*b^4*c^4 - 8*B*a*b^3*c^3*d + 8*B*a^3*b*c*d^3 - B*a^4*d^4 - 12*(B*b^4*c*d^3 - B*a*b^3*d^4)*x^3 - 18*(B*b^4*c^2*d^2 - B*a^2*b^2*d^4)*x^2 - 4*(B*b^4*c^3*d + 6*B*a*b^3*c^2*d^2 - 6*B*a^2*b^2*c*d^3 - B*a^3*b*d^4)*x - 12*(B*b^4*d^4*x^4 + B*a^2*b^2*c^2*d^2 + 2*(B*b^4*c*d^3 + B*a*b^3*d^4)*x^3 + (B*b^4*c^2*d^2 + 4*B*a*b^3*c*d^3 + B*a^2*b^2*d^4)*x^2 + 2*(B*a*b^3*c^2*d^2 + B*a^2*b^2*c*d^3)*x)*log((b*x + a)/(d*x + c)))*log(e) - 2*(12*A*b^4*d^4*x^4 + 12*A*a^2*b^2*c^2*d^2 + 12*(2*A*b^4*c*d^3 + 2*A*a*b^3*d^4 + (B*b^4*c*d^3 - B*a*b^3*d^4)*n)*x^3 + 6*(2*A*b^4*c^2*d^2 + 8*A*a*b^3*c*d^3 + 2*A*a^2*b^2*d^4 + 3*(B*b^4*c^2*d^2 - B*a^2*b^2*d^4)*n)*x^2 - (B*b^4*c^4 - 8*B*a*b^3*c^3*d + 8*B*a^3*b*c*d^3 - B*a^4*d^4)*n + 4*(6*A*a*b^3*c^2*d^2 + 6*A*a^2*b^2*c*d^3 + (B*b^4*c^3*d + 6*B*a*b^3*c^2*d^2 - 6*B*a^2*b^2*c*d^3 - B*a^3*b*d^4)*n)*x)*log((b*x + a)/(d*x + c)))/((b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*g^3*i^3*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*g^3*i^3*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*g^3*i^3*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*g^3*i^3*x + (a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5)*g^3*i^3)","B",0
158,1,2181,0,0.544458," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))/(b*g*x+a*g)^4/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{12 \, A b^{5} c^{5} - 90 \, A a b^{4} c^{4} d + 360 \, A a^{2} b^{3} c^{3} d^{2} - 120 \, A a^{3} b^{2} c^{2} d^{3} - 180 \, A a^{4} b c d^{4} + 18 \, A a^{5} d^{5} + 120 \, {\left(3 \, A b^{5} c d^{4} - 3 \, A a b^{4} d^{5} + {\left(B b^{5} c d^{4} - B a b^{4} d^{5}\right)} n\right)} x^{4} + 60 \, {\left(9 \, A b^{5} c^{2} d^{3} + 6 \, A a b^{4} c d^{4} - 15 \, A a^{2} b^{3} d^{5} + 2 \, {\left(3 \, B b^{5} c^{2} d^{3} - 2 \, B a b^{4} c d^{4} - B a^{2} b^{3} d^{5}\right)} n\right)} x^{3} + 20 \, {\left(6 \, A b^{5} c^{3} d^{2} + 63 \, A a b^{4} c^{2} d^{3} - 36 \, A a^{2} b^{3} c d^{4} - 33 \, A a^{3} b^{2} d^{5} + {\left(11 \, B b^{5} c^{3} d^{2} + 21 \, B a b^{4} c^{2} d^{3} - 39 \, B a^{2} b^{3} c d^{4} + 7 \, B a^{3} b^{2} d^{5}\right)} n\right)} x^{2} + 180 \, {\left(B b^{5} d^{5} n x^{5} + B a^{3} b^{2} c^{2} d^{3} n + {\left(2 \, B b^{5} c d^{4} + 3 \, B a b^{4} d^{5}\right)} n x^{4} + {\left(B b^{5} c^{2} d^{3} + 6 \, B a b^{4} c d^{4} + 3 \, B a^{2} b^{3} d^{5}\right)} n x^{3} + {\left(3 \, B a b^{4} c^{2} d^{3} + 6 \, B a^{2} b^{3} c d^{4} + B a^{3} b^{2} d^{5}\right)} n x^{2} + {\left(3 \, B a^{2} b^{3} c^{2} d^{3} + 2 \, B a^{3} b^{2} c d^{4}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(4 \, B b^{5} c^{5} - 45 \, B a b^{4} c^{4} d + 360 \, B a^{2} b^{3} c^{3} d^{2} - 490 \, B a^{3} b^{2} c^{2} d^{3} + 180 \, B a^{4} b c d^{4} - 9 \, B a^{5} d^{5}\right)} n - 5 \, {\left(6 \, A b^{5} c^{4} d - 72 \, A a b^{4} c^{3} d^{2} - 144 \, A a^{2} b^{3} c^{2} d^{3} + 192 \, A a^{3} b^{2} c d^{4} + 18 \, A a^{4} b d^{5} + {\left(5 \, B b^{5} c^{4} d - 108 \, B a b^{4} c^{3} d^{2} + 78 \, B a^{2} b^{3} c^{2} d^{3} + 52 \, B a^{3} b^{2} c d^{4} - 27 \, B a^{4} b d^{5}\right)} n\right)} x + 6 \, {\left(2 \, B b^{5} c^{5} - 15 \, B a b^{4} c^{4} d + 60 \, B a^{2} b^{3} c^{3} d^{2} - 20 \, B a^{3} b^{2} c^{2} d^{3} - 30 \, B a^{4} b c d^{4} + 3 \, B a^{5} d^{5} + 60 \, {\left(B b^{5} c d^{4} - B a b^{4} d^{5}\right)} x^{4} + 30 \, {\left(3 \, B b^{5} c^{2} d^{3} + 2 \, B a b^{4} c d^{4} - 5 \, B a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(2 \, B b^{5} c^{3} d^{2} + 21 \, B a b^{4} c^{2} d^{3} - 12 \, B a^{2} b^{3} c d^{4} - 11 \, B a^{3} b^{2} d^{5}\right)} x^{2} - 5 \, {\left(B b^{5} c^{4} d - 12 \, B a b^{4} c^{3} d^{2} - 24 \, B a^{2} b^{3} c^{2} d^{3} + 32 \, B a^{3} b^{2} c d^{4} + 3 \, B a^{4} b d^{5}\right)} x + 60 \, {\left(B b^{5} d^{5} x^{5} + B a^{3} b^{2} c^{2} d^{3} + {\left(2 \, B b^{5} c d^{4} + 3 \, B a b^{4} d^{5}\right)} x^{4} + {\left(B b^{5} c^{2} d^{3} + 6 \, B a b^{4} c d^{4} + 3 \, B a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, B a b^{4} c^{2} d^{3} + 6 \, B a^{2} b^{3} c d^{4} + B a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, B a^{2} b^{3} c^{2} d^{3} + 2 \, B a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left(60 \, A a^{3} b^{2} c^{2} d^{3} + 20 \, {\left(B b^{5} d^{5} n + 3 \, A b^{5} d^{5}\right)} x^{5} + 20 \, {\left(5 \, B b^{5} c d^{4} n + 6 \, A b^{5} c d^{4} + 9 \, A a b^{4} d^{5}\right)} x^{4} + 10 \, {\left(6 \, A b^{5} c^{2} d^{3} + 36 \, A a b^{4} c d^{4} + 18 \, A a^{2} b^{3} d^{5} + {\left(11 \, B b^{5} c^{2} d^{3} + 18 \, B a b^{4} c d^{4} - 9 \, B a^{2} b^{3} d^{5}\right)} n\right)} x^{3} + 10 \, {\left(18 \, A a b^{4} c^{2} d^{3} + 36 \, A a^{2} b^{3} c d^{4} + 6 \, A a^{3} b^{2} d^{5} + {\left(2 \, B b^{5} c^{3} d^{2} + 27 \, B a b^{4} c^{2} d^{3} - 9 \, B a^{3} b^{2} d^{5}\right)} n\right)} x^{2} + {\left(2 \, B b^{5} c^{5} - 15 \, B a b^{4} c^{4} d + 60 \, B a^{2} b^{3} c^{3} d^{2} - 30 \, B a^{4} b c d^{4} + 3 \, B a^{5} d^{5}\right)} n + 5 \, {\left(36 \, A a^{2} b^{3} c^{2} d^{3} + 24 \, A a^{3} b^{2} c d^{4} - {\left(B b^{5} c^{4} d - 12 \, B a b^{4} c^{3} d^{2} - 36 \, B a^{2} b^{3} c^{2} d^{3} + 24 \, B a^{3} b^{2} c d^{4} + 3 \, B a^{4} b d^{5}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{36 \, {\left({\left(b^{9} c^{6} d^{2} - 6 \, a b^{8} c^{5} d^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} - 20 \, a^{3} b^{6} c^{3} d^{5} + 15 \, a^{4} b^{5} c^{2} d^{6} - 6 \, a^{5} b^{4} c d^{7} + a^{6} b^{3} d^{8}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{9} c^{7} d - 9 \, a b^{8} c^{6} d^{2} + 12 \, a^{2} b^{7} c^{5} d^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} - 30 \, a^{4} b^{5} c^{3} d^{5} + 33 \, a^{5} b^{4} c^{2} d^{6} - 16 \, a^{6} b^{3} c d^{7} + 3 \, a^{7} b^{2} d^{8}\right)} g^{4} i^{3} x^{4} + {\left(b^{9} c^{8} - 18 \, a^{2} b^{7} c^{6} d^{2} + 52 \, a^{3} b^{6} c^{5} d^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} + 24 \, a^{5} b^{4} c^{3} d^{5} + 10 \, a^{6} b^{3} c^{2} d^{6} - 12 \, a^{7} b^{2} c d^{7} + 3 \, a^{8} b d^{8}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{8} c^{8} - 12 \, a^{2} b^{7} c^{7} d + 10 \, a^{3} b^{6} c^{6} d^{2} + 24 \, a^{4} b^{5} c^{5} d^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} + 52 \, a^{6} b^{3} c^{3} d^{5} - 18 \, a^{7} b^{2} c^{2} d^{6} + a^{9} d^{8}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} - 16 \, a^{3} b^{6} c^{7} d + 33 \, a^{4} b^{5} c^{6} d^{2} - 30 \, a^{5} b^{4} c^{5} d^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} + 12 \, a^{7} b^{2} c^{3} d^{5} - 9 \, a^{8} b c^{2} d^{6} + 2 \, a^{9} c d^{7}\right)} g^{4} i^{3} x + {\left(a^{3} b^{6} c^{8} - 6 \, a^{4} b^{5} c^{7} d + 15 \, a^{5} b^{4} c^{6} d^{2} - 20 \, a^{6} b^{3} c^{5} d^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} - 6 \, a^{8} b c^{3} d^{5} + a^{9} c^{2} d^{6}\right)} g^{4} i^{3}\right)}}"," ",0,"-1/36*(12*A*b^5*c^5 - 90*A*a*b^4*c^4*d + 360*A*a^2*b^3*c^3*d^2 - 120*A*a^3*b^2*c^2*d^3 - 180*A*a^4*b*c*d^4 + 18*A*a^5*d^5 + 120*(3*A*b^5*c*d^4 - 3*A*a*b^4*d^5 + (B*b^5*c*d^4 - B*a*b^4*d^5)*n)*x^4 + 60*(9*A*b^5*c^2*d^3 + 6*A*a*b^4*c*d^4 - 15*A*a^2*b^3*d^5 + 2*(3*B*b^5*c^2*d^3 - 2*B*a*b^4*c*d^4 - B*a^2*b^3*d^5)*n)*x^3 + 20*(6*A*b^5*c^3*d^2 + 63*A*a*b^4*c^2*d^3 - 36*A*a^2*b^3*c*d^4 - 33*A*a^3*b^2*d^5 + (11*B*b^5*c^3*d^2 + 21*B*a*b^4*c^2*d^3 - 39*B*a^2*b^3*c*d^4 + 7*B*a^3*b^2*d^5)*n)*x^2 + 180*(B*b^5*d^5*n*x^5 + B*a^3*b^2*c^2*d^3*n + (2*B*b^5*c*d^4 + 3*B*a*b^4*d^5)*n*x^4 + (B*b^5*c^2*d^3 + 6*B*a*b^4*c*d^4 + 3*B*a^2*b^3*d^5)*n*x^3 + (3*B*a*b^4*c^2*d^3 + 6*B*a^2*b^3*c*d^4 + B*a^3*b^2*d^5)*n*x^2 + (3*B*a^2*b^3*c^2*d^3 + 2*B*a^3*b^2*c*d^4)*n*x)*log((b*x + a)/(d*x + c))^2 + (4*B*b^5*c^5 - 45*B*a*b^4*c^4*d + 360*B*a^2*b^3*c^3*d^2 - 490*B*a^3*b^2*c^2*d^3 + 180*B*a^4*b*c*d^4 - 9*B*a^5*d^5)*n - 5*(6*A*b^5*c^4*d - 72*A*a*b^4*c^3*d^2 - 144*A*a^2*b^3*c^2*d^3 + 192*A*a^3*b^2*c*d^4 + 18*A*a^4*b*d^5 + (5*B*b^5*c^4*d - 108*B*a*b^4*c^3*d^2 + 78*B*a^2*b^3*c^2*d^3 + 52*B*a^3*b^2*c*d^4 - 27*B*a^4*b*d^5)*n)*x + 6*(2*B*b^5*c^5 - 15*B*a*b^4*c^4*d + 60*B*a^2*b^3*c^3*d^2 - 20*B*a^3*b^2*c^2*d^3 - 30*B*a^4*b*c*d^4 + 3*B*a^5*d^5 + 60*(B*b^5*c*d^4 - B*a*b^4*d^5)*x^4 + 30*(3*B*b^5*c^2*d^3 + 2*B*a*b^4*c*d^4 - 5*B*a^2*b^3*d^5)*x^3 + 10*(2*B*b^5*c^3*d^2 + 21*B*a*b^4*c^2*d^3 - 12*B*a^2*b^3*c*d^4 - 11*B*a^3*b^2*d^5)*x^2 - 5*(B*b^5*c^4*d - 12*B*a*b^4*c^3*d^2 - 24*B*a^2*b^3*c^2*d^3 + 32*B*a^3*b^2*c*d^4 + 3*B*a^4*b*d^5)*x + 60*(B*b^5*d^5*x^5 + B*a^3*b^2*c^2*d^3 + (2*B*b^5*c*d^4 + 3*B*a*b^4*d^5)*x^4 + (B*b^5*c^2*d^3 + 6*B*a*b^4*c*d^4 + 3*B*a^2*b^3*d^5)*x^3 + (3*B*a*b^4*c^2*d^3 + 6*B*a^2*b^3*c*d^4 + B*a^3*b^2*d^5)*x^2 + (3*B*a^2*b^3*c^2*d^3 + 2*B*a^3*b^2*c*d^4)*x)*log((b*x + a)/(d*x + c)))*log(e) + 6*(60*A*a^3*b^2*c^2*d^3 + 20*(B*b^5*d^5*n + 3*A*b^5*d^5)*x^5 + 20*(5*B*b^5*c*d^4*n + 6*A*b^5*c*d^4 + 9*A*a*b^4*d^5)*x^4 + 10*(6*A*b^5*c^2*d^3 + 36*A*a*b^4*c*d^4 + 18*A*a^2*b^3*d^5 + (11*B*b^5*c^2*d^3 + 18*B*a*b^4*c*d^4 - 9*B*a^2*b^3*d^5)*n)*x^3 + 10*(18*A*a*b^4*c^2*d^3 + 36*A*a^2*b^3*c*d^4 + 6*A*a^3*b^2*d^5 + (2*B*b^5*c^3*d^2 + 27*B*a*b^4*c^2*d^3 - 9*B*a^3*b^2*d^5)*n)*x^2 + (2*B*b^5*c^5 - 15*B*a*b^4*c^4*d + 60*B*a^2*b^3*c^3*d^2 - 30*B*a^4*b*c*d^4 + 3*B*a^5*d^5)*n + 5*(36*A*a^2*b^3*c^2*d^3 + 24*A*a^3*b^2*c*d^4 - (B*b^5*c^4*d - 12*B*a*b^4*c^3*d^2 - 36*B*a^2*b^3*c^2*d^3 + 24*B*a^3*b^2*c*d^4 + 3*B*a^4*b*d^5)*n)*x)*log((b*x + a)/(d*x + c)))/((b^9*c^6*d^2 - 6*a*b^8*c^5*d^3 + 15*a^2*b^7*c^4*d^4 - 20*a^3*b^6*c^3*d^5 + 15*a^4*b^5*c^2*d^6 - 6*a^5*b^4*c*d^7 + a^6*b^3*d^8)*g^4*i^3*x^5 + (2*b^9*c^7*d - 9*a*b^8*c^6*d^2 + 12*a^2*b^7*c^5*d^3 + 5*a^3*b^6*c^4*d^4 - 30*a^4*b^5*c^3*d^5 + 33*a^5*b^4*c^2*d^6 - 16*a^6*b^3*c*d^7 + 3*a^7*b^2*d^8)*g^4*i^3*x^4 + (b^9*c^8 - 18*a^2*b^7*c^6*d^2 + 52*a^3*b^6*c^5*d^3 - 60*a^4*b^5*c^4*d^4 + 24*a^5*b^4*c^3*d^5 + 10*a^6*b^3*c^2*d^6 - 12*a^7*b^2*c*d^7 + 3*a^8*b*d^8)*g^4*i^3*x^3 + (3*a*b^8*c^8 - 12*a^2*b^7*c^7*d + 10*a^3*b^6*c^6*d^2 + 24*a^4*b^5*c^5*d^3 - 60*a^5*b^4*c^4*d^4 + 52*a^6*b^3*c^3*d^5 - 18*a^7*b^2*c^2*d^6 + a^9*d^8)*g^4*i^3*x^2 + (3*a^2*b^7*c^8 - 16*a^3*b^6*c^7*d + 33*a^4*b^5*c^6*d^2 - 30*a^5*b^4*c^5*d^3 + 5*a^6*b^3*c^4*d^4 + 12*a^7*b^2*c^3*d^5 - 9*a^8*b*c^2*d^6 + 2*a^9*c*d^7)*g^4*i^3*x + (a^3*b^6*c^8 - 6*a^4*b^5*c^7*d + 15*a^5*b^4*c^6*d^2 - 20*a^6*b^3*c^5*d^3 + 15*a^7*b^2*c^4*d^4 - 6*a^8*b*c^3*d^5 + a^9*c^2*d^6)*g^4*i^3)","B",0
159,0,0,0,0.458037," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{3} d g^{3} i x^{4} + A^{2} a^{3} c g^{3} i + {\left(A^{2} b^{3} c + 3 \, A^{2} a b^{2} d\right)} g^{3} i x^{3} + 3 \, {\left(A^{2} a b^{2} c + A^{2} a^{2} b d\right)} g^{3} i x^{2} + {\left(3 \, A^{2} a^{2} b c + A^{2} a^{3} d\right)} g^{3} i x + {\left(B^{2} b^{3} d g^{3} i x^{4} + B^{2} a^{3} c g^{3} i + {\left(B^{2} b^{3} c + 3 \, B^{2} a b^{2} d\right)} g^{3} i x^{3} + 3 \, {\left(B^{2} a b^{2} c + B^{2} a^{2} b d\right)} g^{3} i x^{2} + {\left(3 \, B^{2} a^{2} b c + B^{2} a^{3} d\right)} g^{3} i x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{3} d g^{3} i x^{4} + A B a^{3} c g^{3} i + {\left(A B b^{3} c + 3 \, A B a b^{2} d\right)} g^{3} i x^{3} + 3 \, {\left(A B a b^{2} c + A B a^{2} b d\right)} g^{3} i x^{2} + {\left(3 \, A B a^{2} b c + A B a^{3} d\right)} g^{3} i x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b^3*d*g^3*i*x^4 + A^2*a^3*c*g^3*i + (A^2*b^3*c + 3*A^2*a*b^2*d)*g^3*i*x^3 + 3*(A^2*a*b^2*c + A^2*a^2*b*d)*g^3*i*x^2 + (3*A^2*a^2*b*c + A^2*a^3*d)*g^3*i*x + (B^2*b^3*d*g^3*i*x^4 + B^2*a^3*c*g^3*i + (B^2*b^3*c + 3*B^2*a*b^2*d)*g^3*i*x^3 + 3*(B^2*a*b^2*c + B^2*a^2*b*d)*g^3*i*x^2 + (3*B^2*a^2*b*c + B^2*a^3*d)*g^3*i*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^3*d*g^3*i*x^4 + A*B*a^3*c*g^3*i + (A*B*b^3*c + 3*A*B*a*b^2*d)*g^3*i*x^3 + 3*(A*B*a*b^2*c + A*B*a^2*b*d)*g^3*i*x^2 + (3*A*B*a^2*b*c + A*B*a^3*d)*g^3*i*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
160,0,0,0,0.452201," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{2} d g^{2} i x^{3} + A^{2} a^{2} c g^{2} i + {\left(A^{2} b^{2} c + 2 \, A^{2} a b d\right)} g^{2} i x^{2} + {\left(2 \, A^{2} a b c + A^{2} a^{2} d\right)} g^{2} i x + {\left(B^{2} b^{2} d g^{2} i x^{3} + B^{2} a^{2} c g^{2} i + {\left(B^{2} b^{2} c + 2 \, B^{2} a b d\right)} g^{2} i x^{2} + {\left(2 \, B^{2} a b c + B^{2} a^{2} d\right)} g^{2} i x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{2} d g^{2} i x^{3} + A B a^{2} c g^{2} i + {\left(A B b^{2} c + 2 \, A B a b d\right)} g^{2} i x^{2} + {\left(2 \, A B a b c + A B a^{2} d\right)} g^{2} i x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b^2*d*g^2*i*x^3 + A^2*a^2*c*g^2*i + (A^2*b^2*c + 2*A^2*a*b*d)*g^2*i*x^2 + (2*A^2*a*b*c + A^2*a^2*d)*g^2*i*x + (B^2*b^2*d*g^2*i*x^3 + B^2*a^2*c*g^2*i + (B^2*b^2*c + 2*B^2*a*b*d)*g^2*i*x^2 + (2*B^2*a*b*c + B^2*a^2*d)*g^2*i*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^2*d*g^2*i*x^3 + A*B*a^2*c*g^2*i + (A*B*b^2*c + 2*A*B*a*b*d)*g^2*i*x^2 + (2*A*B*a*b*c + A*B*a^2*d)*g^2*i*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
161,0,0,0,0.441108," ","integrate((b*g*x+a*g)*(d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b d g i x^{2} + A^{2} a c g i + {\left(A^{2} b c + A^{2} a d\right)} g i x + {\left(B^{2} b d g i x^{2} + B^{2} a c g i + {\left(B^{2} b c + B^{2} a d\right)} g i x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b d g i x^{2} + A B a c g i + {\left(A B b c + A B a d\right)} g i x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b*d*g*i*x^2 + A^2*a*c*g*i + (A^2*b*c + A^2*a*d)*g*i*x + (B^2*b*d*g*i*x^2 + B^2*a*c*g*i + (B^2*b*c + B^2*a*d)*g*i*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b*d*g*i*x^2 + A*B*a*c*g*i + (A*B*b*c + A*B*a*d)*g*i*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
162,0,0,0,0.445711," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} d i x + A^{2} c i + {\left(B^{2} d i x + B^{2} c i\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d i x + A B c i\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*d*i*x + A^2*c*i + (B^2*d*i*x + B^2*c*i)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d*i*x + A*B*c*i)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
163,0,0,0,0.425500," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d i x + A^{2} c i + {\left(B^{2} d i x + B^{2} c i\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d i x + A B c i\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b g x + a g}, x\right)"," ",0,"integral((A^2*d*i*x + A^2*c*i + (B^2*d*i*x + B^2*c*i)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d*i*x + A*B*c*i)*log(e*((b*x + a)/(d*x + c))^n))/(b*g*x + a*g), x)","F",0
164,0,0,0,0.423891," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d i x + A^{2} c i + {\left(B^{2} d i x + B^{2} c i\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d i x + A B c i\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A^2*d*i*x + A^2*c*i + (B^2*d*i*x + B^2*c*i)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d*i*x + A*B*c*i)*log(e*((b*x + a)/(d*x + c))^n))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
165,1,600,0,0.451501," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3,x, algorithm=""fricas"")","-\frac{{\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} i n^{2} + 2 \, {\left(A B b^{2} c^{2} - A B a^{2} d^{2}\right)} i n + 2 \, {\left(2 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} i x + {\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} i\right)} \log\left(e\right)^{2} + 2 \, {\left(B^{2} b^{2} d^{2} i n^{2} x^{2} + 2 \, B^{2} b^{2} c d i n^{2} x + B^{2} b^{2} c^{2} i n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(A^{2} b^{2} c^{2} - A^{2} a^{2} d^{2}\right)} i + 2 \, {\left({\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} i n^{2} + 2 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} i n + 2 \, {\left(A^{2} b^{2} c d - A^{2} a b d^{2}\right)} i\right)} x + 2 \, {\left({\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} i n + 2 \, {\left(A B b^{2} c^{2} - A B a^{2} d^{2}\right)} i + 2 \, {\left({\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} i n + 2 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} i\right)} x + 2 \, {\left(B^{2} b^{2} d^{2} i n x^{2} + 2 \, B^{2} b^{2} c d i n x + B^{2} b^{2} c^{2} i n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left(B^{2} b^{2} c^{2} i n^{2} + 2 \, A B b^{2} c^{2} i n + {\left(B^{2} b^{2} d^{2} i n^{2} + 2 \, A B b^{2} d^{2} i n\right)} x^{2} + 2 \, {\left(B^{2} b^{2} c d i n^{2} + 2 \, A B b^{2} c d i n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{5} c - a b^{4} d\right)} g^{3} x^{2} + 2 \, {\left(a b^{4} c - a^{2} b^{3} d\right)} g^{3} x + {\left(a^{2} b^{3} c - a^{3} b^{2} d\right)} g^{3}\right)}}"," ",0,"-1/4*((B^2*b^2*c^2 - B^2*a^2*d^2)*i*n^2 + 2*(A*B*b^2*c^2 - A*B*a^2*d^2)*i*n + 2*(2*(B^2*b^2*c*d - B^2*a*b*d^2)*i*x + (B^2*b^2*c^2 - B^2*a^2*d^2)*i)*log(e)^2 + 2*(B^2*b^2*d^2*i*n^2*x^2 + 2*B^2*b^2*c*d*i*n^2*x + B^2*b^2*c^2*i*n^2)*log((b*x + a)/(d*x + c))^2 + 2*(A^2*b^2*c^2 - A^2*a^2*d^2)*i + 2*((B^2*b^2*c*d - B^2*a*b*d^2)*i*n^2 + 2*(A*B*b^2*c*d - A*B*a*b*d^2)*i*n + 2*(A^2*b^2*c*d - A^2*a*b*d^2)*i)*x + 2*((B^2*b^2*c^2 - B^2*a^2*d^2)*i*n + 2*(A*B*b^2*c^2 - A*B*a^2*d^2)*i + 2*((B^2*b^2*c*d - B^2*a*b*d^2)*i*n + 2*(A*B*b^2*c*d - A*B*a*b*d^2)*i)*x + 2*(B^2*b^2*d^2*i*n*x^2 + 2*B^2*b^2*c*d*i*n*x + B^2*b^2*c^2*i*n)*log((b*x + a)/(d*x + c)))*log(e) + 2*(B^2*b^2*c^2*i*n^2 + 2*A*B*b^2*c^2*i*n + (B^2*b^2*d^2*i*n^2 + 2*A*B*b^2*d^2*i*n)*x^2 + 2*(B^2*b^2*c*d*i*n^2 + 2*A*B*b^2*c*d*i*n)*x)*log((b*x + a)/(d*x + c)))/((b^5*c - a*b^4*d)*g^3*x^2 + 2*(a*b^4*c - a^2*b^3*d)*g^3*x + (a^2*b^3*c - a^3*b^2*d)*g^3)","B",0
166,1,1167,0,0.487669," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4,x, algorithm=""fricas"")","-\frac{{\left(8 \, B^{2} b^{3} c^{3} - 27 \, B^{2} a b^{2} c^{2} d + 19 \, B^{2} a^{3} d^{3}\right)} i n^{2} + 6 \, {\left(4 \, A B b^{3} c^{3} - 9 \, A B a b^{2} c^{2} d + 5 \, A B a^{3} d^{3}\right)} i n - 6 \, {\left(5 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} i n^{2} + 6 \, {\left(A B b^{3} c d^{2} - A B a b^{2} d^{3}\right)} i n\right)} x^{2} + 18 \, {\left(3 \, {\left(B^{2} b^{3} c^{2} d - 2 \, B^{2} a b^{2} c d^{2} + B^{2} a^{2} b d^{3}\right)} i x + {\left(2 \, B^{2} b^{3} c^{3} - 3 \, B^{2} a b^{2} c^{2} d + B^{2} a^{3} d^{3}\right)} i\right)} \log\left(e\right)^{2} - 18 \, {\left(B^{2} b^{3} d^{3} i n^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} i n^{2} x^{2} - 3 \, {\left(B^{2} b^{3} c^{2} d - 2 \, B^{2} a b^{2} c d^{2}\right)} i n^{2} x - {\left(2 \, B^{2} b^{3} c^{3} - 3 \, B^{2} a b^{2} c^{2} d\right)} i n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 18 \, {\left(2 \, A^{2} b^{3} c^{3} - 3 \, A^{2} a b^{2} c^{2} d + A^{2} a^{3} d^{3}\right)} i - 3 \, {\left({\left(B^{2} b^{3} c^{2} d + 18 \, B^{2} a b^{2} c d^{2} - 19 \, B^{2} a^{2} b d^{3}\right)} i n^{2} - 6 \, {\left(A B b^{3} c^{2} d - 6 \, A B a b^{2} c d^{2} + 5 \, A B a^{2} b d^{3}\right)} i n - 18 \, {\left(A^{2} b^{3} c^{2} d - 2 \, A^{2} a b^{2} c d^{2} + A^{2} a^{2} b d^{3}\right)} i\right)} x - 6 \, {\left(6 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} i n x^{2} - {\left(4 \, B^{2} b^{3} c^{3} - 9 \, B^{2} a b^{2} c^{2} d + 5 \, B^{2} a^{3} d^{3}\right)} i n - 6 \, {\left(2 \, A B b^{3} c^{3} - 3 \, A B a b^{2} c^{2} d + A B a^{3} d^{3}\right)} i - 3 \, {\left({\left(B^{2} b^{3} c^{2} d - 6 \, B^{2} a b^{2} c d^{2} + 5 \, B^{2} a^{2} b d^{3}\right)} i n + 6 \, {\left(A B b^{3} c^{2} d - 2 \, A B a b^{2} c d^{2} + A B a^{2} b d^{3}\right)} i\right)} x + 6 \, {\left(B^{2} b^{3} d^{3} i n x^{3} + 3 \, B^{2} a b^{2} d^{3} i n x^{2} - 3 \, {\left(B^{2} b^{3} c^{2} d - 2 \, B^{2} a b^{2} c d^{2}\right)} i n x - {\left(2 \, B^{2} b^{3} c^{3} - 3 \, B^{2} a b^{2} c^{2} d\right)} i n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left({\left(4 \, B^{2} b^{3} c^{3} - 9 \, B^{2} a b^{2} c^{2} d\right)} i n^{2} - {\left(5 \, B^{2} b^{3} d^{3} i n^{2} + 6 \, A B b^{3} d^{3} i n\right)} x^{3} + 6 \, {\left(2 \, A B b^{3} c^{3} - 3 \, A B a b^{2} c^{2} d\right)} i n - 3 \, {\left(6 \, A B a b^{2} d^{3} i n + {\left(2 \, B^{2} b^{3} c d^{2} + 3 \, B^{2} a b^{2} d^{3}\right)} i n^{2}\right)} x^{2} + 3 \, {\left({\left(B^{2} b^{3} c^{2} d - 6 \, B^{2} a b^{2} c d^{2}\right)} i n^{2} + 6 \, {\left(A B b^{3} c^{2} d - 2 \, A B a b^{2} c d^{2}\right)} i n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{108 \, {\left({\left(b^{7} c^{2} - 2 \, a b^{6} c d + a^{2} b^{5} d^{2}\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c^{2} - 2 \, a^{2} b^{5} c d + a^{3} b^{4} d^{2}\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c^{2} - 2 \, a^{3} b^{4} c d + a^{4} b^{3} d^{2}\right)} g^{4} x + {\left(a^{3} b^{4} c^{2} - 2 \, a^{4} b^{3} c d + a^{5} b^{2} d^{2}\right)} g^{4}\right)}}"," ",0,"-1/108*((8*B^2*b^3*c^3 - 27*B^2*a*b^2*c^2*d + 19*B^2*a^3*d^3)*i*n^2 + 6*(4*A*B*b^3*c^3 - 9*A*B*a*b^2*c^2*d + 5*A*B*a^3*d^3)*i*n - 6*(5*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*i*n^2 + 6*(A*B*b^3*c*d^2 - A*B*a*b^2*d^3)*i*n)*x^2 + 18*(3*(B^2*b^3*c^2*d - 2*B^2*a*b^2*c*d^2 + B^2*a^2*b*d^3)*i*x + (2*B^2*b^3*c^3 - 3*B^2*a*b^2*c^2*d + B^2*a^3*d^3)*i)*log(e)^2 - 18*(B^2*b^3*d^3*i*n^2*x^3 + 3*B^2*a*b^2*d^3*i*n^2*x^2 - 3*(B^2*b^3*c^2*d - 2*B^2*a*b^2*c*d^2)*i*n^2*x - (2*B^2*b^3*c^3 - 3*B^2*a*b^2*c^2*d)*i*n^2)*log((b*x + a)/(d*x + c))^2 + 18*(2*A^2*b^3*c^3 - 3*A^2*a*b^2*c^2*d + A^2*a^3*d^3)*i - 3*((B^2*b^3*c^2*d + 18*B^2*a*b^2*c*d^2 - 19*B^2*a^2*b*d^3)*i*n^2 - 6*(A*B*b^3*c^2*d - 6*A*B*a*b^2*c*d^2 + 5*A*B*a^2*b*d^3)*i*n - 18*(A^2*b^3*c^2*d - 2*A^2*a*b^2*c*d^2 + A^2*a^2*b*d^3)*i)*x - 6*(6*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*i*n*x^2 - (4*B^2*b^3*c^3 - 9*B^2*a*b^2*c^2*d + 5*B^2*a^3*d^3)*i*n - 6*(2*A*B*b^3*c^3 - 3*A*B*a*b^2*c^2*d + A*B*a^3*d^3)*i - 3*((B^2*b^3*c^2*d - 6*B^2*a*b^2*c*d^2 + 5*B^2*a^2*b*d^3)*i*n + 6*(A*B*b^3*c^2*d - 2*A*B*a*b^2*c*d^2 + A*B*a^2*b*d^3)*i)*x + 6*(B^2*b^3*d^3*i*n*x^3 + 3*B^2*a*b^2*d^3*i*n*x^2 - 3*(B^2*b^3*c^2*d - 2*B^2*a*b^2*c*d^2)*i*n*x - (2*B^2*b^3*c^3 - 3*B^2*a*b^2*c^2*d)*i*n)*log((b*x + a)/(d*x + c)))*log(e) + 6*((4*B^2*b^3*c^3 - 9*B^2*a*b^2*c^2*d)*i*n^2 - (5*B^2*b^3*d^3*i*n^2 + 6*A*B*b^3*d^3*i*n)*x^3 + 6*(2*A*B*b^3*c^3 - 3*A*B*a*b^2*c^2*d)*i*n - 3*(6*A*B*a*b^2*d^3*i*n + (2*B^2*b^3*c*d^2 + 3*B^2*a*b^2*d^3)*i*n^2)*x^2 + 3*((B^2*b^3*c^2*d - 6*B^2*a*b^2*c*d^2)*i*n^2 + 6*(A*B*b^3*c^2*d - 2*A*B*a*b^2*c*d^2)*i*n)*x)*log((b*x + a)/(d*x + c)))/((b^7*c^2 - 2*a*b^6*c*d + a^2*b^5*d^2)*g^4*x^3 + 3*(a*b^6*c^2 - 2*a^2*b^5*c*d + a^3*b^4*d^2)*g^4*x^2 + 3*(a^2*b^5*c^2 - 2*a^3*b^4*c*d + a^4*b^3*d^2)*g^4*x + (a^3*b^4*c^2 - 2*a^4*b^3*c*d + a^5*b^2*d^2)*g^4)","B",0
167,1,1868,0,0.537557," ","integrate((d*i*x+c*i)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^5,x, algorithm=""fricas"")","-\frac{{\left(27 \, B^{2} b^{4} c^{4} - 128 \, B^{2} a b^{3} c^{3} d + 216 \, B^{2} a^{2} b^{2} c^{2} d^{2} - 115 \, B^{2} a^{4} d^{4}\right)} i n^{2} + 12 \, {\left(13 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} i n^{2} + 12 \, {\left(A B b^{4} c d^{3} - A B a b^{3} d^{4}\right)} i n\right)} x^{3} + 12 \, {\left(9 \, A B b^{4} c^{4} - 32 \, A B a b^{3} c^{3} d + 36 \, A B a^{2} b^{2} c^{2} d^{2} - 13 \, A B a^{4} d^{4}\right)} i n - 6 \, {\left({\left(B^{2} b^{4} c^{2} d^{2} - 80 \, B^{2} a b^{3} c d^{3} + 79 \, B^{2} a^{2} b^{2} d^{4}\right)} i n^{2} + 12 \, {\left(A B b^{4} c^{2} d^{2} - 8 \, A B a b^{3} c d^{3} + 7 \, A B a^{2} b^{2} d^{4}\right)} i n\right)} x^{2} + 72 \, {\left(4 \, {\left(B^{2} b^{4} c^{3} d - 3 \, B^{2} a b^{3} c^{2} d^{2} + 3 \, B^{2} a^{2} b^{2} c d^{3} - B^{2} a^{3} b d^{4}\right)} i x + {\left(3 \, B^{2} b^{4} c^{4} - 8 \, B^{2} a b^{3} c^{3} d + 6 \, B^{2} a^{2} b^{2} c^{2} d^{2} - B^{2} a^{4} d^{4}\right)} i\right)} \log\left(e\right)^{2} + 72 \, {\left(B^{2} b^{4} d^{4} i n^{2} x^{4} + 4 \, B^{2} a b^{3} d^{4} i n^{2} x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} i n^{2} x^{2} + 4 \, {\left(B^{2} b^{4} c^{3} d - 3 \, B^{2} a b^{3} c^{2} d^{2} + 3 \, B^{2} a^{2} b^{2} c d^{3}\right)} i n^{2} x + {\left(3 \, B^{2} b^{4} c^{4} - 8 \, B^{2} a b^{3} c^{3} d + 6 \, B^{2} a^{2} b^{2} c^{2} d^{2}\right)} i n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 72 \, {\left(3 \, A^{2} b^{4} c^{4} - 8 \, A^{2} a b^{3} c^{3} d + 6 \, A^{2} a^{2} b^{2} c^{2} d^{2} - A^{2} a^{4} d^{4}\right)} i - 4 \, {\left({\left(5 \, B^{2} b^{4} c^{3} d - 12 \, B^{2} a b^{3} c^{2} d^{2} - 108 \, B^{2} a^{2} b^{2} c d^{3} + 115 \, B^{2} a^{3} b d^{4}\right)} i n^{2} - 12 \, {\left(A B b^{4} c^{3} d - 6 \, A B a b^{3} c^{2} d^{2} + 18 \, A B a^{2} b^{2} c d^{3} - 13 \, A B a^{3} b d^{4}\right)} i n - 72 \, {\left(A^{2} b^{4} c^{3} d - 3 \, A^{2} a b^{3} c^{2} d^{2} + 3 \, A^{2} a^{2} b^{2} c d^{3} - A^{2} a^{3} b d^{4}\right)} i\right)} x + 12 \, {\left(12 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} i n x^{3} - 6 \, {\left(B^{2} b^{4} c^{2} d^{2} - 8 \, B^{2} a b^{3} c d^{3} + 7 \, B^{2} a^{2} b^{2} d^{4}\right)} i n x^{2} + {\left(9 \, B^{2} b^{4} c^{4} - 32 \, B^{2} a b^{3} c^{3} d + 36 \, B^{2} a^{2} b^{2} c^{2} d^{2} - 13 \, B^{2} a^{4} d^{4}\right)} i n + 12 \, {\left(3 \, A B b^{4} c^{4} - 8 \, A B a b^{3} c^{3} d + 6 \, A B a^{2} b^{2} c^{2} d^{2} - A B a^{4} d^{4}\right)} i + 4 \, {\left({\left(B^{2} b^{4} c^{3} d - 6 \, B^{2} a b^{3} c^{2} d^{2} + 18 \, B^{2} a^{2} b^{2} c d^{3} - 13 \, B^{2} a^{3} b d^{4}\right)} i n + 12 \, {\left(A B b^{4} c^{3} d - 3 \, A B a b^{3} c^{2} d^{2} + 3 \, A B a^{2} b^{2} c d^{3} - A B a^{3} b d^{4}\right)} i\right)} x + 12 \, {\left(B^{2} b^{4} d^{4} i n x^{4} + 4 \, B^{2} a b^{3} d^{4} i n x^{3} + 6 \, B^{2} a^{2} b^{2} d^{4} i n x^{2} + 4 \, {\left(B^{2} b^{4} c^{3} d - 3 \, B^{2} a b^{3} c^{2} d^{2} + 3 \, B^{2} a^{2} b^{2} c d^{3}\right)} i n x + {\left(3 \, B^{2} b^{4} c^{4} - 8 \, B^{2} a b^{3} c^{3} d + 6 \, B^{2} a^{2} b^{2} c^{2} d^{2}\right)} i n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 12 \, {\left({\left(13 \, B^{2} b^{4} d^{4} i n^{2} + 12 \, A B b^{4} d^{4} i n\right)} x^{4} + {\left(9 \, B^{2} b^{4} c^{4} - 32 \, B^{2} a b^{3} c^{3} d + 36 \, B^{2} a^{2} b^{2} c^{2} d^{2}\right)} i n^{2} + 4 \, {\left(12 \, A B a b^{3} d^{4} i n + {\left(3 \, B^{2} b^{4} c d^{3} + 10 \, B^{2} a b^{3} d^{4}\right)} i n^{2}\right)} x^{3} + 12 \, {\left(3 \, A B b^{4} c^{4} - 8 \, A B a b^{3} c^{3} d + 6 \, A B a^{2} b^{2} c^{2} d^{2}\right)} i n + 6 \, {\left(12 \, A B a^{2} b^{2} d^{4} i n - {\left(B^{2} b^{4} c^{2} d^{2} - 8 \, B^{2} a b^{3} c d^{3} - 6 \, B^{2} a^{2} b^{2} d^{4}\right)} i n^{2}\right)} x^{2} + 4 \, {\left({\left(B^{2} b^{4} c^{3} d - 6 \, B^{2} a b^{3} c^{2} d^{2} + 18 \, B^{2} a^{2} b^{2} c d^{3}\right)} i n^{2} + 12 \, {\left(A B b^{4} c^{3} d - 3 \, A B a b^{3} c^{2} d^{2} + 3 \, A B a^{2} b^{2} c d^{3}\right)} i n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{864 \, {\left({\left(b^{9} c^{3} - 3 \, a b^{8} c^{2} d + 3 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{3} - 3 \, a^{2} b^{7} c^{2} d + 3 \, a^{3} b^{6} c d^{2} - a^{4} b^{5} d^{3}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{3} - 3 \, a^{3} b^{6} c^{2} d + 3 \, a^{4} b^{5} c d^{2} - a^{5} b^{4} d^{3}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{3} - 3 \, a^{4} b^{5} c^{2} d + 3 \, a^{5} b^{4} c d^{2} - a^{6} b^{3} d^{3}\right)} g^{5} x + {\left(a^{4} b^{5} c^{3} - 3 \, a^{5} b^{4} c^{2} d + 3 \, a^{6} b^{3} c d^{2} - a^{7} b^{2} d^{3}\right)} g^{5}\right)}}"," ",0,"-1/864*((27*B^2*b^4*c^4 - 128*B^2*a*b^3*c^3*d + 216*B^2*a^2*b^2*c^2*d^2 - 115*B^2*a^4*d^4)*i*n^2 + 12*(13*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*i*n^2 + 12*(A*B*b^4*c*d^3 - A*B*a*b^3*d^4)*i*n)*x^3 + 12*(9*A*B*b^4*c^4 - 32*A*B*a*b^3*c^3*d + 36*A*B*a^2*b^2*c^2*d^2 - 13*A*B*a^4*d^4)*i*n - 6*((B^2*b^4*c^2*d^2 - 80*B^2*a*b^3*c*d^3 + 79*B^2*a^2*b^2*d^4)*i*n^2 + 12*(A*B*b^4*c^2*d^2 - 8*A*B*a*b^3*c*d^3 + 7*A*B*a^2*b^2*d^4)*i*n)*x^2 + 72*(4*(B^2*b^4*c^3*d - 3*B^2*a*b^3*c^2*d^2 + 3*B^2*a^2*b^2*c*d^3 - B^2*a^3*b*d^4)*i*x + (3*B^2*b^4*c^4 - 8*B^2*a*b^3*c^3*d + 6*B^2*a^2*b^2*c^2*d^2 - B^2*a^4*d^4)*i)*log(e)^2 + 72*(B^2*b^4*d^4*i*n^2*x^4 + 4*B^2*a*b^3*d^4*i*n^2*x^3 + 6*B^2*a^2*b^2*d^4*i*n^2*x^2 + 4*(B^2*b^4*c^3*d - 3*B^2*a*b^3*c^2*d^2 + 3*B^2*a^2*b^2*c*d^3)*i*n^2*x + (3*B^2*b^4*c^4 - 8*B^2*a*b^3*c^3*d + 6*B^2*a^2*b^2*c^2*d^2)*i*n^2)*log((b*x + a)/(d*x + c))^2 + 72*(3*A^2*b^4*c^4 - 8*A^2*a*b^3*c^3*d + 6*A^2*a^2*b^2*c^2*d^2 - A^2*a^4*d^4)*i - 4*((5*B^2*b^4*c^3*d - 12*B^2*a*b^3*c^2*d^2 - 108*B^2*a^2*b^2*c*d^3 + 115*B^2*a^3*b*d^4)*i*n^2 - 12*(A*B*b^4*c^3*d - 6*A*B*a*b^3*c^2*d^2 + 18*A*B*a^2*b^2*c*d^3 - 13*A*B*a^3*b*d^4)*i*n - 72*(A^2*b^4*c^3*d - 3*A^2*a*b^3*c^2*d^2 + 3*A^2*a^2*b^2*c*d^3 - A^2*a^3*b*d^4)*i)*x + 12*(12*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*i*n*x^3 - 6*(B^2*b^4*c^2*d^2 - 8*B^2*a*b^3*c*d^3 + 7*B^2*a^2*b^2*d^4)*i*n*x^2 + (9*B^2*b^4*c^4 - 32*B^2*a*b^3*c^3*d + 36*B^2*a^2*b^2*c^2*d^2 - 13*B^2*a^4*d^4)*i*n + 12*(3*A*B*b^4*c^4 - 8*A*B*a*b^3*c^3*d + 6*A*B*a^2*b^2*c^2*d^2 - A*B*a^4*d^4)*i + 4*((B^2*b^4*c^3*d - 6*B^2*a*b^3*c^2*d^2 + 18*B^2*a^2*b^2*c*d^3 - 13*B^2*a^3*b*d^4)*i*n + 12*(A*B*b^4*c^3*d - 3*A*B*a*b^3*c^2*d^2 + 3*A*B*a^2*b^2*c*d^3 - A*B*a^3*b*d^4)*i)*x + 12*(B^2*b^4*d^4*i*n*x^4 + 4*B^2*a*b^3*d^4*i*n*x^3 + 6*B^2*a^2*b^2*d^4*i*n*x^2 + 4*(B^2*b^4*c^3*d - 3*B^2*a*b^3*c^2*d^2 + 3*B^2*a^2*b^2*c*d^3)*i*n*x + (3*B^2*b^4*c^4 - 8*B^2*a*b^3*c^3*d + 6*B^2*a^2*b^2*c^2*d^2)*i*n)*log((b*x + a)/(d*x + c)))*log(e) + 12*((13*B^2*b^4*d^4*i*n^2 + 12*A*B*b^4*d^4*i*n)*x^4 + (9*B^2*b^4*c^4 - 32*B^2*a*b^3*c^3*d + 36*B^2*a^2*b^2*c^2*d^2)*i*n^2 + 4*(12*A*B*a*b^3*d^4*i*n + (3*B^2*b^4*c*d^3 + 10*B^2*a*b^3*d^4)*i*n^2)*x^3 + 12*(3*A*B*b^4*c^4 - 8*A*B*a*b^3*c^3*d + 6*A*B*a^2*b^2*c^2*d^2)*i*n + 6*(12*A*B*a^2*b^2*d^4*i*n - (B^2*b^4*c^2*d^2 - 8*B^2*a*b^3*c*d^3 - 6*B^2*a^2*b^2*d^4)*i*n^2)*x^2 + 4*((B^2*b^4*c^3*d - 6*B^2*a*b^3*c^2*d^2 + 18*B^2*a^2*b^2*c*d^3)*i*n^2 + 12*(A*B*b^4*c^3*d - 3*A*B*a*b^3*c^2*d^2 + 3*A*B*a^2*b^2*c*d^3)*i*n)*x)*log((b*x + a)/(d*x + c)))/((b^9*c^3 - 3*a*b^8*c^2*d + 3*a^2*b^7*c*d^2 - a^3*b^6*d^3)*g^5*x^4 + 4*(a*b^8*c^3 - 3*a^2*b^7*c^2*d + 3*a^3*b^6*c*d^2 - a^4*b^5*d^3)*g^5*x^3 + 6*(a^2*b^7*c^3 - 3*a^3*b^6*c^2*d + 3*a^4*b^5*c*d^2 - a^5*b^4*d^3)*g^5*x^2 + 4*(a^3*b^6*c^3 - 3*a^4*b^5*c^2*d + 3*a^5*b^4*c*d^2 - a^6*b^3*d^3)*g^5*x + (a^4*b^5*c^3 - 3*a^5*b^4*c^2*d + 3*a^6*b^3*c*d^2 - a^7*b^2*d^3)*g^5)","B",0
168,0,0,0,0.482004," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{3} d^{2} g^{3} i^{2} x^{5} + A^{2} a^{3} c^{2} g^{3} i^{2} + {\left(2 \, A^{2} b^{3} c d + 3 \, A^{2} a b^{2} d^{2}\right)} g^{3} i^{2} x^{4} + {\left(A^{2} b^{3} c^{2} + 6 \, A^{2} a b^{2} c d + 3 \, A^{2} a^{2} b d^{2}\right)} g^{3} i^{2} x^{3} + {\left(3 \, A^{2} a b^{2} c^{2} + 6 \, A^{2} a^{2} b c d + A^{2} a^{3} d^{2}\right)} g^{3} i^{2} x^{2} + {\left(3 \, A^{2} a^{2} b c^{2} + 2 \, A^{2} a^{3} c d\right)} g^{3} i^{2} x + {\left(B^{2} b^{3} d^{2} g^{3} i^{2} x^{5} + B^{2} a^{3} c^{2} g^{3} i^{2} + {\left(2 \, B^{2} b^{3} c d + 3 \, B^{2} a b^{2} d^{2}\right)} g^{3} i^{2} x^{4} + {\left(B^{2} b^{3} c^{2} + 6 \, B^{2} a b^{2} c d + 3 \, B^{2} a^{2} b d^{2}\right)} g^{3} i^{2} x^{3} + {\left(3 \, B^{2} a b^{2} c^{2} + 6 \, B^{2} a^{2} b c d + B^{2} a^{3} d^{2}\right)} g^{3} i^{2} x^{2} + {\left(3 \, B^{2} a^{2} b c^{2} + 2 \, B^{2} a^{3} c d\right)} g^{3} i^{2} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{3} d^{2} g^{3} i^{2} x^{5} + A B a^{3} c^{2} g^{3} i^{2} + {\left(2 \, A B b^{3} c d + 3 \, A B a b^{2} d^{2}\right)} g^{3} i^{2} x^{4} + {\left(A B b^{3} c^{2} + 6 \, A B a b^{2} c d + 3 \, A B a^{2} b d^{2}\right)} g^{3} i^{2} x^{3} + {\left(3 \, A B a b^{2} c^{2} + 6 \, A B a^{2} b c d + A B a^{3} d^{2}\right)} g^{3} i^{2} x^{2} + {\left(3 \, A B a^{2} b c^{2} + 2 \, A B a^{3} c d\right)} g^{3} i^{2} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b^3*d^2*g^3*i^2*x^5 + A^2*a^3*c^2*g^3*i^2 + (2*A^2*b^3*c*d + 3*A^2*a*b^2*d^2)*g^3*i^2*x^4 + (A^2*b^3*c^2 + 6*A^2*a*b^2*c*d + 3*A^2*a^2*b*d^2)*g^3*i^2*x^3 + (3*A^2*a*b^2*c^2 + 6*A^2*a^2*b*c*d + A^2*a^3*d^2)*g^3*i^2*x^2 + (3*A^2*a^2*b*c^2 + 2*A^2*a^3*c*d)*g^3*i^2*x + (B^2*b^3*d^2*g^3*i^2*x^5 + B^2*a^3*c^2*g^3*i^2 + (2*B^2*b^3*c*d + 3*B^2*a*b^2*d^2)*g^3*i^2*x^4 + (B^2*b^3*c^2 + 6*B^2*a*b^2*c*d + 3*B^2*a^2*b*d^2)*g^3*i^2*x^3 + (3*B^2*a*b^2*c^2 + 6*B^2*a^2*b*c*d + B^2*a^3*d^2)*g^3*i^2*x^2 + (3*B^2*a^2*b*c^2 + 2*B^2*a^3*c*d)*g^3*i^2*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^3*d^2*g^3*i^2*x^5 + A*B*a^3*c^2*g^3*i^2 + (2*A*B*b^3*c*d + 3*A*B*a*b^2*d^2)*g^3*i^2*x^4 + (A*B*b^3*c^2 + 6*A*B*a*b^2*c*d + 3*A*B*a^2*b*d^2)*g^3*i^2*x^3 + (3*A*B*a*b^2*c^2 + 6*A*B*a^2*b*c*d + A*B*a^3*d^2)*g^3*i^2*x^2 + (3*A*B*a^2*b*c^2 + 2*A*B*a^3*c*d)*g^3*i^2*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
169,0,0,0,0.487888," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{2} d^{2} g^{2} i^{2} x^{4} + A^{2} a^{2} c^{2} g^{2} i^{2} + 2 \, {\left(A^{2} b^{2} c d + A^{2} a b d^{2}\right)} g^{2} i^{2} x^{3} + {\left(A^{2} b^{2} c^{2} + 4 \, A^{2} a b c d + A^{2} a^{2} d^{2}\right)} g^{2} i^{2} x^{2} + 2 \, {\left(A^{2} a b c^{2} + A^{2} a^{2} c d\right)} g^{2} i^{2} x + {\left(B^{2} b^{2} d^{2} g^{2} i^{2} x^{4} + B^{2} a^{2} c^{2} g^{2} i^{2} + 2 \, {\left(B^{2} b^{2} c d + B^{2} a b d^{2}\right)} g^{2} i^{2} x^{3} + {\left(B^{2} b^{2} c^{2} + 4 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right)} g^{2} i^{2} x^{2} + 2 \, {\left(B^{2} a b c^{2} + B^{2} a^{2} c d\right)} g^{2} i^{2} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{2} d^{2} g^{2} i^{2} x^{4} + A B a^{2} c^{2} g^{2} i^{2} + 2 \, {\left(A B b^{2} c d + A B a b d^{2}\right)} g^{2} i^{2} x^{3} + {\left(A B b^{2} c^{2} + 4 \, A B a b c d + A B a^{2} d^{2}\right)} g^{2} i^{2} x^{2} + 2 \, {\left(A B a b c^{2} + A B a^{2} c d\right)} g^{2} i^{2} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b^2*d^2*g^2*i^2*x^4 + A^2*a^2*c^2*g^2*i^2 + 2*(A^2*b^2*c*d + A^2*a*b*d^2)*g^2*i^2*x^3 + (A^2*b^2*c^2 + 4*A^2*a*b*c*d + A^2*a^2*d^2)*g^2*i^2*x^2 + 2*(A^2*a*b*c^2 + A^2*a^2*c*d)*g^2*i^2*x + (B^2*b^2*d^2*g^2*i^2*x^4 + B^2*a^2*c^2*g^2*i^2 + 2*(B^2*b^2*c*d + B^2*a*b*d^2)*g^2*i^2*x^3 + (B^2*b^2*c^2 + 4*B^2*a*b*c*d + B^2*a^2*d^2)*g^2*i^2*x^2 + 2*(B^2*a*b*c^2 + B^2*a^2*c*d)*g^2*i^2*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^2*d^2*g^2*i^2*x^4 + A*B*a^2*c^2*g^2*i^2 + 2*(A*B*b^2*c*d + A*B*a*b*d^2)*g^2*i^2*x^3 + (A*B*b^2*c^2 + 4*A*B*a*b*c*d + A*B*a^2*d^2)*g^2*i^2*x^2 + 2*(A*B*a*b*c^2 + A*B*a^2*c*d)*g^2*i^2*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
170,0,0,0,0.439205," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b d^{2} g i^{2} x^{3} + A^{2} a c^{2} g i^{2} + {\left(2 \, A^{2} b c d + A^{2} a d^{2}\right)} g i^{2} x^{2} + {\left(A^{2} b c^{2} + 2 \, A^{2} a c d\right)} g i^{2} x + {\left(B^{2} b d^{2} g i^{2} x^{3} + B^{2} a c^{2} g i^{2} + {\left(2 \, B^{2} b c d + B^{2} a d^{2}\right)} g i^{2} x^{2} + {\left(B^{2} b c^{2} + 2 \, B^{2} a c d\right)} g i^{2} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b d^{2} g i^{2} x^{3} + A B a c^{2} g i^{2} + {\left(2 \, A B b c d + A B a d^{2}\right)} g i^{2} x^{2} + {\left(A B b c^{2} + 2 \, A B a c d\right)} g i^{2} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b*d^2*g*i^2*x^3 + A^2*a*c^2*g*i^2 + (2*A^2*b*c*d + A^2*a*d^2)*g*i^2*x^2 + (A^2*b*c^2 + 2*A^2*a*c*d)*g*i^2*x + (B^2*b*d^2*g*i^2*x^3 + B^2*a*c^2*g*i^2 + (2*B^2*b*c*d + B^2*a*d^2)*g*i^2*x^2 + (B^2*b*c^2 + 2*B^2*a*c*d)*g*i^2*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b*d^2*g*i^2*x^3 + A*B*a*c^2*g*i^2 + (2*A*B*b*c*d + A*B*a*d^2)*g*i^2*x^2 + (A*B*b*c^2 + 2*A*B*a*c*d)*g*i^2*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
171,0,0,0,0.430357," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left(B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*d^2*i^2*x^2 + 2*A^2*c*d*i^2*x + A^2*c^2*i^2 + (B^2*d^2*i^2*x^2 + 2*B^2*c*d*i^2*x + B^2*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^2*i^2*x^2 + 2*A*B*c*d*i^2*x + A*B*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
172,0,0,0,0.447195," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left(B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b g x + a g}, x\right)"," ",0,"integral((A^2*d^2*i^2*x^2 + 2*A^2*c*d*i^2*x + A^2*c^2*i^2 + (B^2*d^2*i^2*x^2 + 2*B^2*c*d*i^2*x + B^2*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^2*i^2*x^2 + 2*A*B*c*d*i^2*x + A*B*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n))/(b*g*x + a*g), x)","F",0
173,0,0,0,0.460466," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left(B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A^2*d^2*i^2*x^2 + 2*A^2*c*d*i^2*x + A^2*c^2*i^2 + (B^2*d^2*i^2*x^2 + 2*B^2*c*d*i^2*x + B^2*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^2*i^2*x^2 + 2*A*B*c*d*i^2*x + A*B*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
174,0,0,0,0.451806," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{2} i^{2} x^{2} + 2 \, A^{2} c d i^{2} x + A^{2} c^{2} i^{2} + {\left(B^{2} d^{2} i^{2} x^{2} + 2 \, B^{2} c d i^{2} x + B^{2} c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{2} i^{2} x^{2} + 2 \, A B c d i^{2} x + A B c^{2} i^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{3} g^{3} x^{3} + 3 \, a b^{2} g^{3} x^{2} + 3 \, a^{2} b g^{3} x + a^{3} g^{3}}, x\right)"," ",0,"integral((A^2*d^2*i^2*x^2 + 2*A^2*c*d*i^2*x + A^2*c^2*i^2 + (B^2*d^2*i^2*x^2 + 2*B^2*c*d*i^2*x + B^2*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^2*i^2*x^2 + 2*A*B*c*d*i^2*x + A*B*c^2*i^2)*log(e*((b*x + a)/(d*x + c))^n))/(b^3*g^3*x^3 + 3*a*b^2*g^3*x^2 + 3*a^2*b*g^3*x + a^3*g^3), x)","F",0
175,1,975,0,0.474408," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(B^{2} b^{3} c^{3} - B^{2} a^{3} d^{3}\right)} i^{2} n^{2} + 6 \, {\left(A B b^{3} c^{3} - A B a^{3} d^{3}\right)} i^{2} n + 9 \, {\left(A^{2} b^{3} c^{3} - A^{2} a^{3} d^{3}\right)} i^{2} + 3 \, {\left(2 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} i^{2} n^{2} + 6 \, {\left(A B b^{3} c d^{2} - A B a b^{2} d^{3}\right)} i^{2} n + 9 \, {\left(A^{2} b^{3} c d^{2} - A^{2} a b^{2} d^{3}\right)} i^{2}\right)} x^{2} + 9 \, {\left(3 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} i^{2} x^{2} + 3 \, {\left(B^{2} b^{3} c^{2} d - B^{2} a^{2} b d^{3}\right)} i^{2} x + {\left(B^{2} b^{3} c^{3} - B^{2} a^{3} d^{3}\right)} i^{2}\right)} \log\left(e\right)^{2} + 9 \, {\left(B^{2} b^{3} d^{3} i^{2} n^{2} x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} n^{2} x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} n^{2} x + B^{2} b^{3} c^{3} i^{2} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 3 \, {\left(2 \, {\left(B^{2} b^{3} c^{2} d - B^{2} a^{2} b d^{3}\right)} i^{2} n^{2} + 6 \, {\left(A B b^{3} c^{2} d - A B a^{2} b d^{3}\right)} i^{2} n + 9 \, {\left(A^{2} b^{3} c^{2} d - A^{2} a^{2} b d^{3}\right)} i^{2}\right)} x + 6 \, {\left({\left(B^{2} b^{3} c^{3} - B^{2} a^{3} d^{3}\right)} i^{2} n + 3 \, {\left(A B b^{3} c^{3} - A B a^{3} d^{3}\right)} i^{2} + 3 \, {\left({\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} i^{2} n + 3 \, {\left(A B b^{3} c d^{2} - A B a b^{2} d^{3}\right)} i^{2}\right)} x^{2} + 3 \, {\left({\left(B^{2} b^{3} c^{2} d - B^{2} a^{2} b d^{3}\right)} i^{2} n + 3 \, {\left(A B b^{3} c^{2} d - A B a^{2} b d^{3}\right)} i^{2}\right)} x + 3 \, {\left(B^{2} b^{3} d^{3} i^{2} n x^{3} + 3 \, B^{2} b^{3} c d^{2} i^{2} n x^{2} + 3 \, B^{2} b^{3} c^{2} d i^{2} n x + B^{2} b^{3} c^{3} i^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left(B^{2} b^{3} c^{3} i^{2} n^{2} + 3 \, A B b^{3} c^{3} i^{2} n + {\left(B^{2} b^{3} d^{3} i^{2} n^{2} + 3 \, A B b^{3} d^{3} i^{2} n\right)} x^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} i^{2} n^{2} + 3 \, A B b^{3} c d^{2} i^{2} n\right)} x^{2} + 3 \, {\left(B^{2} b^{3} c^{2} d i^{2} n^{2} + 3 \, A B b^{3} c^{2} d i^{2} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{27 \, {\left({\left(b^{7} c - a b^{6} d\right)} g^{4} x^{3} + 3 \, {\left(a b^{6} c - a^{2} b^{5} d\right)} g^{4} x^{2} + 3 \, {\left(a^{2} b^{5} c - a^{3} b^{4} d\right)} g^{4} x + {\left(a^{3} b^{4} c - a^{4} b^{3} d\right)} g^{4}\right)}}"," ",0,"-1/27*(2*(B^2*b^3*c^3 - B^2*a^3*d^3)*i^2*n^2 + 6*(A*B*b^3*c^3 - A*B*a^3*d^3)*i^2*n + 9*(A^2*b^3*c^3 - A^2*a^3*d^3)*i^2 + 3*(2*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*i^2*n^2 + 6*(A*B*b^3*c*d^2 - A*B*a*b^2*d^3)*i^2*n + 9*(A^2*b^3*c*d^2 - A^2*a*b^2*d^3)*i^2)*x^2 + 9*(3*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*i^2*x^2 + 3*(B^2*b^3*c^2*d - B^2*a^2*b*d^3)*i^2*x + (B^2*b^3*c^3 - B^2*a^3*d^3)*i^2)*log(e)^2 + 9*(B^2*b^3*d^3*i^2*n^2*x^3 + 3*B^2*b^3*c*d^2*i^2*n^2*x^2 + 3*B^2*b^3*c^2*d*i^2*n^2*x + B^2*b^3*c^3*i^2*n^2)*log((b*x + a)/(d*x + c))^2 + 3*(2*(B^2*b^3*c^2*d - B^2*a^2*b*d^3)*i^2*n^2 + 6*(A*B*b^3*c^2*d - A*B*a^2*b*d^3)*i^2*n + 9*(A^2*b^3*c^2*d - A^2*a^2*b*d^3)*i^2)*x + 6*((B^2*b^3*c^3 - B^2*a^3*d^3)*i^2*n + 3*(A*B*b^3*c^3 - A*B*a^3*d^3)*i^2 + 3*((B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*i^2*n + 3*(A*B*b^3*c*d^2 - A*B*a*b^2*d^3)*i^2)*x^2 + 3*((B^2*b^3*c^2*d - B^2*a^2*b*d^3)*i^2*n + 3*(A*B*b^3*c^2*d - A*B*a^2*b*d^3)*i^2)*x + 3*(B^2*b^3*d^3*i^2*n*x^3 + 3*B^2*b^3*c*d^2*i^2*n*x^2 + 3*B^2*b^3*c^2*d*i^2*n*x + B^2*b^3*c^3*i^2*n)*log((b*x + a)/(d*x + c)))*log(e) + 6*(B^2*b^3*c^3*i^2*n^2 + 3*A*B*b^3*c^3*i^2*n + (B^2*b^3*d^3*i^2*n^2 + 3*A*B*b^3*d^3*i^2*n)*x^3 + 3*(B^2*b^3*c*d^2*i^2*n^2 + 3*A*B*b^3*c*d^2*i^2*n)*x^2 + 3*(B^2*b^3*c^2*d*i^2*n^2 + 3*A*B*b^3*c^2*d*i^2*n)*x)*log((b*x + a)/(d*x + c)))/((b^7*c - a*b^6*d)*g^4*x^3 + 3*(a*b^6*c - a^2*b^5*d)*g^4*x^2 + 3*(a^2*b^5*c - a^3*b^4*d)*g^4*x + (a^3*b^4*c - a^4*b^3*d)*g^4)","B",0
176,1,1729,0,0.521396," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^5,x, algorithm=""fricas"")","-\frac{{\left(27 \, B^{2} b^{4} c^{4} - 64 \, B^{2} a b^{3} c^{3} d + 37 \, B^{2} a^{4} d^{4}\right)} i^{2} n^{2} + 12 \, {\left(9 \, A B b^{4} c^{4} - 16 \, A B a b^{3} c^{3} d + 7 \, A B a^{4} d^{4}\right)} i^{2} n - 12 \, {\left(7 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} i^{2} n^{2} + 12 \, {\left(A B b^{4} c d^{3} - A B a b^{3} d^{4}\right)} i^{2} n\right)} x^{3} + 72 \, {\left(3 \, A^{2} b^{4} c^{4} - 4 \, A^{2} a b^{3} c^{3} d + A^{2} a^{4} d^{4}\right)} i^{2} - 6 \, {\left({\left(5 \, B^{2} b^{4} c^{2} d^{2} + 32 \, B^{2} a b^{3} c d^{3} - 37 \, B^{2} a^{2} b^{2} d^{4}\right)} i^{2} n^{2} - 12 \, {\left(A B b^{4} c^{2} d^{2} - 8 \, A B a b^{3} c d^{3} + 7 \, A B a^{2} b^{2} d^{4}\right)} i^{2} n - 72 \, {\left(A^{2} b^{4} c^{2} d^{2} - 2 \, A^{2} a b^{3} c d^{3} + A^{2} a^{2} b^{2} d^{4}\right)} i^{2}\right)} x^{2} + 72 \, {\left(6 \, {\left(B^{2} b^{4} c^{2} d^{2} - 2 \, B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} i^{2} x^{2} + 4 \, {\left(2 \, B^{2} b^{4} c^{3} d - 3 \, B^{2} a b^{3} c^{2} d^{2} + B^{2} a^{3} b d^{4}\right)} i^{2} x + {\left(3 \, B^{2} b^{4} c^{4} - 4 \, B^{2} a b^{3} c^{3} d + B^{2} a^{4} d^{4}\right)} i^{2}\right)} \log\left(e\right)^{2} - 72 \, {\left(B^{2} b^{4} d^{4} i^{2} n^{2} x^{4} + 4 \, B^{2} a b^{3} d^{4} i^{2} n^{2} x^{3} - 6 \, {\left(B^{2} b^{4} c^{2} d^{2} - 2 \, B^{2} a b^{3} c d^{3}\right)} i^{2} n^{2} x^{2} - 4 \, {\left(2 \, B^{2} b^{4} c^{3} d - 3 \, B^{2} a b^{3} c^{2} d^{2}\right)} i^{2} n^{2} x - {\left(3 \, B^{2} b^{4} c^{4} - 4 \, B^{2} a b^{3} c^{3} d\right)} i^{2} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 4 \, {\left({\left(11 \, B^{2} b^{4} c^{3} d - 48 \, B^{2} a b^{3} c^{2} d^{2} + 37 \, B^{2} a^{3} b d^{4}\right)} i^{2} n^{2} + 12 \, {\left(5 \, A B b^{4} c^{3} d - 12 \, A B a b^{3} c^{2} d^{2} + 7 \, A B a^{3} b d^{4}\right)} i^{2} n + 72 \, {\left(2 \, A^{2} b^{4} c^{3} d - 3 \, A^{2} a b^{3} c^{2} d^{2} + A^{2} a^{3} b d^{4}\right)} i^{2}\right)} x - 12 \, {\left(12 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} i^{2} n x^{3} - {\left(9 \, B^{2} b^{4} c^{4} - 16 \, B^{2} a b^{3} c^{3} d + 7 \, B^{2} a^{4} d^{4}\right)} i^{2} n - 12 \, {\left(3 \, A B b^{4} c^{4} - 4 \, A B a b^{3} c^{3} d + A B a^{4} d^{4}\right)} i^{2} - 6 \, {\left({\left(B^{2} b^{4} c^{2} d^{2} - 8 \, B^{2} a b^{3} c d^{3} + 7 \, B^{2} a^{2} b^{2} d^{4}\right)} i^{2} n + 12 \, {\left(A B b^{4} c^{2} d^{2} - 2 \, A B a b^{3} c d^{3} + A B a^{2} b^{2} d^{4}\right)} i^{2}\right)} x^{2} - 4 \, {\left({\left(5 \, B^{2} b^{4} c^{3} d - 12 \, B^{2} a b^{3} c^{2} d^{2} + 7 \, B^{2} a^{3} b d^{4}\right)} i^{2} n + 12 \, {\left(2 \, A B b^{4} c^{3} d - 3 \, A B a b^{3} c^{2} d^{2} + A B a^{3} b d^{4}\right)} i^{2}\right)} x + 12 \, {\left(B^{2} b^{4} d^{4} i^{2} n x^{4} + 4 \, B^{2} a b^{3} d^{4} i^{2} n x^{3} - 6 \, {\left(B^{2} b^{4} c^{2} d^{2} - 2 \, B^{2} a b^{3} c d^{3}\right)} i^{2} n x^{2} - 4 \, {\left(2 \, B^{2} b^{4} c^{3} d - 3 \, B^{2} a b^{3} c^{2} d^{2}\right)} i^{2} n x - {\left(3 \, B^{2} b^{4} c^{4} - 4 \, B^{2} a b^{3} c^{3} d\right)} i^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 12 \, {\left({\left(9 \, B^{2} b^{4} c^{4} - 16 \, B^{2} a b^{3} c^{3} d\right)} i^{2} n^{2} - {\left(7 \, B^{2} b^{4} d^{4} i^{2} n^{2} + 12 \, A B b^{4} d^{4} i^{2} n\right)} x^{4} + 12 \, {\left(3 \, A B b^{4} c^{4} - 4 \, A B a b^{3} c^{3} d\right)} i^{2} n - 4 \, {\left(12 \, A B a b^{3} d^{4} i^{2} n + {\left(3 \, B^{2} b^{4} c d^{3} + 4 \, B^{2} a b^{3} d^{4}\right)} i^{2} n^{2}\right)} x^{3} + 6 \, {\left({\left(B^{2} b^{4} c^{2} d^{2} - 8 \, B^{2} a b^{3} c d^{3}\right)} i^{2} n^{2} + 12 \, {\left(A B b^{4} c^{2} d^{2} - 2 \, A B a b^{3} c d^{3}\right)} i^{2} n\right)} x^{2} + 4 \, {\left({\left(5 \, B^{2} b^{4} c^{3} d - 12 \, B^{2} a b^{3} c^{2} d^{2}\right)} i^{2} n^{2} + 12 \, {\left(2 \, A B b^{4} c^{3} d - 3 \, A B a b^{3} c^{2} d^{2}\right)} i^{2} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{864 \, {\left({\left(b^{9} c^{2} - 2 \, a b^{8} c d + a^{2} b^{7} d^{2}\right)} g^{5} x^{4} + 4 \, {\left(a b^{8} c^{2} - 2 \, a^{2} b^{7} c d + a^{3} b^{6} d^{2}\right)} g^{5} x^{3} + 6 \, {\left(a^{2} b^{7} c^{2} - 2 \, a^{3} b^{6} c d + a^{4} b^{5} d^{2}\right)} g^{5} x^{2} + 4 \, {\left(a^{3} b^{6} c^{2} - 2 \, a^{4} b^{5} c d + a^{5} b^{4} d^{2}\right)} g^{5} x + {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} g^{5}\right)}}"," ",0,"-1/864*((27*B^2*b^4*c^4 - 64*B^2*a*b^3*c^3*d + 37*B^2*a^4*d^4)*i^2*n^2 + 12*(9*A*B*b^4*c^4 - 16*A*B*a*b^3*c^3*d + 7*A*B*a^4*d^4)*i^2*n - 12*(7*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*i^2*n^2 + 12*(A*B*b^4*c*d^3 - A*B*a*b^3*d^4)*i^2*n)*x^3 + 72*(3*A^2*b^4*c^4 - 4*A^2*a*b^3*c^3*d + A^2*a^4*d^4)*i^2 - 6*((5*B^2*b^4*c^2*d^2 + 32*B^2*a*b^3*c*d^3 - 37*B^2*a^2*b^2*d^4)*i^2*n^2 - 12*(A*B*b^4*c^2*d^2 - 8*A*B*a*b^3*c*d^3 + 7*A*B*a^2*b^2*d^4)*i^2*n - 72*(A^2*b^4*c^2*d^2 - 2*A^2*a*b^3*c*d^3 + A^2*a^2*b^2*d^4)*i^2)*x^2 + 72*(6*(B^2*b^4*c^2*d^2 - 2*B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*i^2*x^2 + 4*(2*B^2*b^4*c^3*d - 3*B^2*a*b^3*c^2*d^2 + B^2*a^3*b*d^4)*i^2*x + (3*B^2*b^4*c^4 - 4*B^2*a*b^3*c^3*d + B^2*a^4*d^4)*i^2)*log(e)^2 - 72*(B^2*b^4*d^4*i^2*n^2*x^4 + 4*B^2*a*b^3*d^4*i^2*n^2*x^3 - 6*(B^2*b^4*c^2*d^2 - 2*B^2*a*b^3*c*d^3)*i^2*n^2*x^2 - 4*(2*B^2*b^4*c^3*d - 3*B^2*a*b^3*c^2*d^2)*i^2*n^2*x - (3*B^2*b^4*c^4 - 4*B^2*a*b^3*c^3*d)*i^2*n^2)*log((b*x + a)/(d*x + c))^2 + 4*((11*B^2*b^4*c^3*d - 48*B^2*a*b^3*c^2*d^2 + 37*B^2*a^3*b*d^4)*i^2*n^2 + 12*(5*A*B*b^4*c^3*d - 12*A*B*a*b^3*c^2*d^2 + 7*A*B*a^3*b*d^4)*i^2*n + 72*(2*A^2*b^4*c^3*d - 3*A^2*a*b^3*c^2*d^2 + A^2*a^3*b*d^4)*i^2)*x - 12*(12*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*i^2*n*x^3 - (9*B^2*b^4*c^4 - 16*B^2*a*b^3*c^3*d + 7*B^2*a^4*d^4)*i^2*n - 12*(3*A*B*b^4*c^4 - 4*A*B*a*b^3*c^3*d + A*B*a^4*d^4)*i^2 - 6*((B^2*b^4*c^2*d^2 - 8*B^2*a*b^3*c*d^3 + 7*B^2*a^2*b^2*d^4)*i^2*n + 12*(A*B*b^4*c^2*d^2 - 2*A*B*a*b^3*c*d^3 + A*B*a^2*b^2*d^4)*i^2)*x^2 - 4*((5*B^2*b^4*c^3*d - 12*B^2*a*b^3*c^2*d^2 + 7*B^2*a^3*b*d^4)*i^2*n + 12*(2*A*B*b^4*c^3*d - 3*A*B*a*b^3*c^2*d^2 + A*B*a^3*b*d^4)*i^2)*x + 12*(B^2*b^4*d^4*i^2*n*x^4 + 4*B^2*a*b^3*d^4*i^2*n*x^3 - 6*(B^2*b^4*c^2*d^2 - 2*B^2*a*b^3*c*d^3)*i^2*n*x^2 - 4*(2*B^2*b^4*c^3*d - 3*B^2*a*b^3*c^2*d^2)*i^2*n*x - (3*B^2*b^4*c^4 - 4*B^2*a*b^3*c^3*d)*i^2*n)*log((b*x + a)/(d*x + c)))*log(e) + 12*((9*B^2*b^4*c^4 - 16*B^2*a*b^3*c^3*d)*i^2*n^2 - (7*B^2*b^4*d^4*i^2*n^2 + 12*A*B*b^4*d^4*i^2*n)*x^4 + 12*(3*A*B*b^4*c^4 - 4*A*B*a*b^3*c^3*d)*i^2*n - 4*(12*A*B*a*b^3*d^4*i^2*n + (3*B^2*b^4*c*d^3 + 4*B^2*a*b^3*d^4)*i^2*n^2)*x^3 + 6*((B^2*b^4*c^2*d^2 - 8*B^2*a*b^3*c*d^3)*i^2*n^2 + 12*(A*B*b^4*c^2*d^2 - 2*A*B*a*b^3*c*d^3)*i^2*n)*x^2 + 4*((5*B^2*b^4*c^3*d - 12*B^2*a*b^3*c^2*d^2)*i^2*n^2 + 12*(2*A*B*b^4*c^3*d - 3*A*B*a*b^3*c^2*d^2)*i^2*n)*x)*log((b*x + a)/(d*x + c)))/((b^9*c^2 - 2*a*b^8*c*d + a^2*b^7*d^2)*g^5*x^4 + 4*(a*b^8*c^2 - 2*a^2*b^7*c*d + a^3*b^6*d^2)*g^5*x^3 + 6*(a^2*b^7*c^2 - 2*a^3*b^6*c*d + a^4*b^5*d^2)*g^5*x^2 + 4*(a^3*b^6*c^2 - 2*a^4*b^5*c*d + a^5*b^4*d^2)*g^5*x + (a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*g^5)","B",0
177,1,2633,0,0.597943," ","integrate((d*i*x+c*i)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^6,x, algorithm=""fricas"")","-\frac{{\left(864 \, B^{2} b^{5} c^{5} - 3375 \, B^{2} a b^{4} c^{4} d + 4000 \, B^{2} a^{2} b^{3} c^{3} d^{2} - 1489 \, B^{2} a^{5} d^{5}\right)} i^{2} n^{2} + 60 \, {\left(47 \, {\left(B^{2} b^{5} c d^{4} - B^{2} a b^{4} d^{5}\right)} i^{2} n^{2} + 60 \, {\left(A B b^{5} c d^{4} - A B a b^{4} d^{5}\right)} i^{2} n\right)} x^{4} + 60 \, {\left(72 \, A B b^{5} c^{5} - 225 \, A B a b^{4} c^{4} d + 200 \, A B a^{2} b^{3} c^{3} d^{2} - 47 \, A B a^{5} d^{5}\right)} i^{2} n + 30 \, {\left({\left(13 \, B^{2} b^{5} c^{2} d^{3} + 350 \, B^{2} a b^{4} c d^{4} - 363 \, B^{2} a^{2} b^{3} d^{5}\right)} i^{2} n^{2} - 60 \, {\left(A B b^{5} c^{2} d^{3} - 10 \, A B a b^{4} c d^{4} + 9 \, A B a^{2} b^{3} d^{5}\right)} i^{2} n\right)} x^{3} + 1800 \, {\left(6 \, A^{2} b^{5} c^{5} - 15 \, A^{2} a b^{4} c^{4} d + 10 \, A^{2} a^{2} b^{3} c^{3} d^{2} - A^{2} a^{5} d^{5}\right)} i^{2} - 10 \, {\left({\left(86 \, B^{2} b^{5} c^{3} d^{2} - 375 \, B^{2} a b^{4} c^{2} d^{3} - 1200 \, B^{2} a^{2} b^{3} c d^{4} + 1489 \, B^{2} a^{3} b^{2} d^{5}\right)} i^{2} n^{2} - 60 \, {\left(2 \, A B b^{5} c^{3} d^{2} - 15 \, A B a b^{4} c^{2} d^{3} + 60 \, A B a^{2} b^{3} c d^{4} - 47 \, A B a^{3} b^{2} d^{5}\right)} i^{2} n - 1800 \, {\left(A^{2} b^{5} c^{3} d^{2} - 3 \, A^{2} a b^{4} c^{2} d^{3} + 3 \, A^{2} a^{2} b^{3} c d^{4} - A^{2} a^{3} b^{2} d^{5}\right)} i^{2}\right)} x^{2} + 1800 \, {\left(10 \, {\left(B^{2} b^{5} c^{3} d^{2} - 3 \, B^{2} a b^{4} c^{2} d^{3} + 3 \, B^{2} a^{2} b^{3} c d^{4} - B^{2} a^{3} b^{2} d^{5}\right)} i^{2} x^{2} + 5 \, {\left(3 \, B^{2} b^{5} c^{4} d - 8 \, B^{2} a b^{4} c^{3} d^{2} + 6 \, B^{2} a^{2} b^{3} c^{2} d^{3} - B^{2} a^{4} b d^{5}\right)} i^{2} x + {\left(6 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 10 \, B^{2} a^{2} b^{3} c^{3} d^{2} - B^{2} a^{5} d^{5}\right)} i^{2}\right)} \log\left(e\right)^{2} + 1800 \, {\left(B^{2} b^{5} d^{5} i^{2} n^{2} x^{5} + 5 \, B^{2} a b^{4} d^{5} i^{2} n^{2} x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} i^{2} n^{2} x^{3} + 10 \, {\left(B^{2} b^{5} c^{3} d^{2} - 3 \, B^{2} a b^{4} c^{2} d^{3} + 3 \, B^{2} a^{2} b^{3} c d^{4}\right)} i^{2} n^{2} x^{2} + 5 \, {\left(3 \, B^{2} b^{5} c^{4} d - 8 \, B^{2} a b^{4} c^{3} d^{2} + 6 \, B^{2} a^{2} b^{3} c^{2} d^{3}\right)} i^{2} n^{2} x + {\left(6 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 10 \, B^{2} a^{2} b^{3} c^{3} d^{2}\right)} i^{2} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 5 \, {\left({\left(189 \, B^{2} b^{5} c^{4} d - 1100 \, B^{2} a b^{4} c^{3} d^{2} + 2400 \, B^{2} a^{2} b^{3} c^{2} d^{3} - 1489 \, B^{2} a^{4} b d^{5}\right)} i^{2} n^{2} + 60 \, {\left(27 \, A B b^{5} c^{4} d - 100 \, A B a b^{4} c^{3} d^{2} + 120 \, A B a^{2} b^{3} c^{2} d^{3} - 47 \, A B a^{4} b d^{5}\right)} i^{2} n + 1800 \, {\left(3 \, A^{2} b^{5} c^{4} d - 8 \, A^{2} a b^{4} c^{3} d^{2} + 6 \, A^{2} a^{2} b^{3} c^{2} d^{3} - A^{2} a^{4} b d^{5}\right)} i^{2}\right)} x + 60 \, {\left(60 \, {\left(B^{2} b^{5} c d^{4} - B^{2} a b^{4} d^{5}\right)} i^{2} n x^{4} - 30 \, {\left(B^{2} b^{5} c^{2} d^{3} - 10 \, B^{2} a b^{4} c d^{4} + 9 \, B^{2} a^{2} b^{3} d^{5}\right)} i^{2} n x^{3} + {\left(72 \, B^{2} b^{5} c^{5} - 225 \, B^{2} a b^{4} c^{4} d + 200 \, B^{2} a^{2} b^{3} c^{3} d^{2} - 47 \, B^{2} a^{5} d^{5}\right)} i^{2} n + 60 \, {\left(6 \, A B b^{5} c^{5} - 15 \, A B a b^{4} c^{4} d + 10 \, A B a^{2} b^{3} c^{3} d^{2} - A B a^{5} d^{5}\right)} i^{2} + 10 \, {\left({\left(2 \, B^{2} b^{5} c^{3} d^{2} - 15 \, B^{2} a b^{4} c^{2} d^{3} + 60 \, B^{2} a^{2} b^{3} c d^{4} - 47 \, B^{2} a^{3} b^{2} d^{5}\right)} i^{2} n + 60 \, {\left(A B b^{5} c^{3} d^{2} - 3 \, A B a b^{4} c^{2} d^{3} + 3 \, A B a^{2} b^{3} c d^{4} - A B a^{3} b^{2} d^{5}\right)} i^{2}\right)} x^{2} + 5 \, {\left({\left(27 \, B^{2} b^{5} c^{4} d - 100 \, B^{2} a b^{4} c^{3} d^{2} + 120 \, B^{2} a^{2} b^{3} c^{2} d^{3} - 47 \, B^{2} a^{4} b d^{5}\right)} i^{2} n + 60 \, {\left(3 \, A B b^{5} c^{4} d - 8 \, A B a b^{4} c^{3} d^{2} + 6 \, A B a^{2} b^{3} c^{2} d^{3} - A B a^{4} b d^{5}\right)} i^{2}\right)} x + 60 \, {\left(B^{2} b^{5} d^{5} i^{2} n x^{5} + 5 \, B^{2} a b^{4} d^{5} i^{2} n x^{4} + 10 \, B^{2} a^{2} b^{3} d^{5} i^{2} n x^{3} + 10 \, {\left(B^{2} b^{5} c^{3} d^{2} - 3 \, B^{2} a b^{4} c^{2} d^{3} + 3 \, B^{2} a^{2} b^{3} c d^{4}\right)} i^{2} n x^{2} + 5 \, {\left(3 \, B^{2} b^{5} c^{4} d - 8 \, B^{2} a b^{4} c^{3} d^{2} + 6 \, B^{2} a^{2} b^{3} c^{2} d^{3}\right)} i^{2} n x + {\left(6 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 10 \, B^{2} a^{2} b^{3} c^{3} d^{2}\right)} i^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 60 \, {\left({\left(47 \, B^{2} b^{5} d^{5} i^{2} n^{2} + 60 \, A B b^{5} d^{5} i^{2} n\right)} x^{5} + {\left(72 \, B^{2} b^{5} c^{5} - 225 \, B^{2} a b^{4} c^{4} d + 200 \, B^{2} a^{2} b^{3} c^{3} d^{2}\right)} i^{2} n^{2} + 5 \, {\left(60 \, A B a b^{4} d^{5} i^{2} n + {\left(12 \, B^{2} b^{5} c d^{4} + 35 \, B^{2} a b^{4} d^{5}\right)} i^{2} n^{2}\right)} x^{4} + 60 \, {\left(6 \, A B b^{5} c^{5} - 15 \, A B a b^{4} c^{4} d + 10 \, A B a^{2} b^{3} c^{3} d^{2}\right)} i^{2} n + 10 \, {\left(60 \, A B a^{2} b^{3} d^{5} i^{2} n - {\left(3 \, B^{2} b^{5} c^{2} d^{3} - 30 \, B^{2} a b^{4} c d^{4} - 20 \, B^{2} a^{2} b^{3} d^{5}\right)} i^{2} n^{2}\right)} x^{3} + 10 \, {\left({\left(2 \, B^{2} b^{5} c^{3} d^{2} - 15 \, B^{2} a b^{4} c^{2} d^{3} + 60 \, B^{2} a^{2} b^{3} c d^{4}\right)} i^{2} n^{2} + 60 \, {\left(A B b^{5} c^{3} d^{2} - 3 \, A B a b^{4} c^{2} d^{3} + 3 \, A B a^{2} b^{3} c d^{4}\right)} i^{2} n\right)} x^{2} + 5 \, {\left({\left(27 \, B^{2} b^{5} c^{4} d - 100 \, B^{2} a b^{4} c^{3} d^{2} + 120 \, B^{2} a^{2} b^{3} c^{2} d^{3}\right)} i^{2} n^{2} + 60 \, {\left(3 \, A B b^{5} c^{4} d - 8 \, A B a b^{4} c^{3} d^{2} + 6 \, A B a^{2} b^{3} c^{2} d^{3}\right)} i^{2} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{54000 \, {\left({\left(b^{11} c^{3} - 3 \, a b^{10} c^{2} d + 3 \, a^{2} b^{9} c d^{2} - a^{3} b^{8} d^{3}\right)} g^{6} x^{5} + 5 \, {\left(a b^{10} c^{3} - 3 \, a^{2} b^{9} c^{2} d + 3 \, a^{3} b^{8} c d^{2} - a^{4} b^{7} d^{3}\right)} g^{6} x^{4} + 10 \, {\left(a^{2} b^{9} c^{3} - 3 \, a^{3} b^{8} c^{2} d + 3 \, a^{4} b^{7} c d^{2} - a^{5} b^{6} d^{3}\right)} g^{6} x^{3} + 10 \, {\left(a^{3} b^{8} c^{3} - 3 \, a^{4} b^{7} c^{2} d + 3 \, a^{5} b^{6} c d^{2} - a^{6} b^{5} d^{3}\right)} g^{6} x^{2} + 5 \, {\left(a^{4} b^{7} c^{3} - 3 \, a^{5} b^{6} c^{2} d + 3 \, a^{6} b^{5} c d^{2} - a^{7} b^{4} d^{3}\right)} g^{6} x + {\left(a^{5} b^{6} c^{3} - 3 \, a^{6} b^{5} c^{2} d + 3 \, a^{7} b^{4} c d^{2} - a^{8} b^{3} d^{3}\right)} g^{6}\right)}}"," ",0,"-1/54000*((864*B^2*b^5*c^5 - 3375*B^2*a*b^4*c^4*d + 4000*B^2*a^2*b^3*c^3*d^2 - 1489*B^2*a^5*d^5)*i^2*n^2 + 60*(47*(B^2*b^5*c*d^4 - B^2*a*b^4*d^5)*i^2*n^2 + 60*(A*B*b^5*c*d^4 - A*B*a*b^4*d^5)*i^2*n)*x^4 + 60*(72*A*B*b^5*c^5 - 225*A*B*a*b^4*c^4*d + 200*A*B*a^2*b^3*c^3*d^2 - 47*A*B*a^5*d^5)*i^2*n + 30*((13*B^2*b^5*c^2*d^3 + 350*B^2*a*b^4*c*d^4 - 363*B^2*a^2*b^3*d^5)*i^2*n^2 - 60*(A*B*b^5*c^2*d^3 - 10*A*B*a*b^4*c*d^4 + 9*A*B*a^2*b^3*d^5)*i^2*n)*x^3 + 1800*(6*A^2*b^5*c^5 - 15*A^2*a*b^4*c^4*d + 10*A^2*a^2*b^3*c^3*d^2 - A^2*a^5*d^5)*i^2 - 10*((86*B^2*b^5*c^3*d^2 - 375*B^2*a*b^4*c^2*d^3 - 1200*B^2*a^2*b^3*c*d^4 + 1489*B^2*a^3*b^2*d^5)*i^2*n^2 - 60*(2*A*B*b^5*c^3*d^2 - 15*A*B*a*b^4*c^2*d^3 + 60*A*B*a^2*b^3*c*d^4 - 47*A*B*a^3*b^2*d^5)*i^2*n - 1800*(A^2*b^5*c^3*d^2 - 3*A^2*a*b^4*c^2*d^3 + 3*A^2*a^2*b^3*c*d^4 - A^2*a^3*b^2*d^5)*i^2)*x^2 + 1800*(10*(B^2*b^5*c^3*d^2 - 3*B^2*a*b^4*c^2*d^3 + 3*B^2*a^2*b^3*c*d^4 - B^2*a^3*b^2*d^5)*i^2*x^2 + 5*(3*B^2*b^5*c^4*d - 8*B^2*a*b^4*c^3*d^2 + 6*B^2*a^2*b^3*c^2*d^3 - B^2*a^4*b*d^5)*i^2*x + (6*B^2*b^5*c^5 - 15*B^2*a*b^4*c^4*d + 10*B^2*a^2*b^3*c^3*d^2 - B^2*a^5*d^5)*i^2)*log(e)^2 + 1800*(B^2*b^5*d^5*i^2*n^2*x^5 + 5*B^2*a*b^4*d^5*i^2*n^2*x^4 + 10*B^2*a^2*b^3*d^5*i^2*n^2*x^3 + 10*(B^2*b^5*c^3*d^2 - 3*B^2*a*b^4*c^2*d^3 + 3*B^2*a^2*b^3*c*d^4)*i^2*n^2*x^2 + 5*(3*B^2*b^5*c^4*d - 8*B^2*a*b^4*c^3*d^2 + 6*B^2*a^2*b^3*c^2*d^3)*i^2*n^2*x + (6*B^2*b^5*c^5 - 15*B^2*a*b^4*c^4*d + 10*B^2*a^2*b^3*c^3*d^2)*i^2*n^2)*log((b*x + a)/(d*x + c))^2 + 5*((189*B^2*b^5*c^4*d - 1100*B^2*a*b^4*c^3*d^2 + 2400*B^2*a^2*b^3*c^2*d^3 - 1489*B^2*a^4*b*d^5)*i^2*n^2 + 60*(27*A*B*b^5*c^4*d - 100*A*B*a*b^4*c^3*d^2 + 120*A*B*a^2*b^3*c^2*d^3 - 47*A*B*a^4*b*d^5)*i^2*n + 1800*(3*A^2*b^5*c^4*d - 8*A^2*a*b^4*c^3*d^2 + 6*A^2*a^2*b^3*c^2*d^3 - A^2*a^4*b*d^5)*i^2)*x + 60*(60*(B^2*b^5*c*d^4 - B^2*a*b^4*d^5)*i^2*n*x^4 - 30*(B^2*b^5*c^2*d^3 - 10*B^2*a*b^4*c*d^4 + 9*B^2*a^2*b^3*d^5)*i^2*n*x^3 + (72*B^2*b^5*c^5 - 225*B^2*a*b^4*c^4*d + 200*B^2*a^2*b^3*c^3*d^2 - 47*B^2*a^5*d^5)*i^2*n + 60*(6*A*B*b^5*c^5 - 15*A*B*a*b^4*c^4*d + 10*A*B*a^2*b^3*c^3*d^2 - A*B*a^5*d^5)*i^2 + 10*((2*B^2*b^5*c^3*d^2 - 15*B^2*a*b^4*c^2*d^3 + 60*B^2*a^2*b^3*c*d^4 - 47*B^2*a^3*b^2*d^5)*i^2*n + 60*(A*B*b^5*c^3*d^2 - 3*A*B*a*b^4*c^2*d^3 + 3*A*B*a^2*b^3*c*d^4 - A*B*a^3*b^2*d^5)*i^2)*x^2 + 5*((27*B^2*b^5*c^4*d - 100*B^2*a*b^4*c^3*d^2 + 120*B^2*a^2*b^3*c^2*d^3 - 47*B^2*a^4*b*d^5)*i^2*n + 60*(3*A*B*b^5*c^4*d - 8*A*B*a*b^4*c^3*d^2 + 6*A*B*a^2*b^3*c^2*d^3 - A*B*a^4*b*d^5)*i^2)*x + 60*(B^2*b^5*d^5*i^2*n*x^5 + 5*B^2*a*b^4*d^5*i^2*n*x^4 + 10*B^2*a^2*b^3*d^5*i^2*n*x^3 + 10*(B^2*b^5*c^3*d^2 - 3*B^2*a*b^4*c^2*d^3 + 3*B^2*a^2*b^3*c*d^4)*i^2*n*x^2 + 5*(3*B^2*b^5*c^4*d - 8*B^2*a*b^4*c^3*d^2 + 6*B^2*a^2*b^3*c^2*d^3)*i^2*n*x + (6*B^2*b^5*c^5 - 15*B^2*a*b^4*c^4*d + 10*B^2*a^2*b^3*c^3*d^2)*i^2*n)*log((b*x + a)/(d*x + c)))*log(e) + 60*((47*B^2*b^5*d^5*i^2*n^2 + 60*A*B*b^5*d^5*i^2*n)*x^5 + (72*B^2*b^5*c^5 - 225*B^2*a*b^4*c^4*d + 200*B^2*a^2*b^3*c^3*d^2)*i^2*n^2 + 5*(60*A*B*a*b^4*d^5*i^2*n + (12*B^2*b^5*c*d^4 + 35*B^2*a*b^4*d^5)*i^2*n^2)*x^4 + 60*(6*A*B*b^5*c^5 - 15*A*B*a*b^4*c^4*d + 10*A*B*a^2*b^3*c^3*d^2)*i^2*n + 10*(60*A*B*a^2*b^3*d^5*i^2*n - (3*B^2*b^5*c^2*d^3 - 30*B^2*a*b^4*c*d^4 - 20*B^2*a^2*b^3*d^5)*i^2*n^2)*x^3 + 10*((2*B^2*b^5*c^3*d^2 - 15*B^2*a*b^4*c^2*d^3 + 60*B^2*a^2*b^3*c*d^4)*i^2*n^2 + 60*(A*B*b^5*c^3*d^2 - 3*A*B*a*b^4*c^2*d^3 + 3*A*B*a^2*b^3*c*d^4)*i^2*n)*x^2 + 5*((27*B^2*b^5*c^4*d - 100*B^2*a*b^4*c^3*d^2 + 120*B^2*a^2*b^3*c^2*d^3)*i^2*n^2 + 60*(3*A*B*b^5*c^4*d - 8*A*B*a*b^4*c^3*d^2 + 6*A*B*a^2*b^3*c^2*d^3)*i^2*n)*x)*log((b*x + a)/(d*x + c)))/((b^11*c^3 - 3*a*b^10*c^2*d + 3*a^2*b^9*c*d^2 - a^3*b^8*d^3)*g^6*x^5 + 5*(a*b^10*c^3 - 3*a^2*b^9*c^2*d + 3*a^3*b^8*c*d^2 - a^4*b^7*d^3)*g^6*x^4 + 10*(a^2*b^9*c^3 - 3*a^3*b^8*c^2*d + 3*a^4*b^7*c*d^2 - a^5*b^6*d^3)*g^6*x^3 + 10*(a^3*b^8*c^3 - 3*a^4*b^7*c^2*d + 3*a^5*b^6*c*d^2 - a^6*b^5*d^3)*g^6*x^2 + 5*(a^4*b^7*c^3 - 3*a^5*b^6*c^2*d + 3*a^6*b^5*c*d^2 - a^7*b^4*d^3)*g^6*x + (a^5*b^6*c^3 - 3*a^6*b^5*c^2*d + 3*a^7*b^4*c*d^2 - a^8*b^3*d^3)*g^6)","B",0
178,0,0,0,0.512136," ","integrate((b*g*x+a*g)^3*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{3} d^{3} g^{3} i^{3} x^{6} + A^{2} a^{3} c^{3} g^{3} i^{3} + 3 \, {\left(A^{2} b^{3} c d^{2} + A^{2} a b^{2} d^{3}\right)} g^{3} i^{3} x^{5} + 3 \, {\left(A^{2} b^{3} c^{2} d + 3 \, A^{2} a b^{2} c d^{2} + A^{2} a^{2} b d^{3}\right)} g^{3} i^{3} x^{4} + {\left(A^{2} b^{3} c^{3} + 9 \, A^{2} a b^{2} c^{2} d + 9 \, A^{2} a^{2} b c d^{2} + A^{2} a^{3} d^{3}\right)} g^{3} i^{3} x^{3} + 3 \, {\left(A^{2} a b^{2} c^{3} + 3 \, A^{2} a^{2} b c^{2} d + A^{2} a^{3} c d^{2}\right)} g^{3} i^{3} x^{2} + 3 \, {\left(A^{2} a^{2} b c^{3} + A^{2} a^{3} c^{2} d\right)} g^{3} i^{3} x + {\left(B^{2} b^{3} d^{3} g^{3} i^{3} x^{6} + B^{2} a^{3} c^{3} g^{3} i^{3} + 3 \, {\left(B^{2} b^{3} c d^{2} + B^{2} a b^{2} d^{3}\right)} g^{3} i^{3} x^{5} + 3 \, {\left(B^{2} b^{3} c^{2} d + 3 \, B^{2} a b^{2} c d^{2} + B^{2} a^{2} b d^{3}\right)} g^{3} i^{3} x^{4} + {\left(B^{2} b^{3} c^{3} + 9 \, B^{2} a b^{2} c^{2} d + 9 \, B^{2} a^{2} b c d^{2} + B^{2} a^{3} d^{3}\right)} g^{3} i^{3} x^{3} + 3 \, {\left(B^{2} a b^{2} c^{3} + 3 \, B^{2} a^{2} b c^{2} d + B^{2} a^{3} c d^{2}\right)} g^{3} i^{3} x^{2} + 3 \, {\left(B^{2} a^{2} b c^{3} + B^{2} a^{3} c^{2} d\right)} g^{3} i^{3} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{3} d^{3} g^{3} i^{3} x^{6} + A B a^{3} c^{3} g^{3} i^{3} + 3 \, {\left(A B b^{3} c d^{2} + A B a b^{2} d^{3}\right)} g^{3} i^{3} x^{5} + 3 \, {\left(A B b^{3} c^{2} d + 3 \, A B a b^{2} c d^{2} + A B a^{2} b d^{3}\right)} g^{3} i^{3} x^{4} + {\left(A B b^{3} c^{3} + 9 \, A B a b^{2} c^{2} d + 9 \, A B a^{2} b c d^{2} + A B a^{3} d^{3}\right)} g^{3} i^{3} x^{3} + 3 \, {\left(A B a b^{2} c^{3} + 3 \, A B a^{2} b c^{2} d + A B a^{3} c d^{2}\right)} g^{3} i^{3} x^{2} + 3 \, {\left(A B a^{2} b c^{3} + A B a^{3} c^{2} d\right)} g^{3} i^{3} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b^3*d^3*g^3*i^3*x^6 + A^2*a^3*c^3*g^3*i^3 + 3*(A^2*b^3*c*d^2 + A^2*a*b^2*d^3)*g^3*i^3*x^5 + 3*(A^2*b^3*c^2*d + 3*A^2*a*b^2*c*d^2 + A^2*a^2*b*d^3)*g^3*i^3*x^4 + (A^2*b^3*c^3 + 9*A^2*a*b^2*c^2*d + 9*A^2*a^2*b*c*d^2 + A^2*a^3*d^3)*g^3*i^3*x^3 + 3*(A^2*a*b^2*c^3 + 3*A^2*a^2*b*c^2*d + A^2*a^3*c*d^2)*g^3*i^3*x^2 + 3*(A^2*a^2*b*c^3 + A^2*a^3*c^2*d)*g^3*i^3*x + (B^2*b^3*d^3*g^3*i^3*x^6 + B^2*a^3*c^3*g^3*i^3 + 3*(B^2*b^3*c*d^2 + B^2*a*b^2*d^3)*g^3*i^3*x^5 + 3*(B^2*b^3*c^2*d + 3*B^2*a*b^2*c*d^2 + B^2*a^2*b*d^3)*g^3*i^3*x^4 + (B^2*b^3*c^3 + 9*B^2*a*b^2*c^2*d + 9*B^2*a^2*b*c*d^2 + B^2*a^3*d^3)*g^3*i^3*x^3 + 3*(B^2*a*b^2*c^3 + 3*B^2*a^2*b*c^2*d + B^2*a^3*c*d^2)*g^3*i^3*x^2 + 3*(B^2*a^2*b*c^3 + B^2*a^3*c^2*d)*g^3*i^3*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^3*d^3*g^3*i^3*x^6 + A*B*a^3*c^3*g^3*i^3 + 3*(A*B*b^3*c*d^2 + A*B*a*b^2*d^3)*g^3*i^3*x^5 + 3*(A*B*b^3*c^2*d + 3*A*B*a*b^2*c*d^2 + A*B*a^2*b*d^3)*g^3*i^3*x^4 + (A*B*b^3*c^3 + 9*A*B*a*b^2*c^2*d + 9*A*B*a^2*b*c*d^2 + A*B*a^3*d^3)*g^3*i^3*x^3 + 3*(A*B*a*b^2*c^3 + 3*A*B*a^2*b*c^2*d + A*B*a^3*c*d^2)*g^3*i^3*x^2 + 3*(A*B*a^2*b*c^3 + A*B*a^3*c^2*d)*g^3*i^3*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
179,0,0,0,0.489957," ","integrate((b*g*x+a*g)^2*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b^{2} d^{3} g^{2} i^{3} x^{5} + A^{2} a^{2} c^{3} g^{2} i^{3} + {\left(3 \, A^{2} b^{2} c d^{2} + 2 \, A^{2} a b d^{3}\right)} g^{2} i^{3} x^{4} + {\left(3 \, A^{2} b^{2} c^{2} d + 6 \, A^{2} a b c d^{2} + A^{2} a^{2} d^{3}\right)} g^{2} i^{3} x^{3} + {\left(A^{2} b^{2} c^{3} + 6 \, A^{2} a b c^{2} d + 3 \, A^{2} a^{2} c d^{2}\right)} g^{2} i^{3} x^{2} + {\left(2 \, A^{2} a b c^{3} + 3 \, A^{2} a^{2} c^{2} d\right)} g^{2} i^{3} x + {\left(B^{2} b^{2} d^{3} g^{2} i^{3} x^{5} + B^{2} a^{2} c^{3} g^{2} i^{3} + {\left(3 \, B^{2} b^{2} c d^{2} + 2 \, B^{2} a b d^{3}\right)} g^{2} i^{3} x^{4} + {\left(3 \, B^{2} b^{2} c^{2} d + 6 \, B^{2} a b c d^{2} + B^{2} a^{2} d^{3}\right)} g^{2} i^{3} x^{3} + {\left(B^{2} b^{2} c^{3} + 6 \, B^{2} a b c^{2} d + 3 \, B^{2} a^{2} c d^{2}\right)} g^{2} i^{3} x^{2} + {\left(2 \, B^{2} a b c^{3} + 3 \, B^{2} a^{2} c^{2} d\right)} g^{2} i^{3} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{2} d^{3} g^{2} i^{3} x^{5} + A B a^{2} c^{3} g^{2} i^{3} + {\left(3 \, A B b^{2} c d^{2} + 2 \, A B a b d^{3}\right)} g^{2} i^{3} x^{4} + {\left(3 \, A B b^{2} c^{2} d + 6 \, A B a b c d^{2} + A B a^{2} d^{3}\right)} g^{2} i^{3} x^{3} + {\left(A B b^{2} c^{3} + 6 \, A B a b c^{2} d + 3 \, A B a^{2} c d^{2}\right)} g^{2} i^{3} x^{2} + {\left(2 \, A B a b c^{3} + 3 \, A B a^{2} c^{2} d\right)} g^{2} i^{3} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b^2*d^3*g^2*i^3*x^5 + A^2*a^2*c^3*g^2*i^3 + (3*A^2*b^2*c*d^2 + 2*A^2*a*b*d^3)*g^2*i^3*x^4 + (3*A^2*b^2*c^2*d + 6*A^2*a*b*c*d^2 + A^2*a^2*d^3)*g^2*i^3*x^3 + (A^2*b^2*c^3 + 6*A^2*a*b*c^2*d + 3*A^2*a^2*c*d^2)*g^2*i^3*x^2 + (2*A^2*a*b*c^3 + 3*A^2*a^2*c^2*d)*g^2*i^3*x + (B^2*b^2*d^3*g^2*i^3*x^5 + B^2*a^2*c^3*g^2*i^3 + (3*B^2*b^2*c*d^2 + 2*B^2*a*b*d^3)*g^2*i^3*x^4 + (3*B^2*b^2*c^2*d + 6*B^2*a*b*c*d^2 + B^2*a^2*d^3)*g^2*i^3*x^3 + (B^2*b^2*c^3 + 6*B^2*a*b*c^2*d + 3*B^2*a^2*c*d^2)*g^2*i^3*x^2 + (2*B^2*a*b*c^3 + 3*B^2*a^2*c^2*d)*g^2*i^3*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^2*d^3*g^2*i^3*x^5 + A*B*a^2*c^3*g^2*i^3 + (3*A*B*b^2*c*d^2 + 2*A*B*a*b*d^3)*g^2*i^3*x^4 + (3*A*B*b^2*c^2*d + 6*A*B*a*b*c*d^2 + A*B*a^2*d^3)*g^2*i^3*x^3 + (A*B*b^2*c^3 + 6*A*B*a*b*c^2*d + 3*A*B*a^2*c*d^2)*g^2*i^3*x^2 + (2*A*B*a*b*c^3 + 3*A*B*a^2*c^2*d)*g^2*i^3*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
180,0,0,0,0.475525," ","integrate((b*g*x+a*g)*(d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} b d^{3} g i^{3} x^{4} + A^{2} a c^{3} g i^{3} + {\left(3 \, A^{2} b c d^{2} + A^{2} a d^{3}\right)} g i^{3} x^{3} + 3 \, {\left(A^{2} b c^{2} d + A^{2} a c d^{2}\right)} g i^{3} x^{2} + {\left(A^{2} b c^{3} + 3 \, A^{2} a c^{2} d\right)} g i^{3} x + {\left(B^{2} b d^{3} g i^{3} x^{4} + B^{2} a c^{3} g i^{3} + {\left(3 \, B^{2} b c d^{2} + B^{2} a d^{3}\right)} g i^{3} x^{3} + 3 \, {\left(B^{2} b c^{2} d + B^{2} a c d^{2}\right)} g i^{3} x^{2} + {\left(B^{2} b c^{3} + 3 \, B^{2} a c^{2} d\right)} g i^{3} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b d^{3} g i^{3} x^{4} + A B a c^{3} g i^{3} + {\left(3 \, A B b c d^{2} + A B a d^{3}\right)} g i^{3} x^{3} + 3 \, {\left(A B b c^{2} d + A B a c d^{2}\right)} g i^{3} x^{2} + {\left(A B b c^{3} + 3 \, A B a c^{2} d\right)} g i^{3} x\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*b*d^3*g*i^3*x^4 + A^2*a*c^3*g*i^3 + (3*A^2*b*c*d^2 + A^2*a*d^3)*g*i^3*x^3 + 3*(A^2*b*c^2*d + A^2*a*c*d^2)*g*i^3*x^2 + (A^2*b*c^3 + 3*A^2*a*c^2*d)*g*i^3*x + (B^2*b*d^3*g*i^3*x^4 + B^2*a*c^3*g*i^3 + (3*B^2*b*c*d^2 + B^2*a*d^3)*g*i^3*x^3 + 3*(B^2*b*c^2*d + B^2*a*c*d^2)*g*i^3*x^2 + (B^2*b*c^3 + 3*B^2*a*c^2*d)*g*i^3*x)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b*d^3*g*i^3*x^4 + A*B*a*c^3*g*i^3 + (3*A*B*b*c*d^2 + A*B*a*d^3)*g*i^3*x^3 + 3*(A*B*b*c^2*d + A*B*a*c*d^2)*g*i^3*x^2 + (A*B*b*c^3 + 3*A*B*a*c^2*d)*g*i^3*x)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
181,0,0,0,0.466760," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right), x\right)"," ",0,"integral(A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n), x)","F",0
182,0,0,0,0.441189," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b g x + a g}, x\right)"," ",0,"integral((A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n))/(b*g*x + a*g), x)","F",0
183,0,0,0,0.440789," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{2} g^{2} x^{2} + 2 \, a b g^{2} x + a^{2} g^{2}}, x\right)"," ",0,"integral((A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n))/(b^2*g^2*x^2 + 2*a*b*g^2*x + a^2*g^2), x)","F",0
184,0,0,0,0.475140," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{3} g^{3} x^{3} + 3 \, a b^{2} g^{3} x^{2} + 3 \, a^{2} b g^{3} x + a^{3} g^{3}}, x\right)"," ",0,"integral((A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n))/(b^3*g^3*x^3 + 3*a*b^2*g^3*x^2 + 3*a^2*b*g^3*x + a^3*g^3), x)","F",0
185,0,0,0,0.442379," ","integrate((d*i*x+c*i)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} d^{3} i^{3} x^{3} + 3 \, A^{2} c d^{2} i^{3} x^{2} + 3 \, A^{2} c^{2} d i^{3} x + A^{2} c^{3} i^{3} + {\left(B^{2} d^{3} i^{3} x^{3} + 3 \, B^{2} c d^{2} i^{3} x^{2} + 3 \, B^{2} c^{2} d i^{3} x + B^{2} c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B d^{3} i^{3} x^{3} + 3 \, A B c d^{2} i^{3} x^{2} + 3 \, A B c^{2} d i^{3} x + A B c^{3} i^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{b^{4} g^{4} x^{4} + 4 \, a b^{3} g^{4} x^{3} + 6 \, a^{2} b^{2} g^{4} x^{2} + 4 \, a^{3} b g^{4} x + a^{4} g^{4}}, x\right)"," ",0,"integral((A^2*d^3*i^3*x^3 + 3*A^2*c*d^2*i^3*x^2 + 3*A^2*c^2*d*i^3*x + A^2*c^3*i^3 + (B^2*d^3*i^3*x^3 + 3*B^2*c*d^2*i^3*x^2 + 3*B^2*c^2*d*i^3*x + B^2*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*d^3*i^3*x^3 + 3*A*B*c*d^2*i^3*x^2 + 3*A*B*c^2*d*i^3*x + A*B*c^3*i^3)*log(e*((b*x + a)/(d*x + c))^n))/(b^4*g^4*x^4 + 4*a*b^3*g^4*x^3 + 6*a^2*b^2*g^4*x^2 + 4*a^3*b*g^4*x + a^4*g^4), x)","F",0
186,0,0,0,0.440215," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{3} g^{3} x^{3} + 3 \, A^{2} a b^{2} g^{3} x^{2} + 3 \, A^{2} a^{2} b g^{3} x + A^{2} a^{3} g^{3} + {\left(B^{2} b^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b g^{3} x + B^{2} a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{3} g^{3} x^{3} + 3 \, A B a b^{2} g^{3} x^{2} + 3 \, A B a^{2} b g^{3} x + A B a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d i x + c i}, x\right)"," ",0,"integral((A^2*b^3*g^3*x^3 + 3*A^2*a*b^2*g^3*x^2 + 3*A^2*a^2*b*g^3*x + A^2*a^3*g^3 + (B^2*b^3*g^3*x^3 + 3*B^2*a*b^2*g^3*x^2 + 3*B^2*a^2*b*g^3*x + B^2*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^3*g^3*x^3 + 3*A*B*a*b^2*g^3*x^2 + 3*A*B*a^2*b*g^3*x + A*B*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n))/(d*i*x + c*i), x)","F",0
187,0,0,0,0.434873," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{2} g^{2} x^{2} + 2 \, A^{2} a b g^{2} x + A^{2} a^{2} g^{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(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{2} g^{2} x^{2} + 2 \, A B a b g^{2} x + A B a^{2} g^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d i x + c i}, x\right)"," ",0,"integral((A^2*b^2*g^2*x^2 + 2*A^2*a*b*g^2*x + A^2*a^2*g^2 + (B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^2*g^2*x^2 + 2*A*B*a*b*g^2*x + A*B*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n))/(d*i*x + c*i), x)","F",0
188,0,0,0,0.424199," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b g x + A^{2} a g + {\left(B^{2} b g x + B^{2} a g\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b g x + A B a g\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d i x + c i}, x\right)"," ",0,"integral((A^2*b*g*x + A^2*a*g + (B^2*b*g*x + B^2*a*g)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b*g*x + A*B*a*g)*log(e*((b*x + a)/(d*x + c))^n))/(d*i*x + c*i), x)","F",0
189,0,0,0,0.422168," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B^{2} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, A B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A^{2}}{d i x + c i}, x\right)"," ",0,"integral((B^2*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*A*B*log(e*((b*x + a)/(d*x + c))^n) + A^2)/(d*i*x + c*i), x)","F",0
190,1,149,0,0.455672," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)/(d*i*x+c*i),x, algorithm=""fricas"")","\frac{B^{2} n^{2} \log\left(\frac{b x + a}{d x + c}\right)^{3} + 3 \, B^{2} \log\left(e\right)^{2} \log\left(\frac{b x + a}{d x + c}\right) + 3 \, A B n \log\left(\frac{b x + a}{d x + c}\right)^{2} + 3 \, A^{2} \log\left(\frac{b x + a}{d x + c}\right) + 3 \, {\left(B^{2} n \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, A B \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)}{3 \, {\left(b c - a d\right)} g i}"," ",0,"1/3*(B^2*n^2*log((b*x + a)/(d*x + c))^3 + 3*B^2*log(e)^2*log((b*x + a)/(d*x + c)) + 3*A*B*n*log((b*x + a)/(d*x + c))^2 + 3*A^2*log((b*x + a)/(d*x + c)) + 3*(B^2*n*log((b*x + a)/(d*x + c))^2 + 2*A*B*log((b*x + a)/(d*x + c)))*log(e))/((b*c - a*d)*g*i)","B",0
191,1,428,0,0.459773," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{3 \, A^{2} b c - 3 \, A^{2} a d + {\left(B^{2} b d n^{2} x + B^{2} a d n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + 6 \, {\left(B^{2} b c - B^{2} a d\right)} n^{2} + 3 \, {\left(B^{2} b c - B^{2} a d + {\left(B^{2} b d x + B^{2} a d\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} + 3 \, {\left(B^{2} b c n^{2} + A B a d n + {\left(B^{2} b d n^{2} + A B b d n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 6 \, {\left(A B b c - A B a d\right)} n + 3 \, {\left(2 \, A B b c - 2 \, A B a d + {\left(B^{2} b d n x + B^{2} a d n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(B^{2} b c - B^{2} a d\right)} n + 2 \, {\left(B^{2} b c n + A B a d + {\left(B^{2} b d n + A B b d\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 3 \, {\left(2 \, B^{2} b c n^{2} + 2 \, A B b c n + A^{2} a d + {\left(2 \, B^{2} b d n^{2} + 2 \, A B b d n + A^{2} b d\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{3 \, {\left({\left(b^{3} c^{2} - 2 \, a b^{2} c d + a^{2} b d^{2}\right)} g^{2} i x + {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} g^{2} i\right)}}"," ",0,"-1/3*(3*A^2*b*c - 3*A^2*a*d + (B^2*b*d*n^2*x + B^2*a*d*n^2)*log((b*x + a)/(d*x + c))^3 + 6*(B^2*b*c - B^2*a*d)*n^2 + 3*(B^2*b*c - B^2*a*d + (B^2*b*d*x + B^2*a*d)*log((b*x + a)/(d*x + c)))*log(e)^2 + 3*(B^2*b*c*n^2 + A*B*a*d*n + (B^2*b*d*n^2 + A*B*b*d*n)*x)*log((b*x + a)/(d*x + c))^2 + 6*(A*B*b*c - A*B*a*d)*n + 3*(2*A*B*b*c - 2*A*B*a*d + (B^2*b*d*n*x + B^2*a*d*n)*log((b*x + a)/(d*x + c))^2 + 2*(B^2*b*c - B^2*a*d)*n + 2*(B^2*b*c*n + A*B*a*d + (B^2*b*d*n + A*B*b*d)*x)*log((b*x + a)/(d*x + c)))*log(e) + 3*(2*B^2*b*c*n^2 + 2*A*B*b*c*n + A^2*a*d + (2*B^2*b*d*n^2 + 2*A*B*b*d*n + A^2*b*d)*x)*log((b*x + a)/(d*x + c)))/((b^3*c^2 - 2*a*b^2*c*d + a^2*b*d^2)*g^2*i*x + (a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*g^2*i)","B",0
192,1,1068,0,0.474708," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{6 \, A^{2} b^{2} c^{2} - 24 \, A^{2} a b c d + 18 \, A^{2} a^{2} d^{2} - 4 \, {\left(B^{2} b^{2} d^{2} n^{2} x^{2} + 2 \, B^{2} a b d^{2} n^{2} x + B^{2} a^{2} d^{2} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + 3 \, {\left(B^{2} b^{2} c^{2} - 16 \, B^{2} a b c d + 15 \, B^{2} a^{2} d^{2}\right)} n^{2} + 6 \, {\left(B^{2} b^{2} c^{2} - 4 \, B^{2} a b c d + 3 \, B^{2} a^{2} d^{2} - 2 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} x - 2 \, {\left(B^{2} b^{2} d^{2} x^{2} + 2 \, B^{2} a b d^{2} x + B^{2} a^{2} d^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} - 6 \, {\left(2 \, A B a^{2} d^{2} n - {\left(B^{2} b^{2} c^{2} - 4 \, B^{2} a b c d\right)} n^{2} + {\left(3 \, B^{2} b^{2} d^{2} n^{2} + 2 \, A B b^{2} d^{2} n\right)} x^{2} + 2 \, {\left(2 \, A B a b d^{2} n + {\left(B^{2} b^{2} c d + 2 \, B^{2} a b d^{2}\right)} n^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 6 \, {\left(A B b^{2} c^{2} - 8 \, A B a b c d + 7 \, A B a^{2} d^{2}\right)} n - 6 \, {\left(2 \, A^{2} b^{2} c d - 2 \, A^{2} a b d^{2} + 7 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n^{2} + 6 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} n\right)} x + 6 \, {\left(2 \, A B b^{2} c^{2} - 8 \, A B a b c d + 6 \, A B a^{2} d^{2} - 2 \, {\left(B^{2} b^{2} d^{2} n x^{2} + 2 \, B^{2} a b d^{2} n x + B^{2} a^{2} d^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B^{2} b^{2} c^{2} - 8 \, B^{2} a b c d + 7 \, B^{2} a^{2} d^{2}\right)} n - 2 \, {\left(2 \, A B b^{2} c d - 2 \, A B a b d^{2} + 3 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n\right)} x - 2 \, {\left(2 \, A B a^{2} d^{2} + {\left(3 \, B^{2} b^{2} d^{2} n + 2 \, A B b^{2} d^{2}\right)} x^{2} - {\left(B^{2} b^{2} c^{2} - 4 \, B^{2} a b c d\right)} n + 2 \, {\left(2 \, A B a b d^{2} + {\left(B^{2} b^{2} c d + 2 \, B^{2} a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) - 6 \, {\left(2 \, A^{2} a^{2} d^{2} - {\left(B^{2} b^{2} c^{2} - 8 \, B^{2} a b c d\right)} n^{2} + {\left(7 \, B^{2} b^{2} d^{2} n^{2} + 6 \, A B b^{2} d^{2} n + 2 \, A^{2} b^{2} d^{2}\right)} x^{2} - 2 \, {\left(A B b^{2} c^{2} - 4 \, A B a b c d\right)} n + 2 \, {\left(2 \, A^{2} a b d^{2} + {\left(3 \, B^{2} b^{2} c d + 4 \, B^{2} a b d^{2}\right)} n^{2} + 2 \, {\left(A B b^{2} c d + 2 \, A B a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{12 \, {\left({\left(b^{5} c^{3} - 3 \, a b^{4} c^{2} d + 3 \, a^{2} b^{3} c d^{2} - a^{3} b^{2} d^{3}\right)} g^{3} i x^{2} + 2 \, {\left(a b^{4} c^{3} - 3 \, a^{2} b^{3} c^{2} d + 3 \, a^{3} b^{2} c d^{2} - a^{4} b d^{3}\right)} g^{3} i x + {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} g^{3} i\right)}}"," ",0,"-1/12*(6*A^2*b^2*c^2 - 24*A^2*a*b*c*d + 18*A^2*a^2*d^2 - 4*(B^2*b^2*d^2*n^2*x^2 + 2*B^2*a*b*d^2*n^2*x + B^2*a^2*d^2*n^2)*log((b*x + a)/(d*x + c))^3 + 3*(B^2*b^2*c^2 - 16*B^2*a*b*c*d + 15*B^2*a^2*d^2)*n^2 + 6*(B^2*b^2*c^2 - 4*B^2*a*b*c*d + 3*B^2*a^2*d^2 - 2*(B^2*b^2*c*d - B^2*a*b*d^2)*x - 2*(B^2*b^2*d^2*x^2 + 2*B^2*a*b*d^2*x + B^2*a^2*d^2)*log((b*x + a)/(d*x + c)))*log(e)^2 - 6*(2*A*B*a^2*d^2*n - (B^2*b^2*c^2 - 4*B^2*a*b*c*d)*n^2 + (3*B^2*b^2*d^2*n^2 + 2*A*B*b^2*d^2*n)*x^2 + 2*(2*A*B*a*b*d^2*n + (B^2*b^2*c*d + 2*B^2*a*b*d^2)*n^2)*x)*log((b*x + a)/(d*x + c))^2 + 6*(A*B*b^2*c^2 - 8*A*B*a*b*c*d + 7*A*B*a^2*d^2)*n - 6*(2*A^2*b^2*c*d - 2*A^2*a*b*d^2 + 7*(B^2*b^2*c*d - B^2*a*b*d^2)*n^2 + 6*(A*B*b^2*c*d - A*B*a*b*d^2)*n)*x + 6*(2*A*B*b^2*c^2 - 8*A*B*a*b*c*d + 6*A*B*a^2*d^2 - 2*(B^2*b^2*d^2*n*x^2 + 2*B^2*a*b*d^2*n*x + B^2*a^2*d^2*n)*log((b*x + a)/(d*x + c))^2 + (B^2*b^2*c^2 - 8*B^2*a*b*c*d + 7*B^2*a^2*d^2)*n - 2*(2*A*B*b^2*c*d - 2*A*B*a*b*d^2 + 3*(B^2*b^2*c*d - B^2*a*b*d^2)*n)*x - 2*(2*A*B*a^2*d^2 + (3*B^2*b^2*d^2*n + 2*A*B*b^2*d^2)*x^2 - (B^2*b^2*c^2 - 4*B^2*a*b*c*d)*n + 2*(2*A*B*a*b*d^2 + (B^2*b^2*c*d + 2*B^2*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) - 6*(2*A^2*a^2*d^2 - (B^2*b^2*c^2 - 8*B^2*a*b*c*d)*n^2 + (7*B^2*b^2*d^2*n^2 + 6*A*B*b^2*d^2*n + 2*A^2*b^2*d^2)*x^2 - 2*(A*B*b^2*c^2 - 4*A*B*a*b*c*d)*n + 2*(2*A^2*a*b*d^2 + (3*B^2*b^2*c*d + 4*B^2*a*b*d^2)*n^2 + 2*(A*B*b^2*c*d + 2*A*B*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))/((b^5*c^3 - 3*a*b^4*c^2*d + 3*a^2*b^3*c*d^2 - a^3*b^2*d^3)*g^3*i*x^2 + 2*(a*b^4*c^3 - 3*a^2*b^3*c^2*d + 3*a^3*b^2*c*d^2 - a^4*b*d^3)*g^3*i*x + (a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*g^3*i)","B",0
193,1,1910,0,0.495483," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4/(d*i*x+c*i),x, algorithm=""fricas"")","-\frac{36 \, A^{2} b^{3} c^{3} - 162 \, A^{2} a b^{2} c^{2} d + 324 \, A^{2} a^{2} b c d^{2} - 198 \, A^{2} a^{3} d^{3} + 36 \, {\left(B^{2} b^{3} d^{3} n^{2} x^{3} + 3 \, B^{2} a b^{2} d^{3} n^{2} x^{2} + 3 \, B^{2} a^{2} b d^{3} n^{2} x + B^{2} a^{3} d^{3} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + {\left(8 \, B^{2} b^{3} c^{3} - 81 \, B^{2} a b^{2} c^{2} d + 648 \, B^{2} a^{2} b c d^{2} - 575 \, B^{2} a^{3} d^{3}\right)} n^{2} + 6 \, {\left(18 \, A^{2} b^{3} c d^{2} - 18 \, A^{2} a b^{2} d^{3} + 85 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} n^{2} + 66 \, {\left(A B b^{3} c d^{2} - A B a b^{2} d^{3}\right)} n\right)} x^{2} + 18 \, {\left(2 \, B^{2} b^{3} c^{3} - 9 \, B^{2} a b^{2} c^{2} d + 18 \, B^{2} a^{2} b c d^{2} - 11 \, B^{2} a^{3} d^{3} + 6 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(B^{2} b^{3} c^{2} d - 6 \, B^{2} a b^{2} c d^{2} + 5 \, B^{2} a^{2} b d^{3}\right)} x + 6 \, {\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 + B^{2} a^{3} d^{3}\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} + 18 \, {\left(6 \, A B a^{3} d^{3} n + {\left(11 \, B^{2} b^{3} d^{3} n^{2} + 6 \, A B b^{3} d^{3} n\right)} x^{3} + {\left(2 \, B^{2} b^{3} c^{3} - 9 \, B^{2} a b^{2} c^{2} d + 18 \, B^{2} a^{2} b c d^{2}\right)} n^{2} + 3 \, {\left(6 \, A B a b^{2} d^{3} n + {\left(2 \, B^{2} b^{3} c d^{2} + 9 \, B^{2} a b^{2} d^{3}\right)} n^{2}\right)} x^{2} + 3 \, {\left(6 \, A B a^{2} b d^{3} n - {\left(B^{2} b^{3} c^{2} d - 6 \, B^{2} a b^{2} c d^{2} - 6 \, B^{2} a^{2} b d^{3}\right)} n^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 6 \, {\left(4 \, A B b^{3} c^{3} - 27 \, A B a b^{2} c^{2} d + 108 \, A B a^{2} b c d^{2} - 85 \, A B a^{3} d^{3}\right)} n - 3 \, {\left(18 \, A^{2} b^{3} c^{2} d - 108 \, A^{2} a b^{2} c d^{2} + 90 \, A^{2} a^{2} b d^{3} + {\left(19 \, B^{2} b^{3} c^{2} d - 378 \, B^{2} a b^{2} c d^{2} + 359 \, B^{2} a^{2} b d^{3}\right)} n^{2} + 6 \, {\left(5 \, A B b^{3} c^{2} d - 54 \, A B a b^{2} c d^{2} + 49 \, A B a^{2} b d^{3}\right)} n\right)} x + 6 \, {\left(12 \, A B b^{3} c^{3} - 54 \, A B a b^{2} c^{2} d + 108 \, A B a^{2} b c d^{2} - 66 \, A B a^{3} d^{3} + 6 \, {\left(6 \, A B b^{3} c d^{2} - 6 \, A B a b^{2} d^{3} + 11 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} n\right)} x^{2} + 18 \, {\left(B^{2} b^{3} d^{3} n x^{3} + 3 \, B^{2} a b^{2} d^{3} n x^{2} + 3 \, B^{2} a^{2} b d^{3} n x + B^{2} a^{3} d^{3} n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(4 \, B^{2} b^{3} c^{3} - 27 \, B^{2} a b^{2} c^{2} d + 108 \, B^{2} a^{2} b c d^{2} - 85 \, B^{2} a^{3} d^{3}\right)} n - 3 \, {\left(6 \, A B b^{3} c^{2} d - 36 \, A B a b^{2} c d^{2} + 30 \, A B a^{2} b d^{3} + {\left(5 \, B^{2} b^{3} c^{2} d - 54 \, B^{2} a b^{2} c d^{2} + 49 \, B^{2} a^{2} b d^{3}\right)} n\right)} x + 6 \, {\left(6 \, A B a^{3} d^{3} + {\left(11 \, B^{2} b^{3} d^{3} n + 6 \, A B b^{3} d^{3}\right)} x^{3} + 3 \, {\left(6 \, A B a b^{2} d^{3} + {\left(2 \, B^{2} b^{3} c d^{2} + 9 \, B^{2} a b^{2} d^{3}\right)} n\right)} x^{2} + {\left(2 \, B^{2} b^{3} c^{3} - 9 \, B^{2} a b^{2} c^{2} d + 18 \, B^{2} a^{2} b c d^{2}\right)} n + 3 \, {\left(6 \, A B a^{2} b d^{3} - {\left(B^{2} b^{3} c^{2} d - 6 \, B^{2} a b^{2} c d^{2} - 6 \, B^{2} a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left(18 \, A^{2} a^{3} d^{3} + {\left(85 \, B^{2} b^{3} d^{3} n^{2} + 66 \, A B b^{3} d^{3} n + 18 \, A^{2} b^{3} d^{3}\right)} x^{3} + {\left(4 \, B^{2} b^{3} c^{3} - 27 \, B^{2} a b^{2} c^{2} d + 108 \, B^{2} a^{2} b c d^{2}\right)} n^{2} + 3 \, {\left(18 \, A^{2} a b^{2} d^{3} + {\left(22 \, B^{2} b^{3} c d^{2} + 63 \, B^{2} a b^{2} d^{3}\right)} n^{2} + 6 \, {\left(2 \, A B b^{3} c d^{2} + 9 \, A B a b^{2} d^{3}\right)} n\right)} x^{2} + 6 \, {\left(2 \, A B b^{3} c^{3} - 9 \, A B a b^{2} c^{2} d + 18 \, A B a^{2} b c d^{2}\right)} n + 3 \, {\left(18 \, A^{2} a^{2} b d^{3} - {\left(5 \, B^{2} b^{3} c^{2} d - 54 \, B^{2} a b^{2} c d^{2} - 36 \, B^{2} a^{2} b d^{3}\right)} n^{2} - 6 \, {\left(A B b^{3} c^{2} d - 6 \, A B a b^{2} c d^{2} - 6 \, A B a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{108 \, {\left({\left(b^{7} c^{4} - 4 \, a b^{6} c^{3} d + 6 \, a^{2} b^{5} c^{2} d^{2} - 4 \, a^{3} b^{4} c d^{3} + a^{4} b^{3} d^{4}\right)} g^{4} i x^{3} + 3 \, {\left(a b^{6} c^{4} - 4 \, a^{2} b^{5} c^{3} d + 6 \, a^{3} b^{4} c^{2} d^{2} - 4 \, a^{4} b^{3} c d^{3} + a^{5} b^{2} d^{4}\right)} g^{4} i x^{2} + 3 \, {\left(a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}\right)} g^{4} i x + {\left(a^{3} b^{4} c^{4} - 4 \, a^{4} b^{3} c^{3} d + 6 \, a^{5} b^{2} c^{2} d^{2} - 4 \, a^{6} b c d^{3} + a^{7} d^{4}\right)} g^{4} i\right)}}"," ",0,"-1/108*(36*A^2*b^3*c^3 - 162*A^2*a*b^2*c^2*d + 324*A^2*a^2*b*c*d^2 - 198*A^2*a^3*d^3 + 36*(B^2*b^3*d^3*n^2*x^3 + 3*B^2*a*b^2*d^3*n^2*x^2 + 3*B^2*a^2*b*d^3*n^2*x + B^2*a^3*d^3*n^2)*log((b*x + a)/(d*x + c))^3 + (8*B^2*b^3*c^3 - 81*B^2*a*b^2*c^2*d + 648*B^2*a^2*b*c*d^2 - 575*B^2*a^3*d^3)*n^2 + 6*(18*A^2*b^3*c*d^2 - 18*A^2*a*b^2*d^3 + 85*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*n^2 + 66*(A*B*b^3*c*d^2 - A*B*a*b^2*d^3)*n)*x^2 + 18*(2*B^2*b^3*c^3 - 9*B^2*a*b^2*c^2*d + 18*B^2*a^2*b*c*d^2 - 11*B^2*a^3*d^3 + 6*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*x^2 - 3*(B^2*b^3*c^2*d - 6*B^2*a*b^2*c*d^2 + 5*B^2*a^2*b*d^3)*x + 6*(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 + B^2*a^3*d^3)*log((b*x + a)/(d*x + c)))*log(e)^2 + 18*(6*A*B*a^3*d^3*n + (11*B^2*b^3*d^3*n^2 + 6*A*B*b^3*d^3*n)*x^3 + (2*B^2*b^3*c^3 - 9*B^2*a*b^2*c^2*d + 18*B^2*a^2*b*c*d^2)*n^2 + 3*(6*A*B*a*b^2*d^3*n + (2*B^2*b^3*c*d^2 + 9*B^2*a*b^2*d^3)*n^2)*x^2 + 3*(6*A*B*a^2*b*d^3*n - (B^2*b^3*c^2*d - 6*B^2*a*b^2*c*d^2 - 6*B^2*a^2*b*d^3)*n^2)*x)*log((b*x + a)/(d*x + c))^2 + 6*(4*A*B*b^3*c^3 - 27*A*B*a*b^2*c^2*d + 108*A*B*a^2*b*c*d^2 - 85*A*B*a^3*d^3)*n - 3*(18*A^2*b^3*c^2*d - 108*A^2*a*b^2*c*d^2 + 90*A^2*a^2*b*d^3 + (19*B^2*b^3*c^2*d - 378*B^2*a*b^2*c*d^2 + 359*B^2*a^2*b*d^3)*n^2 + 6*(5*A*B*b^3*c^2*d - 54*A*B*a*b^2*c*d^2 + 49*A*B*a^2*b*d^3)*n)*x + 6*(12*A*B*b^3*c^3 - 54*A*B*a*b^2*c^2*d + 108*A*B*a^2*b*c*d^2 - 66*A*B*a^3*d^3 + 6*(6*A*B*b^3*c*d^2 - 6*A*B*a*b^2*d^3 + 11*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*n)*x^2 + 18*(B^2*b^3*d^3*n*x^3 + 3*B^2*a*b^2*d^3*n*x^2 + 3*B^2*a^2*b*d^3*n*x + B^2*a^3*d^3*n)*log((b*x + a)/(d*x + c))^2 + (4*B^2*b^3*c^3 - 27*B^2*a*b^2*c^2*d + 108*B^2*a^2*b*c*d^2 - 85*B^2*a^3*d^3)*n - 3*(6*A*B*b^3*c^2*d - 36*A*B*a*b^2*c*d^2 + 30*A*B*a^2*b*d^3 + (5*B^2*b^3*c^2*d - 54*B^2*a*b^2*c*d^2 + 49*B^2*a^2*b*d^3)*n)*x + 6*(6*A*B*a^3*d^3 + (11*B^2*b^3*d^3*n + 6*A*B*b^3*d^3)*x^3 + 3*(6*A*B*a*b^2*d^3 + (2*B^2*b^3*c*d^2 + 9*B^2*a*b^2*d^3)*n)*x^2 + (2*B^2*b^3*c^3 - 9*B^2*a*b^2*c^2*d + 18*B^2*a^2*b*c*d^2)*n + 3*(6*A*B*a^2*b*d^3 - (B^2*b^3*c^2*d - 6*B^2*a*b^2*c*d^2 - 6*B^2*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) + 6*(18*A^2*a^3*d^3 + (85*B^2*b^3*d^3*n^2 + 66*A*B*b^3*d^3*n + 18*A^2*b^3*d^3)*x^3 + (4*B^2*b^3*c^3 - 27*B^2*a*b^2*c^2*d + 108*B^2*a^2*b*c*d^2)*n^2 + 3*(18*A^2*a*b^2*d^3 + (22*B^2*b^3*c*d^2 + 63*B^2*a*b^2*d^3)*n^2 + 6*(2*A*B*b^3*c*d^2 + 9*A*B*a*b^2*d^3)*n)*x^2 + 6*(2*A*B*b^3*c^3 - 9*A*B*a*b^2*c^2*d + 18*A*B*a^2*b*c*d^2)*n + 3*(18*A^2*a^2*b*d^3 - (5*B^2*b^3*c^2*d - 54*B^2*a*b^2*c*d^2 - 36*B^2*a^2*b*d^3)*n^2 - 6*(A*B*b^3*c^2*d - 6*A*B*a*b^2*c*d^2 - 6*A*B*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))/((b^7*c^4 - 4*a*b^6*c^3*d + 6*a^2*b^5*c^2*d^2 - 4*a^3*b^4*c*d^3 + a^4*b^3*d^4)*g^4*i*x^3 + 3*(a*b^6*c^4 - 4*a^2*b^5*c^3*d + 6*a^3*b^4*c^2*d^2 - 4*a^4*b^3*c*d^3 + a^5*b^2*d^4)*g^4*i*x^2 + 3*(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 6*a^4*b^3*c^2*d^2 - 4*a^5*b^2*c*d^3 + a^6*b*d^4)*g^4*i*x + (a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3 + a^7*d^4)*g^4*i)","B",0
194,0,0,0,0.447033," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{3} g^{3} x^{3} + 3 \, A^{2} a b^{2} g^{3} x^{2} + 3 \, A^{2} a^{2} b g^{3} x + A^{2} a^{3} g^{3} + {\left(B^{2} b^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b g^{3} x + B^{2} a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{3} g^{3} x^{3} + 3 \, A B a b^{2} g^{3} x^{2} + 3 \, A B a^{2} b g^{3} x + A B a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A^2*b^3*g^3*x^3 + 3*A^2*a*b^2*g^3*x^2 + 3*A^2*a^2*b*g^3*x + A^2*a^3*g^3 + (B^2*b^3*g^3*x^3 + 3*B^2*a*b^2*g^3*x^2 + 3*B^2*a^2*b*g^3*x + B^2*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^3*g^3*x^3 + 3*A*B*a*b^2*g^3*x^2 + 3*A*B*a^2*b*g^3*x + A*B*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
195,0,0,0,0.435814," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{2} g^{2} x^{2} + 2 \, A^{2} a b g^{2} x + A^{2} a^{2} g^{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(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{2} g^{2} x^{2} + 2 \, A B a b g^{2} x + A B a^{2} g^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A^2*b^2*g^2*x^2 + 2*A^2*a*b*g^2*x + A^2*a^2*g^2 + (B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^2*g^2*x^2 + 2*A*B*a*b*g^2*x + A*B*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
196,0,0,0,0.425335," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b g x + A^{2} a g + {\left(B^{2} b g x + B^{2} a g\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b g x + A B a g\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{2} i^{2} x^{2} + 2 \, c d i^{2} x + c^{2} i^{2}}, x\right)"," ",0,"integral((A^2*b*g*x + A^2*a*g + (B^2*b*g*x + B^2*a*g)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b*g*x + A*B*a*g)*log(e*((b*x + a)/(d*x + c))^n))/(d^2*i^2*x^2 + 2*c*d*i^2*x + c^2*i^2), x)","F",0
197,1,263,0,0.435807," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{A^{2} b c - A^{2} a d + 2 \, {\left(B^{2} b c - B^{2} a d\right)} n^{2} + {\left(B^{2} b c - B^{2} a d\right)} \log\left(e\right)^{2} - {\left(B^{2} b d n^{2} x + B^{2} a d n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 2 \, {\left(A B b c - A B a d\right)} n + 2 \, {\left(A B b c - A B a d - {\left(B^{2} b c - B^{2} a d\right)} n - {\left(B^{2} b d n x + B^{2} a d n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left(B^{2} a d n^{2} - A B a d n + {\left(B^{2} b d n^{2} - A B b d n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{{\left(b c d^{2} - a d^{3}\right)} i^{2} x + {\left(b c^{2} d - a c d^{2}\right)} i^{2}}"," ",0,"-(A^2*b*c - A^2*a*d + 2*(B^2*b*c - B^2*a*d)*n^2 + (B^2*b*c - B^2*a*d)*log(e)^2 - (B^2*b*d*n^2*x + B^2*a*d*n^2)*log((b*x + a)/(d*x + c))^2 - 2*(A*B*b*c - A*B*a*d)*n + 2*(A*B*b*c - A*B*a*d - (B^2*b*c - B^2*a*d)*n - (B^2*b*d*n*x + B^2*a*d*n)*log((b*x + a)/(d*x + c)))*log(e) + 2*(B^2*a*d*n^2 - A*B*a*d*n + (B^2*b*d*n^2 - A*B*b*d*n)*x)*log((b*x + a)/(d*x + c)))/((b*c*d^2 - a*d^3)*i^2*x + (b*c^2*d - a*c*d^2)*i^2)","A",0
198,1,432,0,0.442534," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)/(d*i*x+c*i)^2,x, algorithm=""fricas"")","\frac{3 \, A^{2} b c - 3 \, A^{2} a d + {\left(B^{2} b d n^{2} x + B^{2} b c n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + 6 \, {\left(B^{2} b c - B^{2} a d\right)} n^{2} + 3 \, {\left(B^{2} b c - B^{2} a d + {\left(B^{2} b d x + B^{2} b c\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} - 3 \, {\left(B^{2} a d n^{2} - A B b c n + {\left(B^{2} b d n^{2} - A B b d n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 6 \, {\left(A B b c - A B a d\right)} n + 3 \, {\left(2 \, A B b c - 2 \, A B a d + {\left(B^{2} b d n x + B^{2} b c n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 2 \, {\left(B^{2} b c - B^{2} a d\right)} n - 2 \, {\left(B^{2} a d n - A B b c + {\left(B^{2} b d n - A B b d\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 3 \, {\left(2 \, B^{2} a d n^{2} - 2 \, A B a d n + A^{2} b c + {\left(2 \, B^{2} b d n^{2} - 2 \, A B b d n + A^{2} b d\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{3 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} g i^{2} x + {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} g i^{2}\right)}}"," ",0,"1/3*(3*A^2*b*c - 3*A^2*a*d + (B^2*b*d*n^2*x + B^2*b*c*n^2)*log((b*x + a)/(d*x + c))^3 + 6*(B^2*b*c - B^2*a*d)*n^2 + 3*(B^2*b*c - B^2*a*d + (B^2*b*d*x + B^2*b*c)*log((b*x + a)/(d*x + c)))*log(e)^2 - 3*(B^2*a*d*n^2 - A*B*b*c*n + (B^2*b*d*n^2 - A*B*b*d*n)*x)*log((b*x + a)/(d*x + c))^2 - 6*(A*B*b*c - A*B*a*d)*n + 3*(2*A*B*b*c - 2*A*B*a*d + (B^2*b*d*n*x + B^2*b*c*n)*log((b*x + a)/(d*x + c))^2 - 2*(B^2*b*c - B^2*a*d)*n - 2*(B^2*a*d*n - A*B*b*c + (B^2*b*d*n - A*B*b*d)*x)*log((b*x + a)/(d*x + c)))*log(e) + 3*(2*B^2*a*d*n^2 - 2*A*B*a*d*n + A^2*b*c + (2*B^2*b*d*n^2 - 2*A*B*b*d*n + A^2*b*d)*x)*log((b*x + a)/(d*x + c)))/((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*g*i^2*x + (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*g*i^2)","A",0
199,1,983,0,0.455855," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{3 \, A^{2} b^{2} c^{2} - 3 \, A^{2} a^{2} d^{2} + 2 \, {\left(B^{2} b^{2} d^{2} n^{2} x^{2} + B^{2} a b c d n^{2} + {\left(B^{2} b^{2} c d + B^{2} a b d^{2}\right)} n^{2} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + 6 \, {\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} n^{2} + 3 \, {\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2} + 2 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} x + 2 \, {\left(B^{2} b^{2} d^{2} x^{2} + B^{2} a b c d + {\left(B^{2} b^{2} c d + B^{2} a b d^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} + 3 \, {\left(2 \, A B b^{2} d^{2} n x^{2} + 2 \, A B a b c d n + {\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} n^{2} + 2 \, {\left({\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n^{2} + {\left(A B b^{2} c d + A B a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 6 \, {\left(A B b^{2} c^{2} - 2 \, A B a b c d + A B a^{2} d^{2}\right)} n + 6 \, {\left(A^{2} b^{2} c d - A^{2} a b d^{2} + 2 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n^{2}\right)} x + 6 \, {\left(A B b^{2} c^{2} - A B a^{2} d^{2} + {\left(B^{2} b^{2} d^{2} n x^{2} + B^{2} a b c d n + {\left(B^{2} b^{2} c d + B^{2} a b d^{2}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B^{2} b^{2} c^{2} - 2 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right)} n + 2 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} x + {\left(2 \, A B b^{2} d^{2} x^{2} + 2 \, A B a b c d + {\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} n + 2 \, {\left(A B b^{2} c d + A B a b d^{2} + {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left(A^{2} a b c d + {\left(B^{2} b^{2} c^{2} + B^{2} a^{2} d^{2}\right)} n^{2} + {\left(2 \, B^{2} b^{2} d^{2} n^{2} + A^{2} b^{2} d^{2}\right)} x^{2} + {\left(A B b^{2} c^{2} - A B a^{2} d^{2}\right)} n + {\left(A^{2} b^{2} c d + A^{2} a b d^{2} + 2 \, {\left(B^{2} b^{2} c d + B^{2} a b d^{2}\right)} n^{2} + 2 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{3 \, {\left({\left(b^{4} c^{3} d - 3 \, a b^{3} c^{2} d^{2} + 3 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} g^{2} i^{2} x^{2} + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} g^{2} i^{2} x + {\left(a b^{3} c^{4} - 3 \, a^{2} b^{2} c^{3} d + 3 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} g^{2} i^{2}\right)}}"," ",0,"-1/3*(3*A^2*b^2*c^2 - 3*A^2*a^2*d^2 + 2*(B^2*b^2*d^2*n^2*x^2 + B^2*a*b*c*d*n^2 + (B^2*b^2*c*d + B^2*a*b*d^2)*n^2*x)*log((b*x + a)/(d*x + c))^3 + 6*(B^2*b^2*c^2 - B^2*a^2*d^2)*n^2 + 3*(B^2*b^2*c^2 - B^2*a^2*d^2 + 2*(B^2*b^2*c*d - B^2*a*b*d^2)*x + 2*(B^2*b^2*d^2*x^2 + B^2*a*b*c*d + (B^2*b^2*c*d + B^2*a*b*d^2)*x)*log((b*x + a)/(d*x + c)))*log(e)^2 + 3*(2*A*B*b^2*d^2*n*x^2 + 2*A*B*a*b*c*d*n + (B^2*b^2*c^2 - B^2*a^2*d^2)*n^2 + 2*((B^2*b^2*c*d - B^2*a*b*d^2)*n^2 + (A*B*b^2*c*d + A*B*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c))^2 + 6*(A*B*b^2*c^2 - 2*A*B*a*b*c*d + A*B*a^2*d^2)*n + 6*(A^2*b^2*c*d - A^2*a*b*d^2 + 2*(B^2*b^2*c*d - B^2*a*b*d^2)*n^2)*x + 6*(A*B*b^2*c^2 - A*B*a^2*d^2 + (B^2*b^2*d^2*n*x^2 + B^2*a*b*c*d*n + (B^2*b^2*c*d + B^2*a*b*d^2)*n*x)*log((b*x + a)/(d*x + c))^2 + (B^2*b^2*c^2 - 2*B^2*a*b*c*d + B^2*a^2*d^2)*n + 2*(A*B*b^2*c*d - A*B*a*b*d^2)*x + (2*A*B*b^2*d^2*x^2 + 2*A*B*a*b*c*d + (B^2*b^2*c^2 - B^2*a^2*d^2)*n + 2*(A*B*b^2*c*d + A*B*a*b*d^2 + (B^2*b^2*c*d - B^2*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) + 6*(A^2*a*b*c*d + (B^2*b^2*c^2 + B^2*a^2*d^2)*n^2 + (2*B^2*b^2*d^2*n^2 + A^2*b^2*d^2)*x^2 + (A*B*b^2*c^2 - A*B*a^2*d^2)*n + (A^2*b^2*c*d + A^2*a*b*d^2 + 2*(B^2*b^2*c*d + B^2*a*b*d^2)*n^2 + 2*(A*B*b^2*c*d - A*B*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))/((b^4*c^3*d - 3*a*b^3*c^2*d^2 + 3*a^2*b^2*c*d^3 - a^3*b*d^4)*g^2*i^2*x^2 + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*g^2*i^2*x + (a*b^3*c^4 - 3*a^2*b^2*c^3*d + 3*a^3*b*c^2*d^2 - a^4*c*d^3)*g^2*i^2)","B",0
200,1,2052,0,0.514839," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{2 \, A^{2} b^{3} c^{3} - 12 \, A^{2} a b^{2} c^{2} d + 6 \, A^{2} a^{2} b c d^{2} + 4 \, A^{2} a^{3} d^{3} - 4 \, {\left(B^{2} b^{3} d^{3} n^{2} x^{3} + B^{2} a^{2} b c d^{2} n^{2} + {\left(B^{2} b^{3} c d^{2} + 2 \, B^{2} a b^{2} d^{3}\right)} n^{2} x^{2} + {\left(2 \, B^{2} a b^{2} c d^{2} + B^{2} a^{2} b d^{3}\right)} n^{2} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + {\left(B^{2} b^{3} c^{3} - 24 \, B^{2} a b^{2} c^{2} d + 15 \, B^{2} a^{2} b c d^{2} + 8 \, B^{2} a^{3} d^{3}\right)} n^{2} - 6 \, {\left(2 \, A^{2} b^{3} c d^{2} - 2 \, A^{2} a b^{2} d^{3} + 5 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} n^{2} + 2 \, {\left(A B b^{3} c d^{2} - A B a b^{2} d^{3}\right)} n\right)} x^{2} + 2 \, {\left(B^{2} b^{3} c^{3} - 6 \, B^{2} a b^{2} c^{2} d + 3 \, B^{2} a^{2} b c d^{2} + 2 \, B^{2} a^{3} d^{3} - 6 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} x^{2} - 3 \, {\left(B^{2} b^{3} c^{2} d + 2 \, B^{2} a b^{2} c d^{2} - 3 \, B^{2} a^{2} b d^{3}\right)} x - 6 \, {\left(B^{2} b^{3} d^{3} x^{3} + B^{2} a^{2} b c d^{2} + {\left(B^{2} b^{3} c d^{2} + 2 \, B^{2} a b^{2} d^{3}\right)} x^{2} + {\left(2 \, B^{2} a b^{2} c d^{2} + B^{2} a^{2} b d^{3}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} - 2 \, {\left(6 \, A B a^{2} b c d^{2} n + 3 \, {\left(B^{2} b^{3} d^{3} n^{2} + 2 \, A B b^{3} d^{3} n\right)} x^{3} - {\left(B^{2} b^{3} c^{3} - 6 \, B^{2} a b^{2} c^{2} d + 2 \, B^{2} a^{3} d^{3}\right)} n^{2} + 3 \, {\left(3 \, B^{2} b^{3} c d^{2} n^{2} + 2 \, {\left(A B b^{3} c d^{2} + 2 \, A B a b^{2} d^{3}\right)} n\right)} x^{2} + 3 \, {\left({\left(B^{2} b^{3} c^{2} d + 4 \, B^{2} a b^{2} c d^{2} - 2 \, B^{2} a^{2} b d^{3}\right)} n^{2} + 2 \, {\left(2 \, A B a b^{2} c d^{2} + A B a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(A B b^{3} c^{3} - 12 \, A B a b^{2} c^{2} d + 15 \, A B a^{2} b c d^{2} - 4 \, A B a^{3} d^{3}\right)} n - 3 \, {\left(2 \, A^{2} b^{3} c^{2} d + 4 \, A^{2} a b^{2} c d^{2} - 6 \, A^{2} a^{2} b d^{3} + {\left(7 \, B^{2} b^{3} c^{2} d + 6 \, B^{2} a b^{2} c d^{2} - 13 \, B^{2} a^{2} b d^{3}\right)} n^{2} + 2 \, {\left(3 \, A B b^{3} c^{2} d - 2 \, A B a b^{2} c d^{2} - A B a^{2} b d^{3}\right)} n\right)} x + 2 \, {\left(2 \, A B b^{3} c^{3} - 12 \, A B a b^{2} c^{2} d + 6 \, A B a^{2} b c d^{2} + 4 \, A B a^{3} d^{3} - 6 \, {\left(2 \, A B b^{3} c d^{2} - 2 \, A B a b^{2} d^{3} + {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} n\right)} x^{2} - 6 \, {\left(B^{2} b^{3} d^{3} n x^{3} + B^{2} a^{2} b c d^{2} n + {\left(B^{2} b^{3} c d^{2} + 2 \, B^{2} a b^{2} d^{3}\right)} n x^{2} + {\left(2 \, B^{2} a b^{2} c d^{2} + B^{2} a^{2} b d^{3}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B^{2} b^{3} c^{3} - 12 \, B^{2} a b^{2} c^{2} d + 15 \, B^{2} a^{2} b c d^{2} - 4 \, B^{2} a^{3} d^{3}\right)} n - 3 \, {\left(2 \, A B b^{3} c^{2} d + 4 \, A B a b^{2} c d^{2} - 6 \, A B a^{2} b d^{3} + {\left(3 \, B^{2} b^{3} c^{2} d - 2 \, B^{2} a b^{2} c d^{2} - B^{2} a^{2} b d^{3}\right)} n\right)} x - 2 \, {\left(6 \, A B a^{2} b c d^{2} + 3 \, {\left(B^{2} b^{3} d^{3} n + 2 \, A B b^{3} d^{3}\right)} x^{3} + 3 \, {\left(3 \, B^{2} b^{3} c d^{2} n + 2 \, A B b^{3} c d^{2} + 4 \, A B a b^{2} d^{3}\right)} x^{2} - {\left(B^{2} b^{3} c^{3} - 6 \, B^{2} a b^{2} c^{2} d + 2 \, B^{2} a^{3} d^{3}\right)} n + 3 \, {\left(4 \, A B a b^{2} c d^{2} + 2 \, A B a^{2} b d^{3} + {\left(B^{2} b^{3} c^{2} d + 4 \, B^{2} a b^{2} c d^{2} - 2 \, B^{2} a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) - 2 \, {\left(6 \, A^{2} a^{2} b c d^{2} + 3 \, {\left(5 \, B^{2} b^{3} d^{3} n^{2} + 2 \, A B b^{3} d^{3} n + 2 \, A^{2} b^{3} d^{3}\right)} x^{3} - {\left(B^{2} b^{3} c^{3} - 12 \, B^{2} a b^{2} c^{2} d - 4 \, B^{2} a^{3} d^{3}\right)} n^{2} + 3 \, {\left(6 \, A B b^{3} c d^{2} n + 2 \, A^{2} b^{3} c d^{2} + 4 \, A^{2} a b^{2} d^{3} + {\left(7 \, B^{2} b^{3} c d^{2} + 8 \, B^{2} a b^{2} d^{3}\right)} n^{2}\right)} x^{2} - 2 \, {\left(A B b^{3} c^{3} - 6 \, A B a b^{2} c^{2} d + 2 \, A B a^{3} d^{3}\right)} n + 3 \, {\left(4 \, A^{2} a b^{2} c d^{2} + 2 \, A^{2} a^{2} b d^{3} + {\left(3 \, B^{2} b^{3} c^{2} d + 8 \, B^{2} a b^{2} c d^{2} + 4 \, B^{2} a^{2} b d^{3}\right)} n^{2} + 2 \, {\left(A B b^{3} c^{2} d + 4 \, A B a b^{2} c d^{2} - 2 \, A B a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{6} c^{4} d - 4 \, a b^{5} c^{3} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{3} - 4 \, a^{3} b^{3} c d^{4} + a^{4} b^{2} d^{5}\right)} g^{3} i^{2} x^{3} + {\left(b^{6} c^{5} - 2 \, a b^{5} c^{4} d - 2 \, a^{2} b^{4} c^{3} d^{2} + 8 \, a^{3} b^{3} c^{2} d^{3} - 7 \, a^{4} b^{2} c d^{4} + 2 \, a^{5} b d^{5}\right)} g^{3} i^{2} x^{2} + {\left(2 \, a b^{5} c^{5} - 7 \, a^{2} b^{4} c^{4} d + 8 \, a^{3} b^{3} c^{3} d^{2} - 2 \, a^{4} b^{2} c^{2} d^{3} - 2 \, a^{5} b c d^{4} + a^{6} d^{5}\right)} g^{3} i^{2} x + {\left(a^{2} b^{4} c^{5} - 4 \, a^{3} b^{3} c^{4} d + 6 \, a^{4} b^{2} c^{3} d^{2} - 4 \, a^{5} b c^{2} d^{3} + a^{6} c d^{4}\right)} g^{3} i^{2}\right)}}"," ",0,"-1/4*(2*A^2*b^3*c^3 - 12*A^2*a*b^2*c^2*d + 6*A^2*a^2*b*c*d^2 + 4*A^2*a^3*d^3 - 4*(B^2*b^3*d^3*n^2*x^3 + B^2*a^2*b*c*d^2*n^2 + (B^2*b^3*c*d^2 + 2*B^2*a*b^2*d^3)*n^2*x^2 + (2*B^2*a*b^2*c*d^2 + B^2*a^2*b*d^3)*n^2*x)*log((b*x + a)/(d*x + c))^3 + (B^2*b^3*c^3 - 24*B^2*a*b^2*c^2*d + 15*B^2*a^2*b*c*d^2 + 8*B^2*a^3*d^3)*n^2 - 6*(2*A^2*b^3*c*d^2 - 2*A^2*a*b^2*d^3 + 5*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*n^2 + 2*(A*B*b^3*c*d^2 - A*B*a*b^2*d^3)*n)*x^2 + 2*(B^2*b^3*c^3 - 6*B^2*a*b^2*c^2*d + 3*B^2*a^2*b*c*d^2 + 2*B^2*a^3*d^3 - 6*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*x^2 - 3*(B^2*b^3*c^2*d + 2*B^2*a*b^2*c*d^2 - 3*B^2*a^2*b*d^3)*x - 6*(B^2*b^3*d^3*x^3 + B^2*a^2*b*c*d^2 + (B^2*b^3*c*d^2 + 2*B^2*a*b^2*d^3)*x^2 + (2*B^2*a*b^2*c*d^2 + B^2*a^2*b*d^3)*x)*log((b*x + a)/(d*x + c)))*log(e)^2 - 2*(6*A*B*a^2*b*c*d^2*n + 3*(B^2*b^3*d^3*n^2 + 2*A*B*b^3*d^3*n)*x^3 - (B^2*b^3*c^3 - 6*B^2*a*b^2*c^2*d + 2*B^2*a^3*d^3)*n^2 + 3*(3*B^2*b^3*c*d^2*n^2 + 2*(A*B*b^3*c*d^2 + 2*A*B*a*b^2*d^3)*n)*x^2 + 3*((B^2*b^3*c^2*d + 4*B^2*a*b^2*c*d^2 - 2*B^2*a^2*b*d^3)*n^2 + 2*(2*A*B*a*b^2*c*d^2 + A*B*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c))^2 + 2*(A*B*b^3*c^3 - 12*A*B*a*b^2*c^2*d + 15*A*B*a^2*b*c*d^2 - 4*A*B*a^3*d^3)*n - 3*(2*A^2*b^3*c^2*d + 4*A^2*a*b^2*c*d^2 - 6*A^2*a^2*b*d^3 + (7*B^2*b^3*c^2*d + 6*B^2*a*b^2*c*d^2 - 13*B^2*a^2*b*d^3)*n^2 + 2*(3*A*B*b^3*c^2*d - 2*A*B*a*b^2*c*d^2 - A*B*a^2*b*d^3)*n)*x + 2*(2*A*B*b^3*c^3 - 12*A*B*a*b^2*c^2*d + 6*A*B*a^2*b*c*d^2 + 4*A*B*a^3*d^3 - 6*(2*A*B*b^3*c*d^2 - 2*A*B*a*b^2*d^3 + (B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*n)*x^2 - 6*(B^2*b^3*d^3*n*x^3 + B^2*a^2*b*c*d^2*n + (B^2*b^3*c*d^2 + 2*B^2*a*b^2*d^3)*n*x^2 + (2*B^2*a*b^2*c*d^2 + B^2*a^2*b*d^3)*n*x)*log((b*x + a)/(d*x + c))^2 + (B^2*b^3*c^3 - 12*B^2*a*b^2*c^2*d + 15*B^2*a^2*b*c*d^2 - 4*B^2*a^3*d^3)*n - 3*(2*A*B*b^3*c^2*d + 4*A*B*a*b^2*c*d^2 - 6*A*B*a^2*b*d^3 + (3*B^2*b^3*c^2*d - 2*B^2*a*b^2*c*d^2 - B^2*a^2*b*d^3)*n)*x - 2*(6*A*B*a^2*b*c*d^2 + 3*(B^2*b^3*d^3*n + 2*A*B*b^3*d^3)*x^3 + 3*(3*B^2*b^3*c*d^2*n + 2*A*B*b^3*c*d^2 + 4*A*B*a*b^2*d^3)*x^2 - (B^2*b^3*c^3 - 6*B^2*a*b^2*c^2*d + 2*B^2*a^3*d^3)*n + 3*(4*A*B*a*b^2*c*d^2 + 2*A*B*a^2*b*d^3 + (B^2*b^3*c^2*d + 4*B^2*a*b^2*c*d^2 - 2*B^2*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) - 2*(6*A^2*a^2*b*c*d^2 + 3*(5*B^2*b^3*d^3*n^2 + 2*A*B*b^3*d^3*n + 2*A^2*b^3*d^3)*x^3 - (B^2*b^3*c^3 - 12*B^2*a*b^2*c^2*d - 4*B^2*a^3*d^3)*n^2 + 3*(6*A*B*b^3*c*d^2*n + 2*A^2*b^3*c*d^2 + 4*A^2*a*b^2*d^3 + (7*B^2*b^3*c*d^2 + 8*B^2*a*b^2*d^3)*n^2)*x^2 - 2*(A*B*b^3*c^3 - 6*A*B*a*b^2*c^2*d + 2*A*B*a^3*d^3)*n + 3*(4*A^2*a*b^2*c*d^2 + 2*A^2*a^2*b*d^3 + (3*B^2*b^3*c^2*d + 8*B^2*a*b^2*c*d^2 + 4*B^2*a^2*b*d^3)*n^2 + 2*(A*B*b^3*c^2*d + 4*A*B*a*b^2*c*d^2 - 2*A*B*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))/((b^6*c^4*d - 4*a*b^5*c^3*d^2 + 6*a^2*b^4*c^2*d^3 - 4*a^3*b^3*c*d^4 + a^4*b^2*d^5)*g^3*i^2*x^3 + (b^6*c^5 - 2*a*b^5*c^4*d - 2*a^2*b^4*c^3*d^2 + 8*a^3*b^3*c^2*d^3 - 7*a^4*b^2*c*d^4 + 2*a^5*b*d^5)*g^3*i^2*x^2 + (2*a*b^5*c^5 - 7*a^2*b^4*c^4*d + 8*a^3*b^3*c^3*d^2 - 2*a^4*b^2*c^2*d^3 - 2*a^5*b*c*d^4 + a^6*d^5)*g^3*i^2*x + (a^2*b^4*c^5 - 4*a^3*b^3*c^4*d + 6*a^4*b^2*c^3*d^2 - 4*a^5*b*c^2*d^3 + a^6*c*d^4)*g^3*i^2)","B",0
201,1,3183,0,0.575559," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4/(d*i*x+c*i)^2,x, algorithm=""fricas"")","-\frac{9 \, A^{2} b^{4} c^{4} - 54 \, A^{2} a b^{3} c^{3} d + 162 \, A^{2} a^{2} b^{2} c^{2} d^{2} - 90 \, A^{2} a^{3} b c d^{3} - 27 \, A^{2} a^{4} d^{4} + 6 \, {\left(18 \, A^{2} b^{4} c d^{3} - 18 \, A^{2} a b^{3} d^{4} + 55 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} n^{2} + 30 \, {\left(A B b^{4} c d^{3} - A B a b^{3} d^{4}\right)} n\right)} x^{3} + 36 \, {\left(B^{2} b^{4} d^{4} n^{2} x^{4} + B^{2} a^{3} b c d^{3} n^{2} + {\left(B^{2} b^{4} c d^{3} + 3 \, B^{2} a b^{3} d^{4}\right)} n^{2} x^{3} + 3 \, {\left(B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} n^{2} x^{2} + {\left(3 \, B^{2} a^{2} b^{2} c d^{3} + B^{2} a^{3} b d^{4}\right)} n^{2} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + {\left(2 \, B^{2} b^{4} c^{4} - 27 \, B^{2} a b^{3} c^{3} d + 324 \, B^{2} a^{2} b^{2} c^{2} d^{2} - 245 \, B^{2} a^{3} b c d^{3} - 54 \, B^{2} a^{4} d^{4}\right)} n^{2} + 3 \, {\left(18 \, A^{2} b^{4} c^{2} d^{2} + 72 \, A^{2} a b^{3} c d^{3} - 90 \, A^{2} a^{2} b^{2} d^{4} + 5 \, {\left(17 \, B^{2} b^{4} c^{2} d^{2} + 32 \, B^{2} a b^{3} c d^{3} - 49 \, B^{2} a^{2} b^{2} d^{4}\right)} n^{2} + 6 \, {\left(11 \, A B b^{4} c^{2} d^{2} + 8 \, A B a b^{3} c d^{3} - 19 \, A B a^{2} b^{2} d^{4}\right)} n\right)} x^{2} + 9 \, {\left(B^{2} b^{4} c^{4} - 6 \, B^{2} a b^{3} c^{3} d + 18 \, B^{2} a^{2} b^{2} c^{2} d^{2} - 10 \, B^{2} a^{3} b c d^{3} - 3 \, B^{2} a^{4} d^{4} + 12 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} x^{3} + 6 \, {\left(B^{2} b^{4} c^{2} d^{2} + 4 \, B^{2} a b^{3} c d^{3} - 5 \, B^{2} a^{2} b^{2} d^{4}\right)} x^{2} - 2 \, {\left(B^{2} b^{4} c^{3} d - 9 \, B^{2} a b^{3} c^{2} d^{2} - 3 \, B^{2} a^{2} b^{2} c d^{3} + 11 \, B^{2} a^{3} b d^{4}\right)} x + 12 \, {\left(B^{2} b^{4} d^{4} x^{4} + B^{2} a^{3} b c d^{3} + {\left(B^{2} b^{4} c d^{3} + 3 \, B^{2} a b^{3} d^{4}\right)} x^{3} + 3 \, {\left(B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} x^{2} + {\left(3 \, B^{2} a^{2} b^{2} c d^{3} + B^{2} a^{3} b d^{4}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} + 9 \, {\left(12 \, A B a^{3} b c d^{3} n + 2 \, {\left(5 \, B^{2} b^{4} d^{4} n^{2} + 6 \, A B b^{4} d^{4} n\right)} x^{4} + 2 \, {\left({\left(11 \, B^{2} b^{4} c d^{3} + 9 \, B^{2} a b^{3} d^{4}\right)} n^{2} + 6 \, {\left(A B b^{4} c d^{3} + 3 \, A B a b^{3} d^{4}\right)} n\right)} x^{3} + {\left(B^{2} b^{4} c^{4} - 6 \, B^{2} a b^{3} c^{3} d + 18 \, B^{2} a^{2} b^{2} c^{2} d^{2} - 3 \, B^{2} a^{4} d^{4}\right)} n^{2} + 6 \, {\left({\left(B^{2} b^{4} c^{2} d^{2} + 9 \, B^{2} a b^{3} c d^{3}\right)} n^{2} + 6 \, {\left(A B a b^{3} c d^{3} + A B a^{2} b^{2} d^{4}\right)} n\right)} x^{2} - 2 \, {\left({\left(B^{2} b^{4} c^{3} d - 9 \, B^{2} a b^{3} c^{2} d^{2} - 18 \, B^{2} a^{2} b^{2} c d^{3} + 6 \, B^{2} a^{3} b d^{4}\right)} n^{2} - 6 \, {\left(3 \, A B a^{2} b^{2} c d^{3} + A B a^{3} b d^{4}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 6 \, {\left(A B b^{4} c^{4} - 9 \, A B a b^{3} c^{3} d + 54 \, A B a^{2} b^{2} c^{2} d^{2} - 55 \, A B a^{3} b c d^{3} + 9 \, A B a^{4} d^{4}\right)} n - {\left(18 \, A^{2} b^{4} c^{3} d - 162 \, A^{2} a b^{3} c^{2} d^{2} - 54 \, A^{2} a^{2} b^{2} c d^{3} + 198 \, A^{2} a^{3} b d^{4} + {\left(19 \, B^{2} b^{4} c^{3} d - 567 \, B^{2} a b^{3} c^{2} d^{2} + 87 \, B^{2} a^{2} b^{2} c d^{3} + 461 \, B^{2} a^{3} b d^{4}\right)} n^{2} + 6 \, {\left(5 \, A B b^{4} c^{3} d - 81 \, A B a b^{3} c^{2} d^{2} + 57 \, A B a^{2} b^{2} c d^{3} + 19 \, A B a^{3} b d^{4}\right)} n\right)} x + 6 \, {\left(3 \, A B b^{4} c^{4} - 18 \, A B a b^{3} c^{3} d + 54 \, A B a^{2} b^{2} c^{2} d^{2} - 30 \, A B a^{3} b c d^{3} - 9 \, A B a^{4} d^{4} + 6 \, {\left(6 \, A B b^{4} c d^{3} - 6 \, A B a b^{3} d^{4} + 5 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} n\right)} x^{3} + 3 \, {\left(6 \, A B b^{4} c^{2} d^{2} + 24 \, A B a b^{3} c d^{3} - 30 \, A B a^{2} b^{2} d^{4} + {\left(11 \, B^{2} b^{4} c^{2} d^{2} + 8 \, B^{2} a b^{3} c d^{3} - 19 \, B^{2} a^{2} b^{2} d^{4}\right)} n\right)} x^{2} + 18 \, {\left(B^{2} b^{4} d^{4} n x^{4} + B^{2} a^{3} b c d^{3} n + {\left(B^{2} b^{4} c d^{3} + 3 \, B^{2} a b^{3} d^{4}\right)} n x^{3} + 3 \, {\left(B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} n x^{2} + {\left(3 \, B^{2} a^{2} b^{2} c d^{3} + B^{2} a^{3} b d^{4}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B^{2} b^{4} c^{4} - 9 \, B^{2} a b^{3} c^{3} d + 54 \, B^{2} a^{2} b^{2} c^{2} d^{2} - 55 \, B^{2} a^{3} b c d^{3} + 9 \, B^{2} a^{4} d^{4}\right)} n - {\left(6 \, A B b^{4} c^{3} d - 54 \, A B a b^{3} c^{2} d^{2} - 18 \, A B a^{2} b^{2} c d^{3} + 66 \, A B a^{3} b d^{4} + {\left(5 \, B^{2} b^{4} c^{3} d - 81 \, B^{2} a b^{3} c^{2} d^{2} + 57 \, B^{2} a^{2} b^{2} c d^{3} + 19 \, B^{2} a^{3} b d^{4}\right)} n\right)} x + 3 \, {\left(12 \, A B a^{3} b c d^{3} + 2 \, {\left(5 \, B^{2} b^{4} d^{4} n + 6 \, A B b^{4} d^{4}\right)} x^{4} + 2 \, {\left(6 \, A B b^{4} c d^{3} + 18 \, A B a b^{3} d^{4} + {\left(11 \, B^{2} b^{4} c d^{3} + 9 \, B^{2} a b^{3} d^{4}\right)} n\right)} x^{3} + 6 \, {\left(6 \, A B a b^{3} c d^{3} + 6 \, A B a^{2} b^{2} d^{4} + {\left(B^{2} b^{4} c^{2} d^{2} + 9 \, B^{2} a b^{3} c d^{3}\right)} n\right)} x^{2} + {\left(B^{2} b^{4} c^{4} - 6 \, B^{2} a b^{3} c^{3} d + 18 \, B^{2} a^{2} b^{2} c^{2} d^{2} - 3 \, B^{2} a^{4} d^{4}\right)} n + 2 \, {\left(18 \, A B a^{2} b^{2} c d^{3} + 6 \, A B a^{3} b d^{4} - {\left(B^{2} b^{4} c^{3} d - 9 \, B^{2} a b^{3} c^{2} d^{2} - 18 \, B^{2} a^{2} b^{2} c d^{3} + 6 \, B^{2} a^{3} b d^{4}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left(18 \, A^{2} a^{3} b c d^{3} + {\left(55 \, B^{2} b^{4} d^{4} n^{2} + 30 \, A B b^{4} d^{4} n + 18 \, A^{2} b^{4} d^{4}\right)} x^{4} + {\left(18 \, A^{2} b^{4} c d^{3} + 54 \, A^{2} a b^{3} d^{4} + 5 \, {\left(17 \, B^{2} b^{4} c d^{3} + 27 \, B^{2} a b^{3} d^{4}\right)} n^{2} + 6 \, {\left(11 \, A B b^{4} c d^{3} + 9 \, A B a b^{3} d^{4}\right)} n\right)} x^{3} + {\left(B^{2} b^{4} c^{4} - 9 \, B^{2} a b^{3} c^{3} d + 54 \, B^{2} a^{2} b^{2} c^{2} d^{2} + 9 \, B^{2} a^{4} d^{4}\right)} n^{2} + 3 \, {\left(18 \, A^{2} a b^{3} c d^{3} + 18 \, A^{2} a^{2} b^{2} d^{4} + {\left(11 \, B^{2} b^{4} c^{2} d^{2} + 63 \, B^{2} a b^{3} c d^{3} + 36 \, B^{2} a^{2} b^{2} d^{4}\right)} n^{2} + 6 \, {\left(A B b^{4} c^{2} d^{2} + 9 \, A B a b^{3} c d^{3}\right)} n\right)} x^{2} + 3 \, {\left(A B b^{4} c^{4} - 6 \, A B a b^{3} c^{3} d + 18 \, A B a^{2} b^{2} c^{2} d^{2} - 3 \, A B a^{4} d^{4}\right)} n + {\left(54 \, A^{2} a^{2} b^{2} c d^{3} + 18 \, A^{2} a^{3} b d^{4} - {\left(5 \, B^{2} b^{4} c^{3} d - 81 \, B^{2} a b^{3} c^{2} d^{2} - 108 \, B^{2} a^{2} b^{2} c d^{3} - 36 \, B^{2} a^{3} b d^{4}\right)} n^{2} - 6 \, {\left(A B b^{4} c^{3} d - 9 \, A B a b^{3} c^{2} d^{2} - 18 \, A B a^{2} b^{2} c d^{3} + 6 \, A B a^{3} b d^{4}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{27 \, {\left({\left(b^{8} c^{5} d - 5 \, a b^{7} c^{4} d^{2} + 10 \, a^{2} b^{6} c^{3} d^{3} - 10 \, a^{3} b^{5} c^{2} d^{4} + 5 \, a^{4} b^{4} c d^{5} - a^{5} b^{3} d^{6}\right)} g^{4} i^{2} x^{4} + {\left(b^{8} c^{6} - 2 \, a b^{7} c^{5} d - 5 \, a^{2} b^{6} c^{4} d^{2} + 20 \, a^{3} b^{5} c^{3} d^{3} - 25 \, a^{4} b^{4} c^{2} d^{4} + 14 \, a^{5} b^{3} c d^{5} - 3 \, a^{6} b^{2} d^{6}\right)} g^{4} i^{2} x^{3} + 3 \, {\left(a b^{7} c^{6} - 4 \, a^{2} b^{6} c^{5} d + 5 \, a^{3} b^{5} c^{4} d^{2} - 5 \, a^{5} b^{3} c^{2} d^{4} + 4 \, a^{6} b^{2} c d^{5} - a^{7} b d^{6}\right)} g^{4} i^{2} x^{2} + {\left(3 \, a^{2} b^{6} c^{6} - 14 \, a^{3} b^{5} c^{5} d + 25 \, a^{4} b^{4} c^{4} d^{2} - 20 \, a^{5} b^{3} c^{3} d^{3} + 5 \, a^{6} b^{2} c^{2} d^{4} + 2 \, a^{7} b c d^{5} - a^{8} d^{6}\right)} g^{4} i^{2} x + {\left(a^{3} b^{5} c^{6} - 5 \, a^{4} b^{4} c^{5} d + 10 \, a^{5} b^{3} c^{4} d^{2} - 10 \, a^{6} b^{2} c^{3} d^{3} + 5 \, a^{7} b c^{2} d^{4} - a^{8} c d^{5}\right)} g^{4} i^{2}\right)}}"," ",0,"-1/27*(9*A^2*b^4*c^4 - 54*A^2*a*b^3*c^3*d + 162*A^2*a^2*b^2*c^2*d^2 - 90*A^2*a^3*b*c*d^3 - 27*A^2*a^4*d^4 + 6*(18*A^2*b^4*c*d^3 - 18*A^2*a*b^3*d^4 + 55*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*n^2 + 30*(A*B*b^4*c*d^3 - A*B*a*b^3*d^4)*n)*x^3 + 36*(B^2*b^4*d^4*n^2*x^4 + B^2*a^3*b*c*d^3*n^2 + (B^2*b^4*c*d^3 + 3*B^2*a*b^3*d^4)*n^2*x^3 + 3*(B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*n^2*x^2 + (3*B^2*a^2*b^2*c*d^3 + B^2*a^3*b*d^4)*n^2*x)*log((b*x + a)/(d*x + c))^3 + (2*B^2*b^4*c^4 - 27*B^2*a*b^3*c^3*d + 324*B^2*a^2*b^2*c^2*d^2 - 245*B^2*a^3*b*c*d^3 - 54*B^2*a^4*d^4)*n^2 + 3*(18*A^2*b^4*c^2*d^2 + 72*A^2*a*b^3*c*d^3 - 90*A^2*a^2*b^2*d^4 + 5*(17*B^2*b^4*c^2*d^2 + 32*B^2*a*b^3*c*d^3 - 49*B^2*a^2*b^2*d^4)*n^2 + 6*(11*A*B*b^4*c^2*d^2 + 8*A*B*a*b^3*c*d^3 - 19*A*B*a^2*b^2*d^4)*n)*x^2 + 9*(B^2*b^4*c^4 - 6*B^2*a*b^3*c^3*d + 18*B^2*a^2*b^2*c^2*d^2 - 10*B^2*a^3*b*c*d^3 - 3*B^2*a^4*d^4 + 12*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*x^3 + 6*(B^2*b^4*c^2*d^2 + 4*B^2*a*b^3*c*d^3 - 5*B^2*a^2*b^2*d^4)*x^2 - 2*(B^2*b^4*c^3*d - 9*B^2*a*b^3*c^2*d^2 - 3*B^2*a^2*b^2*c*d^3 + 11*B^2*a^3*b*d^4)*x + 12*(B^2*b^4*d^4*x^4 + B^2*a^3*b*c*d^3 + (B^2*b^4*c*d^3 + 3*B^2*a*b^3*d^4)*x^3 + 3*(B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*x^2 + (3*B^2*a^2*b^2*c*d^3 + B^2*a^3*b*d^4)*x)*log((b*x + a)/(d*x + c)))*log(e)^2 + 9*(12*A*B*a^3*b*c*d^3*n + 2*(5*B^2*b^4*d^4*n^2 + 6*A*B*b^4*d^4*n)*x^4 + 2*((11*B^2*b^4*c*d^3 + 9*B^2*a*b^3*d^4)*n^2 + 6*(A*B*b^4*c*d^3 + 3*A*B*a*b^3*d^4)*n)*x^3 + (B^2*b^4*c^4 - 6*B^2*a*b^3*c^3*d + 18*B^2*a^2*b^2*c^2*d^2 - 3*B^2*a^4*d^4)*n^2 + 6*((B^2*b^4*c^2*d^2 + 9*B^2*a*b^3*c*d^3)*n^2 + 6*(A*B*a*b^3*c*d^3 + A*B*a^2*b^2*d^4)*n)*x^2 - 2*((B^2*b^4*c^3*d - 9*B^2*a*b^3*c^2*d^2 - 18*B^2*a^2*b^2*c*d^3 + 6*B^2*a^3*b*d^4)*n^2 - 6*(3*A*B*a^2*b^2*c*d^3 + A*B*a^3*b*d^4)*n)*x)*log((b*x + a)/(d*x + c))^2 + 6*(A*B*b^4*c^4 - 9*A*B*a*b^3*c^3*d + 54*A*B*a^2*b^2*c^2*d^2 - 55*A*B*a^3*b*c*d^3 + 9*A*B*a^4*d^4)*n - (18*A^2*b^4*c^3*d - 162*A^2*a*b^3*c^2*d^2 - 54*A^2*a^2*b^2*c*d^3 + 198*A^2*a^3*b*d^4 + (19*B^2*b^4*c^3*d - 567*B^2*a*b^3*c^2*d^2 + 87*B^2*a^2*b^2*c*d^3 + 461*B^2*a^3*b*d^4)*n^2 + 6*(5*A*B*b^4*c^3*d - 81*A*B*a*b^3*c^2*d^2 + 57*A*B*a^2*b^2*c*d^3 + 19*A*B*a^3*b*d^4)*n)*x + 6*(3*A*B*b^4*c^4 - 18*A*B*a*b^3*c^3*d + 54*A*B*a^2*b^2*c^2*d^2 - 30*A*B*a^3*b*c*d^3 - 9*A*B*a^4*d^4 + 6*(6*A*B*b^4*c*d^3 - 6*A*B*a*b^3*d^4 + 5*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*n)*x^3 + 3*(6*A*B*b^4*c^2*d^2 + 24*A*B*a*b^3*c*d^3 - 30*A*B*a^2*b^2*d^4 + (11*B^2*b^4*c^2*d^2 + 8*B^2*a*b^3*c*d^3 - 19*B^2*a^2*b^2*d^4)*n)*x^2 + 18*(B^2*b^4*d^4*n*x^4 + B^2*a^3*b*c*d^3*n + (B^2*b^4*c*d^3 + 3*B^2*a*b^3*d^4)*n*x^3 + 3*(B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*n*x^2 + (3*B^2*a^2*b^2*c*d^3 + B^2*a^3*b*d^4)*n*x)*log((b*x + a)/(d*x + c))^2 + (B^2*b^4*c^4 - 9*B^2*a*b^3*c^3*d + 54*B^2*a^2*b^2*c^2*d^2 - 55*B^2*a^3*b*c*d^3 + 9*B^2*a^4*d^4)*n - (6*A*B*b^4*c^3*d - 54*A*B*a*b^3*c^2*d^2 - 18*A*B*a^2*b^2*c*d^3 + 66*A*B*a^3*b*d^4 + (5*B^2*b^4*c^3*d - 81*B^2*a*b^3*c^2*d^2 + 57*B^2*a^2*b^2*c*d^3 + 19*B^2*a^3*b*d^4)*n)*x + 3*(12*A*B*a^3*b*c*d^3 + 2*(5*B^2*b^4*d^4*n + 6*A*B*b^4*d^4)*x^4 + 2*(6*A*B*b^4*c*d^3 + 18*A*B*a*b^3*d^4 + (11*B^2*b^4*c*d^3 + 9*B^2*a*b^3*d^4)*n)*x^3 + 6*(6*A*B*a*b^3*c*d^3 + 6*A*B*a^2*b^2*d^4 + (B^2*b^4*c^2*d^2 + 9*B^2*a*b^3*c*d^3)*n)*x^2 + (B^2*b^4*c^4 - 6*B^2*a*b^3*c^3*d + 18*B^2*a^2*b^2*c^2*d^2 - 3*B^2*a^4*d^4)*n + 2*(18*A*B*a^2*b^2*c*d^3 + 6*A*B*a^3*b*d^4 - (B^2*b^4*c^3*d - 9*B^2*a*b^3*c^2*d^2 - 18*B^2*a^2*b^2*c*d^3 + 6*B^2*a^3*b*d^4)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) + 6*(18*A^2*a^3*b*c*d^3 + (55*B^2*b^4*d^4*n^2 + 30*A*B*b^4*d^4*n + 18*A^2*b^4*d^4)*x^4 + (18*A^2*b^4*c*d^3 + 54*A^2*a*b^3*d^4 + 5*(17*B^2*b^4*c*d^3 + 27*B^2*a*b^3*d^4)*n^2 + 6*(11*A*B*b^4*c*d^3 + 9*A*B*a*b^3*d^4)*n)*x^3 + (B^2*b^4*c^4 - 9*B^2*a*b^3*c^3*d + 54*B^2*a^2*b^2*c^2*d^2 + 9*B^2*a^4*d^4)*n^2 + 3*(18*A^2*a*b^3*c*d^3 + 18*A^2*a^2*b^2*d^4 + (11*B^2*b^4*c^2*d^2 + 63*B^2*a*b^3*c*d^3 + 36*B^2*a^2*b^2*d^4)*n^2 + 6*(A*B*b^4*c^2*d^2 + 9*A*B*a*b^3*c*d^3)*n)*x^2 + 3*(A*B*b^4*c^4 - 6*A*B*a*b^3*c^3*d + 18*A*B*a^2*b^2*c^2*d^2 - 3*A*B*a^4*d^4)*n + (54*A^2*a^2*b^2*c*d^3 + 18*A^2*a^3*b*d^4 - (5*B^2*b^4*c^3*d - 81*B^2*a*b^3*c^2*d^2 - 108*B^2*a^2*b^2*c*d^3 - 36*B^2*a^3*b*d^4)*n^2 - 6*(A*B*b^4*c^3*d - 9*A*B*a*b^3*c^2*d^2 - 18*A*B*a^2*b^2*c*d^3 + 6*A*B*a^3*b*d^4)*n)*x)*log((b*x + a)/(d*x + c)))/((b^8*c^5*d - 5*a*b^7*c^4*d^2 + 10*a^2*b^6*c^3*d^3 - 10*a^3*b^5*c^2*d^4 + 5*a^4*b^4*c*d^5 - a^5*b^3*d^6)*g^4*i^2*x^4 + (b^8*c^6 - 2*a*b^7*c^5*d - 5*a^2*b^6*c^4*d^2 + 20*a^3*b^5*c^3*d^3 - 25*a^4*b^4*c^2*d^4 + 14*a^5*b^3*c*d^5 - 3*a^6*b^2*d^6)*g^4*i^2*x^3 + 3*(a*b^7*c^6 - 4*a^2*b^6*c^5*d + 5*a^3*b^5*c^4*d^2 - 5*a^5*b^3*c^2*d^4 + 4*a^6*b^2*c*d^5 - a^7*b*d^6)*g^4*i^2*x^2 + (3*a^2*b^6*c^6 - 14*a^3*b^5*c^5*d + 25*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 5*a^6*b^2*c^2*d^4 + 2*a^7*b*c*d^5 - a^8*d^6)*g^4*i^2*x + (a^3*b^5*c^6 - 5*a^4*b^4*c^5*d + 10*a^5*b^3*c^4*d^2 - 10*a^6*b^2*c^3*d^3 + 5*a^7*b*c^2*d^4 - a^8*c*d^5)*g^4*i^2)","B",0
202,0,0,0,0.439718," ","integrate((b*g*x+a*g)^3*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{3} g^{3} x^{3} + 3 \, A^{2} a b^{2} g^{3} x^{2} + 3 \, A^{2} a^{2} b g^{3} x + A^{2} a^{3} g^{3} + {\left(B^{2} b^{3} g^{3} x^{3} + 3 \, B^{2} a b^{2} g^{3} x^{2} + 3 \, B^{2} a^{2} b g^{3} x + B^{2} a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{3} g^{3} x^{3} + 3 \, A B a b^{2} g^{3} x^{2} + 3 \, A B a^{2} b g^{3} x + A B a^{3} g^{3}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{3} i^{3} x^{3} + 3 \, c d^{2} i^{3} x^{2} + 3 \, c^{2} d i^{3} x + c^{3} i^{3}}, x\right)"," ",0,"integral((A^2*b^3*g^3*x^3 + 3*A^2*a*b^2*g^3*x^2 + 3*A^2*a^2*b*g^3*x + A^2*a^3*g^3 + (B^2*b^3*g^3*x^3 + 3*B^2*a*b^2*g^3*x^2 + 3*B^2*a^2*b*g^3*x + B^2*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^3*g^3*x^3 + 3*A*B*a*b^2*g^3*x^2 + 3*A*B*a^2*b*g^3*x + A*B*a^3*g^3)*log(e*((b*x + a)/(d*x + c))^n))/(d^3*i^3*x^3 + 3*c*d^2*i^3*x^2 + 3*c^2*d*i^3*x + c^3*i^3), x)","F",0
203,0,0,0,0.431385," ","integrate((b*g*x+a*g)^2*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{A^{2} b^{2} g^{2} x^{2} + 2 \, A^{2} a b g^{2} x + A^{2} a^{2} g^{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(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)^{2} + 2 \, {\left(A B b^{2} g^{2} x^{2} + 2 \, A B a b g^{2} x + A B a^{2} g^{2}\right)} \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right)}{d^{3} i^{3} x^{3} + 3 \, c d^{2} i^{3} x^{2} + 3 \, c^{2} d i^{3} x + c^{3} i^{3}}, x\right)"," ",0,"integral((A^2*b^2*g^2*x^2 + 2*A^2*a*b*g^2*x + A^2*a^2*g^2 + (B^2*b^2*g^2*x^2 + 2*B^2*a*b*g^2*x + B^2*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n)^2 + 2*(A*B*b^2*g^2*x^2 + 2*A*B*a*b*g^2*x + A*B*a^2*g^2)*log(e*((b*x + a)/(d*x + c))^n))/(d^3*i^3*x^3 + 3*c*d^2*i^3*x^2 + 3*c^2*d*i^3*x + c^3*i^3), x)","F",0
204,1,600,0,0.450588," ","integrate((b*g*x+a*g)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{{\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} g n^{2} - 2 \, {\left(A B b^{2} c^{2} - A B a^{2} d^{2}\right)} g n + 2 \, {\left(2 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} g x + {\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} g\right)} \log\left(e\right)^{2} - 2 \, {\left(B^{2} b^{2} d^{2} g n^{2} x^{2} + 2 \, B^{2} a b d^{2} g n^{2} x + B^{2} a^{2} d^{2} g n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(A^{2} b^{2} c^{2} - A^{2} a^{2} d^{2}\right)} g + 2 \, {\left({\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} g n^{2} - 2 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} g n + 2 \, {\left(A^{2} b^{2} c d - A^{2} a b d^{2}\right)} g\right)} x - 2 \, {\left({\left(B^{2} b^{2} c^{2} - B^{2} a^{2} d^{2}\right)} g n - 2 \, {\left(A B b^{2} c^{2} - A B a^{2} d^{2}\right)} g + 2 \, {\left({\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} g n - 2 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} g\right)} x + 2 \, {\left(B^{2} b^{2} d^{2} g n x^{2} + 2 \, B^{2} a b d^{2} g n x + B^{2} a^{2} d^{2} g n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left(B^{2} a^{2} d^{2} g n^{2} - 2 \, A B a^{2} d^{2} g n + {\left(B^{2} b^{2} d^{2} g n^{2} - 2 \, A B b^{2} d^{2} g n\right)} x^{2} + 2 \, {\left(B^{2} a b d^{2} g n^{2} - 2 \, A B a b d^{2} g n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b c d^{4} - a d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b c^{2} d^{3} - a c d^{4}\right)} i^{3} x + {\left(b c^{3} d^{2} - a c^{2} d^{3}\right)} i^{3}\right)}}"," ",0,"-1/4*((B^2*b^2*c^2 - B^2*a^2*d^2)*g*n^2 - 2*(A*B*b^2*c^2 - A*B*a^2*d^2)*g*n + 2*(2*(B^2*b^2*c*d - B^2*a*b*d^2)*g*x + (B^2*b^2*c^2 - B^2*a^2*d^2)*g)*log(e)^2 - 2*(B^2*b^2*d^2*g*n^2*x^2 + 2*B^2*a*b*d^2*g*n^2*x + B^2*a^2*d^2*g*n^2)*log((b*x + a)/(d*x + c))^2 + 2*(A^2*b^2*c^2 - A^2*a^2*d^2)*g + 2*((B^2*b^2*c*d - B^2*a*b*d^2)*g*n^2 - 2*(A*B*b^2*c*d - A*B*a*b*d^2)*g*n + 2*(A^2*b^2*c*d - A^2*a*b*d^2)*g)*x - 2*((B^2*b^2*c^2 - B^2*a^2*d^2)*g*n - 2*(A*B*b^2*c^2 - A*B*a^2*d^2)*g + 2*((B^2*b^2*c*d - B^2*a*b*d^2)*g*n - 2*(A*B*b^2*c*d - A*B*a*b*d^2)*g)*x + 2*(B^2*b^2*d^2*g*n*x^2 + 2*B^2*a*b*d^2*g*n*x + B^2*a^2*d^2*g*n)*log((b*x + a)/(d*x + c)))*log(e) + 2*(B^2*a^2*d^2*g*n^2 - 2*A*B*a^2*d^2*g*n + (B^2*b^2*d^2*g*n^2 - 2*A*B*b^2*d^2*g*n)*x^2 + 2*(B^2*a*b*d^2*g*n^2 - 2*A*B*a*b*d^2*g*n)*x)*log((b*x + a)/(d*x + c)))/((b*c*d^4 - a*d^5)*i^3*x^2 + 2*(b*c^2*d^3 - a*c*d^4)*i^3*x + (b*c^3*d^2 - a*c^2*d^3)*i^3)","B",0
205,1,654,0,0.447129," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{2 \, A^{2} b^{2} c^{2} - 4 \, A^{2} a b c d + 2 \, A^{2} a^{2} d^{2} + {\left(7 \, B^{2} b^{2} c^{2} - 8 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right)} n^{2} + 2 \, {\left(B^{2} b^{2} c^{2} - 2 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right)} \log\left(e\right)^{2} - 2 \, {\left(B^{2} b^{2} d^{2} n^{2} x^{2} + 2 \, B^{2} b^{2} c d n^{2} x + {\left(2 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right)} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 2 \, {\left(3 \, A B b^{2} c^{2} - 4 \, A B a b c d + A B a^{2} d^{2}\right)} n + 2 \, {\left(3 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n^{2} - 2 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} n\right)} x + 2 \, {\left(2 \, A B b^{2} c^{2} - 4 \, A B a b c d + 2 \, A B a^{2} d^{2} - 2 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n x - {\left(3 \, B^{2} b^{2} c^{2} - 4 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right)} n - 2 \, {\left(B^{2} b^{2} d^{2} n x^{2} + 2 \, B^{2} b^{2} c d n x + {\left(2 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right)} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left({\left(4 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right)} n^{2} + {\left(3 \, B^{2} b^{2} d^{2} n^{2} - 2 \, A B b^{2} d^{2} n\right)} x^{2} - 2 \, {\left(2 \, A B a b c d - A B a^{2} d^{2}\right)} n - 2 \, {\left(2 \, A B b^{2} c d n - {\left(2 \, B^{2} b^{2} c d + B^{2} a b d^{2}\right)} n^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}\right)} i^{3} x^{2} + 2 \, {\left(b^{2} c^{3} d^{2} - 2 \, a b c^{2} d^{3} + a^{2} c d^{4}\right)} i^{3} x + {\left(b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} i^{3}\right)}}"," ",0,"-1/4*(2*A^2*b^2*c^2 - 4*A^2*a*b*c*d + 2*A^2*a^2*d^2 + (7*B^2*b^2*c^2 - 8*B^2*a*b*c*d + B^2*a^2*d^2)*n^2 + 2*(B^2*b^2*c^2 - 2*B^2*a*b*c*d + B^2*a^2*d^2)*log(e)^2 - 2*(B^2*b^2*d^2*n^2*x^2 + 2*B^2*b^2*c*d*n^2*x + (2*B^2*a*b*c*d - B^2*a^2*d^2)*n^2)*log((b*x + a)/(d*x + c))^2 - 2*(3*A*B*b^2*c^2 - 4*A*B*a*b*c*d + A*B*a^2*d^2)*n + 2*(3*(B^2*b^2*c*d - B^2*a*b*d^2)*n^2 - 2*(A*B*b^2*c*d - A*B*a*b*d^2)*n)*x + 2*(2*A*B*b^2*c^2 - 4*A*B*a*b*c*d + 2*A*B*a^2*d^2 - 2*(B^2*b^2*c*d - B^2*a*b*d^2)*n*x - (3*B^2*b^2*c^2 - 4*B^2*a*b*c*d + B^2*a^2*d^2)*n - 2*(B^2*b^2*d^2*n*x^2 + 2*B^2*b^2*c*d*n*x + (2*B^2*a*b*c*d - B^2*a^2*d^2)*n)*log((b*x + a)/(d*x + c)))*log(e) + 2*((4*B^2*a*b*c*d - B^2*a^2*d^2)*n^2 + (3*B^2*b^2*d^2*n^2 - 2*A*B*b^2*d^2*n)*x^2 - 2*(2*A*B*a*b*c*d - A*B*a^2*d^2)*n - 2*(2*A*B*b^2*c*d*n - (2*B^2*b^2*c*d + B^2*a*b*d^2)*n^2)*x)*log((b*x + a)/(d*x + c)))/((b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5)*i^3*x^2 + 2*(b^2*c^3*d^2 - 2*a*b*c^2*d^3 + a^2*c*d^4)*i^3*x + (b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3)*i^3)","B",0
206,1,1076,0,0.473980," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)/(d*i*x+c*i)^3,x, algorithm=""fricas"")","\frac{18 \, A^{2} b^{2} c^{2} - 24 \, A^{2} a b c d + 6 \, A^{2} a^{2} d^{2} + 4 \, {\left(B^{2} b^{2} d^{2} n^{2} x^{2} + 2 \, B^{2} b^{2} c d n^{2} x + B^{2} b^{2} c^{2} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + 3 \, {\left(15 \, B^{2} b^{2} c^{2} - 16 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right)} n^{2} + 6 \, {\left(3 \, B^{2} b^{2} c^{2} - 4 \, B^{2} a b c d + B^{2} a^{2} d^{2} + 2 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} x + 2 \, {\left(B^{2} b^{2} d^{2} x^{2} + 2 \, B^{2} b^{2} c d x + B^{2} b^{2} c^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} + 6 \, {\left(2 \, A B b^{2} c^{2} n - {\left(4 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right)} n^{2} - {\left(3 \, B^{2} b^{2} d^{2} n^{2} - 2 \, A B b^{2} d^{2} n\right)} x^{2} + 2 \, {\left(2 \, A B b^{2} c d n - {\left(2 \, B^{2} b^{2} c d + B^{2} a b d^{2}\right)} n^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 6 \, {\left(7 \, A B b^{2} c^{2} - 8 \, A B a b c d + A B a^{2} d^{2}\right)} n + 6 \, {\left(2 \, A^{2} b^{2} c d - 2 \, A^{2} a b d^{2} + 7 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n^{2} - 6 \, {\left(A B b^{2} c d - A B a b d^{2}\right)} n\right)} x + 6 \, {\left(6 \, A B b^{2} c^{2} - 8 \, A B a b c d + 2 \, A B a^{2} d^{2} + 2 \, {\left(B^{2} b^{2} d^{2} n x^{2} + 2 \, B^{2} b^{2} c d n x + B^{2} b^{2} c^{2} n\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - {\left(7 \, B^{2} b^{2} c^{2} - 8 \, B^{2} a b c d + B^{2} a^{2} d^{2}\right)} n + 2 \, {\left(2 \, A B b^{2} c d - 2 \, A B a b d^{2} - 3 \, {\left(B^{2} b^{2} c d - B^{2} a b d^{2}\right)} n\right)} x + 2 \, {\left(2 \, A B b^{2} c^{2} - {\left(3 \, B^{2} b^{2} d^{2} n - 2 \, A B b^{2} d^{2}\right)} x^{2} - {\left(4 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right)} n + 2 \, {\left(2 \, A B b^{2} c d - {\left(2 \, B^{2} b^{2} c d + B^{2} a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left(2 \, A^{2} b^{2} c^{2} + {\left(8 \, B^{2} a b c d - B^{2} a^{2} d^{2}\right)} n^{2} + {\left(7 \, B^{2} b^{2} d^{2} n^{2} - 6 \, A B b^{2} d^{2} n + 2 \, A^{2} b^{2} d^{2}\right)} x^{2} - 2 \, {\left(4 \, A B a b c d - A B a^{2} d^{2}\right)} n + 2 \, {\left(2 \, A^{2} b^{2} c d + {\left(4 \, B^{2} b^{2} c d + 3 \, B^{2} a b d^{2}\right)} n^{2} - 2 \, {\left(2 \, A B b^{2} c d + A B a b d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{12 \, {\left({\left(b^{3} c^{3} d^{2} - 3 \, a b^{2} c^{2} d^{3} + 3 \, a^{2} b c d^{4} - a^{3} d^{5}\right)} g i^{3} x^{2} + 2 \, {\left(b^{3} c^{4} d - 3 \, a b^{2} c^{3} d^{2} + 3 \, a^{2} b c^{2} d^{3} - a^{3} c d^{4}\right)} g i^{3} x + {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} g i^{3}\right)}}"," ",0,"1/12*(18*A^2*b^2*c^2 - 24*A^2*a*b*c*d + 6*A^2*a^2*d^2 + 4*(B^2*b^2*d^2*n^2*x^2 + 2*B^2*b^2*c*d*n^2*x + B^2*b^2*c^2*n^2)*log((b*x + a)/(d*x + c))^3 + 3*(15*B^2*b^2*c^2 - 16*B^2*a*b*c*d + B^2*a^2*d^2)*n^2 + 6*(3*B^2*b^2*c^2 - 4*B^2*a*b*c*d + B^2*a^2*d^2 + 2*(B^2*b^2*c*d - B^2*a*b*d^2)*x + 2*(B^2*b^2*d^2*x^2 + 2*B^2*b^2*c*d*x + B^2*b^2*c^2)*log((b*x + a)/(d*x + c)))*log(e)^2 + 6*(2*A*B*b^2*c^2*n - (4*B^2*a*b*c*d - B^2*a^2*d^2)*n^2 - (3*B^2*b^2*d^2*n^2 - 2*A*B*b^2*d^2*n)*x^2 + 2*(2*A*B*b^2*c*d*n - (2*B^2*b^2*c*d + B^2*a*b*d^2)*n^2)*x)*log((b*x + a)/(d*x + c))^2 - 6*(7*A*B*b^2*c^2 - 8*A*B*a*b*c*d + A*B*a^2*d^2)*n + 6*(2*A^2*b^2*c*d - 2*A^2*a*b*d^2 + 7*(B^2*b^2*c*d - B^2*a*b*d^2)*n^2 - 6*(A*B*b^2*c*d - A*B*a*b*d^2)*n)*x + 6*(6*A*B*b^2*c^2 - 8*A*B*a*b*c*d + 2*A*B*a^2*d^2 + 2*(B^2*b^2*d^2*n*x^2 + 2*B^2*b^2*c*d*n*x + B^2*b^2*c^2*n)*log((b*x + a)/(d*x + c))^2 - (7*B^2*b^2*c^2 - 8*B^2*a*b*c*d + B^2*a^2*d^2)*n + 2*(2*A*B*b^2*c*d - 2*A*B*a*b*d^2 - 3*(B^2*b^2*c*d - B^2*a*b*d^2)*n)*x + 2*(2*A*B*b^2*c^2 - (3*B^2*b^2*d^2*n - 2*A*B*b^2*d^2)*x^2 - (4*B^2*a*b*c*d - B^2*a^2*d^2)*n + 2*(2*A*B*b^2*c*d - (2*B^2*b^2*c*d + B^2*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) + 6*(2*A^2*b^2*c^2 + (8*B^2*a*b*c*d - B^2*a^2*d^2)*n^2 + (7*B^2*b^2*d^2*n^2 - 6*A*B*b^2*d^2*n + 2*A^2*b^2*d^2)*x^2 - 2*(4*A*B*a*b*c*d - A*B*a^2*d^2)*n + 2*(2*A^2*b^2*c*d + (4*B^2*b^2*c*d + 3*B^2*a*b*d^2)*n^2 - 2*(2*A*B*b^2*c*d + A*B*a*b*d^2)*n)*x)*log((b*x + a)/(d*x + c)))/((b^3*c^3*d^2 - 3*a*b^2*c^2*d^3 + 3*a^2*b*c*d^4 - a^3*d^5)*g*i^3*x^2 + 2*(b^3*c^4*d - 3*a*b^2*c^3*d^2 + 3*a^2*b*c^2*d^3 - a^3*c*d^4)*g*i^3*x + (b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*g*i^3)","B",0
207,1,2057,0,0.525957," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^2/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{4 \, A^{2} b^{3} c^{3} + 6 \, A^{2} a b^{2} c^{2} d - 12 \, A^{2} a^{2} b c d^{2} + 2 \, A^{2} a^{3} d^{3} + 4 \, {\left(B^{2} b^{3} d^{3} n^{2} x^{3} + B^{2} a b^{2} c^{2} d n^{2} + {\left(2 \, B^{2} b^{3} c d^{2} + B^{2} a b^{2} d^{3}\right)} n^{2} x^{2} + {\left(B^{2} b^{3} c^{2} d + 2 \, B^{2} a b^{2} c d^{2}\right)} n^{2} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + {\left(8 \, B^{2} b^{3} c^{3} + 15 \, B^{2} a b^{2} c^{2} d - 24 \, B^{2} a^{2} b c d^{2} + B^{2} a^{3} d^{3}\right)} n^{2} + 6 \, {\left(2 \, A^{2} b^{3} c d^{2} - 2 \, A^{2} a b^{2} d^{3} + 5 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} n^{2} - 2 \, {\left(A B b^{3} c d^{2} - A B a b^{2} d^{3}\right)} n\right)} x^{2} + 2 \, {\left(2 \, B^{2} b^{3} c^{3} + 3 \, B^{2} a b^{2} c^{2} d - 6 \, B^{2} a^{2} b c d^{2} + B^{2} a^{3} d^{3} + 6 \, {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} x^{2} + 3 \, {\left(3 \, B^{2} b^{3} c^{2} d - 2 \, B^{2} a b^{2} c d^{2} - B^{2} a^{2} b d^{3}\right)} x + 6 \, {\left(B^{2} b^{3} d^{3} x^{3} + B^{2} a b^{2} c^{2} d + {\left(2 \, B^{2} b^{3} c d^{2} + B^{2} a b^{2} d^{3}\right)} x^{2} + {\left(B^{2} b^{3} c^{2} d + 2 \, B^{2} a b^{2} c d^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} + 2 \, {\left(6 \, A B a b^{2} c^{2} d n - 3 \, {\left(B^{2} b^{3} d^{3} n^{2} - 2 \, A B b^{3} d^{3} n\right)} x^{3} + {\left(2 \, B^{2} b^{3} c^{3} - 6 \, B^{2} a^{2} b c d^{2} + B^{2} a^{3} d^{3}\right)} n^{2} - 3 \, {\left(3 \, B^{2} a b^{2} d^{3} n^{2} - 2 \, {\left(2 \, A B b^{3} c d^{2} + A B a b^{2} d^{3}\right)} n\right)} x^{2} + 3 \, {\left({\left(2 \, B^{2} b^{3} c^{2} d - 4 \, B^{2} a b^{2} c d^{2} - B^{2} a^{2} b d^{3}\right)} n^{2} + 2 \, {\left(A B b^{3} c^{2} d + 2 \, A B a b^{2} c d^{2}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(4 \, A B b^{3} c^{3} - 15 \, A B a b^{2} c^{2} d + 12 \, A B a^{2} b c d^{2} - A B a^{3} d^{3}\right)} n + 3 \, {\left(6 \, A^{2} b^{3} c^{2} d - 4 \, A^{2} a b^{2} c d^{2} - 2 \, A^{2} a^{2} b d^{3} + {\left(13 \, B^{2} b^{3} c^{2} d - 6 \, B^{2} a b^{2} c d^{2} - 7 \, B^{2} a^{2} b d^{3}\right)} n^{2} - 2 \, {\left(A B b^{3} c^{2} d + 2 \, A B a b^{2} c d^{2} - 3 \, A B a^{2} b d^{3}\right)} n\right)} x + 2 \, {\left(4 \, A B b^{3} c^{3} + 6 \, A B a b^{2} c^{2} d - 12 \, A B a^{2} b c d^{2} + 2 \, A B a^{3} d^{3} + 6 \, {\left(2 \, A B b^{3} c d^{2} - 2 \, A B a b^{2} d^{3} - {\left(B^{2} b^{3} c d^{2} - B^{2} a b^{2} d^{3}\right)} n\right)} x^{2} + 6 \, {\left(B^{2} b^{3} d^{3} n x^{3} + B^{2} a b^{2} c^{2} d n + {\left(2 \, B^{2} b^{3} c d^{2} + B^{2} a b^{2} d^{3}\right)} n x^{2} + {\left(B^{2} b^{3} c^{2} d + 2 \, B^{2} a b^{2} c d^{2}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(4 \, B^{2} b^{3} c^{3} - 15 \, B^{2} a b^{2} c^{2} d + 12 \, B^{2} a^{2} b c d^{2} - B^{2} a^{3} d^{3}\right)} n + 3 \, {\left(6 \, A B b^{3} c^{2} d - 4 \, A B a b^{2} c d^{2} - 2 \, A B a^{2} b d^{3} - {\left(B^{2} b^{3} c^{2} d + 2 \, B^{2} a b^{2} c d^{2} - 3 \, B^{2} a^{2} b d^{3}\right)} n\right)} x + 2 \, {\left(6 \, A B a b^{2} c^{2} d - 3 \, {\left(B^{2} b^{3} d^{3} n - 2 \, A B b^{3} d^{3}\right)} x^{3} - 3 \, {\left(3 \, B^{2} a b^{2} d^{3} n - 4 \, A B b^{3} c d^{2} - 2 \, A B a b^{2} d^{3}\right)} x^{2} + {\left(2 \, B^{2} b^{3} c^{3} - 6 \, B^{2} a^{2} b c d^{2} + B^{2} a^{3} d^{3}\right)} n + 3 \, {\left(2 \, A B b^{3} c^{2} d + 4 \, A B a b^{2} c d^{2} + {\left(2 \, B^{2} b^{3} c^{2} d - 4 \, B^{2} a b^{2} c d^{2} - B^{2} a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left(6 \, A^{2} a b^{2} c^{2} d + 3 \, {\left(5 \, B^{2} b^{3} d^{3} n^{2} - 2 \, A B b^{3} d^{3} n + 2 \, A^{2} b^{3} d^{3}\right)} x^{3} + {\left(4 \, B^{2} b^{3} c^{3} + 12 \, B^{2} a^{2} b c d^{2} - B^{2} a^{3} d^{3}\right)} n^{2} - 3 \, {\left(6 \, A B a b^{2} d^{3} n - 4 \, A^{2} b^{3} c d^{2} - 2 \, A^{2} a b^{2} d^{3} - {\left(8 \, B^{2} b^{3} c d^{2} + 7 \, B^{2} a b^{2} d^{3}\right)} n^{2}\right)} x^{2} + 2 \, {\left(2 \, A B b^{3} c^{3} - 6 \, A B a^{2} b c d^{2} + A B a^{3} d^{3}\right)} n + 3 \, {\left(2 \, A^{2} b^{3} c^{2} d + 4 \, A^{2} a b^{2} c d^{2} + {\left(4 \, B^{2} b^{3} c^{2} d + 8 \, B^{2} a b^{2} c d^{2} + 3 \, B^{2} a^{2} b d^{3}\right)} n^{2} + 2 \, {\left(2 \, A B b^{3} c^{2} d - 4 \, A B a b^{2} c d^{2} - A B a^{2} b d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{5} c^{4} d^{2} - 4 \, a b^{4} c^{3} d^{3} + 6 \, a^{2} b^{3} c^{2} d^{4} - 4 \, a^{3} b^{2} c d^{5} + a^{4} b d^{6}\right)} g^{2} i^{3} x^{3} + {\left(2 \, b^{5} c^{5} d - 7 \, a b^{4} c^{4} d^{2} + 8 \, a^{2} b^{3} c^{3} d^{3} - 2 \, a^{3} b^{2} c^{2} d^{4} - 2 \, a^{4} b c d^{5} + a^{5} d^{6}\right)} g^{2} i^{3} x^{2} + {\left(b^{5} c^{6} - 2 \, a b^{4} c^{5} d - 2 \, a^{2} b^{3} c^{4} d^{2} + 8 \, a^{3} b^{2} c^{3} d^{3} - 7 \, a^{4} b c^{2} d^{4} + 2 \, a^{5} c d^{5}\right)} g^{2} i^{3} x + {\left(a b^{4} c^{6} - 4 \, a^{2} b^{3} c^{5} d + 6 \, a^{3} b^{2} c^{4} d^{2} - 4 \, a^{4} b c^{3} d^{3} + a^{5} c^{2} d^{4}\right)} g^{2} i^{3}\right)}}"," ",0,"-1/4*(4*A^2*b^3*c^3 + 6*A^2*a*b^2*c^2*d - 12*A^2*a^2*b*c*d^2 + 2*A^2*a^3*d^3 + 4*(B^2*b^3*d^3*n^2*x^3 + B^2*a*b^2*c^2*d*n^2 + (2*B^2*b^3*c*d^2 + B^2*a*b^2*d^3)*n^2*x^2 + (B^2*b^3*c^2*d + 2*B^2*a*b^2*c*d^2)*n^2*x)*log((b*x + a)/(d*x + c))^3 + (8*B^2*b^3*c^3 + 15*B^2*a*b^2*c^2*d - 24*B^2*a^2*b*c*d^2 + B^2*a^3*d^3)*n^2 + 6*(2*A^2*b^3*c*d^2 - 2*A^2*a*b^2*d^3 + 5*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*n^2 - 2*(A*B*b^3*c*d^2 - A*B*a*b^2*d^3)*n)*x^2 + 2*(2*B^2*b^3*c^3 + 3*B^2*a*b^2*c^2*d - 6*B^2*a^2*b*c*d^2 + B^2*a^3*d^3 + 6*(B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*x^2 + 3*(3*B^2*b^3*c^2*d - 2*B^2*a*b^2*c*d^2 - B^2*a^2*b*d^3)*x + 6*(B^2*b^3*d^3*x^3 + B^2*a*b^2*c^2*d + (2*B^2*b^3*c*d^2 + B^2*a*b^2*d^3)*x^2 + (B^2*b^3*c^2*d + 2*B^2*a*b^2*c*d^2)*x)*log((b*x + a)/(d*x + c)))*log(e)^2 + 2*(6*A*B*a*b^2*c^2*d*n - 3*(B^2*b^3*d^3*n^2 - 2*A*B*b^3*d^3*n)*x^3 + (2*B^2*b^3*c^3 - 6*B^2*a^2*b*c*d^2 + B^2*a^3*d^3)*n^2 - 3*(3*B^2*a*b^2*d^3*n^2 - 2*(2*A*B*b^3*c*d^2 + A*B*a*b^2*d^3)*n)*x^2 + 3*((2*B^2*b^3*c^2*d - 4*B^2*a*b^2*c*d^2 - B^2*a^2*b*d^3)*n^2 + 2*(A*B*b^3*c^2*d + 2*A*B*a*b^2*c*d^2)*n)*x)*log((b*x + a)/(d*x + c))^2 + 2*(4*A*B*b^3*c^3 - 15*A*B*a*b^2*c^2*d + 12*A*B*a^2*b*c*d^2 - A*B*a^3*d^3)*n + 3*(6*A^2*b^3*c^2*d - 4*A^2*a*b^2*c*d^2 - 2*A^2*a^2*b*d^3 + (13*B^2*b^3*c^2*d - 6*B^2*a*b^2*c*d^2 - 7*B^2*a^2*b*d^3)*n^2 - 2*(A*B*b^3*c^2*d + 2*A*B*a*b^2*c*d^2 - 3*A*B*a^2*b*d^3)*n)*x + 2*(4*A*B*b^3*c^3 + 6*A*B*a*b^2*c^2*d - 12*A*B*a^2*b*c*d^2 + 2*A*B*a^3*d^3 + 6*(2*A*B*b^3*c*d^2 - 2*A*B*a*b^2*d^3 - (B^2*b^3*c*d^2 - B^2*a*b^2*d^3)*n)*x^2 + 6*(B^2*b^3*d^3*n*x^3 + B^2*a*b^2*c^2*d*n + (2*B^2*b^3*c*d^2 + B^2*a*b^2*d^3)*n*x^2 + (B^2*b^3*c^2*d + 2*B^2*a*b^2*c*d^2)*n*x)*log((b*x + a)/(d*x + c))^2 + (4*B^2*b^3*c^3 - 15*B^2*a*b^2*c^2*d + 12*B^2*a^2*b*c*d^2 - B^2*a^3*d^3)*n + 3*(6*A*B*b^3*c^2*d - 4*A*B*a*b^2*c*d^2 - 2*A*B*a^2*b*d^3 - (B^2*b^3*c^2*d + 2*B^2*a*b^2*c*d^2 - 3*B^2*a^2*b*d^3)*n)*x + 2*(6*A*B*a*b^2*c^2*d - 3*(B^2*b^3*d^3*n - 2*A*B*b^3*d^3)*x^3 - 3*(3*B^2*a*b^2*d^3*n - 4*A*B*b^3*c*d^2 - 2*A*B*a*b^2*d^3)*x^2 + (2*B^2*b^3*c^3 - 6*B^2*a^2*b*c*d^2 + B^2*a^3*d^3)*n + 3*(2*A*B*b^3*c^2*d + 4*A*B*a*b^2*c*d^2 + (2*B^2*b^3*c^2*d - 4*B^2*a*b^2*c*d^2 - B^2*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) + 2*(6*A^2*a*b^2*c^2*d + 3*(5*B^2*b^3*d^3*n^2 - 2*A*B*b^3*d^3*n + 2*A^2*b^3*d^3)*x^3 + (4*B^2*b^3*c^3 + 12*B^2*a^2*b*c*d^2 - B^2*a^3*d^3)*n^2 - 3*(6*A*B*a*b^2*d^3*n - 4*A^2*b^3*c*d^2 - 2*A^2*a*b^2*d^3 - (8*B^2*b^3*c*d^2 + 7*B^2*a*b^2*d^3)*n^2)*x^2 + 2*(2*A*B*b^3*c^3 - 6*A*B*a^2*b*c*d^2 + A*B*a^3*d^3)*n + 3*(2*A^2*b^3*c^2*d + 4*A^2*a*b^2*c*d^2 + (4*B^2*b^3*c^2*d + 8*B^2*a*b^2*c*d^2 + 3*B^2*a^2*b*d^3)*n^2 + 2*(2*A*B*b^3*c^2*d - 4*A*B*a*b^2*c*d^2 - A*B*a^2*b*d^3)*n)*x)*log((b*x + a)/(d*x + c)))/((b^5*c^4*d^2 - 4*a*b^4*c^3*d^3 + 6*a^2*b^3*c^2*d^4 - 4*a^3*b^2*c*d^5 + a^4*b*d^6)*g^2*i^3*x^3 + (2*b^5*c^5*d - 7*a*b^4*c^4*d^2 + 8*a^2*b^3*c^3*d^3 - 2*a^3*b^2*c^2*d^4 - 2*a^4*b*c*d^5 + a^5*d^6)*g^2*i^3*x^2 + (b^5*c^6 - 2*a*b^4*c^5*d - 2*a^2*b^3*c^4*d^2 + 8*a^3*b^2*c^3*d^3 - 7*a^4*b*c^2*d^4 + 2*a^5*c*d^5)*g^2*i^3*x + (a*b^4*c^6 - 4*a^2*b^3*c^5*d + 6*a^3*b^2*c^4*d^2 - 4*a^4*b*c^3*d^3 + a^5*c^2*d^4)*g^2*i^3)","B",0
208,1,3062,0,0.553650," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^3/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{2 \, A^{2} b^{4} c^{4} - 16 \, A^{2} a b^{3} c^{3} d + 16 \, A^{2} a^{3} b c d^{3} - 2 \, A^{2} a^{4} d^{4} - 12 \, {\left(2 \, A^{2} b^{4} c d^{3} - 2 \, A^{2} a b^{3} d^{4} + 5 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} n^{2}\right)} x^{3} - 8 \, {\left(B^{2} b^{4} d^{4} n^{2} x^{4} + B^{2} a^{2} b^{2} c^{2} d^{2} n^{2} + 2 \, {\left(B^{2} b^{4} c d^{3} + B^{2} a b^{3} d^{4}\right)} n^{2} x^{3} + {\left(B^{2} b^{4} c^{2} d^{2} + 4 \, B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} n^{2} x^{2} + 2 \, {\left(B^{2} a b^{3} c^{2} d^{2} + B^{2} a^{2} b^{2} c d^{3}\right)} n^{2} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + {\left(B^{2} b^{4} c^{4} - 32 \, B^{2} a b^{3} c^{3} d + 32 \, B^{2} a^{3} b c d^{3} - B^{2} a^{4} d^{4}\right)} n^{2} - 6 \, {\left(6 \, A^{2} b^{4} c^{2} d^{2} - 6 \, A^{2} a^{2} b^{2} d^{4} + 15 \, {\left(B^{2} b^{4} c^{2} d^{2} - B^{2} a^{2} b^{2} d^{4}\right)} n^{2} + 4 \, {\left(A B b^{4} c^{2} d^{2} - 2 \, A B a b^{3} c d^{3} + A B a^{2} b^{2} d^{4}\right)} n\right)} x^{2} + 2 \, {\left(B^{2} b^{4} c^{4} - 8 \, B^{2} a b^{3} c^{3} d + 8 \, B^{2} a^{3} b c d^{3} - B^{2} a^{4} d^{4} - 12 \, {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} x^{3} - 18 \, {\left(B^{2} b^{4} c^{2} d^{2} - B^{2} a^{2} b^{2} d^{4}\right)} x^{2} - 4 \, {\left(B^{2} b^{4} c^{3} d + 6 \, B^{2} a b^{3} c^{2} d^{2} - 6 \, B^{2} a^{2} b^{2} c d^{3} - B^{2} a^{3} b d^{4}\right)} x - 12 \, {\left(B^{2} b^{4} d^{4} x^{4} + B^{2} a^{2} b^{2} c^{2} d^{2} + 2 \, {\left(B^{2} b^{4} c d^{3} + B^{2} a b^{3} d^{4}\right)} x^{3} + {\left(B^{2} b^{4} c^{2} d^{2} + 4 \, B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} x^{2} + 2 \, {\left(B^{2} a b^{3} c^{2} d^{2} + B^{2} a^{2} b^{2} c d^{3}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} - 2 \, {\left(12 \, A B b^{4} d^{4} n x^{4} + 12 \, A B a^{2} b^{2} c^{2} d^{2} n + 12 \, {\left({\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} n^{2} + 2 \, {\left(A B b^{4} c d^{3} + A B a b^{3} d^{4}\right)} n\right)} x^{3} - {\left(B^{2} b^{4} c^{4} - 8 \, B^{2} a b^{3} c^{3} d + 8 \, B^{2} a^{3} b c d^{3} - B^{2} a^{4} d^{4}\right)} n^{2} + 6 \, {\left(3 \, {\left(B^{2} b^{4} c^{2} d^{2} - B^{2} a^{2} b^{2} d^{4}\right)} n^{2} + 2 \, {\left(A B b^{4} c^{2} d^{2} + 4 \, A B a b^{3} c d^{3} + A B a^{2} b^{2} d^{4}\right)} n\right)} x^{2} + 4 \, {\left({\left(B^{2} b^{4} c^{3} d + 6 \, B^{2} a b^{3} c^{2} d^{2} - 6 \, B^{2} a^{2} b^{2} c d^{3} - B^{2} a^{3} b d^{4}\right)} n^{2} + 6 \, {\left(A B a b^{3} c^{2} d^{2} + A B a^{2} b^{2} c d^{3}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(A B b^{4} c^{4} - 16 \, A B a b^{3} c^{3} d + 30 \, A B a^{2} b^{2} c^{2} d^{2} - 16 \, A B a^{3} b c d^{3} + A B a^{4} d^{4}\right)} n - 4 \, {\left(2 \, A^{2} b^{4} c^{3} d + 12 \, A^{2} a b^{3} c^{2} d^{2} - 12 \, A^{2} a^{2} b^{2} c d^{3} - 2 \, A^{2} a^{3} b d^{4} + {\left(7 \, B^{2} b^{4} c^{3} d + 24 \, B^{2} a b^{3} c^{2} d^{2} - 24 \, B^{2} a^{2} b^{2} c d^{3} - 7 \, B^{2} a^{3} b d^{4}\right)} n^{2} + 6 \, {\left(A B b^{4} c^{3} d - A B a b^{3} c^{2} d^{2} - A B a^{2} b^{2} c d^{3} + A B a^{3} b d^{4}\right)} n\right)} x + 2 \, {\left(2 \, A B b^{4} c^{4} - 16 \, A B a b^{3} c^{3} d + 16 \, A B a^{3} b c d^{3} - 2 \, A B a^{4} d^{4} - 24 \, {\left(A B b^{4} c d^{3} - A B a b^{3} d^{4}\right)} x^{3} - 12 \, {\left(3 \, A B b^{4} c^{2} d^{2} - 3 \, A B a^{2} b^{2} d^{4} + {\left(B^{2} b^{4} c^{2} d^{2} - 2 \, B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} n\right)} x^{2} - 12 \, {\left(B^{2} b^{4} d^{4} n x^{4} + B^{2} a^{2} b^{2} c^{2} d^{2} n + 2 \, {\left(B^{2} b^{4} c d^{3} + B^{2} a b^{3} d^{4}\right)} n x^{3} + {\left(B^{2} b^{4} c^{2} d^{2} + 4 \, B^{2} a b^{3} c d^{3} + B^{2} a^{2} b^{2} d^{4}\right)} n x^{2} + 2 \, {\left(B^{2} a b^{3} c^{2} d^{2} + B^{2} a^{2} b^{2} c d^{3}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B^{2} b^{4} c^{4} - 16 \, B^{2} a b^{3} c^{3} d + 30 \, B^{2} a^{2} b^{2} c^{2} d^{2} - 16 \, B^{2} a^{3} b c d^{3} + B^{2} a^{4} d^{4}\right)} n - 4 \, {\left(2 \, A B b^{4} c^{3} d + 12 \, A B a b^{3} c^{2} d^{2} - 12 \, A B a^{2} b^{2} c d^{3} - 2 \, A B a^{3} b d^{4} + 3 \, {\left(B^{2} b^{4} c^{3} d - B^{2} a b^{3} c^{2} d^{2} - B^{2} a^{2} b^{2} c d^{3} + B^{2} a^{3} b d^{4}\right)} n\right)} x - 2 \, {\left(12 \, A B b^{4} d^{4} x^{4} + 12 \, A B a^{2} b^{2} c^{2} d^{2} + 12 \, {\left(2 \, A B b^{4} c d^{3} + 2 \, A B a b^{3} d^{4} + {\left(B^{2} b^{4} c d^{3} - B^{2} a b^{3} d^{4}\right)} n\right)} x^{3} + 6 \, {\left(2 \, A B b^{4} c^{2} d^{2} + 8 \, A B a b^{3} c d^{3} + 2 \, A B a^{2} b^{2} d^{4} + 3 \, {\left(B^{2} b^{4} c^{2} d^{2} - B^{2} a^{2} b^{2} d^{4}\right)} n\right)} x^{2} - {\left(B^{2} b^{4} c^{4} - 8 \, B^{2} a b^{3} c^{3} d + 8 \, B^{2} a^{3} b c d^{3} - B^{2} a^{4} d^{4}\right)} n + 4 \, {\left(6 \, A B a b^{3} c^{2} d^{2} + 6 \, A B a^{2} b^{2} c d^{3} + {\left(B^{2} b^{4} c^{3} d + 6 \, B^{2} a b^{3} c^{2} d^{2} - 6 \, B^{2} a^{2} b^{2} c d^{3} - B^{2} a^{3} b d^{4}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) - 2 \, {\left(12 \, A^{2} a^{2} b^{2} c^{2} d^{2} + 6 \, {\left(5 \, B^{2} b^{4} d^{4} n^{2} + 2 \, A^{2} b^{4} d^{4}\right)} x^{4} + 12 \, {\left(2 \, A^{2} b^{4} c d^{3} + 2 \, A^{2} a b^{3} d^{4} + 5 \, {\left(B^{2} b^{4} c d^{3} + B^{2} a b^{3} d^{4}\right)} n^{2} + 2 \, {\left(A B b^{4} c d^{3} - A B a b^{3} d^{4}\right)} n\right)} x^{3} - {\left(B^{2} b^{4} c^{4} - 16 \, B^{2} a b^{3} c^{3} d - 16 \, B^{2} a^{3} b c d^{3} + B^{2} a^{4} d^{4}\right)} n^{2} + 6 \, {\left(2 \, A^{2} b^{4} c^{2} d^{2} + 8 \, A^{2} a b^{3} c d^{3} + 2 \, A^{2} a^{2} b^{2} d^{4} + {\left(7 \, B^{2} b^{4} c^{2} d^{2} + 16 \, B^{2} a b^{3} c d^{3} + 7 \, B^{2} a^{2} b^{2} d^{4}\right)} n^{2} + 6 \, {\left(A B b^{4} c^{2} d^{2} - A B a^{2} b^{2} d^{4}\right)} n\right)} x^{2} - 2 \, {\left(A B b^{4} c^{4} - 8 \, A B a b^{3} c^{3} d + 8 \, A B a^{3} b c d^{3} - A B a^{4} d^{4}\right)} n + 4 \, {\left(6 \, A^{2} a b^{3} c^{2} d^{2} + 6 \, A^{2} a^{2} b^{2} c d^{3} + 3 \, {\left(B^{2} b^{4} c^{3} d + 4 \, B^{2} a b^{3} c^{2} d^{2} + 4 \, B^{2} a^{2} b^{2} c d^{3} + B^{2} a^{3} b d^{4}\right)} n^{2} + 2 \, {\left(A B b^{4} c^{3} d + 6 \, A B a b^{3} c^{2} d^{2} - 6 \, A B a^{2} b^{2} c d^{3} - A B a^{3} b d^{4}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{4 \, {\left({\left(b^{7} c^{5} d^{2} - 5 \, a b^{6} c^{4} d^{3} + 10 \, a^{2} b^{5} c^{3} d^{4} - 10 \, a^{3} b^{4} c^{2} d^{5} + 5 \, a^{4} b^{3} c d^{6} - a^{5} b^{2} d^{7}\right)} g^{3} i^{3} x^{4} + 2 \, {\left(b^{7} c^{6} d - 4 \, a b^{6} c^{5} d^{2} + 5 \, a^{2} b^{5} c^{4} d^{3} - 5 \, a^{4} b^{3} c^{2} d^{5} + 4 \, a^{5} b^{2} c d^{6} - a^{6} b d^{7}\right)} g^{3} i^{3} x^{3} + {\left(b^{7} c^{7} - a b^{6} c^{6} d - 9 \, a^{2} b^{5} c^{5} d^{2} + 25 \, a^{3} b^{4} c^{4} d^{3} - 25 \, a^{4} b^{3} c^{3} d^{4} + 9 \, a^{5} b^{2} c^{2} d^{5} + a^{6} b c d^{6} - a^{7} d^{7}\right)} g^{3} i^{3} x^{2} + 2 \, {\left(a b^{6} c^{7} - 4 \, a^{2} b^{5} c^{6} d + 5 \, a^{3} b^{4} c^{5} d^{2} - 5 \, a^{5} b^{2} c^{3} d^{4} + 4 \, a^{6} b c^{2} d^{5} - a^{7} c d^{6}\right)} g^{3} i^{3} x + {\left(a^{2} b^{5} c^{7} - 5 \, a^{3} b^{4} c^{6} d + 10 \, a^{4} b^{3} c^{5} d^{2} - 10 \, a^{5} b^{2} c^{4} d^{3} + 5 \, a^{6} b c^{3} d^{4} - a^{7} c^{2} d^{5}\right)} g^{3} i^{3}\right)}}"," ",0,"-1/4*(2*A^2*b^4*c^4 - 16*A^2*a*b^3*c^3*d + 16*A^2*a^3*b*c*d^3 - 2*A^2*a^4*d^4 - 12*(2*A^2*b^4*c*d^3 - 2*A^2*a*b^3*d^4 + 5*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*n^2)*x^3 - 8*(B^2*b^4*d^4*n^2*x^4 + B^2*a^2*b^2*c^2*d^2*n^2 + 2*(B^2*b^4*c*d^3 + B^2*a*b^3*d^4)*n^2*x^3 + (B^2*b^4*c^2*d^2 + 4*B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*n^2*x^2 + 2*(B^2*a*b^3*c^2*d^2 + B^2*a^2*b^2*c*d^3)*n^2*x)*log((b*x + a)/(d*x + c))^3 + (B^2*b^4*c^4 - 32*B^2*a*b^3*c^3*d + 32*B^2*a^3*b*c*d^3 - B^2*a^4*d^4)*n^2 - 6*(6*A^2*b^4*c^2*d^2 - 6*A^2*a^2*b^2*d^4 + 15*(B^2*b^4*c^2*d^2 - B^2*a^2*b^2*d^4)*n^2 + 4*(A*B*b^4*c^2*d^2 - 2*A*B*a*b^3*c*d^3 + A*B*a^2*b^2*d^4)*n)*x^2 + 2*(B^2*b^4*c^4 - 8*B^2*a*b^3*c^3*d + 8*B^2*a^3*b*c*d^3 - B^2*a^4*d^4 - 12*(B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*x^3 - 18*(B^2*b^4*c^2*d^2 - B^2*a^2*b^2*d^4)*x^2 - 4*(B^2*b^4*c^3*d + 6*B^2*a*b^3*c^2*d^2 - 6*B^2*a^2*b^2*c*d^3 - B^2*a^3*b*d^4)*x - 12*(B^2*b^4*d^4*x^4 + B^2*a^2*b^2*c^2*d^2 + 2*(B^2*b^4*c*d^3 + B^2*a*b^3*d^4)*x^3 + (B^2*b^4*c^2*d^2 + 4*B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*x^2 + 2*(B^2*a*b^3*c^2*d^2 + B^2*a^2*b^2*c*d^3)*x)*log((b*x + a)/(d*x + c)))*log(e)^2 - 2*(12*A*B*b^4*d^4*n*x^4 + 12*A*B*a^2*b^2*c^2*d^2*n + 12*((B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*n^2 + 2*(A*B*b^4*c*d^3 + A*B*a*b^3*d^4)*n)*x^3 - (B^2*b^4*c^4 - 8*B^2*a*b^3*c^3*d + 8*B^2*a^3*b*c*d^3 - B^2*a^4*d^4)*n^2 + 6*(3*(B^2*b^4*c^2*d^2 - B^2*a^2*b^2*d^4)*n^2 + 2*(A*B*b^4*c^2*d^2 + 4*A*B*a*b^3*c*d^3 + A*B*a^2*b^2*d^4)*n)*x^2 + 4*((B^2*b^4*c^3*d + 6*B^2*a*b^3*c^2*d^2 - 6*B^2*a^2*b^2*c*d^3 - B^2*a^3*b*d^4)*n^2 + 6*(A*B*a*b^3*c^2*d^2 + A*B*a^2*b^2*c*d^3)*n)*x)*log((b*x + a)/(d*x + c))^2 + 2*(A*B*b^4*c^4 - 16*A*B*a*b^3*c^3*d + 30*A*B*a^2*b^2*c^2*d^2 - 16*A*B*a^3*b*c*d^3 + A*B*a^4*d^4)*n - 4*(2*A^2*b^4*c^3*d + 12*A^2*a*b^3*c^2*d^2 - 12*A^2*a^2*b^2*c*d^3 - 2*A^2*a^3*b*d^4 + (7*B^2*b^4*c^3*d + 24*B^2*a*b^3*c^2*d^2 - 24*B^2*a^2*b^2*c*d^3 - 7*B^2*a^3*b*d^4)*n^2 + 6*(A*B*b^4*c^3*d - A*B*a*b^3*c^2*d^2 - A*B*a^2*b^2*c*d^3 + A*B*a^3*b*d^4)*n)*x + 2*(2*A*B*b^4*c^4 - 16*A*B*a*b^3*c^3*d + 16*A*B*a^3*b*c*d^3 - 2*A*B*a^4*d^4 - 24*(A*B*b^4*c*d^3 - A*B*a*b^3*d^4)*x^3 - 12*(3*A*B*b^4*c^2*d^2 - 3*A*B*a^2*b^2*d^4 + (B^2*b^4*c^2*d^2 - 2*B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*n)*x^2 - 12*(B^2*b^4*d^4*n*x^4 + B^2*a^2*b^2*c^2*d^2*n + 2*(B^2*b^4*c*d^3 + B^2*a*b^3*d^4)*n*x^3 + (B^2*b^4*c^2*d^2 + 4*B^2*a*b^3*c*d^3 + B^2*a^2*b^2*d^4)*n*x^2 + 2*(B^2*a*b^3*c^2*d^2 + B^2*a^2*b^2*c*d^3)*n*x)*log((b*x + a)/(d*x + c))^2 + (B^2*b^4*c^4 - 16*B^2*a*b^3*c^3*d + 30*B^2*a^2*b^2*c^2*d^2 - 16*B^2*a^3*b*c*d^3 + B^2*a^4*d^4)*n - 4*(2*A*B*b^4*c^3*d + 12*A*B*a*b^3*c^2*d^2 - 12*A*B*a^2*b^2*c*d^3 - 2*A*B*a^3*b*d^4 + 3*(B^2*b^4*c^3*d - B^2*a*b^3*c^2*d^2 - B^2*a^2*b^2*c*d^3 + B^2*a^3*b*d^4)*n)*x - 2*(12*A*B*b^4*d^4*x^4 + 12*A*B*a^2*b^2*c^2*d^2 + 12*(2*A*B*b^4*c*d^3 + 2*A*B*a*b^3*d^4 + (B^2*b^4*c*d^3 - B^2*a*b^3*d^4)*n)*x^3 + 6*(2*A*B*b^4*c^2*d^2 + 8*A*B*a*b^3*c*d^3 + 2*A*B*a^2*b^2*d^4 + 3*(B^2*b^4*c^2*d^2 - B^2*a^2*b^2*d^4)*n)*x^2 - (B^2*b^4*c^4 - 8*B^2*a*b^3*c^3*d + 8*B^2*a^3*b*c*d^3 - B^2*a^4*d^4)*n + 4*(6*A*B*a*b^3*c^2*d^2 + 6*A*B*a^2*b^2*c*d^3 + (B^2*b^4*c^3*d + 6*B^2*a*b^3*c^2*d^2 - 6*B^2*a^2*b^2*c*d^3 - B^2*a^3*b*d^4)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) - 2*(12*A^2*a^2*b^2*c^2*d^2 + 6*(5*B^2*b^4*d^4*n^2 + 2*A^2*b^4*d^4)*x^4 + 12*(2*A^2*b^4*c*d^3 + 2*A^2*a*b^3*d^4 + 5*(B^2*b^4*c*d^3 + B^2*a*b^3*d^4)*n^2 + 2*(A*B*b^4*c*d^3 - A*B*a*b^3*d^4)*n)*x^3 - (B^2*b^4*c^4 - 16*B^2*a*b^3*c^3*d - 16*B^2*a^3*b*c*d^3 + B^2*a^4*d^4)*n^2 + 6*(2*A^2*b^4*c^2*d^2 + 8*A^2*a*b^3*c*d^3 + 2*A^2*a^2*b^2*d^4 + (7*B^2*b^4*c^2*d^2 + 16*B^2*a*b^3*c*d^3 + 7*B^2*a^2*b^2*d^4)*n^2 + 6*(A*B*b^4*c^2*d^2 - A*B*a^2*b^2*d^4)*n)*x^2 - 2*(A*B*b^4*c^4 - 8*A*B*a*b^3*c^3*d + 8*A*B*a^3*b*c*d^3 - A*B*a^4*d^4)*n + 4*(6*A^2*a*b^3*c^2*d^2 + 6*A^2*a^2*b^2*c*d^3 + 3*(B^2*b^4*c^3*d + 4*B^2*a*b^3*c^2*d^2 + 4*B^2*a^2*b^2*c*d^3 + B^2*a^3*b*d^4)*n^2 + 2*(A*B*b^4*c^3*d + 6*A*B*a*b^3*c^2*d^2 - 6*A*B*a^2*b^2*c*d^3 - A*B*a^3*b*d^4)*n)*x)*log((b*x + a)/(d*x + c)))/((b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 10*a^2*b^5*c^3*d^4 - 10*a^3*b^4*c^2*d^5 + 5*a^4*b^3*c*d^6 - a^5*b^2*d^7)*g^3*i^3*x^4 + 2*(b^7*c^6*d - 4*a*b^6*c^5*d^2 + 5*a^2*b^5*c^4*d^3 - 5*a^4*b^3*c^2*d^5 + 4*a^5*b^2*c*d^6 - a^6*b*d^7)*g^3*i^3*x^3 + (b^7*c^7 - a*b^6*c^6*d - 9*a^2*b^5*c^5*d^2 + 25*a^3*b^4*c^4*d^3 - 25*a^4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 + a^6*b*c*d^6 - a^7*d^7)*g^3*i^3*x^2 + 2*(a*b^6*c^7 - 4*a^2*b^5*c^6*d + 5*a^3*b^4*c^5*d^2 - 5*a^5*b^2*c^3*d^4 + 4*a^6*b*c^2*d^5 - a^7*c*d^6)*g^3*i^3*x + (a^2*b^5*c^7 - 5*a^3*b^4*c^6*d + 10*a^4*b^3*c^5*d^2 - 10*a^5*b^2*c^4*d^3 + 5*a^6*b*c^3*d^4 - a^7*c^2*d^5)*g^3*i^3)","B",0
209,1,4725,0,0.649821," ","integrate((A+B*log(e*((b*x+a)/(d*x+c))^n))^2/(b*g*x+a*g)^4/(d*i*x+c*i)^3,x, algorithm=""fricas"")","-\frac{36 \, A^{2} b^{5} c^{5} - 270 \, A^{2} a b^{4} c^{4} d + 1080 \, A^{2} a^{2} b^{3} c^{3} d^{2} - 360 \, A^{2} a^{3} b^{2} c^{2} d^{3} - 540 \, A^{2} a^{4} b c d^{4} + 54 \, A^{2} a^{5} d^{5} + 60 \, {\left(18 \, A^{2} b^{5} c d^{4} - 18 \, A^{2} a b^{4} d^{5} + 49 \, {\left(B^{2} b^{5} c d^{4} - B^{2} a b^{4} d^{5}\right)} n^{2} + 12 \, {\left(A B b^{5} c d^{4} - A B a b^{4} d^{5}\right)} n\right)} x^{4} + 30 \, {\left(54 \, A^{2} b^{5} c^{2} d^{3} + 36 \, A^{2} a b^{4} c d^{4} - 90 \, A^{2} a^{2} b^{3} d^{5} + {\left(159 \, B^{2} b^{5} c^{2} d^{3} + 74 \, B^{2} a b^{4} c d^{4} - 233 \, B^{2} a^{2} b^{3} d^{5}\right)} n^{2} + 24 \, {\left(3 \, A B b^{5} c^{2} d^{3} - 2 \, A B a b^{4} c d^{4} - A B a^{2} b^{3} d^{5}\right)} n\right)} x^{3} + 360 \, {\left(B^{2} b^{5} d^{5} n^{2} x^{5} + B^{2} a^{3} b^{2} c^{2} d^{3} n^{2} + {\left(2 \, B^{2} b^{5} c d^{4} + 3 \, B^{2} a b^{4} d^{5}\right)} n^{2} x^{4} + {\left(B^{2} b^{5} c^{2} d^{3} + 6 \, B^{2} a b^{4} c d^{4} + 3 \, B^{2} a^{2} b^{3} d^{5}\right)} n^{2} x^{3} + {\left(3 \, B^{2} a b^{4} c^{2} d^{3} + 6 \, B^{2} a^{2} b^{3} c d^{4} + B^{2} a^{3} b^{2} d^{5}\right)} n^{2} x^{2} + {\left(3 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 2 \, B^{2} a^{3} b^{2} c d^{4}\right)} n^{2} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + {\left(8 \, B^{2} b^{5} c^{5} - 135 \, B^{2} a b^{4} c^{4} d + 2160 \, B^{2} a^{2} b^{3} c^{3} d^{2} - 980 \, B^{2} a^{3} b^{2} c^{2} d^{3} - 1080 \, B^{2} a^{4} b c d^{4} + 27 \, B^{2} a^{5} d^{5}\right)} n^{2} + 10 \, {\left(36 \, A^{2} b^{5} c^{3} d^{2} + 378 \, A^{2} a b^{4} c^{2} d^{3} - 216 \, A^{2} a^{2} b^{3} c d^{4} - 198 \, A^{2} a^{3} b^{2} d^{5} + {\left(170 \, B^{2} b^{5} c^{3} d^{2} + 921 \, B^{2} a b^{4} c^{2} d^{3} - 588 \, B^{2} a^{2} b^{3} c d^{4} - 503 \, B^{2} a^{3} b^{2} d^{5}\right)} n^{2} + 12 \, {\left(11 \, A B b^{5} c^{3} d^{2} + 21 \, A B a b^{4} c^{2} d^{3} - 39 \, A B a^{2} b^{3} c d^{4} + 7 \, A B a^{3} b^{2} d^{5}\right)} n\right)} x^{2} + 18 \, {\left(2 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 60 \, B^{2} a^{2} b^{3} c^{3} d^{2} - 20 \, B^{2} a^{3} b^{2} c^{2} d^{3} - 30 \, B^{2} a^{4} b c d^{4} + 3 \, B^{2} a^{5} d^{5} + 60 \, {\left(B^{2} b^{5} c d^{4} - B^{2} a b^{4} d^{5}\right)} x^{4} + 30 \, {\left(3 \, B^{2} b^{5} c^{2} d^{3} + 2 \, B^{2} a b^{4} c d^{4} - 5 \, B^{2} a^{2} b^{3} d^{5}\right)} x^{3} + 10 \, {\left(2 \, B^{2} b^{5} c^{3} d^{2} + 21 \, B^{2} a b^{4} c^{2} d^{3} - 12 \, B^{2} a^{2} b^{3} c d^{4} - 11 \, B^{2} a^{3} b^{2} d^{5}\right)} x^{2} - 5 \, {\left(B^{2} b^{5} c^{4} d - 12 \, B^{2} a b^{4} c^{3} d^{2} - 24 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 32 \, B^{2} a^{3} b^{2} c d^{4} + 3 \, B^{2} a^{4} b d^{5}\right)} x + 60 \, {\left(B^{2} b^{5} d^{5} x^{5} + B^{2} a^{3} b^{2} c^{2} d^{3} + {\left(2 \, B^{2} b^{5} c d^{4} + 3 \, B^{2} a b^{4} d^{5}\right)} x^{4} + {\left(B^{2} b^{5} c^{2} d^{3} + 6 \, B^{2} a b^{4} c d^{4} + 3 \, B^{2} a^{2} b^{3} d^{5}\right)} x^{3} + {\left(3 \, B^{2} a b^{4} c^{2} d^{3} + 6 \, B^{2} a^{2} b^{3} c d^{4} + B^{2} a^{3} b^{2} d^{5}\right)} x^{2} + {\left(3 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 2 \, B^{2} a^{3} b^{2} c d^{4}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} + 18 \, {\left(60 \, A B a^{3} b^{2} c^{2} d^{3} n + 20 \, {\left(B^{2} b^{5} d^{5} n^{2} + 3 \, A B b^{5} d^{5} n\right)} x^{5} + 20 \, {\left(5 \, B^{2} b^{5} c d^{4} n^{2} + 3 \, {\left(2 \, A B b^{5} c d^{4} + 3 \, A B a b^{4} d^{5}\right)} n\right)} x^{4} + 10 \, {\left({\left(11 \, B^{2} b^{5} c^{2} d^{3} + 18 \, B^{2} a b^{4} c d^{4} - 9 \, B^{2} a^{2} b^{3} d^{5}\right)} n^{2} + 6 \, {\left(A B b^{5} c^{2} d^{3} + 6 \, A B a b^{4} c d^{4} + 3 \, A B a^{2} b^{3} d^{5}\right)} n\right)} x^{3} + {\left(2 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 60 \, B^{2} a^{2} b^{3} c^{3} d^{2} - 30 \, B^{2} a^{4} b c d^{4} + 3 \, B^{2} a^{5} d^{5}\right)} n^{2} + 10 \, {\left({\left(2 \, B^{2} b^{5} c^{3} d^{2} + 27 \, B^{2} a b^{4} c^{2} d^{3} - 9 \, B^{2} a^{3} b^{2} d^{5}\right)} n^{2} + 6 \, {\left(3 \, A B a b^{4} c^{2} d^{3} + 6 \, A B a^{2} b^{3} c d^{4} + A B a^{3} b^{2} d^{5}\right)} n\right)} x^{2} - 5 \, {\left({\left(B^{2} b^{5} c^{4} d - 12 \, B^{2} a b^{4} c^{3} d^{2} - 36 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 24 \, B^{2} a^{3} b^{2} c d^{4} + 3 \, B^{2} a^{4} b d^{5}\right)} n^{2} - 12 \, {\left(3 \, A B a^{2} b^{3} c^{2} d^{3} + 2 \, A B a^{3} b^{2} c d^{4}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 6 \, {\left(4 \, A B b^{5} c^{5} - 45 \, A B a b^{4} c^{4} d + 360 \, A B a^{2} b^{3} c^{3} d^{2} - 490 \, A B a^{3} b^{2} c^{2} d^{3} + 180 \, A B a^{4} b c d^{4} - 9 \, A B a^{5} d^{5}\right)} n - 5 \, {\left(18 \, A^{2} b^{5} c^{4} d - 216 \, A^{2} a b^{4} c^{3} d^{2} - 432 \, A^{2} a^{2} b^{3} c^{2} d^{3} + 576 \, A^{2} a^{3} b^{2} c d^{4} + 54 \, A^{2} a^{4} b d^{5} + {\left(19 \, B^{2} b^{5} c^{4} d - 756 \, B^{2} a b^{4} c^{3} d^{2} - 708 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 1256 \, B^{2} a^{3} b^{2} c d^{4} + 189 \, B^{2} a^{4} b d^{5}\right)} n^{2} + 6 \, {\left(5 \, A B b^{5} c^{4} d - 108 \, A B a b^{4} c^{3} d^{2} + 78 \, A B a^{2} b^{3} c^{2} d^{3} + 52 \, A B a^{3} b^{2} c d^{4} - 27 \, A B a^{4} b d^{5}\right)} n\right)} x + 6 \, {\left(12 \, A B b^{5} c^{5} - 90 \, A B a b^{4} c^{4} d + 360 \, A B a^{2} b^{3} c^{3} d^{2} - 120 \, A B a^{3} b^{2} c^{2} d^{3} - 180 \, A B a^{4} b c d^{4} + 18 \, A B a^{5} d^{5} + 120 \, {\left(3 \, A B b^{5} c d^{4} - 3 \, A B a b^{4} d^{5} + {\left(B^{2} b^{5} c d^{4} - B^{2} a b^{4} d^{5}\right)} n\right)} x^{4} + 60 \, {\left(9 \, A B b^{5} c^{2} d^{3} + 6 \, A B a b^{4} c d^{4} - 15 \, A B a^{2} b^{3} d^{5} + 2 \, {\left(3 \, B^{2} b^{5} c^{2} d^{3} - 2 \, B^{2} a b^{4} c d^{4} - B^{2} a^{2} b^{3} d^{5}\right)} n\right)} x^{3} + 20 \, {\left(6 \, A B b^{5} c^{3} d^{2} + 63 \, A B a b^{4} c^{2} d^{3} - 36 \, A B a^{2} b^{3} c d^{4} - 33 \, A B a^{3} b^{2} d^{5} + {\left(11 \, B^{2} b^{5} c^{3} d^{2} + 21 \, B^{2} a b^{4} c^{2} d^{3} - 39 \, B^{2} a^{2} b^{3} c d^{4} + 7 \, B^{2} a^{3} b^{2} d^{5}\right)} n\right)} x^{2} + 180 \, {\left(B^{2} b^{5} d^{5} n x^{5} + B^{2} a^{3} b^{2} c^{2} d^{3} n + {\left(2 \, B^{2} b^{5} c d^{4} + 3 \, B^{2} a b^{4} d^{5}\right)} n x^{4} + {\left(B^{2} b^{5} c^{2} d^{3} + 6 \, B^{2} a b^{4} c d^{4} + 3 \, B^{2} a^{2} b^{3} d^{5}\right)} n x^{3} + {\left(3 \, B^{2} a b^{4} c^{2} d^{3} + 6 \, B^{2} a^{2} b^{3} c d^{4} + B^{2} a^{3} b^{2} d^{5}\right)} n x^{2} + {\left(3 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 2 \, B^{2} a^{3} b^{2} c d^{4}\right)} n x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(4 \, B^{2} b^{5} c^{5} - 45 \, B^{2} a b^{4} c^{4} d + 360 \, B^{2} a^{2} b^{3} c^{3} d^{2} - 490 \, B^{2} a^{3} b^{2} c^{2} d^{3} + 180 \, B^{2} a^{4} b c d^{4} - 9 \, B^{2} a^{5} d^{5}\right)} n - 5 \, {\left(6 \, A B b^{5} c^{4} d - 72 \, A B a b^{4} c^{3} d^{2} - 144 \, A B a^{2} b^{3} c^{2} d^{3} + 192 \, A B a^{3} b^{2} c d^{4} + 18 \, A B a^{4} b d^{5} + {\left(5 \, B^{2} b^{5} c^{4} d - 108 \, B^{2} a b^{4} c^{3} d^{2} + 78 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 52 \, B^{2} a^{3} b^{2} c d^{4} - 27 \, B^{2} a^{4} b d^{5}\right)} n\right)} x + 6 \, {\left(60 \, A B a^{3} b^{2} c^{2} d^{3} + 20 \, {\left(B^{2} b^{5} d^{5} n + 3 \, A B b^{5} d^{5}\right)} x^{5} + 20 \, {\left(5 \, B^{2} b^{5} c d^{4} n + 6 \, A B b^{5} c d^{4} + 9 \, A B a b^{4} d^{5}\right)} x^{4} + 10 \, {\left(6 \, A B b^{5} c^{2} d^{3} + 36 \, A B a b^{4} c d^{4} + 18 \, A B a^{2} b^{3} d^{5} + {\left(11 \, B^{2} b^{5} c^{2} d^{3} + 18 \, B^{2} a b^{4} c d^{4} - 9 \, B^{2} a^{2} b^{3} d^{5}\right)} n\right)} x^{3} + 10 \, {\left(18 \, A B a b^{4} c^{2} d^{3} + 36 \, A B a^{2} b^{3} c d^{4} + 6 \, A B a^{3} b^{2} d^{5} + {\left(2 \, B^{2} b^{5} c^{3} d^{2} + 27 \, B^{2} a b^{4} c^{2} d^{3} - 9 \, B^{2} a^{3} b^{2} d^{5}\right)} n\right)} x^{2} + {\left(2 \, B^{2} b^{5} c^{5} - 15 \, B^{2} a b^{4} c^{4} d + 60 \, B^{2} a^{2} b^{3} c^{3} d^{2} - 30 \, B^{2} a^{4} b c d^{4} + 3 \, B^{2} a^{5} d^{5}\right)} n + 5 \, {\left(36 \, A B a^{2} b^{3} c^{2} d^{3} + 24 \, A B a^{3} b^{2} c d^{4} - {\left(B^{2} b^{5} c^{4} d - 12 \, B^{2} a b^{4} c^{3} d^{2} - 36 \, B^{2} a^{2} b^{3} c^{2} d^{3} + 24 \, B^{2} a^{3} b^{2} c d^{4} + 3 \, B^{2} a^{4} b d^{5}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 6 \, {\left(180 \, A^{2} a^{3} b^{2} c^{2} d^{3} + 10 \, {\left(49 \, B^{2} b^{5} d^{5} n^{2} + 12 \, A B b^{5} d^{5} n + 18 \, A^{2} b^{5} d^{5}\right)} x^{5} + 10 \, {\left(60 \, A B b^{5} c d^{4} n + 36 \, A^{2} b^{5} c d^{4} + 54 \, A^{2} a b^{4} d^{5} + 5 \, {\left(22 \, B^{2} b^{5} c d^{4} + 27 \, B^{2} a b^{4} d^{5}\right)} n^{2}\right)} x^{4} + 10 \, {\left(18 \, A^{2} b^{5} c^{2} d^{3} + 108 \, A^{2} a b^{4} c d^{4} + 54 \, A^{2} a^{2} b^{3} d^{5} + 5 \, {\left(17 \, B^{2} b^{5} c^{2} d^{3} + 54 \, B^{2} a b^{4} c d^{4} + 27 \, B^{2} a^{2} b^{3} d^{5}\right)} n^{2} + 6 \, {\left(11 \, A B b^{5} c^{2} d^{3} + 18 \, A B a b^{4} c d^{4} - 9 \, A B a^{2} b^{3} d^{5}\right)} n\right)} x^{3} + {\left(4 \, B^{2} b^{5} c^{5} - 45 \, B^{2} a b^{4} c^{4} d + 360 \, B^{2} a^{2} b^{3} c^{3} d^{2} + 180 \, B^{2} a^{4} b c d^{4} - 9 \, B^{2} a^{5} d^{5}\right)} n^{2} + 10 \, {\left(54 \, A^{2} a b^{4} c^{2} d^{3} + 108 \, A^{2} a^{2} b^{3} c d^{4} + 18 \, A^{2} a^{3} b^{2} d^{5} + {\left(22 \, B^{2} b^{5} c^{3} d^{2} + 189 \, B^{2} a b^{4} c^{2} d^{3} + 216 \, B^{2} a^{2} b^{3} c d^{4} + 63 \, B^{2} a^{3} b^{2} d^{5}\right)} n^{2} + 6 \, {\left(2 \, A B b^{5} c^{3} d^{2} + 27 \, A B a b^{4} c^{2} d^{3} - 9 \, A B a^{3} b^{2} d^{5}\right)} n\right)} x^{2} + 6 \, {\left(2 \, A B b^{5} c^{5} - 15 \, A B a b^{4} c^{4} d + 60 \, A B a^{2} b^{3} c^{3} d^{2} - 30 \, A B a^{4} b c d^{4} + 3 \, A B a^{5} d^{5}\right)} n + 5 \, {\left(108 \, A^{2} a^{2} b^{3} c^{2} d^{3} + 72 \, A^{2} a^{3} b^{2} c d^{4} - {\left(5 \, B^{2} b^{5} c^{4} d - 108 \, B^{2} a b^{4} c^{3} d^{2} - 216 \, B^{2} a^{2} b^{3} c^{2} d^{3} - 144 \, B^{2} a^{3} b^{2} c d^{4} - 27 \, B^{2} a^{4} b d^{5}\right)} n^{2} - 6 \, {\left(A B b^{5} c^{4} d - 12 \, A B a b^{4} c^{3} d^{2} - 36 \, A B a^{2} b^{3} c^{2} d^{3} + 24 \, A B a^{3} b^{2} c d^{4} + 3 \, A B a^{4} b d^{5}\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)}{108 \, {\left({\left(b^{9} c^{6} d^{2} - 6 \, a b^{8} c^{5} d^{3} + 15 \, a^{2} b^{7} c^{4} d^{4} - 20 \, a^{3} b^{6} c^{3} d^{5} + 15 \, a^{4} b^{5} c^{2} d^{6} - 6 \, a^{5} b^{4} c d^{7} + a^{6} b^{3} d^{8}\right)} g^{4} i^{3} x^{5} + {\left(2 \, b^{9} c^{7} d - 9 \, a b^{8} c^{6} d^{2} + 12 \, a^{2} b^{7} c^{5} d^{3} + 5 \, a^{3} b^{6} c^{4} d^{4} - 30 \, a^{4} b^{5} c^{3} d^{5} + 33 \, a^{5} b^{4} c^{2} d^{6} - 16 \, a^{6} b^{3} c d^{7} + 3 \, a^{7} b^{2} d^{8}\right)} g^{4} i^{3} x^{4} + {\left(b^{9} c^{8} - 18 \, a^{2} b^{7} c^{6} d^{2} + 52 \, a^{3} b^{6} c^{5} d^{3} - 60 \, a^{4} b^{5} c^{4} d^{4} + 24 \, a^{5} b^{4} c^{3} d^{5} + 10 \, a^{6} b^{3} c^{2} d^{6} - 12 \, a^{7} b^{2} c d^{7} + 3 \, a^{8} b d^{8}\right)} g^{4} i^{3} x^{3} + {\left(3 \, a b^{8} c^{8} - 12 \, a^{2} b^{7} c^{7} d + 10 \, a^{3} b^{6} c^{6} d^{2} + 24 \, a^{4} b^{5} c^{5} d^{3} - 60 \, a^{5} b^{4} c^{4} d^{4} + 52 \, a^{6} b^{3} c^{3} d^{5} - 18 \, a^{7} b^{2} c^{2} d^{6} + a^{9} d^{8}\right)} g^{4} i^{3} x^{2} + {\left(3 \, a^{2} b^{7} c^{8} - 16 \, a^{3} b^{6} c^{7} d + 33 \, a^{4} b^{5} c^{6} d^{2} - 30 \, a^{5} b^{4} c^{5} d^{3} + 5 \, a^{6} b^{3} c^{4} d^{4} + 12 \, a^{7} b^{2} c^{3} d^{5} - 9 \, a^{8} b c^{2} d^{6} + 2 \, a^{9} c d^{7}\right)} g^{4} i^{3} x + {\left(a^{3} b^{6} c^{8} - 6 \, a^{4} b^{5} c^{7} d + 15 \, a^{5} b^{4} c^{6} d^{2} - 20 \, a^{6} b^{3} c^{5} d^{3} + 15 \, a^{7} b^{2} c^{4} d^{4} - 6 \, a^{8} b c^{3} d^{5} + a^{9} c^{2} d^{6}\right)} g^{4} i^{3}\right)}}"," ",0,"-1/108*(36*A^2*b^5*c^5 - 270*A^2*a*b^4*c^4*d + 1080*A^2*a^2*b^3*c^3*d^2 - 360*A^2*a^3*b^2*c^2*d^3 - 540*A^2*a^4*b*c*d^4 + 54*A^2*a^5*d^5 + 60*(18*A^2*b^5*c*d^4 - 18*A^2*a*b^4*d^5 + 49*(B^2*b^5*c*d^4 - B^2*a*b^4*d^5)*n^2 + 12*(A*B*b^5*c*d^4 - A*B*a*b^4*d^5)*n)*x^4 + 30*(54*A^2*b^5*c^2*d^3 + 36*A^2*a*b^4*c*d^4 - 90*A^2*a^2*b^3*d^5 + (159*B^2*b^5*c^2*d^3 + 74*B^2*a*b^4*c*d^4 - 233*B^2*a^2*b^3*d^5)*n^2 + 24*(3*A*B*b^5*c^2*d^3 - 2*A*B*a*b^4*c*d^4 - A*B*a^2*b^3*d^5)*n)*x^3 + 360*(B^2*b^5*d^5*n^2*x^5 + B^2*a^3*b^2*c^2*d^3*n^2 + (2*B^2*b^5*c*d^4 + 3*B^2*a*b^4*d^5)*n^2*x^4 + (B^2*b^5*c^2*d^3 + 6*B^2*a*b^4*c*d^4 + 3*B^2*a^2*b^3*d^5)*n^2*x^3 + (3*B^2*a*b^4*c^2*d^3 + 6*B^2*a^2*b^3*c*d^4 + B^2*a^3*b^2*d^5)*n^2*x^2 + (3*B^2*a^2*b^3*c^2*d^3 + 2*B^2*a^3*b^2*c*d^4)*n^2*x)*log((b*x + a)/(d*x + c))^3 + (8*B^2*b^5*c^5 - 135*B^2*a*b^4*c^4*d + 2160*B^2*a^2*b^3*c^3*d^2 - 980*B^2*a^3*b^2*c^2*d^3 - 1080*B^2*a^4*b*c*d^4 + 27*B^2*a^5*d^5)*n^2 + 10*(36*A^2*b^5*c^3*d^2 + 378*A^2*a*b^4*c^2*d^3 - 216*A^2*a^2*b^3*c*d^4 - 198*A^2*a^3*b^2*d^5 + (170*B^2*b^5*c^3*d^2 + 921*B^2*a*b^4*c^2*d^3 - 588*B^2*a^2*b^3*c*d^4 - 503*B^2*a^3*b^2*d^5)*n^2 + 12*(11*A*B*b^5*c^3*d^2 + 21*A*B*a*b^4*c^2*d^3 - 39*A*B*a^2*b^3*c*d^4 + 7*A*B*a^3*b^2*d^5)*n)*x^2 + 18*(2*B^2*b^5*c^5 - 15*B^2*a*b^4*c^4*d + 60*B^2*a^2*b^3*c^3*d^2 - 20*B^2*a^3*b^2*c^2*d^3 - 30*B^2*a^4*b*c*d^4 + 3*B^2*a^5*d^5 + 60*(B^2*b^5*c*d^4 - B^2*a*b^4*d^5)*x^4 + 30*(3*B^2*b^5*c^2*d^3 + 2*B^2*a*b^4*c*d^4 - 5*B^2*a^2*b^3*d^5)*x^3 + 10*(2*B^2*b^5*c^3*d^2 + 21*B^2*a*b^4*c^2*d^3 - 12*B^2*a^2*b^3*c*d^4 - 11*B^2*a^3*b^2*d^5)*x^2 - 5*(B^2*b^5*c^4*d - 12*B^2*a*b^4*c^3*d^2 - 24*B^2*a^2*b^3*c^2*d^3 + 32*B^2*a^3*b^2*c*d^4 + 3*B^2*a^4*b*d^5)*x + 60*(B^2*b^5*d^5*x^5 + B^2*a^3*b^2*c^2*d^3 + (2*B^2*b^5*c*d^4 + 3*B^2*a*b^4*d^5)*x^4 + (B^2*b^5*c^2*d^3 + 6*B^2*a*b^4*c*d^4 + 3*B^2*a^2*b^3*d^5)*x^3 + (3*B^2*a*b^4*c^2*d^3 + 6*B^2*a^2*b^3*c*d^4 + B^2*a^3*b^2*d^5)*x^2 + (3*B^2*a^2*b^3*c^2*d^3 + 2*B^2*a^3*b^2*c*d^4)*x)*log((b*x + a)/(d*x + c)))*log(e)^2 + 18*(60*A*B*a^3*b^2*c^2*d^3*n + 20*(B^2*b^5*d^5*n^2 + 3*A*B*b^5*d^5*n)*x^5 + 20*(5*B^2*b^5*c*d^4*n^2 + 3*(2*A*B*b^5*c*d^4 + 3*A*B*a*b^4*d^5)*n)*x^4 + 10*((11*B^2*b^5*c^2*d^3 + 18*B^2*a*b^4*c*d^4 - 9*B^2*a^2*b^3*d^5)*n^2 + 6*(A*B*b^5*c^2*d^3 + 6*A*B*a*b^4*c*d^4 + 3*A*B*a^2*b^3*d^5)*n)*x^3 + (2*B^2*b^5*c^5 - 15*B^2*a*b^4*c^4*d + 60*B^2*a^2*b^3*c^3*d^2 - 30*B^2*a^4*b*c*d^4 + 3*B^2*a^5*d^5)*n^2 + 10*((2*B^2*b^5*c^3*d^2 + 27*B^2*a*b^4*c^2*d^3 - 9*B^2*a^3*b^2*d^5)*n^2 + 6*(3*A*B*a*b^4*c^2*d^3 + 6*A*B*a^2*b^3*c*d^4 + A*B*a^3*b^2*d^5)*n)*x^2 - 5*((B^2*b^5*c^4*d - 12*B^2*a*b^4*c^3*d^2 - 36*B^2*a^2*b^3*c^2*d^3 + 24*B^2*a^3*b^2*c*d^4 + 3*B^2*a^4*b*d^5)*n^2 - 12*(3*A*B*a^2*b^3*c^2*d^3 + 2*A*B*a^3*b^2*c*d^4)*n)*x)*log((b*x + a)/(d*x + c))^2 + 6*(4*A*B*b^5*c^5 - 45*A*B*a*b^4*c^4*d + 360*A*B*a^2*b^3*c^3*d^2 - 490*A*B*a^3*b^2*c^2*d^3 + 180*A*B*a^4*b*c*d^4 - 9*A*B*a^5*d^5)*n - 5*(18*A^2*b^5*c^4*d - 216*A^2*a*b^4*c^3*d^2 - 432*A^2*a^2*b^3*c^2*d^3 + 576*A^2*a^3*b^2*c*d^4 + 54*A^2*a^4*b*d^5 + (19*B^2*b^5*c^4*d - 756*B^2*a*b^4*c^3*d^2 - 708*B^2*a^2*b^3*c^2*d^3 + 1256*B^2*a^3*b^2*c*d^4 + 189*B^2*a^4*b*d^5)*n^2 + 6*(5*A*B*b^5*c^4*d - 108*A*B*a*b^4*c^3*d^2 + 78*A*B*a^2*b^3*c^2*d^3 + 52*A*B*a^3*b^2*c*d^4 - 27*A*B*a^4*b*d^5)*n)*x + 6*(12*A*B*b^5*c^5 - 90*A*B*a*b^4*c^4*d + 360*A*B*a^2*b^3*c^3*d^2 - 120*A*B*a^3*b^2*c^2*d^3 - 180*A*B*a^4*b*c*d^4 + 18*A*B*a^5*d^5 + 120*(3*A*B*b^5*c*d^4 - 3*A*B*a*b^4*d^5 + (B^2*b^5*c*d^4 - B^2*a*b^4*d^5)*n)*x^4 + 60*(9*A*B*b^5*c^2*d^3 + 6*A*B*a*b^4*c*d^4 - 15*A*B*a^2*b^3*d^5 + 2*(3*B^2*b^5*c^2*d^3 - 2*B^2*a*b^4*c*d^4 - B^2*a^2*b^3*d^5)*n)*x^3 + 20*(6*A*B*b^5*c^3*d^2 + 63*A*B*a*b^4*c^2*d^3 - 36*A*B*a^2*b^3*c*d^4 - 33*A*B*a^3*b^2*d^5 + (11*B^2*b^5*c^3*d^2 + 21*B^2*a*b^4*c^2*d^3 - 39*B^2*a^2*b^3*c*d^4 + 7*B^2*a^3*b^2*d^5)*n)*x^2 + 180*(B^2*b^5*d^5*n*x^5 + B^2*a^3*b^2*c^2*d^3*n + (2*B^2*b^5*c*d^4 + 3*B^2*a*b^4*d^5)*n*x^4 + (B^2*b^5*c^2*d^3 + 6*B^2*a*b^4*c*d^4 + 3*B^2*a^2*b^3*d^5)*n*x^3 + (3*B^2*a*b^4*c^2*d^3 + 6*B^2*a^2*b^3*c*d^4 + B^2*a^3*b^2*d^5)*n*x^2 + (3*B^2*a^2*b^3*c^2*d^3 + 2*B^2*a^3*b^2*c*d^4)*n*x)*log((b*x + a)/(d*x + c))^2 + (4*B^2*b^5*c^5 - 45*B^2*a*b^4*c^4*d + 360*B^2*a^2*b^3*c^3*d^2 - 490*B^2*a^3*b^2*c^2*d^3 + 180*B^2*a^4*b*c*d^4 - 9*B^2*a^5*d^5)*n - 5*(6*A*B*b^5*c^4*d - 72*A*B*a*b^4*c^3*d^2 - 144*A*B*a^2*b^3*c^2*d^3 + 192*A*B*a^3*b^2*c*d^4 + 18*A*B*a^4*b*d^5 + (5*B^2*b^5*c^4*d - 108*B^2*a*b^4*c^3*d^2 + 78*B^2*a^2*b^3*c^2*d^3 + 52*B^2*a^3*b^2*c*d^4 - 27*B^2*a^4*b*d^5)*n)*x + 6*(60*A*B*a^3*b^2*c^2*d^3 + 20*(B^2*b^5*d^5*n + 3*A*B*b^5*d^5)*x^5 + 20*(5*B^2*b^5*c*d^4*n + 6*A*B*b^5*c*d^4 + 9*A*B*a*b^4*d^5)*x^4 + 10*(6*A*B*b^5*c^2*d^3 + 36*A*B*a*b^4*c*d^4 + 18*A*B*a^2*b^3*d^5 + (11*B^2*b^5*c^2*d^3 + 18*B^2*a*b^4*c*d^4 - 9*B^2*a^2*b^3*d^5)*n)*x^3 + 10*(18*A*B*a*b^4*c^2*d^3 + 36*A*B*a^2*b^3*c*d^4 + 6*A*B*a^3*b^2*d^5 + (2*B^2*b^5*c^3*d^2 + 27*B^2*a*b^4*c^2*d^3 - 9*B^2*a^3*b^2*d^5)*n)*x^2 + (2*B^2*b^5*c^5 - 15*B^2*a*b^4*c^4*d + 60*B^2*a^2*b^3*c^3*d^2 - 30*B^2*a^4*b*c*d^4 + 3*B^2*a^5*d^5)*n + 5*(36*A*B*a^2*b^3*c^2*d^3 + 24*A*B*a^3*b^2*c*d^4 - (B^2*b^5*c^4*d - 12*B^2*a*b^4*c^3*d^2 - 36*B^2*a^2*b^3*c^2*d^3 + 24*B^2*a^3*b^2*c*d^4 + 3*B^2*a^4*b*d^5)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) + 6*(180*A^2*a^3*b^2*c^2*d^3 + 10*(49*B^2*b^5*d^5*n^2 + 12*A*B*b^5*d^5*n + 18*A^2*b^5*d^5)*x^5 + 10*(60*A*B*b^5*c*d^4*n + 36*A^2*b^5*c*d^4 + 54*A^2*a*b^4*d^5 + 5*(22*B^2*b^5*c*d^4 + 27*B^2*a*b^4*d^5)*n^2)*x^4 + 10*(18*A^2*b^5*c^2*d^3 + 108*A^2*a*b^4*c*d^4 + 54*A^2*a^2*b^3*d^5 + 5*(17*B^2*b^5*c^2*d^3 + 54*B^2*a*b^4*c*d^4 + 27*B^2*a^2*b^3*d^5)*n^2 + 6*(11*A*B*b^5*c^2*d^3 + 18*A*B*a*b^4*c*d^4 - 9*A*B*a^2*b^3*d^5)*n)*x^3 + (4*B^2*b^5*c^5 - 45*B^2*a*b^4*c^4*d + 360*B^2*a^2*b^3*c^3*d^2 + 180*B^2*a^4*b*c*d^4 - 9*B^2*a^5*d^5)*n^2 + 10*(54*A^2*a*b^4*c^2*d^3 + 108*A^2*a^2*b^3*c*d^4 + 18*A^2*a^3*b^2*d^5 + (22*B^2*b^5*c^3*d^2 + 189*B^2*a*b^4*c^2*d^3 + 216*B^2*a^2*b^3*c*d^4 + 63*B^2*a^3*b^2*d^5)*n^2 + 6*(2*A*B*b^5*c^3*d^2 + 27*A*B*a*b^4*c^2*d^3 - 9*A*B*a^3*b^2*d^5)*n)*x^2 + 6*(2*A*B*b^5*c^5 - 15*A*B*a*b^4*c^4*d + 60*A*B*a^2*b^3*c^3*d^2 - 30*A*B*a^4*b*c*d^4 + 3*A*B*a^5*d^5)*n + 5*(108*A^2*a^2*b^3*c^2*d^3 + 72*A^2*a^3*b^2*c*d^4 - (5*B^2*b^5*c^4*d - 108*B^2*a*b^4*c^3*d^2 - 216*B^2*a^2*b^3*c^2*d^3 - 144*B^2*a^3*b^2*c*d^4 - 27*B^2*a^4*b*d^5)*n^2 - 6*(A*B*b^5*c^4*d - 12*A*B*a*b^4*c^3*d^2 - 36*A*B*a^2*b^3*c^2*d^3 + 24*A*B*a^3*b^2*c*d^4 + 3*A*B*a^4*b*d^5)*n)*x)*log((b*x + a)/(d*x + c)))/((b^9*c^6*d^2 - 6*a*b^8*c^5*d^3 + 15*a^2*b^7*c^4*d^4 - 20*a^3*b^6*c^3*d^5 + 15*a^4*b^5*c^2*d^6 - 6*a^5*b^4*c*d^7 + a^6*b^3*d^8)*g^4*i^3*x^5 + (2*b^9*c^7*d - 9*a*b^8*c^6*d^2 + 12*a^2*b^7*c^5*d^3 + 5*a^3*b^6*c^4*d^4 - 30*a^4*b^5*c^3*d^5 + 33*a^5*b^4*c^2*d^6 - 16*a^6*b^3*c*d^7 + 3*a^7*b^2*d^8)*g^4*i^3*x^4 + (b^9*c^8 - 18*a^2*b^7*c^6*d^2 + 52*a^3*b^6*c^5*d^3 - 60*a^4*b^5*c^4*d^4 + 24*a^5*b^4*c^3*d^5 + 10*a^6*b^3*c^2*d^6 - 12*a^7*b^2*c*d^7 + 3*a^8*b*d^8)*g^4*i^3*x^3 + (3*a*b^8*c^8 - 12*a^2*b^7*c^7*d + 10*a^3*b^6*c^6*d^2 + 24*a^4*b^5*c^5*d^3 - 60*a^5*b^4*c^4*d^4 + 52*a^6*b^3*c^3*d^5 - 18*a^7*b^2*c^2*d^6 + a^9*d^8)*g^4*i^3*x^2 + (3*a^2*b^7*c^8 - 16*a^3*b^6*c^7*d + 33*a^4*b^5*c^6*d^2 - 30*a^5*b^4*c^5*d^3 + 5*a^6*b^3*c^4*d^4 + 12*a^7*b^2*c^3*d^5 - 9*a^8*b*c^2*d^6 + 2*a^9*c*d^7)*g^4*i^3*x + (a^3*b^6*c^8 - 6*a^4*b^5*c^7*d + 15*a^5*b^4*c^6*d^2 - 20*a^6*b^3*c^5*d^3 + 15*a^7*b^2*c^4*d^4 - 6*a^8*b*c^3*d^5 + a^9*c^2*d^6)*g^4*i^3)","B",0
210,0,0,0,0.477530," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b g x + a g\right)}^{m} {\left(d i x + c i\right)}^{-m - 2} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}^{p}, x\right)"," ",0,"integral((b*g*x + a*g)^m*(d*i*x + c*i)^(-m - 2)*(B*log(e*((b*x + a)/(d*x + c))^n) + A)^p, x)","F",0
211,0,0,0,0.450073," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*((b*x+a)/(d*x+c))^n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b g x + a g\right)}^{-m - 2} {\left(d i x + c i\right)}^{m} {\left(B \log\left(e \left(\frac{b x + a}{d x + c}\right)^{n}\right) + A\right)}^{p}, x\right)"," ",0,"integral((b*g*x + a*g)^(-m - 2)*(d*i*x + c*i)^m*(B*log(e*((b*x + a)/(d*x + c))^n) + A)^p, x)","F",0
212,1,2680,0,0.556372," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^3,x, algorithm=""fricas"")","\frac{{\left(A^{3} a c m^{3} - 6 \, B^{3} a c n^{3} + 3 \, A^{3} a c m^{2} + 3 \, A^{3} a c m + A^{3} a c + {\left(B^{3} a c m^{3} + 3 \, B^{3} a c m^{2} + 3 \, B^{3} a c m + B^{3} a c + {\left(B^{3} b d m^{3} + 3 \, B^{3} b d m^{2} + 3 \, B^{3} b d m + B^{3} b d\right)} x^{2} + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{3} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} x\right)} \log\left(e\right)^{3} + {\left({\left(B^{3} b d m^{3} + 3 \, B^{3} b d m^{2} + 3 \, B^{3} b d m + B^{3} b d\right)} n^{3} x^{2} + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{3} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{3} x + {\left(B^{3} a c m^{3} + 3 \, B^{3} a c m^{2} + 3 \, B^{3} a c m + B^{3} a c\right)} n^{3}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + 6 \, {\left(A B^{2} a c m + A B^{2} a c\right)} n^{2} + {\left(A^{3} b d m^{3} - 6 \, B^{3} b d n^{3} + 3 \, A^{3} b d m^{2} + 3 \, A^{3} b d m + A^{3} b d + 6 \, {\left(A B^{2} b d m + A B^{2} b d\right)} n^{2} - 3 \, {\left(A^{2} B b d m^{2} + 2 \, A^{2} B b d m + A^{2} B b d\right)} n\right)} x^{2} + 3 \, {\left(A B^{2} a c m^{3} + 3 \, A B^{2} a c m^{2} + 3 \, A B^{2} a c m + A B^{2} a c + {\left(A B^{2} b d m^{3} + 3 \, A B^{2} b d m^{2} + 3 \, A B^{2} b d m + A B^{2} b d - {\left(B^{3} b d m^{2} + 2 \, B^{3} b d m + B^{3} b d\right)} n\right)} x^{2} - {\left(B^{3} a c m^{2} + 2 \, B^{3} a c m + B^{3} a c\right)} n + {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{3} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m - {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 2 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n\right)} x + {\left({\left(B^{3} b d m^{3} + 3 \, B^{3} b d m^{2} + 3 \, B^{3} b d m + B^{3} b d\right)} n x^{2} + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{3} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n x + {\left(B^{3} a c m^{3} + 3 \, B^{3} a c m^{2} + 3 \, B^{3} a c m + B^{3} a c\right)} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} - 3 \, {\left({\left(B^{3} a c m^{2} + 2 \, B^{3} a c m + B^{3} a c\right)} n^{3} - {\left(A B^{2} a c m^{3} + 3 \, A B^{2} a c m^{2} + 3 \, A B^{2} a c m + A B^{2} a c\right)} n^{2} + {\left({\left(B^{3} b d m^{2} + 2 \, B^{3} b d m + B^{3} b d\right)} n^{3} - {\left(A B^{2} b d m^{3} + 3 \, A B^{2} b d m^{2} + 3 \, A B^{2} b d m + A B^{2} b d\right)} n^{2}\right)} x^{2} + {\left({\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 2 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{3} - {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{3} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 3 \, {\left(A^{2} B a c m^{2} + 2 \, A^{2} B a c m + A^{2} B a c\right)} n + {\left(A^{3} b c + A^{3} a d + {\left(A^{3} b c + A^{3} a d\right)} m^{3} - 6 \, {\left(B^{3} b c + B^{3} a d\right)} n^{3} + 3 \, {\left(A^{3} b c + A^{3} a d\right)} m^{2} + 6 \, {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n^{2} + 3 \, {\left(A^{3} b c + A^{3} a d\right)} m - 3 \, {\left(A^{2} B b c + A^{2} B a d + {\left(A^{2} B b c + A^{2} B a d\right)} m^{2} + 2 \, {\left(A^{2} B b c + A^{2} B a d\right)} m\right)} n\right)} x + 3 \, {\left(A^{2} B a c m^{3} + 3 \, A^{2} B a c m^{2} + 3 \, A^{2} B a c m + A^{2} B a c + 2 \, {\left(B^{3} a c m + B^{3} a c\right)} n^{2} + {\left(A^{2} B b d m^{3} + 3 \, A^{2} B b d m^{2} + 3 \, A^{2} B b d m + A^{2} B b d + 2 \, {\left(B^{3} b d m + B^{3} b d\right)} n^{2} - 2 \, {\left(A B^{2} b d m^{2} + 2 \, A B^{2} b d m + A B^{2} b d\right)} n\right)} x^{2} + {\left({\left(B^{3} b d m^{3} + 3 \, B^{3} b d m^{2} + 3 \, B^{3} b d m + B^{3} b d\right)} n^{2} x^{2} + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{3} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{2} x + {\left(B^{3} a c m^{3} + 3 \, B^{3} a c m^{2} + 3 \, B^{3} a c m + B^{3} a c\right)} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 2 \, {\left(A B^{2} a c m^{2} + 2 \, A B^{2} a c m + A B^{2} a c\right)} n + {\left(A^{2} B b c + A^{2} B a d + {\left(A^{2} B b c + A^{2} B a d\right)} m^{3} + 3 \, {\left(A^{2} B b c + A^{2} B a d\right)} m^{2} + 2 \, {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{2} + 3 \, {\left(A^{2} B b c + A^{2} B a d\right)} m - 2 \, {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 2 \, {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n\right)} x - 2 \, {\left({\left(B^{3} a c m^{2} + 2 \, B^{3} a c m + B^{3} a c\right)} n^{2} + {\left({\left(B^{3} b d m^{2} + 2 \, B^{3} b d m + B^{3} b d\right)} n^{2} - {\left(A B^{2} b d m^{3} + 3 \, A B^{2} b d m^{2} + 3 \, A B^{2} b d m + A B^{2} b d\right)} n\right)} x^{2} - {\left(A B^{2} a c m^{3} + 3 \, A B^{2} a c m^{2} + 3 \, A B^{2} a c m + A B^{2} a c\right)} n + {\left({\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 2 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{2} - {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{3} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 3 \, {\left(2 \, {\left(B^{3} a c m + B^{3} a c\right)} n^{3} - 2 \, {\left(A B^{2} a c m^{2} + 2 \, A B^{2} a c m + A B^{2} a c\right)} n^{2} + {\left(2 \, {\left(B^{3} b d m + B^{3} b d\right)} n^{3} - 2 \, {\left(A B^{2} b d m^{2} + 2 \, A B^{2} b d m + A B^{2} b d\right)} n^{2} + {\left(A^{2} B b d m^{3} + 3 \, A^{2} B b d m^{2} + 3 \, A^{2} B b d m + A^{2} B b d\right)} n\right)} x^{2} + {\left(A^{2} B a c m^{3} + 3 \, A^{2} B a c m^{2} + 3 \, A^{2} B a c m + A^{2} B a c\right)} n + {\left(2 \, {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{3} - 2 \, {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 2 \, {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n^{2} + {\left(A^{2} B b c + A^{2} B a d + {\left(A^{2} B b c + A^{2} B a d\right)} m^{3} + 3 \, {\left(A^{2} B b c + A^{2} B a d\right)} m^{2} + 3 \, {\left(A^{2} B b c + A^{2} B a d\right)} m\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} {\left(b g x + a g\right)}^{m} e^{\left(-{\left(m + 2\right)} \log\left(b g x + a g\right) + {\left(m + 2\right)} \log\left(\frac{b x + a}{d x + c}\right) - {\left(m + 2\right)} \log\left(\frac{i}{g}\right)\right)}}{{\left(b c - a d\right)} m^{4} + 4 \, {\left(b c - a d\right)} m^{3} + 6 \, {\left(b c - a d\right)} m^{2} + b c - a d + 4 \, {\left(b c - a d\right)} m}"," ",0,"(A^3*a*c*m^3 - 6*B^3*a*c*n^3 + 3*A^3*a*c*m^2 + 3*A^3*a*c*m + A^3*a*c + (B^3*a*c*m^3 + 3*B^3*a*c*m^2 + 3*B^3*a*c*m + B^3*a*c + (B^3*b*d*m^3 + 3*B^3*b*d*m^2 + 3*B^3*b*d*m + B^3*b*d)*x^2 + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^3 + 3*(B^3*b*c + B^3*a*d)*m^2 + 3*(B^3*b*c + B^3*a*d)*m)*x)*log(e)^3 + ((B^3*b*d*m^3 + 3*B^3*b*d*m^2 + 3*B^3*b*d*m + B^3*b*d)*n^3*x^2 + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^3 + 3*(B^3*b*c + B^3*a*d)*m^2 + 3*(B^3*b*c + B^3*a*d)*m)*n^3*x + (B^3*a*c*m^3 + 3*B^3*a*c*m^2 + 3*B^3*a*c*m + B^3*a*c)*n^3)*log((b*x + a)/(d*x + c))^3 + 6*(A*B^2*a*c*m + A*B^2*a*c)*n^2 + (A^3*b*d*m^3 - 6*B^3*b*d*n^3 + 3*A^3*b*d*m^2 + 3*A^3*b*d*m + A^3*b*d + 6*(A*B^2*b*d*m + A*B^2*b*d)*n^2 - 3*(A^2*B*b*d*m^2 + 2*A^2*B*b*d*m + A^2*B*b*d)*n)*x^2 + 3*(A*B^2*a*c*m^3 + 3*A*B^2*a*c*m^2 + 3*A*B^2*a*c*m + A*B^2*a*c + (A*B^2*b*d*m^3 + 3*A*B^2*b*d*m^2 + 3*A*B^2*b*d*m + A*B^2*b*d - (B^3*b*d*m^2 + 2*B^3*b*d*m + B^3*b*d)*n)*x^2 - (B^3*a*c*m^2 + 2*B^3*a*c*m + B^3*a*c)*n + (A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^3 + 3*(A*B^2*b*c + A*B^2*a*d)*m^2 + 3*(A*B^2*b*c + A*B^2*a*d)*m - (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^2 + 2*(B^3*b*c + B^3*a*d)*m)*n)*x + ((B^3*b*d*m^3 + 3*B^3*b*d*m^2 + 3*B^3*b*d*m + B^3*b*d)*n*x^2 + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^3 + 3*(B^3*b*c + B^3*a*d)*m^2 + 3*(B^3*b*c + B^3*a*d)*m)*n*x + (B^3*a*c*m^3 + 3*B^3*a*c*m^2 + 3*B^3*a*c*m + B^3*a*c)*n)*log((b*x + a)/(d*x + c)))*log(e)^2 - 3*((B^3*a*c*m^2 + 2*B^3*a*c*m + B^3*a*c)*n^3 - (A*B^2*a*c*m^3 + 3*A*B^2*a*c*m^2 + 3*A*B^2*a*c*m + A*B^2*a*c)*n^2 + ((B^3*b*d*m^2 + 2*B^3*b*d*m + B^3*b*d)*n^3 - (A*B^2*b*d*m^3 + 3*A*B^2*b*d*m^2 + 3*A*B^2*b*d*m + A*B^2*b*d)*n^2)*x^2 + ((B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^2 + 2*(B^3*b*c + B^3*a*d)*m)*n^3 - (A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^3 + 3*(A*B^2*b*c + A*B^2*a*d)*m^2 + 3*(A*B^2*b*c + A*B^2*a*d)*m)*n^2)*x)*log((b*x + a)/(d*x + c))^2 - 3*(A^2*B*a*c*m^2 + 2*A^2*B*a*c*m + A^2*B*a*c)*n + (A^3*b*c + A^3*a*d + (A^3*b*c + A^3*a*d)*m^3 - 6*(B^3*b*c + B^3*a*d)*n^3 + 3*(A^3*b*c + A^3*a*d)*m^2 + 6*(A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m)*n^2 + 3*(A^3*b*c + A^3*a*d)*m - 3*(A^2*B*b*c + A^2*B*a*d + (A^2*B*b*c + A^2*B*a*d)*m^2 + 2*(A^2*B*b*c + A^2*B*a*d)*m)*n)*x + 3*(A^2*B*a*c*m^3 + 3*A^2*B*a*c*m^2 + 3*A^2*B*a*c*m + A^2*B*a*c + 2*(B^3*a*c*m + B^3*a*c)*n^2 + (A^2*B*b*d*m^3 + 3*A^2*B*b*d*m^2 + 3*A^2*B*b*d*m + A^2*B*b*d + 2*(B^3*b*d*m + B^3*b*d)*n^2 - 2*(A*B^2*b*d*m^2 + 2*A*B^2*b*d*m + A*B^2*b*d)*n)*x^2 + ((B^3*b*d*m^3 + 3*B^3*b*d*m^2 + 3*B^3*b*d*m + B^3*b*d)*n^2*x^2 + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^3 + 3*(B^3*b*c + B^3*a*d)*m^2 + 3*(B^3*b*c + B^3*a*d)*m)*n^2*x + (B^3*a*c*m^3 + 3*B^3*a*c*m^2 + 3*B^3*a*c*m + B^3*a*c)*n^2)*log((b*x + a)/(d*x + c))^2 - 2*(A*B^2*a*c*m^2 + 2*A*B^2*a*c*m + A*B^2*a*c)*n + (A^2*B*b*c + A^2*B*a*d + (A^2*B*b*c + A^2*B*a*d)*m^3 + 3*(A^2*B*b*c + A^2*B*a*d)*m^2 + 2*(B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m)*n^2 + 3*(A^2*B*b*c + A^2*B*a*d)*m - 2*(A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^2 + 2*(A*B^2*b*c + A*B^2*a*d)*m)*n)*x - 2*((B^3*a*c*m^2 + 2*B^3*a*c*m + B^3*a*c)*n^2 + ((B^3*b*d*m^2 + 2*B^3*b*d*m + B^3*b*d)*n^2 - (A*B^2*b*d*m^3 + 3*A*B^2*b*d*m^2 + 3*A*B^2*b*d*m + A*B^2*b*d)*n)*x^2 - (A*B^2*a*c*m^3 + 3*A*B^2*a*c*m^2 + 3*A*B^2*a*c*m + A*B^2*a*c)*n + ((B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^2 + 2*(B^3*b*c + B^3*a*d)*m)*n^2 - (A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^3 + 3*(A*B^2*b*c + A*B^2*a*d)*m^2 + 3*(A*B^2*b*c + A*B^2*a*d)*m)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) + 3*(2*(B^3*a*c*m + B^3*a*c)*n^3 - 2*(A*B^2*a*c*m^2 + 2*A*B^2*a*c*m + A*B^2*a*c)*n^2 + (2*(B^3*b*d*m + B^3*b*d)*n^3 - 2*(A*B^2*b*d*m^2 + 2*A*B^2*b*d*m + A*B^2*b*d)*n^2 + (A^2*B*b*d*m^3 + 3*A^2*B*b*d*m^2 + 3*A^2*B*b*d*m + A^2*B*b*d)*n)*x^2 + (A^2*B*a*c*m^3 + 3*A^2*B*a*c*m^2 + 3*A^2*B*a*c*m + A^2*B*a*c)*n + (2*(B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m)*n^3 - 2*(A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^2 + 2*(A*B^2*b*c + A*B^2*a*d)*m)*n^2 + (A^2*B*b*c + A^2*B*a*d + (A^2*B*b*c + A^2*B*a*d)*m^3 + 3*(A^2*B*b*c + A^2*B*a*d)*m^2 + 3*(A^2*B*b*c + A^2*B*a*d)*m)*n)*x)*log((b*x + a)/(d*x + c)))*(b*g*x + a*g)^m*e^(-(m + 2)*log(b*g*x + a*g) + (m + 2)*log((b*x + a)/(d*x + c)) - (m + 2)*log(i/g))/((b*c - a*d)*m^4 + 4*(b*c - a*d)*m^3 + 6*(b*c - a*d)*m^2 + b*c - a*d + 4*(b*c - a*d)*m)","B",0
213,1,991,0,0.494769," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","\frac{{\left(A^{2} a c m^{2} + 2 \, B^{2} a c n^{2} + 2 \, A^{2} a c m + A^{2} a c + {\left(A^{2} b d m^{2} + 2 \, B^{2} b d n^{2} + 2 \, A^{2} b d m + A^{2} b d - 2 \, {\left(A B b d m + A B b d\right)} n\right)} x^{2} + {\left(B^{2} a c m^{2} + 2 \, B^{2} a c m + B^{2} a c + {\left(B^{2} b d m^{2} + 2 \, B^{2} b d m + B^{2} b d\right)} x^{2} + {\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m^{2} + 2 \, {\left(B^{2} b c + B^{2} a d\right)} m\right)} x\right)} \log\left(e\right)^{2} + {\left({\left(B^{2} b d m^{2} + 2 \, B^{2} b d m + B^{2} b d\right)} n^{2} x^{2} + {\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m^{2} + 2 \, {\left(B^{2} b c + B^{2} a d\right)} m\right)} n^{2} x + {\left(B^{2} a c m^{2} + 2 \, B^{2} a c m + B^{2} a c\right)} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} - 2 \, {\left(A B a c m + A B a c\right)} n + {\left(A^{2} b c + A^{2} a d + {\left(A^{2} b c + A^{2} a d\right)} m^{2} + 2 \, {\left(B^{2} b c + B^{2} a d\right)} n^{2} + 2 \, {\left(A^{2} b c + A^{2} a d\right)} m - 2 \, {\left(A B b c + A B a d + {\left(A B b c + A B a d\right)} m\right)} n\right)} x + 2 \, {\left(A B a c m^{2} + 2 \, A B a c m + A B a c + {\left(A B b d m^{2} + 2 \, A B b d m + A B b d - {\left(B^{2} b d m + B^{2} b d\right)} n\right)} x^{2} - {\left(B^{2} a c m + B^{2} a c\right)} n + {\left(A B b c + A B a d + {\left(A B b c + A B a d\right)} m^{2} + 2 \, {\left(A B b c + A B a d\right)} m - {\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m\right)} n\right)} x + {\left({\left(B^{2} b d m^{2} + 2 \, B^{2} b d m + B^{2} b d\right)} n x^{2} + {\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m^{2} + 2 \, {\left(B^{2} b c + B^{2} a d\right)} m\right)} n x + {\left(B^{2} a c m^{2} + 2 \, B^{2} a c m + B^{2} a c\right)} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) - 2 \, {\left({\left(B^{2} a c m + B^{2} a c\right)} n^{2} + {\left({\left(B^{2} b d m + B^{2} b d\right)} n^{2} - {\left(A B b d m^{2} + 2 \, A B b d m + A B b d\right)} n\right)} x^{2} - {\left(A B a c m^{2} + 2 \, A B a c m + A B a c\right)} n + {\left({\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m\right)} n^{2} - {\left(A B b c + A B a d + {\left(A B b c + A B a d\right)} m^{2} + 2 \, {\left(A B b c + A B a d\right)} m\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} {\left(b g x + a g\right)}^{m} e^{\left(-{\left(m + 2\right)} \log\left(b g x + a g\right) + {\left(m + 2\right)} \log\left(\frac{b x + a}{d x + c}\right) - {\left(m + 2\right)} \log\left(\frac{i}{g}\right)\right)}}{{\left(b c - a d\right)} m^{3} + 3 \, {\left(b c - a d\right)} m^{2} + b c - a d + 3 \, {\left(b c - a d\right)} m}"," ",0,"(A^2*a*c*m^2 + 2*B^2*a*c*n^2 + 2*A^2*a*c*m + A^2*a*c + (A^2*b*d*m^2 + 2*B^2*b*d*n^2 + 2*A^2*b*d*m + A^2*b*d - 2*(A*B*b*d*m + A*B*b*d)*n)*x^2 + (B^2*a*c*m^2 + 2*B^2*a*c*m + B^2*a*c + (B^2*b*d*m^2 + 2*B^2*b*d*m + B^2*b*d)*x^2 + (B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m^2 + 2*(B^2*b*c + B^2*a*d)*m)*x)*log(e)^2 + ((B^2*b*d*m^2 + 2*B^2*b*d*m + B^2*b*d)*n^2*x^2 + (B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m^2 + 2*(B^2*b*c + B^2*a*d)*m)*n^2*x + (B^2*a*c*m^2 + 2*B^2*a*c*m + B^2*a*c)*n^2)*log((b*x + a)/(d*x + c))^2 - 2*(A*B*a*c*m + A*B*a*c)*n + (A^2*b*c + A^2*a*d + (A^2*b*c + A^2*a*d)*m^2 + 2*(B^2*b*c + B^2*a*d)*n^2 + 2*(A^2*b*c + A^2*a*d)*m - 2*(A*B*b*c + A*B*a*d + (A*B*b*c + A*B*a*d)*m)*n)*x + 2*(A*B*a*c*m^2 + 2*A*B*a*c*m + A*B*a*c + (A*B*b*d*m^2 + 2*A*B*b*d*m + A*B*b*d - (B^2*b*d*m + B^2*b*d)*n)*x^2 - (B^2*a*c*m + B^2*a*c)*n + (A*B*b*c + A*B*a*d + (A*B*b*c + A*B*a*d)*m^2 + 2*(A*B*b*c + A*B*a*d)*m - (B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m)*n)*x + ((B^2*b*d*m^2 + 2*B^2*b*d*m + B^2*b*d)*n*x^2 + (B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m^2 + 2*(B^2*b*c + B^2*a*d)*m)*n*x + (B^2*a*c*m^2 + 2*B^2*a*c*m + B^2*a*c)*n)*log((b*x + a)/(d*x + c)))*log(e) - 2*((B^2*a*c*m + B^2*a*c)*n^2 + ((B^2*b*d*m + B^2*b*d)*n^2 - (A*B*b*d*m^2 + 2*A*B*b*d*m + A*B*b*d)*n)*x^2 - (A*B*a*c*m^2 + 2*A*B*a*c*m + A*B*a*c)*n + ((B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m)*n^2 - (A*B*b*c + A*B*a*d + (A*B*b*c + A*B*a*d)*m^2 + 2*(A*B*b*c + A*B*a*d)*m)*n)*x)*log((b*x + a)/(d*x + c)))*(b*g*x + a*g)^m*e^(-(m + 2)*log(b*g*x + a*g) + (m + 2)*log((b*x + a)/(d*x + c)) - (m + 2)*log(i/g))/((b*c - a*d)*m^3 + 3*(b*c - a*d)*m^2 + b*c - a*d + 3*(b*c - a*d)*m)","B",0
214,1,274,0,0.457750," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{{\left(A a c m - B a c n + A a c + {\left(A b d m - B b d n + A b d\right)} x^{2} + {\left(A b c + A a d + {\left(A b c + A a d\right)} m - {\left(B b c + B a d\right)} n\right)} x + {\left(B a c m + B a c + {\left(B b d m + B b d\right)} x^{2} + {\left(B b c + B a d + {\left(B b c + B a d\right)} m\right)} x\right)} \log\left(e\right) + {\left({\left(B b d m + B b d\right)} n x^{2} + {\left(B b c + B a d + {\left(B b c + B a d\right)} m\right)} n x + {\left(B a c m + B a c\right)} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} {\left(b g x + a g\right)}^{m} e^{\left(-{\left(m + 2\right)} \log\left(b g x + a g\right) + {\left(m + 2\right)} \log\left(\frac{b x + a}{d x + c}\right) - {\left(m + 2\right)} \log\left(\frac{i}{g}\right)\right)}}{{\left(b c - a d\right)} m^{2} + b c - a d + 2 \, {\left(b c - a d\right)} m}"," ",0,"(A*a*c*m - B*a*c*n + A*a*c + (A*b*d*m - B*b*d*n + A*b*d)*x^2 + (A*b*c + A*a*d + (A*b*c + A*a*d)*m - (B*b*c + B*a*d)*n)*x + (B*a*c*m + B*a*c + (B*b*d*m + B*b*d)*x^2 + (B*b*c + B*a*d + (B*b*c + B*a*d)*m)*x)*log(e) + ((B*b*d*m + B*b*d)*n*x^2 + (B*b*c + B*a*d + (B*b*c + B*a*d)*m)*n*x + (B*a*c*m + B*a*c)*n)*log((b*x + a)/(d*x + c)))*(b*g*x + a*g)^m*e^(-(m + 2)*log(b*g*x + a*g) + (m + 2)*log((b*x + a)/(d*x + c)) - (m + 2)*log(i/g))/((b*c - a*d)*m^2 + b*c - a*d + 2*(b*c - a*d)*m)","B",0
215,1,98,0,0.429064," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{{\rm Ei}\left(\frac{{\left(B m + B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right) e^{\left(-\frac{{\left(B m + 2 \, B\right)} n \log\left(\frac{i}{g}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right)}}{{\left(B b c - B a d\right)} g^{2} n}"," ",0,"Ei(((B*m + B)*n*log((b*x + a)/(d*x + c)) + A*m + (B*m + B)*log(e) + A)/(B*n))*e^(-((B*m + 2*B)*n*log(i/g) + A*m + (B*m + B)*log(e) + A)/(B*n))/((B*b*c - B*a*d)*g^2*n)","A",0
216,1,293,0,0.434257," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","-\frac{{\left(B b d g^{2} n x^{2} + B a c g^{2} n + {\left(B b c + B a d\right)} g^{2} n x\right)} {\left(b g x + a g\right)}^{m} e^{\left(-{\left(m + 2\right)} \log\left(b g x + a g\right) + {\left(m + 2\right)} \log\left(\frac{b x + a}{d x + c}\right) - {\left(m + 2\right)} \log\left(\frac{i}{g}\right)\right)} - {\left({\left(B m + B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A\right)} {\rm Ei}\left(\frac{{\left(B m + B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right) e^{\left(-\frac{{\left(B m + 2 \, B\right)} n \log\left(\frac{i}{g}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right)}}{{\left(B^{3} b c - B^{3} a d\right)} g^{2} n^{3} \log\left(\frac{b x + a}{d x + c}\right) + {\left(B^{3} b c - B^{3} a d\right)} g^{2} n^{2} \log\left(e\right) + {\left(A B^{2} b c - A B^{2} a d\right)} g^{2} n^{2}}"," ",0,"-((B*b*d*g^2*n*x^2 + B*a*c*g^2*n + (B*b*c + B*a*d)*g^2*n*x)*(b*g*x + a*g)^m*e^(-(m + 2)*log(b*g*x + a*g) + (m + 2)*log((b*x + a)/(d*x + c)) - (m + 2)*log(i/g)) - ((B*m + B)*n*log((b*x + a)/(d*x + c)) + A*m + (B*m + B)*log(e) + A)*Ei(((B*m + B)*n*log((b*x + a)/(d*x + c)) + A*m + (B*m + B)*log(e) + A)/(B*n))*e^(-((B*m + 2*B)*n*log(i/g) + A*m + (B*m + B)*log(e) + A)/(B*n)))/((B^3*b*c - B^3*a*d)*g^2*n^3*log((b*x + a)/(d*x + c)) + (B^3*b*c - B^3*a*d)*g^2*n^2*log(e) + (A*B^2*b*c - A*B^2*a*d)*g^2*n^2)","A",0
217,1,818,0,0.465924," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)/(A+B*log(e*((b*x+a)/(d*x+c))^n))^3,x, algorithm=""fricas"")","-\frac{{\left(B^{2} a c g^{2} n^{2} + {\left(B^{2} b d g^{2} n^{2} + {\left(A B b d g^{2} m + A B b d g^{2}\right)} n\right)} x^{2} + {\left(A B a c g^{2} m + A B a c g^{2}\right)} n + {\left({\left(B^{2} b c + B^{2} a d\right)} g^{2} n^{2} + {\left({\left(A B b c + A B a d\right)} g^{2} m + {\left(A B b c + A B a d\right)} g^{2}\right)} n\right)} x + {\left({\left(B^{2} b d g^{2} m + B^{2} b d g^{2}\right)} n x^{2} + {\left({\left(B^{2} b c + B^{2} a d\right)} g^{2} m + {\left(B^{2} b c + B^{2} a d\right)} g^{2}\right)} n x + {\left(B^{2} a c g^{2} m + B^{2} a c g^{2}\right)} n\right)} \log\left(e\right) + {\left({\left(B^{2} b d g^{2} m + B^{2} b d g^{2}\right)} n^{2} x^{2} + {\left({\left(B^{2} b c + B^{2} a d\right)} g^{2} m + {\left(B^{2} b c + B^{2} a d\right)} g^{2}\right)} n^{2} x + {\left(B^{2} a c g^{2} m + B^{2} a c g^{2}\right)} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} {\left(b g x + a g\right)}^{m} e^{\left(-{\left(m + 2\right)} \log\left(b g x + a g\right) + {\left(m + 2\right)} \log\left(\frac{b x + a}{d x + c}\right) - {\left(m + 2\right)} \log\left(\frac{i}{g}\right)\right)} - {\left({\left(B^{2} m^{2} + 2 \, B^{2} m + B^{2}\right)} n^{2} \log\left(\frac{b x + a}{d x + c}\right)^{2} + A^{2} m^{2} + 2 \, A^{2} m + {\left(B^{2} m^{2} + 2 \, B^{2} m + B^{2}\right)} \log\left(e\right)^{2} + 2 \, {\left(A B m^{2} + 2 \, A B m + A B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A^{2} + 2 \, {\left(A B m^{2} + 2 \, A B m + {\left(B^{2} m^{2} + 2 \, B^{2} m + B^{2}\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A B\right)} \log\left(e\right)\right)} {\rm Ei}\left(\frac{{\left(B m + B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right) e^{\left(-\frac{{\left(B m + 2 \, B\right)} n \log\left(\frac{i}{g}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right)}}{2 \, {\left({\left(B^{5} b c - B^{5} a d\right)} g^{2} n^{5} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B^{5} b c - B^{5} a d\right)} g^{2} n^{3} \log\left(e\right)^{2} + 2 \, {\left(A B^{4} b c - A B^{4} a d\right)} g^{2} n^{4} \log\left(\frac{b x + a}{d x + c}\right) + {\left(A^{2} B^{3} b c - A^{2} B^{3} a d\right)} g^{2} n^{3} + 2 \, {\left({\left(B^{5} b c - B^{5} a d\right)} g^{2} n^{4} \log\left(\frac{b x + a}{d x + c}\right) + {\left(A B^{4} b c - A B^{4} a d\right)} g^{2} n^{3}\right)} \log\left(e\right)\right)}}"," ",0,"-1/2*((B^2*a*c*g^2*n^2 + (B^2*b*d*g^2*n^2 + (A*B*b*d*g^2*m + A*B*b*d*g^2)*n)*x^2 + (A*B*a*c*g^2*m + A*B*a*c*g^2)*n + ((B^2*b*c + B^2*a*d)*g^2*n^2 + ((A*B*b*c + A*B*a*d)*g^2*m + (A*B*b*c + A*B*a*d)*g^2)*n)*x + ((B^2*b*d*g^2*m + B^2*b*d*g^2)*n*x^2 + ((B^2*b*c + B^2*a*d)*g^2*m + (B^2*b*c + B^2*a*d)*g^2)*n*x + (B^2*a*c*g^2*m + B^2*a*c*g^2)*n)*log(e) + ((B^2*b*d*g^2*m + B^2*b*d*g^2)*n^2*x^2 + ((B^2*b*c + B^2*a*d)*g^2*m + (B^2*b*c + B^2*a*d)*g^2)*n^2*x + (B^2*a*c*g^2*m + B^2*a*c*g^2)*n^2)*log((b*x + a)/(d*x + c)))*(b*g*x + a*g)^m*e^(-(m + 2)*log(b*g*x + a*g) + (m + 2)*log((b*x + a)/(d*x + c)) - (m + 2)*log(i/g)) - ((B^2*m^2 + 2*B^2*m + B^2)*n^2*log((b*x + a)/(d*x + c))^2 + A^2*m^2 + 2*A^2*m + (B^2*m^2 + 2*B^2*m + B^2)*log(e)^2 + 2*(A*B*m^2 + 2*A*B*m + A*B)*n*log((b*x + a)/(d*x + c)) + A^2 + 2*(A*B*m^2 + 2*A*B*m + (B^2*m^2 + 2*B^2*m + B^2)*n*log((b*x + a)/(d*x + c)) + A*B)*log(e))*Ei(((B*m + B)*n*log((b*x + a)/(d*x + c)) + A*m + (B*m + B)*log(e) + A)/(B*n))*e^(-((B*m + 2*B)*n*log(i/g) + A*m + (B*m + B)*log(e) + A)/(B*n)))/((B^5*b*c - B^5*a*d)*g^2*n^5*log((b*x + a)/(d*x + c))^2 + (B^5*b*c - B^5*a*d)*g^2*n^3*log(e)^2 + 2*(A*B^4*b*c - A*B^4*a*d)*g^2*n^4*log((b*x + a)/(d*x + c)) + (A^2*B^3*b*c - A^2*B^3*a*d)*g^2*n^3 + 2*((B^5*b*c - B^5*a*d)*g^2*n^4*log((b*x + a)/(d*x + c)) + (A*B^4*b*c - A*B^4*a*d)*g^2*n^3)*log(e))","B",0
218,1,2669,0,0.552255," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*((b*x+a)/(d*x+c))^n))^3,x, algorithm=""fricas"")","-\frac{{\left(A^{3} a c m^{3} + 6 \, B^{3} a c n^{3} + 3 \, A^{3} a c m^{2} + 3 \, A^{3} a c m + A^{3} a c + {\left(B^{3} a c m^{3} + 3 \, B^{3} a c m^{2} + 3 \, B^{3} a c m + B^{3} a c + {\left(B^{3} b d m^{3} + 3 \, B^{3} b d m^{2} + 3 \, B^{3} b d m + B^{3} b d\right)} x^{2} + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{3} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} x\right)} \log\left(e\right)^{3} + {\left({\left(B^{3} b d m^{3} + 3 \, B^{3} b d m^{2} + 3 \, B^{3} b d m + B^{3} b d\right)} n^{3} x^{2} + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{3} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{3} x + {\left(B^{3} a c m^{3} + 3 \, B^{3} a c m^{2} + 3 \, B^{3} a c m + B^{3} a c\right)} n^{3}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{3} + 6 \, {\left(A B^{2} a c m + A B^{2} a c\right)} n^{2} + {\left(A^{3} b d m^{3} + 6 \, B^{3} b d n^{3} + 3 \, A^{3} b d m^{2} + 3 \, A^{3} b d m + A^{3} b d + 6 \, {\left(A B^{2} b d m + A B^{2} b d\right)} n^{2} + 3 \, {\left(A^{2} B b d m^{2} + 2 \, A^{2} B b d m + A^{2} B b d\right)} n\right)} x^{2} + 3 \, {\left(A B^{2} a c m^{3} + 3 \, A B^{2} a c m^{2} + 3 \, A B^{2} a c m + A B^{2} a c + {\left(A B^{2} b d m^{3} + 3 \, A B^{2} b d m^{2} + 3 \, A B^{2} b d m + A B^{2} b d + {\left(B^{3} b d m^{2} + 2 \, B^{3} b d m + B^{3} b d\right)} n\right)} x^{2} + {\left(B^{3} a c m^{2} + 2 \, B^{3} a c m + B^{3} a c\right)} n + {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{3} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 2 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n\right)} x + {\left({\left(B^{3} b d m^{3} + 3 \, B^{3} b d m^{2} + 3 \, B^{3} b d m + B^{3} b d\right)} n x^{2} + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{3} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n x + {\left(B^{3} a c m^{3} + 3 \, B^{3} a c m^{2} + 3 \, B^{3} a c m + B^{3} a c\right)} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right)^{2} + 3 \, {\left({\left(B^{3} a c m^{2} + 2 \, B^{3} a c m + B^{3} a c\right)} n^{3} + {\left(A B^{2} a c m^{3} + 3 \, A B^{2} a c m^{2} + 3 \, A B^{2} a c m + A B^{2} a c\right)} n^{2} + {\left({\left(B^{3} b d m^{2} + 2 \, B^{3} b d m + B^{3} b d\right)} n^{3} + {\left(A B^{2} b d m^{3} + 3 \, A B^{2} b d m^{2} + 3 \, A B^{2} b d m + A B^{2} b d\right)} n^{2}\right)} x^{2} + {\left({\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 2 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{3} + {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{3} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n^{2}\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 3 \, {\left(A^{2} B a c m^{2} + 2 \, A^{2} B a c m + A^{2} B a c\right)} n + {\left(A^{3} b c + A^{3} a d + {\left(A^{3} b c + A^{3} a d\right)} m^{3} + 6 \, {\left(B^{3} b c + B^{3} a d\right)} n^{3} + 3 \, {\left(A^{3} b c + A^{3} a d\right)} m^{2} + 6 \, {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n^{2} + 3 \, {\left(A^{3} b c + A^{3} a d\right)} m + 3 \, {\left(A^{2} B b c + A^{2} B a d + {\left(A^{2} B b c + A^{2} B a d\right)} m^{2} + 2 \, {\left(A^{2} B b c + A^{2} B a d\right)} m\right)} n\right)} x + 3 \, {\left(A^{2} B a c m^{3} + 3 \, A^{2} B a c m^{2} + 3 \, A^{2} B a c m + A^{2} B a c + 2 \, {\left(B^{3} a c m + B^{3} a c\right)} n^{2} + {\left(A^{2} B b d m^{3} + 3 \, A^{2} B b d m^{2} + 3 \, A^{2} B b d m + A^{2} B b d + 2 \, {\left(B^{3} b d m + B^{3} b d\right)} n^{2} + 2 \, {\left(A B^{2} b d m^{2} + 2 \, A B^{2} b d m + A B^{2} b d\right)} n\right)} x^{2} + {\left({\left(B^{3} b d m^{3} + 3 \, B^{3} b d m^{2} + 3 \, B^{3} b d m + B^{3} b d\right)} n^{2} x^{2} + {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{3} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 3 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{2} x + {\left(B^{3} a c m^{3} + 3 \, B^{3} a c m^{2} + 3 \, B^{3} a c m + B^{3} a c\right)} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(A B^{2} a c m^{2} + 2 \, A B^{2} a c m + A B^{2} a c\right)} n + {\left(A^{2} B b c + A^{2} B a d + {\left(A^{2} B b c + A^{2} B a d\right)} m^{3} + 3 \, {\left(A^{2} B b c + A^{2} B a d\right)} m^{2} + 2 \, {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{2} + 3 \, {\left(A^{2} B b c + A^{2} B a d\right)} m + 2 \, {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 2 \, {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n\right)} x + 2 \, {\left({\left(B^{3} a c m^{2} + 2 \, B^{3} a c m + B^{3} a c\right)} n^{2} + {\left({\left(B^{3} b d m^{2} + 2 \, B^{3} b d m + B^{3} b d\right)} n^{2} + {\left(A B^{2} b d m^{3} + 3 \, A B^{2} b d m^{2} + 3 \, A B^{2} b d m + A B^{2} b d\right)} n\right)} x^{2} + {\left(A B^{2} a c m^{3} + 3 \, A B^{2} a c m^{2} + 3 \, A B^{2} a c m + A B^{2} a c\right)} n + {\left({\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m^{2} + 2 \, {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{2} + {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{3} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 3 \, {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 3 \, {\left(2 \, {\left(B^{3} a c m + B^{3} a c\right)} n^{3} + 2 \, {\left(A B^{2} a c m^{2} + 2 \, A B^{2} a c m + A B^{2} a c\right)} n^{2} + {\left(2 \, {\left(B^{3} b d m + B^{3} b d\right)} n^{3} + 2 \, {\left(A B^{2} b d m^{2} + 2 \, A B^{2} b d m + A B^{2} b d\right)} n^{2} + {\left(A^{2} B b d m^{3} + 3 \, A^{2} B b d m^{2} + 3 \, A^{2} B b d m + A^{2} B b d\right)} n\right)} x^{2} + {\left(A^{2} B a c m^{3} + 3 \, A^{2} B a c m^{2} + 3 \, A^{2} B a c m + A^{2} B a c\right)} n + {\left(2 \, {\left(B^{3} b c + B^{3} a d + {\left(B^{3} b c + B^{3} a d\right)} m\right)} n^{3} + 2 \, {\left(A B^{2} b c + A B^{2} a d + {\left(A B^{2} b c + A B^{2} a d\right)} m^{2} + 2 \, {\left(A B^{2} b c + A B^{2} a d\right)} m\right)} n^{2} + {\left(A^{2} B b c + A^{2} B a d + {\left(A^{2} B b c + A^{2} B a d\right)} m^{3} + 3 \, {\left(A^{2} B b c + A^{2} B a d\right)} m^{2} + 3 \, {\left(A^{2} B b c + A^{2} B a d\right)} m\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} {\left(b g x + a g\right)}^{-m - 2} e^{\left(m \log\left(b g x + a g\right) - m \log\left(\frac{b x + a}{d x + c}\right) + m \log\left(\frac{i}{g}\right)\right)}}{{\left(b c - a d\right)} m^{4} + 4 \, {\left(b c - a d\right)} m^{3} + 6 \, {\left(b c - a d\right)} m^{2} + b c - a d + 4 \, {\left(b c - a d\right)} m}"," ",0,"-(A^3*a*c*m^3 + 6*B^3*a*c*n^3 + 3*A^3*a*c*m^2 + 3*A^3*a*c*m + A^3*a*c + (B^3*a*c*m^3 + 3*B^3*a*c*m^2 + 3*B^3*a*c*m + B^3*a*c + (B^3*b*d*m^3 + 3*B^3*b*d*m^2 + 3*B^3*b*d*m + B^3*b*d)*x^2 + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^3 + 3*(B^3*b*c + B^3*a*d)*m^2 + 3*(B^3*b*c + B^3*a*d)*m)*x)*log(e)^3 + ((B^3*b*d*m^3 + 3*B^3*b*d*m^2 + 3*B^3*b*d*m + B^3*b*d)*n^3*x^2 + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^3 + 3*(B^3*b*c + B^3*a*d)*m^2 + 3*(B^3*b*c + B^3*a*d)*m)*n^3*x + (B^3*a*c*m^3 + 3*B^3*a*c*m^2 + 3*B^3*a*c*m + B^3*a*c)*n^3)*log((b*x + a)/(d*x + c))^3 + 6*(A*B^2*a*c*m + A*B^2*a*c)*n^2 + (A^3*b*d*m^3 + 6*B^3*b*d*n^3 + 3*A^3*b*d*m^2 + 3*A^3*b*d*m + A^3*b*d + 6*(A*B^2*b*d*m + A*B^2*b*d)*n^2 + 3*(A^2*B*b*d*m^2 + 2*A^2*B*b*d*m + A^2*B*b*d)*n)*x^2 + 3*(A*B^2*a*c*m^3 + 3*A*B^2*a*c*m^2 + 3*A*B^2*a*c*m + A*B^2*a*c + (A*B^2*b*d*m^3 + 3*A*B^2*b*d*m^2 + 3*A*B^2*b*d*m + A*B^2*b*d + (B^3*b*d*m^2 + 2*B^3*b*d*m + B^3*b*d)*n)*x^2 + (B^3*a*c*m^2 + 2*B^3*a*c*m + B^3*a*c)*n + (A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^3 + 3*(A*B^2*b*c + A*B^2*a*d)*m^2 + 3*(A*B^2*b*c + A*B^2*a*d)*m + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^2 + 2*(B^3*b*c + B^3*a*d)*m)*n)*x + ((B^3*b*d*m^3 + 3*B^3*b*d*m^2 + 3*B^3*b*d*m + B^3*b*d)*n*x^2 + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^3 + 3*(B^3*b*c + B^3*a*d)*m^2 + 3*(B^3*b*c + B^3*a*d)*m)*n*x + (B^3*a*c*m^3 + 3*B^3*a*c*m^2 + 3*B^3*a*c*m + B^3*a*c)*n)*log((b*x + a)/(d*x + c)))*log(e)^2 + 3*((B^3*a*c*m^2 + 2*B^3*a*c*m + B^3*a*c)*n^3 + (A*B^2*a*c*m^3 + 3*A*B^2*a*c*m^2 + 3*A*B^2*a*c*m + A*B^2*a*c)*n^2 + ((B^3*b*d*m^2 + 2*B^3*b*d*m + B^3*b*d)*n^3 + (A*B^2*b*d*m^3 + 3*A*B^2*b*d*m^2 + 3*A*B^2*b*d*m + A*B^2*b*d)*n^2)*x^2 + ((B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^2 + 2*(B^3*b*c + B^3*a*d)*m)*n^3 + (A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^3 + 3*(A*B^2*b*c + A*B^2*a*d)*m^2 + 3*(A*B^2*b*c + A*B^2*a*d)*m)*n^2)*x)*log((b*x + a)/(d*x + c))^2 + 3*(A^2*B*a*c*m^2 + 2*A^2*B*a*c*m + A^2*B*a*c)*n + (A^3*b*c + A^3*a*d + (A^3*b*c + A^3*a*d)*m^3 + 6*(B^3*b*c + B^3*a*d)*n^3 + 3*(A^3*b*c + A^3*a*d)*m^2 + 6*(A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m)*n^2 + 3*(A^3*b*c + A^3*a*d)*m + 3*(A^2*B*b*c + A^2*B*a*d + (A^2*B*b*c + A^2*B*a*d)*m^2 + 2*(A^2*B*b*c + A^2*B*a*d)*m)*n)*x + 3*(A^2*B*a*c*m^3 + 3*A^2*B*a*c*m^2 + 3*A^2*B*a*c*m + A^2*B*a*c + 2*(B^3*a*c*m + B^3*a*c)*n^2 + (A^2*B*b*d*m^3 + 3*A^2*B*b*d*m^2 + 3*A^2*B*b*d*m + A^2*B*b*d + 2*(B^3*b*d*m + B^3*b*d)*n^2 + 2*(A*B^2*b*d*m^2 + 2*A*B^2*b*d*m + A*B^2*b*d)*n)*x^2 + ((B^3*b*d*m^3 + 3*B^3*b*d*m^2 + 3*B^3*b*d*m + B^3*b*d)*n^2*x^2 + (B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^3 + 3*(B^3*b*c + B^3*a*d)*m^2 + 3*(B^3*b*c + B^3*a*d)*m)*n^2*x + (B^3*a*c*m^3 + 3*B^3*a*c*m^2 + 3*B^3*a*c*m + B^3*a*c)*n^2)*log((b*x + a)/(d*x + c))^2 + 2*(A*B^2*a*c*m^2 + 2*A*B^2*a*c*m + A*B^2*a*c)*n + (A^2*B*b*c + A^2*B*a*d + (A^2*B*b*c + A^2*B*a*d)*m^3 + 3*(A^2*B*b*c + A^2*B*a*d)*m^2 + 2*(B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m)*n^2 + 3*(A^2*B*b*c + A^2*B*a*d)*m + 2*(A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^2 + 2*(A*B^2*b*c + A*B^2*a*d)*m)*n)*x + 2*((B^3*a*c*m^2 + 2*B^3*a*c*m + B^3*a*c)*n^2 + ((B^3*b*d*m^2 + 2*B^3*b*d*m + B^3*b*d)*n^2 + (A*B^2*b*d*m^3 + 3*A*B^2*b*d*m^2 + 3*A*B^2*b*d*m + A*B^2*b*d)*n)*x^2 + (A*B^2*a*c*m^3 + 3*A*B^2*a*c*m^2 + 3*A*B^2*a*c*m + A*B^2*a*c)*n + ((B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m^2 + 2*(B^3*b*c + B^3*a*d)*m)*n^2 + (A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^3 + 3*(A*B^2*b*c + A*B^2*a*d)*m^2 + 3*(A*B^2*b*c + A*B^2*a*d)*m)*n)*x)*log((b*x + a)/(d*x + c)))*log(e) + 3*(2*(B^3*a*c*m + B^3*a*c)*n^3 + 2*(A*B^2*a*c*m^2 + 2*A*B^2*a*c*m + A*B^2*a*c)*n^2 + (2*(B^3*b*d*m + B^3*b*d)*n^3 + 2*(A*B^2*b*d*m^2 + 2*A*B^2*b*d*m + A*B^2*b*d)*n^2 + (A^2*B*b*d*m^3 + 3*A^2*B*b*d*m^2 + 3*A^2*B*b*d*m + A^2*B*b*d)*n)*x^2 + (A^2*B*a*c*m^3 + 3*A^2*B*a*c*m^2 + 3*A^2*B*a*c*m + A^2*B*a*c)*n + (2*(B^3*b*c + B^3*a*d + (B^3*b*c + B^3*a*d)*m)*n^3 + 2*(A*B^2*b*c + A*B^2*a*d + (A*B^2*b*c + A*B^2*a*d)*m^2 + 2*(A*B^2*b*c + A*B^2*a*d)*m)*n^2 + (A^2*B*b*c + A^2*B*a*d + (A^2*B*b*c + A^2*B*a*d)*m^3 + 3*(A^2*B*b*c + A^2*B*a*d)*m^2 + 3*(A^2*B*b*c + A^2*B*a*d)*m)*n)*x)*log((b*x + a)/(d*x + c)))*(b*g*x + a*g)^(-m - 2)*e^(m*log(b*g*x + a*g) - m*log((b*x + a)/(d*x + c)) + m*log(i/g))/((b*c - a*d)*m^4 + 4*(b*c - a*d)*m^3 + 6*(b*c - a*d)*m^2 + b*c - a*d + 4*(b*c - a*d)*m)","B",0
219,1,983,0,0.489643," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","-\frac{{\left(A^{2} a c m^{2} + 2 \, B^{2} a c n^{2} + 2 \, A^{2} a c m + A^{2} a c + {\left(A^{2} b d m^{2} + 2 \, B^{2} b d n^{2} + 2 \, A^{2} b d m + A^{2} b d + 2 \, {\left(A B b d m + A B b d\right)} n\right)} x^{2} + {\left(B^{2} a c m^{2} + 2 \, B^{2} a c m + B^{2} a c + {\left(B^{2} b d m^{2} + 2 \, B^{2} b d m + B^{2} b d\right)} x^{2} + {\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m^{2} + 2 \, {\left(B^{2} b c + B^{2} a d\right)} m\right)} x\right)} \log\left(e\right)^{2} + {\left({\left(B^{2} b d m^{2} + 2 \, B^{2} b d m + B^{2} b d\right)} n^{2} x^{2} + {\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m^{2} + 2 \, {\left(B^{2} b c + B^{2} a d\right)} m\right)} n^{2} x + {\left(B^{2} a c m^{2} + 2 \, B^{2} a c m + B^{2} a c\right)} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)^{2} + 2 \, {\left(A B a c m + A B a c\right)} n + {\left(A^{2} b c + A^{2} a d + {\left(A^{2} b c + A^{2} a d\right)} m^{2} + 2 \, {\left(B^{2} b c + B^{2} a d\right)} n^{2} + 2 \, {\left(A^{2} b c + A^{2} a d\right)} m + 2 \, {\left(A B b c + A B a d + {\left(A B b c + A B a d\right)} m\right)} n\right)} x + 2 \, {\left(A B a c m^{2} + 2 \, A B a c m + A B a c + {\left(A B b d m^{2} + 2 \, A B b d m + A B b d + {\left(B^{2} b d m + B^{2} b d\right)} n\right)} x^{2} + {\left(B^{2} a c m + B^{2} a c\right)} n + {\left(A B b c + A B a d + {\left(A B b c + A B a d\right)} m^{2} + 2 \, {\left(A B b c + A B a d\right)} m + {\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m\right)} n\right)} x + {\left({\left(B^{2} b d m^{2} + 2 \, B^{2} b d m + B^{2} b d\right)} n x^{2} + {\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m^{2} + 2 \, {\left(B^{2} b c + B^{2} a d\right)} m\right)} n x + {\left(B^{2} a c m^{2} + 2 \, B^{2} a c m + B^{2} a c\right)} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} \log\left(e\right) + 2 \, {\left({\left(B^{2} a c m + B^{2} a c\right)} n^{2} + {\left({\left(B^{2} b d m + B^{2} b d\right)} n^{2} + {\left(A B b d m^{2} + 2 \, A B b d m + A B b d\right)} n\right)} x^{2} + {\left(A B a c m^{2} + 2 \, A B a c m + A B a c\right)} n + {\left({\left(B^{2} b c + B^{2} a d + {\left(B^{2} b c + B^{2} a d\right)} m\right)} n^{2} + {\left(A B b c + A B a d + {\left(A B b c + A B a d\right)} m^{2} + 2 \, {\left(A B b c + A B a d\right)} m\right)} n\right)} x\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} {\left(b g x + a g\right)}^{-m - 2} e^{\left(m \log\left(b g x + a g\right) - m \log\left(\frac{b x + a}{d x + c}\right) + m \log\left(\frac{i}{g}\right)\right)}}{{\left(b c - a d\right)} m^{3} + 3 \, {\left(b c - a d\right)} m^{2} + b c - a d + 3 \, {\left(b c - a d\right)} m}"," ",0,"-(A^2*a*c*m^2 + 2*B^2*a*c*n^2 + 2*A^2*a*c*m + A^2*a*c + (A^2*b*d*m^2 + 2*B^2*b*d*n^2 + 2*A^2*b*d*m + A^2*b*d + 2*(A*B*b*d*m + A*B*b*d)*n)*x^2 + (B^2*a*c*m^2 + 2*B^2*a*c*m + B^2*a*c + (B^2*b*d*m^2 + 2*B^2*b*d*m + B^2*b*d)*x^2 + (B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m^2 + 2*(B^2*b*c + B^2*a*d)*m)*x)*log(e)^2 + ((B^2*b*d*m^2 + 2*B^2*b*d*m + B^2*b*d)*n^2*x^2 + (B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m^2 + 2*(B^2*b*c + B^2*a*d)*m)*n^2*x + (B^2*a*c*m^2 + 2*B^2*a*c*m + B^2*a*c)*n^2)*log((b*x + a)/(d*x + c))^2 + 2*(A*B*a*c*m + A*B*a*c)*n + (A^2*b*c + A^2*a*d + (A^2*b*c + A^2*a*d)*m^2 + 2*(B^2*b*c + B^2*a*d)*n^2 + 2*(A^2*b*c + A^2*a*d)*m + 2*(A*B*b*c + A*B*a*d + (A*B*b*c + A*B*a*d)*m)*n)*x + 2*(A*B*a*c*m^2 + 2*A*B*a*c*m + A*B*a*c + (A*B*b*d*m^2 + 2*A*B*b*d*m + A*B*b*d + (B^2*b*d*m + B^2*b*d)*n)*x^2 + (B^2*a*c*m + B^2*a*c)*n + (A*B*b*c + A*B*a*d + (A*B*b*c + A*B*a*d)*m^2 + 2*(A*B*b*c + A*B*a*d)*m + (B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m)*n)*x + ((B^2*b*d*m^2 + 2*B^2*b*d*m + B^2*b*d)*n*x^2 + (B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m^2 + 2*(B^2*b*c + B^2*a*d)*m)*n*x + (B^2*a*c*m^2 + 2*B^2*a*c*m + B^2*a*c)*n)*log((b*x + a)/(d*x + c)))*log(e) + 2*((B^2*a*c*m + B^2*a*c)*n^2 + ((B^2*b*d*m + B^2*b*d)*n^2 + (A*B*b*d*m^2 + 2*A*B*b*d*m + A*B*b*d)*n)*x^2 + (A*B*a*c*m^2 + 2*A*B*a*c*m + A*B*a*c)*n + ((B^2*b*c + B^2*a*d + (B^2*b*c + B^2*a*d)*m)*n^2 + (A*B*b*c + A*B*a*d + (A*B*b*c + A*B*a*d)*m^2 + 2*(A*B*b*c + A*B*a*d)*m)*n)*x)*log((b*x + a)/(d*x + c)))*(b*g*x + a*g)^(-m - 2)*e^(m*log(b*g*x + a*g) - m*log((b*x + a)/(d*x + c)) + m*log(i/g))/((b*c - a*d)*m^3 + 3*(b*c - a*d)*m^2 + b*c - a*d + 3*(b*c - a*d)*m)","B",0
220,1,269,0,0.447620," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","-\frac{{\left(A a c m + B a c n + A a c + {\left(A b d m + B b d n + A b d\right)} x^{2} + {\left(A b c + A a d + {\left(A b c + A a d\right)} m + {\left(B b c + B a d\right)} n\right)} x + {\left(B a c m + B a c + {\left(B b d m + B b d\right)} x^{2} + {\left(B b c + B a d + {\left(B b c + B a d\right)} m\right)} x\right)} \log\left(e\right) + {\left({\left(B b d m + B b d\right)} n x^{2} + {\left(B b c + B a d + {\left(B b c + B a d\right)} m\right)} n x + {\left(B a c m + B a c\right)} n\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} {\left(b g x + a g\right)}^{-m - 2} e^{\left(m \log\left(b g x + a g\right) - m \log\left(\frac{b x + a}{d x + c}\right) + m \log\left(\frac{i}{g}\right)\right)}}{{\left(b c - a d\right)} m^{2} + b c - a d + 2 \, {\left(b c - a d\right)} m}"," ",0,"-(A*a*c*m + B*a*c*n + A*a*c + (A*b*d*m + B*b*d*n + A*b*d)*x^2 + (A*b*c + A*a*d + (A*b*c + A*a*d)*m + (B*b*c + B*a*d)*n)*x + (B*a*c*m + B*a*c + (B*b*d*m + B*b*d)*x^2 + (B*b*c + B*a*d + (B*b*c + B*a*d)*m)*x)*log(e) + ((B*b*d*m + B*b*d)*n*x^2 + (B*b*c + B*a*d + (B*b*c + B*a*d)*m)*n*x + (B*a*c*m + B*a*c)*n)*log((b*x + a)/(d*x + c)))*(b*g*x + a*g)^(-m - 2)*e^(m*log(b*g*x + a*g) - m*log((b*x + a)/(d*x + c)) + m*log(i/g))/((b*c - a*d)*m^2 + b*c - a*d + 2*(b*c - a*d)*m)","A",0
221,1,93,0,0.429353," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m/(A+B*log(e*((b*x+a)/(d*x+c))^n)),x, algorithm=""fricas"")","\frac{{\rm Ei}\left(-\frac{{\left(B m + B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right) e^{\left(\frac{B m n \log\left(\frac{i}{g}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right)}}{{\left(B b c - B a d\right)} g^{2} n}"," ",0,"Ei(-((B*m + B)*n*log((b*x + a)/(d*x + c)) + A*m + (B*m + B)*log(e) + A)/(B*n))*e^((B*m*n*log(i/g) + A*m + (B*m + B)*log(e) + A)/(B*n))/((B*b*c - B*a*d)*g^2*n)","A",0
222,1,284,0,0.442664," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m/(A+B*log(e*((b*x+a)/(d*x+c))^n))^2,x, algorithm=""fricas"")","-\frac{{\left(B b d g^{2} n x^{2} + B a c g^{2} n + {\left(B b c + B a d\right)} g^{2} n x\right)} {\left(b g x + a g\right)}^{-m - 2} e^{\left(m \log\left(b g x + a g\right) - m \log\left(\frac{b x + a}{d x + c}\right) + m \log\left(\frac{i}{g}\right)\right)} + {\left({\left(B m + B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A\right)} {\rm Ei}\left(-\frac{{\left(B m + B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right) e^{\left(\frac{B m n \log\left(\frac{i}{g}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right)}}{{\left(B^{3} b c - B^{3} a d\right)} g^{2} n^{3} \log\left(\frac{b x + a}{d x + c}\right) + {\left(B^{3} b c - B^{3} a d\right)} g^{2} n^{2} \log\left(e\right) + {\left(A B^{2} b c - A B^{2} a d\right)} g^{2} n^{2}}"," ",0,"-((B*b*d*g^2*n*x^2 + B*a*c*g^2*n + (B*b*c + B*a*d)*g^2*n*x)*(b*g*x + a*g)^(-m - 2)*e^(m*log(b*g*x + a*g) - m*log((b*x + a)/(d*x + c)) + m*log(i/g)) + ((B*m + B)*n*log((b*x + a)/(d*x + c)) + A*m + (B*m + B)*log(e) + A)*Ei(-((B*m + B)*n*log((b*x + a)/(d*x + c)) + A*m + (B*m + B)*log(e) + A)/(B*n))*e^((B*m*n*log(i/g) + A*m + (B*m + B)*log(e) + A)/(B*n)))/((B^3*b*c - B^3*a*d)*g^2*n^3*log((b*x + a)/(d*x + c)) + (B^3*b*c - B^3*a*d)*g^2*n^2*log(e) + (A*B^2*b*c - A*B^2*a*d)*g^2*n^2)","A",0
223,1,815,0,0.455631," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m/(A+B*log(e*((b*x+a)/(d*x+c))^n))^3,x, algorithm=""fricas"")","-\frac{{\left(B^{2} a c g^{2} n^{2} + {\left(B^{2} b d g^{2} n^{2} - {\left(A B b d g^{2} m + A B b d g^{2}\right)} n\right)} x^{2} - {\left(A B a c g^{2} m + A B a c g^{2}\right)} n + {\left({\left(B^{2} b c + B^{2} a d\right)} g^{2} n^{2} - {\left({\left(A B b c + A B a d\right)} g^{2} m + {\left(A B b c + A B a d\right)} g^{2}\right)} n\right)} x - {\left({\left(B^{2} b d g^{2} m + B^{2} b d g^{2}\right)} n x^{2} + {\left({\left(B^{2} b c + B^{2} a d\right)} g^{2} m + {\left(B^{2} b c + B^{2} a d\right)} g^{2}\right)} n x + {\left(B^{2} a c g^{2} m + B^{2} a c g^{2}\right)} n\right)} \log\left(e\right) - {\left({\left(B^{2} b d g^{2} m + B^{2} b d g^{2}\right)} n^{2} x^{2} + {\left({\left(B^{2} b c + B^{2} a d\right)} g^{2} m + {\left(B^{2} b c + B^{2} a d\right)} g^{2}\right)} n^{2} x + {\left(B^{2} a c g^{2} m + B^{2} a c g^{2}\right)} n^{2}\right)} \log\left(\frac{b x + a}{d x + c}\right)\right)} {\left(b g x + a g\right)}^{-m - 2} e^{\left(m \log\left(b g x + a g\right) - m \log\left(\frac{b x + a}{d x + c}\right) + m \log\left(\frac{i}{g}\right)\right)} - {\left({\left(B^{2} m^{2} + 2 \, B^{2} m + B^{2}\right)} n^{2} \log\left(\frac{b x + a}{d x + c}\right)^{2} + A^{2} m^{2} + 2 \, A^{2} m + {\left(B^{2} m^{2} + 2 \, B^{2} m + B^{2}\right)} \log\left(e\right)^{2} + 2 \, {\left(A B m^{2} + 2 \, A B m + A B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A^{2} + 2 \, {\left(A B m^{2} + 2 \, A B m + {\left(B^{2} m^{2} + 2 \, B^{2} m + B^{2}\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A B\right)} \log\left(e\right)\right)} {\rm Ei}\left(-\frac{{\left(B m + B\right)} n \log\left(\frac{b x + a}{d x + c}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right) e^{\left(\frac{B m n \log\left(\frac{i}{g}\right) + A m + {\left(B m + B\right)} \log\left(e\right) + A}{B n}\right)}}{2 \, {\left({\left(B^{5} b c - B^{5} a d\right)} g^{2} n^{5} \log\left(\frac{b x + a}{d x + c}\right)^{2} + {\left(B^{5} b c - B^{5} a d\right)} g^{2} n^{3} \log\left(e\right)^{2} + 2 \, {\left(A B^{4} b c - A B^{4} a d\right)} g^{2} n^{4} \log\left(\frac{b x + a}{d x + c}\right) + {\left(A^{2} B^{3} b c - A^{2} B^{3} a d\right)} g^{2} n^{3} + 2 \, {\left({\left(B^{5} b c - B^{5} a d\right)} g^{2} n^{4} \log\left(\frac{b x + a}{d x + c}\right) + {\left(A B^{4} b c - A B^{4} a d\right)} g^{2} n^{3}\right)} \log\left(e\right)\right)}}"," ",0,"-1/2*((B^2*a*c*g^2*n^2 + (B^2*b*d*g^2*n^2 - (A*B*b*d*g^2*m + A*B*b*d*g^2)*n)*x^2 - (A*B*a*c*g^2*m + A*B*a*c*g^2)*n + ((B^2*b*c + B^2*a*d)*g^2*n^2 - ((A*B*b*c + A*B*a*d)*g^2*m + (A*B*b*c + A*B*a*d)*g^2)*n)*x - ((B^2*b*d*g^2*m + B^2*b*d*g^2)*n*x^2 + ((B^2*b*c + B^2*a*d)*g^2*m + (B^2*b*c + B^2*a*d)*g^2)*n*x + (B^2*a*c*g^2*m + B^2*a*c*g^2)*n)*log(e) - ((B^2*b*d*g^2*m + B^2*b*d*g^2)*n^2*x^2 + ((B^2*b*c + B^2*a*d)*g^2*m + (B^2*b*c + B^2*a*d)*g^2)*n^2*x + (B^2*a*c*g^2*m + B^2*a*c*g^2)*n^2)*log((b*x + a)/(d*x + c)))*(b*g*x + a*g)^(-m - 2)*e^(m*log(b*g*x + a*g) - m*log((b*x + a)/(d*x + c)) + m*log(i/g)) - ((B^2*m^2 + 2*B^2*m + B^2)*n^2*log((b*x + a)/(d*x + c))^2 + A^2*m^2 + 2*A^2*m + (B^2*m^2 + 2*B^2*m + B^2)*log(e)^2 + 2*(A*B*m^2 + 2*A*B*m + A*B)*n*log((b*x + a)/(d*x + c)) + A^2 + 2*(A*B*m^2 + 2*A*B*m + (B^2*m^2 + 2*B^2*m + B^2)*n*log((b*x + a)/(d*x + c)) + A*B)*log(e))*Ei(-((B*m + B)*n*log((b*x + a)/(d*x + c)) + A*m + (B*m + B)*log(e) + A)/(B*n))*e^((B*m*n*log(i/g) + A*m + (B*m + B)*log(e) + A)/(B*n)))/((B^5*b*c - B^5*a*d)*g^2*n^5*log((b*x + a)/(d*x + c))^2 + (B^5*b*c - B^5*a*d)*g^2*n^3*log(e)^2 + 2*(A*B^4*b*c - A*B^4*a*d)*g^2*n^4*log((b*x + a)/(d*x + c)) + (A^2*B^3*b*c - A^2*B^3*a*d)*g^2*n^3 + 2*((B^5*b*c - B^5*a*d)*g^2*n^4*log((b*x + a)/(d*x + c)) + (A*B^4*b*c - A*B^4*a*d)*g^2*n^3)*log(e))","B",0
224,1,65,0,0.444585," ","integrate(log(e*((b*x+a)/(d*x+c))^n)^p/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(n \log\left(\frac{b x + a}{d x + c}\right) + \log\left(e\right)\right)} {\left(n \log\left(\frac{b x + a}{d x + c}\right) + \log\left(e\right)\right)}^{p}}{{\left(b c - a d\right)} n p + {\left(b c - a d\right)} n}"," ",0,"(n*log((b*x + a)/(d*x + c)) + log(e))*(n*log((b*x + a)/(d*x + c)) + log(e))^p/((b*c - a*d)*n*p + (b*c - a*d)*n)","A",0
225,1,65,0,0.442743," ","integrate(log(e*((b*x+a)/(d*x+c))^n)^p/(a*c+(a*d+b*c)*x+b*d*x^2),x, algorithm=""fricas"")","\frac{{\left(n \log\left(\frac{b x + a}{d x + c}\right) + \log\left(e\right)\right)} {\left(n \log\left(\frac{b x + a}{d x + c}\right) + \log\left(e\right)\right)}^{p}}{{\left(b c - a d\right)} n p + {\left(b c - a d\right)} n}"," ",0,"(n*log((b*x + a)/(d*x + c)) + log(e))*(n*log((b*x + a)/(d*x + c)) + log(e))^p/((b*c - a*d)*n*p + (b*c - a*d)*n)","A",0
226,0,0,0,0.458681," ","integrate((b*g*x+a*g)^m*(d*i*x+c*i)^(-2-m)*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b g x + a g\right)}^{m} {\left(d i x + c i\right)}^{-m - 2} {\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}^{p}, x\right)"," ",0,"integral((b*g*x + a*g)^m*(d*i*x + c*i)^(-m - 2)*(B*log((b*x + a)^n*e/(d*x + c)^n) + A)^p, x)","F",0
227,0,0,0,0.486925," ","integrate((b*g*x+a*g)^(-2-m)*(d*i*x+c*i)^m*(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b g x + a g\right)}^{-m - 2} {\left(d i x + c i\right)}^{m} {\left(B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A\right)}^{p}, x\right)"," ",0,"integral((b*g*x + a*g)^(-m - 2)*(d*i*x + c*i)^m*(B*log((b*x + a)^n*e/(d*x + c)^n) + A)^p, x)","F",0
228,1,375,0,0.446727," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{B^{3} n^{3} \log\left(b x + a\right)^{4} + B^{3} n^{3} \log\left(d x + c\right)^{4} + 4 \, {\left(B^{3} n^{2} \log\left(e\right) + A B^{2} n^{2}\right)} \log\left(b x + a\right)^{3} - 4 \, {\left(B^{3} n^{3} \log\left(b x + a\right) + B^{3} n^{2} \log\left(e\right) + A B^{2} n^{2}\right)} \log\left(d x + c\right)^{3} + 6 \, {\left(B^{3} n \log\left(e\right)^{2} + 2 \, A B^{2} n \log\left(e\right) + A^{2} B n\right)} \log\left(b x + a\right)^{2} + 6 \, {\left(B^{3} n^{3} \log\left(b x + a\right)^{2} + B^{3} n \log\left(e\right)^{2} + 2 \, A B^{2} n \log\left(e\right) + A^{2} B n + 2 \, {\left(B^{3} n^{2} \log\left(e\right) + A B^{2} n^{2}\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)^{2} + 4 \, {\left(B^{3} \log\left(e\right)^{3} + 3 \, A B^{2} \log\left(e\right)^{2} + 3 \, A^{2} B \log\left(e\right) + A^{3}\right)} \log\left(b x + a\right) - 4 \, {\left(B^{3} n^{3} \log\left(b x + a\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) + A^{3} + 3 \, {\left(B^{3} n^{2} \log\left(e\right) + A B^{2} n^{2}\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(B^{3} n \log\left(e\right)^{2} + 2 \, A B^{2} n \log\left(e\right) + A^{2} B n\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{4 \, {\left(b c - a d\right)}}"," ",0,"1/4*(B^3*n^3*log(b*x + a)^4 + B^3*n^3*log(d*x + c)^4 + 4*(B^3*n^2*log(e) + A*B^2*n^2)*log(b*x + a)^3 - 4*(B^3*n^3*log(b*x + a) + B^3*n^2*log(e) + A*B^2*n^2)*log(d*x + c)^3 + 6*(B^3*n*log(e)^2 + 2*A*B^2*n*log(e) + A^2*B*n)*log(b*x + a)^2 + 6*(B^3*n^3*log(b*x + a)^2 + B^3*n*log(e)^2 + 2*A*B^2*n*log(e) + A^2*B*n + 2*(B^3*n^2*log(e) + A*B^2*n^2)*log(b*x + a))*log(d*x + c)^2 + 4*(B^3*log(e)^3 + 3*A*B^2*log(e)^2 + 3*A^2*B*log(e) + A^3)*log(b*x + a) - 4*(B^3*n^3*log(b*x + a)^3 + B^3*log(e)^3 + 3*A*B^2*log(e)^2 + 3*A^2*B*log(e) + A^3 + 3*(B^3*n^2*log(e) + A*B^2*n^2)*log(b*x + a)^2 + 3*(B^3*n*log(e)^2 + 2*A*B^2*n*log(e) + A^2*B*n)*log(b*x + a))*log(d*x + c))/(b*c - a*d)","B",0
229,1,188,0,0.435156," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{B^{2} n^{2} \log\left(b x + a\right)^{3} - B^{2} n^{2} \log\left(d x + c\right)^{3} + 3 \, {\left(B^{2} n \log\left(e\right) + A B n\right)} \log\left(b x + a\right)^{2} + 3 \, {\left(B^{2} n^{2} \log\left(b x + a\right) + B^{2} n \log\left(e\right) + A B n\right)} \log\left(d x + c\right)^{2} + 3 \, {\left(B^{2} \log\left(e\right)^{2} + 2 \, A B \log\left(e\right) + A^{2}\right)} \log\left(b x + a\right) - 3 \, {\left(B^{2} n^{2} \log\left(b x + a\right)^{2} + B^{2} \log\left(e\right)^{2} + 2 \, A B \log\left(e\right) + A^{2} + 2 \, {\left(B^{2} n \log\left(e\right) + A B n\right)} \log\left(b x + a\right)\right)} \log\left(d x + c\right)}{3 \, {\left(b c - a d\right)}}"," ",0,"1/3*(B^2*n^2*log(b*x + a)^3 - B^2*n^2*log(d*x + c)^3 + 3*(B^2*n*log(e) + A*B*n)*log(b*x + a)^2 + 3*(B^2*n^2*log(b*x + a) + B^2*n*log(e) + A*B*n)*log(d*x + c)^2 + 3*(B^2*log(e)^2 + 2*A*B*log(e) + A^2)*log(b*x + a) - 3*(B^2*n^2*log(b*x + a)^2 + B^2*log(e)^2 + 2*A*B*log(e) + A^2 + 2*(B^2*n*log(e) + A*B*n)*log(b*x + a))*log(d*x + c))/(b*c - a*d)","B",0
230,1,72,0,0.430989," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{B n \log\left(b x + a\right)^{2} + B n \log\left(d x + c\right)^{2} + 2 \, {\left(B \log\left(e\right) + A\right)} \log\left(b x + a\right) - 2 \, {\left(B n \log\left(b x + a\right) + B \log\left(e\right) + A\right)} \log\left(d x + c\right)}{2 \, {\left(b c - a d\right)}}"," ",0,"1/2*(B*n*log(b*x + a)^2 + B*n*log(d*x + c)^2 + 2*(B*log(e) + A)*log(b*x + a) - 2*(B*n*log(b*x + a) + B*log(e) + A)*log(d*x + c))/(b*c - a*d)","A",0
231,1,45,0,0.425048," ","integrate(1/(b*x+a)/(d*x+c)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""fricas"")","\frac{\log\left(-B n \log\left(b x + a\right) + B n \log\left(d x + c\right) - B \log\left(e\right) - A\right)}{{\left(B b c - B a d\right)} n}"," ",0,"log(-B*n*log(b*x + a) + B*n*log(d*x + c) - B*log(e) - A)/((B*b*c - B*a*d)*n)","A",0
232,1,86,0,0.427004," ","integrate(1/(b*x+a)/(d*x+c)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""fricas"")","-\frac{1}{{\left(B^{2} b c - B^{2} a d\right)} n^{2} \log\left(b x + a\right) - {\left(B^{2} b c - B^{2} a d\right)} n^{2} \log\left(d x + c\right) + {\left(B^{2} b c - B^{2} a d\right)} n \log\left(e\right) + {\left(A B b c - A B a d\right)} n}"," ",0,"-1/((B^2*b*c - B^2*a*d)*n^2*log(b*x + a) - (B^2*b*c - B^2*a*d)*n^2*log(d*x + c) + (B^2*b*c - B^2*a*d)*n*log(e) + (A*B*b*c - A*B*a*d)*n)","A",0
233,1,238,0,0.457787," ","integrate(1/(b*x+a)/(d*x+c)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left({\left(B^{3} b c - B^{3} a d\right)} n^{3} \log\left(b x + a\right)^{2} + {\left(B^{3} b c - B^{3} a d\right)} n^{3} \log\left(d x + c\right)^{2} + {\left(B^{3} b c - B^{3} a d\right)} n \log\left(e\right)^{2} + 2 \, {\left(A B^{2} b c - A B^{2} a d\right)} n \log\left(e\right) + {\left(A^{2} B b c - A^{2} B a d\right)} n + 2 \, {\left({\left(B^{3} b c - B^{3} a d\right)} n^{2} \log\left(e\right) + {\left(A B^{2} b c - A B^{2} a d\right)} n^{2}\right)} \log\left(b x + a\right) - 2 \, {\left({\left(B^{3} b c - B^{3} a d\right)} n^{3} \log\left(b x + a\right) + {\left(B^{3} b c - B^{3} a d\right)} n^{2} \log\left(e\right) + {\left(A B^{2} b c - A B^{2} a d\right)} n^{2}\right)} \log\left(d x + c\right)\right)}}"," ",0,"-1/2/((B^3*b*c - B^3*a*d)*n^3*log(b*x + a)^2 + (B^3*b*c - B^3*a*d)*n^3*log(d*x + c)^2 + (B^3*b*c - B^3*a*d)*n*log(e)^2 + 2*(A*B^2*b*c - A*B^2*a*d)*n*log(e) + (A^2*B*b*c - A^2*B*a*d)*n + 2*((B^3*b*c - B^3*a*d)*n^2*log(e) + (A*B^2*b*c - A*B^2*a*d)*n^2)*log(b*x + a) - 2*((B^3*b*c - B^3*a*d)*n^3*log(b*x + a) + (B^3*b*c - B^3*a*d)*n^2*log(e) + (A*B^2*b*c - A*B^2*a*d)*n^2)*log(d*x + c))","B",0
234,1,81,0,0.445527," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(B n \log\left(b x + a\right) - B n \log\left(d x + c\right) + B \log\left(e\right) + A\right)} {\left(B n \log\left(b x + a\right) - B n \log\left(d x + c\right) + B \log\left(e\right) + A\right)}^{p}}{{\left(B b c - B a d\right)} n p + {\left(B b c - B a d\right)} n}"," ",0,"(B*n*log(b*x + a) - B*n*log(d*x + c) + B*log(e) + A)*(B*n*log(b*x + a) - B*n*log(d*x + c) + B*log(e) + A)^p/((B*b*c - B*a*d)*n*p + (B*b*c - B*a*d)*n)","A",0
235,1,85,0,0.451097," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p/(b*f*x+a*f)/(d*g*x+c*g),x, algorithm=""fricas"")","\frac{{\left(B n \log\left(b x + a\right) - B n \log\left(d x + c\right) + B \log\left(e\right) + A\right)} {\left(B n \log\left(b x + a\right) - B n \log\left(d x + c\right) + B \log\left(e\right) + A\right)}^{p}}{{\left(B b c - B a d\right)} f g n p + {\left(B b c - B a d\right)} f g n}"," ",0,"(B*n*log(b*x + a) - B*n*log(d*x + c) + B*log(e) + A)*(B*n*log(b*x + a) - B*n*log(d*x + c) + B*log(e) + A)^p/((B*b*c - B*a*d)*f*g*n*p + (B*b*c - B*a*d)*f*g*n)","A",0
236,1,83,0,0.445561," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^p/(a*c*f+(a*d+b*c)*f*x+b*d*f*x^2),x, algorithm=""fricas"")","\frac{{\left(B n \log\left(b x + a\right) - B n \log\left(d x + c\right) + B \log\left(e\right) + A\right)} {\left(B n \log\left(b x + a\right) - B n \log\left(d x + c\right) + B \log\left(e\right) + A\right)}^{p}}{{\left(B b c - B a d\right)} f n p + {\left(B b c - B a d\right)} f n}"," ",0,"(B*n*log(b*x + a) - B*n*log(d*x + c) + B*log(e) + A)*(B*n*log(b*x + a) - B*n*log(d*x + c) + B*log(e) + A)^p/((B*b*c - B*a*d)*f*n*p + (B*b*c - B*a*d)*f*n)","A",0
237,1,45,0,0.422658," ","integrate(1/(b*x+a)/(d*x+c)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""fricas"")","\frac{\log\left(-B n \log\left(b x + a\right) + B n \log\left(d x + c\right) - B \log\left(e\right) - A\right)}{{\left(B b c - B a d\right)} n}"," ",0,"log(-B*n*log(b*x + a) + B*n*log(d*x + c) - B*log(e) - A)/((B*b*c - B*a*d)*n)","A",0
238,1,51,0,0.425307," ","integrate(1/(b*f*x+a*f)/(d*g*x+c*g)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""fricas"")","\frac{\log\left(-B n \log\left(b x + a\right) + B n \log\left(d x + c\right) - B \log\left(e\right) - A\right)}{{\left(B b c - B a d\right)} f g n}"," ",0,"log(-B*n*log(b*x + a) + B*n*log(d*x + c) - B*log(e) - A)/((B*b*c - B*a*d)*f*g*n)","A",0
239,1,48,0,0.438904," ","integrate(1/(a*c*f+(a*d+b*c)*f*x+b*d*f*x^2)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""fricas"")","\frac{\log\left(-B n \log\left(b x + a\right) + B n \log\left(d x + c\right) - B \log\left(e\right) - A\right)}{{\left(B b c - B a d\right)} f n}"," ",0,"log(-B*n*log(b*x + a) + B*n*log(d*x + c) - B*log(e) - A)/((B*b*c - B*a*d)*f*n)","A",0
240,0,0,0,0.430320," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)/log(e*(b*x+a)^n/((d*x+c)^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}}{\log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^(-m - 2)/log((b*x + a)^n*e/(d*x + c)^n), x)","F",0
241,1,110,0,0.431197," ","integrate((b*x+a)^3/(d*x+c)^5/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(\frac{{\left(b^{4} x^{4} + 4 \, a b^{3} x^{3} + 6 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x + a^{4}\right)} e^{\frac{4}{n}}}{d^{4} x^{4} + 4 \, c d^{3} x^{3} + 6 \, c^{2} d^{2} x^{2} + 4 \, c^{3} d x + c^{4}}\right)}{{\left(b c - a d\right)} e^{\frac{4}{n}} n}"," ",0,"log_integral((b^4*x^4 + 4*a*b^3*x^3 + 6*a^2*b^2*x^2 + 4*a^3*b*x + a^4)*e^(4/n)/(d^4*x^4 + 4*c*d^3*x^3 + 6*c^2*d^2*x^2 + 4*c^3*d*x + c^4))/((b*c - a*d)*e^(4/n)*n)","A",0
242,1,88,0,0.424575," ","integrate((b*x+a)^2/(d*x+c)^4/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(\frac{{\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} e^{\frac{3}{n}}}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{{\left(b c - a d\right)} e^{\frac{3}{n}} n}"," ",0,"log_integral((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*e^(3/n)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/((b*c - a*d)*e^(3/n)*n)","A",0
243,1,66,0,0.423976," ","integrate((b*x+a)/(d*x+c)^3/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} e^{\frac{2}{n}}}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{{\left(b c - a d\right)} e^{\frac{2}{n}} n}"," ",0,"log_integral((b^2*x^2 + 2*a*b*x + a^2)*e^(2/n)/(d^2*x^2 + 2*c*d*x + c^2))/((b*c - a*d)*e^(2/n)*n)","A",0
244,1,40,0,0.424742," ","integrate(1/(d*x+c)^2/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(\frac{{\left(b x + a\right)} e^{\left(\frac{1}{n}\right)}}{d x + c}\right)}{{\left(b c - a d\right)} e^{\left(\frac{1}{n}\right)} n}"," ",0,"log_integral((b*x + a)*e^(1/n)/(d*x + c))/((b*c - a*d)*e^(1/n)*n)","A",0
245,1,34,0,0.446431," ","integrate(1/(b*x+a)/(d*x+c)/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""fricas"")","\frac{\log\left(n \log\left(\frac{b x + a}{d x + c}\right) + \log\left(e\right)\right)}{{\left(b c - a d\right)} n}"," ",0,"log(n*log((b*x + a)/(d*x + c)) + log(e))/((b*c - a*d)*n)","A",0
246,1,40,0,0.456161," ","integrate(1/(b*x+a)^2/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""fricas"")","\frac{e^{\left(\frac{1}{n}\right)} \operatorname{log\_integral}\left(\frac{d x + c}{{\left(b x + a\right)} e^{\left(\frac{1}{n}\right)}}\right)}{{\left(b c - a d\right)} n}"," ",0,"e^(1/n)*log_integral((d*x + c)/((b*x + a)*e^(1/n)))/((b*c - a*d)*n)","A",0
247,1,66,0,0.435011," ","integrate((d*x+c)/(b*x+a)^3/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""fricas"")","\frac{e^{\frac{2}{n}} \operatorname{log\_integral}\left(\frac{d^{2} x^{2} + 2 \, c d x + c^{2}}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} e^{\frac{2}{n}}}\right)}{{\left(b c - a d\right)} n}"," ",0,"e^(2/n)*log_integral((d^2*x^2 + 2*c*d*x + c^2)/((b^2*x^2 + 2*a*b*x + a^2)*e^(2/n)))/((b*c - a*d)*n)","A",0
248,1,88,0,0.430146," ","integrate((d*x+c)^2/(b*x+a)^4/log(e*((b*x+a)/(d*x+c))^n),x, algorithm=""fricas"")","\frac{e^{\frac{3}{n}} \operatorname{log\_integral}\left(\frac{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}{{\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x + a^{3}\right)} e^{\frac{3}{n}}}\right)}{{\left(b c - a d\right)} n}"," ",0,"e^(3/n)*log_integral((d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)/((b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x + a^3)*e^(3/n)))/((b*c - a*d)*n)","A",0
249,0,0,0,0.437643," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^4/(g*x+f)/(b*h*x+a*h),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B^{4} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{4} + 4 \, A B^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{3} + 6 \, A^{2} B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 4 \, A^{3} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{4}}{b g h x^{2} + a f h + {\left(b f + a g\right)} h x}, x\right)"," ",0,"integral((B^4*log((b*x + a)^n*e/(d*x + c)^n)^4 + 4*A*B^3*log((b*x + a)^n*e/(d*x + c)^n)^3 + 6*A^2*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2 + 4*A^3*B*log((b*x + a)^n*e/(d*x + c)^n) + A^4)/(b*g*h*x^2 + a*f*h + (b*f + a*g)*h*x), x)","F",0
250,0,0,0,0.449775," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(g*x+f)/(b*h*x+a*h),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{3} + 3 \, A B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 3 \, A^{2} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3}}{b g h x^{2} + a f h + {\left(b f + a g\right)} h x}, x\right)"," ",0,"integral((B^3*log((b*x + a)^n*e/(d*x + c)^n)^3 + 3*A*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2 + 3*A^2*B*log((b*x + a)^n*e/(d*x + c)^n) + A^3)/(b*g*h*x^2 + a*f*h + (b*f + a*g)*h*x), x)","F",0
251,0,0,0,0.424712," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(g*x+f)/(b*h*x+a*h),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 2 \, A B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2}}{b g h x^{2} + a f h + {\left(b f + a g\right)} h x}, x\right)"," ",0,"integral((B^2*log((b*x + a)^n*e/(d*x + c)^n)^2 + 2*A*B*log((b*x + a)^n*e/(d*x + c)^n) + A^2)/(b*g*h*x^2 + a*f*h + (b*f + a*g)*h*x), x)","F",0
252,0,0,0,0.435808," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(g*x+f)/(b*h*x+a*h),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A}{b g h x^{2} + a f h + {\left(b f + a g\right)} h x}, x\right)"," ",0,"integral((B*log((b*x + a)^n*e/(d*x + c)^n) + A)/(b*g*h*x^2 + a*f*h + (b*f + a*g)*h*x), x)","F",0
253,0,0,0,0.439504," ","integrate(1/(g*x+f)/(b*h*x+a*h)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{A b g h x^{2} + A a f h + {\left(A b f + A a g\right)} h x + {\left(B b g h x^{2} + B a f h + {\left(B b f + B a g\right)} h x\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}, x\right)"," ",0,"integral(1/(A*b*g*h*x^2 + A*a*f*h + (A*b*f + A*a*g)*h*x + (B*b*g*h*x^2 + B*a*f*h + (B*b*f + B*a*g)*h*x)*log((b*x + a)^n*e/(d*x + c)^n)), x)","F",0
254,0,0,0,0.426260," ","integrate(1/(g*x+f)/(b*h*x+a*h)/(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{A^{2} b g h x^{2} + A^{2} a f h + {\left(A^{2} b f + A^{2} a g\right)} h x + {\left(B^{2} b g h x^{2} + B^{2} a f h + {\left(B^{2} b f + B^{2} a g\right)} h x\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 2 \, {\left(A B b g h x^{2} + A B a f h + {\left(A B b f + A B a g\right)} h x\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}, x\right)"," ",0,"integral(1/(A^2*b*g*h*x^2 + A^2*a*f*h + (A^2*b*f + A^2*a*g)*h*x + (B^2*b*g*h*x^2 + B^2*a*f*h + (B^2*b*f + B^2*a*g)*h*x)*log((b*x + a)^n*e/(d*x + c)^n)^2 + 2*(A*B*b*g*h*x^2 + A*B*a*f*h + (A*B*b*f + A*B*a*g)*h*x)*log((b*x + a)^n*e/(d*x + c)^n)), x)","F",0
255,1,32,0,0.419061," ","integrate(log((d*x+c)/(b*x+a))/(b*x+a)/((a-c)*h+(b-d)*h*x),x, algorithm=""fricas"")","-\frac{{\rm Li}_2\left(-\frac{d x + c}{b x + a} + 1\right)}{{\left(b c - a d\right)} h}"," ",0,"-dilog(-(d*x + c)/(b*x + a) + 1)/((b*c - a*d)*h)","A",0
256,1,38,0,0.441301," ","integrate(log((a-c*g+(-d*g+b)*x)/(b*x+a))/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\rm Li}_2\left(\frac{c g + {\left(d g - b\right)} x - a}{b x + a} + 1\right)}{b c - a d}"," ",0,"dilog((c*g + (d*g - b)*x - a)/(b*x + a) + 1)/(b*c - a*d)","A",0
257,1,38,0,0.422503," ","integrate(log(1-g*(d*x+c)/(b*x+a))/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\rm Li}_2\left(\frac{c g + {\left(d g - b\right)} x - a}{b x + a} + 1\right)}{b c - a d}"," ",0,"dilog((c*g + (d*g - b)*x - a)/(b*x + a) + 1)/(b*c - a*d)","A",0
258,1,38,0,0.419942," ","integrate(log((-d*g*x+b*x-c*g+a)/(b*x+a))/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\rm Li}_2\left(\frac{c g + {\left(d g - b\right)} x - a}{b x + a} + 1\right)}{b c - a d}"," ",0,"dilog((c*g + (d*g - b)*x - a)/(b*x + a) + 1)/(b*c - a*d)","A",0
259,0,0,0,0.434971," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^3/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B^{3} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{3} + 3 \, A B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 3 \, A^{2} B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{3}}{b g h x^{2} + a f h + {\left(b f + a g\right)} h x}, x\right)"," ",0,"integral((B^3*log((b*x + a)^n*e/(d*x + c)^n)^3 + 3*A*B^2*log((b*x + a)^n*e/(d*x + c)^n)^2 + 3*A^2*B*log((b*x + a)^n*e/(d*x + c)^n) + A^3)/(b*g*h*x^2 + a*f*h + (b*f + a*g)*h*x), x)","F",0
260,0,0,0,0.423147," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B^{2} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 2 \, A B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A^{2}}{b g h x^{2} + a f h + {\left(b f + a g\right)} h x}, x\right)"," ",0,"integral((B^2*log((b*x + a)^n*e/(d*x + c)^n)^2 + 2*A*B*log((b*x + a)^n*e/(d*x + c)^n) + A^2)/(b*g*h*x^2 + a*f*h + (b*f + a*g)*h*x), x)","F",0
261,0,0,0,0.432154," ","integrate((A+B*log(e*(b*x+a)^n/((d*x+c)^n)))/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right) + A}{b g h x^{2} + a f h + {\left(b f + a g\right)} h x}, x\right)"," ",0,"integral((B*log((b*x + a)^n*e/(d*x + c)^n) + A)/(b*g*h*x^2 + a*f*h + (b*f + a*g)*h*x), x)","F",0
262,0,0,0,0.433008," ","integrate(1/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x))/(A+B*log(e*(b*x+a)^n/((d*x+c)^n))),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{A b g h x^{2} + A a f h + {\left(A b f + A a g\right)} h x + {\left(B b g h x^{2} + B a f h + {\left(B b f + B a g\right)} h x\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}, x\right)"," ",0,"integral(1/(A*b*g*h*x^2 + A*a*f*h + (A*b*f + A*a*g)*h*x + (B*b*g*h*x^2 + B*a*f*h + (B*b*f + B*a*g)*h*x)*log((b*x + a)^n*e/(d*x + c)^n)), x)","F",0
263,0,0,0,0.466186," ","integrate(1/(a*f*h+b*g*h*x^2+h*(a*g*x+b*f*x))/(A+B*log(e*(b*x+a)^n/((d*x+c)^n)))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{A^{2} b g h x^{2} + A^{2} a f h + {\left(A^{2} b f + A^{2} a g\right)} h x + {\left(B^{2} b g h x^{2} + B^{2} a f h + {\left(B^{2} b f + B^{2} a g\right)} h x\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)^{2} + 2 \, {\left(A B b g h x^{2} + A B a f h + {\left(A B b f + A B a g\right)} h x\right)} \log\left(\frac{{\left(b x + a\right)}^{n} e}{{\left(d x + c\right)}^{n}}\right)}, x\right)"," ",0,"integral(1/(A^2*b*g*h*x^2 + A^2*a*f*h + (A^2*b*f + A^2*a*g)*h*x + (B^2*b*g*h*x^2 + B^2*a*f*h + (B^2*b*f + B^2*a*g)*h*x)*log((b*x + a)^n*e/(d*x + c)^n)^2 + 2*(A*B*b*g*h*x^2 + A*B*a*f*h + (A*B*b*f + A*B*a*g)*h*x)*log((b*x + a)^n*e/(d*x + c)^n)), x)","F",0
