1,1,142,0,0.997543," ","integrate((b*x+a)*(d*x+c)*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","\frac{1}{5} x^{5} h f d b + \frac{1}{4} x^{4} g f d b + \frac{1}{4} x^{4} h e d b + \frac{1}{4} x^{4} h f c b + \frac{1}{4} x^{4} h f d a + \frac{1}{3} x^{3} g e d b + \frac{1}{3} x^{3} g f c b + \frac{1}{3} x^{3} h e c b + \frac{1}{3} x^{3} g f d a + \frac{1}{3} x^{3} h e d a + \frac{1}{3} x^{3} h f c a + \frac{1}{2} x^{2} g e c b + \frac{1}{2} x^{2} g e d a + \frac{1}{2} x^{2} g f c a + \frac{1}{2} x^{2} h e c a + x g e c a"," ",0,"1/5*x^5*h*f*d*b + 1/4*x^4*g*f*d*b + 1/4*x^4*h*e*d*b + 1/4*x^4*h*f*c*b + 1/4*x^4*h*f*d*a + 1/3*x^3*g*e*d*b + 1/3*x^3*g*f*c*b + 1/3*x^3*h*e*c*b + 1/3*x^3*g*f*d*a + 1/3*x^3*h*e*d*a + 1/3*x^3*h*f*c*a + 1/2*x^2*g*e*c*b + 1/2*x^2*g*e*d*a + 1/2*x^2*g*f*c*a + 1/2*x^2*h*e*c*a + x*g*e*c*a","A",0
2,1,163,0,0.695249," ","integrate((b*x+a)*(d*x+c)*(f*x+e)/(h*x+g),x, algorithm=""fricas"")","\frac{2 \, b d f h^{3} x^{3} - 3 \, {\left(b d f g h^{2} - {\left(b d e + {\left(b c + a d\right)} f\right)} h^{3}\right)} x^{2} + 6 \, {\left(b d f g^{2} h - {\left(b d e + {\left(b c + a d\right)} f\right)} g h^{2} + {\left(a c f + {\left(b c + a d\right)} e\right)} h^{3}\right)} x - 6 \, {\left(b d f g^{3} - a c e h^{3} - {\left(b d e + {\left(b c + a d\right)} f\right)} g^{2} h + {\left(a c f + {\left(b c + a d\right)} e\right)} g h^{2}\right)} \log\left(h x + g\right)}{6 \, h^{4}}"," ",0,"1/6*(2*b*d*f*h^3*x^3 - 3*(b*d*f*g*h^2 - (b*d*e + (b*c + a*d)*f)*h^3)*x^2 + 6*(b*d*f*g^2*h - (b*d*e + (b*c + a*d)*f)*g*h^2 + (a*c*f + (b*c + a*d)*e)*h^3)*x - 6*(b*d*f*g^3 - a*c*e*h^3 - (b*d*e + (b*c + a*d)*f)*g^2*h + (a*c*f + (b*c + a*d)*e)*g*h^2)*log(h*x + g))/h^4","A",0
3,1,117,0,1.316305," ","integrate((b*x+a)*(d*x+c)/(f*x+e)/(h*x+g),x, algorithm=""fricas"")","\frac{{\left(b d e^{2} + a c f^{2} - {\left(b c + a d\right)} e f\right)} h^{2} \log\left(f x + e\right) + {\left(b d f^{2} g h - b d e f h^{2}\right)} x - {\left(b d f^{2} g^{2} + a c f^{2} h^{2} - {\left(b c + a d\right)} f^{2} g h\right)} \log\left(h x + g\right)}{f^{3} g h^{2} - e f^{2} h^{3}}"," ",0,"((b*d*e^2 + a*c*f^2 - (b*c + a*d)*e*f)*h^2*log(f*x + e) + (b*d*f^2*g*h - b*d*e*f*h^2)*x - (b*d*f^2*g^2 + a*c*f^2*h^2 - (b*c + a*d)*f^2*g*h)*log(h*x + g))/(f^3*g*h^2 - e*f^2*h^3)","A",0
4,-1,0,0,0.000000," ","integrate((b*x+a)/(d*x+c)/(f*x+e)/(h*x+g),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
5,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)/(f*x+e)/(h*x+g),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,1,19,0,1.708952," ","integrate(x/(1+x)/(2+x)/(3+x),x, algorithm=""fricas"")","-\frac{3}{2} \, \log\left(x + 3\right) + 2 \, \log\left(x + 2\right) - \frac{1}{2} \, \log\left(x + 1\right)"," ",0,"-3/2*log(x + 3) + 2*log(x + 2) - 1/2*log(x + 1)","A",0
7,1,53,0,1.440434," ","integrate((x^3-x^2)/(-6+x)/(3+5*x)^3,x, algorithm=""fricas"")","\frac{1493 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(5 \, x + 3\right) + 2500 \, {\left(25 \, x^{2} + 30 \, x + 9\right)} \log\left(x - 6\right) + 33165 \, x + 15543}{499125 \, {\left(25 \, x^{2} + 30 \, x + 9\right)}}"," ",0,"1/499125*(1493*(25*x^2 + 30*x + 9)*log(5*x + 3) + 2500*(25*x^2 + 30*x + 9)*log(x - 6) + 33165*x + 15543)/(25*x^2 + 30*x + 9)","A",0
8,1,649,0,1.293814," ","integrate((b*x+a)^3*(f*x+e)*(d*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{315 \, a^{3} \sqrt{c} d^{4} e \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(35 \, b^{3} d^{4} f x^{4} + 5 \, {\left(9 \, b^{3} d^{4} e + {\left(b^{3} c d^{3} + 27 \, a b^{2} d^{4}\right)} f\right)} x^{3} + 3 \, {\left(3 \, {\left(b^{3} c d^{3} + 21 \, a b^{2} d^{4}\right)} e - {\left(2 \, b^{3} c^{2} d^{2} - 9 \, a b^{2} c d^{3} - 63 \, a^{2} b d^{4}\right)} f\right)} x^{2} + 3 \, {\left(8 \, b^{3} c^{3} d - 42 \, a b^{2} c^{2} d^{2} + 105 \, a^{2} b c d^{3} + 105 \, a^{3} d^{4}\right)} e - {\left(16 \, b^{3} c^{4} - 72 \, a b^{2} c^{3} d + 126 \, a^{2} b c^{2} d^{2} - 105 \, a^{3} c d^{3}\right)} f - {\left(3 \, {\left(4 \, b^{3} c^{2} d^{2} - 21 \, a b^{2} c d^{3} - 105 \, a^{2} b d^{4}\right)} e - {\left(8 \, b^{3} c^{3} d - 36 \, a b^{2} c^{2} d^{2} + 63 \, a^{2} b c d^{3} + 105 \, a^{3} d^{4}\right)} f\right)} x\right)} \sqrt{d x + c}}{315 \, d^{4}}, \frac{2 \, {\left(315 \, a^{3} \sqrt{-c} d^{4} e \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(35 \, b^{3} d^{4} f x^{4} + 5 \, {\left(9 \, b^{3} d^{4} e + {\left(b^{3} c d^{3} + 27 \, a b^{2} d^{4}\right)} f\right)} x^{3} + 3 \, {\left(3 \, {\left(b^{3} c d^{3} + 21 \, a b^{2} d^{4}\right)} e - {\left(2 \, b^{3} c^{2} d^{2} - 9 \, a b^{2} c d^{3} - 63 \, a^{2} b d^{4}\right)} f\right)} x^{2} + 3 \, {\left(8 \, b^{3} c^{3} d - 42 \, a b^{2} c^{2} d^{2} + 105 \, a^{2} b c d^{3} + 105 \, a^{3} d^{4}\right)} e - {\left(16 \, b^{3} c^{4} - 72 \, a b^{2} c^{3} d + 126 \, a^{2} b c^{2} d^{2} - 105 \, a^{3} c d^{3}\right)} f - {\left(3 \, {\left(4 \, b^{3} c^{2} d^{2} - 21 \, a b^{2} c d^{3} - 105 \, a^{2} b d^{4}\right)} e - {\left(8 \, b^{3} c^{3} d - 36 \, a b^{2} c^{2} d^{2} + 63 \, a^{2} b c d^{3} + 105 \, a^{3} d^{4}\right)} f\right)} x\right)} \sqrt{d x + c}\right)}}{315 \, d^{4}}\right]"," ",0,"[1/315*(315*a^3*sqrt(c)*d^4*e*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(35*b^3*d^4*f*x^4 + 5*(9*b^3*d^4*e + (b^3*c*d^3 + 27*a*b^2*d^4)*f)*x^3 + 3*(3*(b^3*c*d^3 + 21*a*b^2*d^4)*e - (2*b^3*c^2*d^2 - 9*a*b^2*c*d^3 - 63*a^2*b*d^4)*f)*x^2 + 3*(8*b^3*c^3*d - 42*a*b^2*c^2*d^2 + 105*a^2*b*c*d^3 + 105*a^3*d^4)*e - (16*b^3*c^4 - 72*a*b^2*c^3*d + 126*a^2*b*c^2*d^2 - 105*a^3*c*d^3)*f - (3*(4*b^3*c^2*d^2 - 21*a*b^2*c*d^3 - 105*a^2*b*d^4)*e - (8*b^3*c^3*d - 36*a*b^2*c^2*d^2 + 63*a^2*b*c*d^3 + 105*a^3*d^4)*f)*x)*sqrt(d*x + c))/d^4, 2/315*(315*a^3*sqrt(-c)*d^4*e*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (35*b^3*d^4*f*x^4 + 5*(9*b^3*d^4*e + (b^3*c*d^3 + 27*a*b^2*d^4)*f)*x^3 + 3*(3*(b^3*c*d^3 + 21*a*b^2*d^4)*e - (2*b^3*c^2*d^2 - 9*a*b^2*c*d^3 - 63*a^2*b*d^4)*f)*x^2 + 3*(8*b^3*c^3*d - 42*a*b^2*c^2*d^2 + 105*a^2*b*c*d^3 + 105*a^3*d^4)*e - (16*b^3*c^4 - 72*a*b^2*c^3*d + 126*a^2*b*c^2*d^2 - 105*a^3*c*d^3)*f - (3*(4*b^3*c^2*d^2 - 21*a*b^2*c*d^3 - 105*a^2*b*d^4)*e - (8*b^3*c^3*d - 36*a*b^2*c^2*d^2 + 63*a^2*b*c*d^3 + 105*a^3*d^4)*f)*x)*sqrt(d*x + c))/d^4]","A",0
9,1,405,0,1.591144," ","integrate((b*x+a)^2*(f*x+e)*(d*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{105 \, a^{2} \sqrt{c} d^{3} e \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(15 \, b^{2} d^{3} f x^{3} + 3 \, {\left(7 \, b^{2} d^{3} e + {\left(b^{2} c d^{2} + 14 \, a b d^{3}\right)} f\right)} x^{2} - 7 \, {\left(2 \, b^{2} c^{2} d - 10 \, a b c d^{2} - 15 \, a^{2} d^{3}\right)} e + {\left(8 \, b^{2} c^{3} - 28 \, a b c^{2} d + 35 \, a^{2} c d^{2}\right)} f + {\left(7 \, {\left(b^{2} c d^{2} + 10 \, a b d^{3}\right)} e - {\left(4 \, b^{2} c^{2} d - 14 \, a b c d^{2} - 35 \, a^{2} d^{3}\right)} f\right)} x\right)} \sqrt{d x + c}}{105 \, d^{3}}, \frac{2 \, {\left(105 \, a^{2} \sqrt{-c} d^{3} e \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(15 \, b^{2} d^{3} f x^{3} + 3 \, {\left(7 \, b^{2} d^{3} e + {\left(b^{2} c d^{2} + 14 \, a b d^{3}\right)} f\right)} x^{2} - 7 \, {\left(2 \, b^{2} c^{2} d - 10 \, a b c d^{2} - 15 \, a^{2} d^{3}\right)} e + {\left(8 \, b^{2} c^{3} - 28 \, a b c^{2} d + 35 \, a^{2} c d^{2}\right)} f + {\left(7 \, {\left(b^{2} c d^{2} + 10 \, a b d^{3}\right)} e - {\left(4 \, b^{2} c^{2} d - 14 \, a b c d^{2} - 35 \, a^{2} d^{3}\right)} f\right)} x\right)} \sqrt{d x + c}\right)}}{105 \, d^{3}}\right]"," ",0,"[1/105*(105*a^2*sqrt(c)*d^3*e*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(15*b^2*d^3*f*x^3 + 3*(7*b^2*d^3*e + (b^2*c*d^2 + 14*a*b*d^3)*f)*x^2 - 7*(2*b^2*c^2*d - 10*a*b*c*d^2 - 15*a^2*d^3)*e + (8*b^2*c^3 - 28*a*b*c^2*d + 35*a^2*c*d^2)*f + (7*(b^2*c*d^2 + 10*a*b*d^3)*e - (4*b^2*c^2*d - 14*a*b*c*d^2 - 35*a^2*d^3)*f)*x)*sqrt(d*x + c))/d^3, 2/105*(105*a^2*sqrt(-c)*d^3*e*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (15*b^2*d^3*f*x^3 + 3*(7*b^2*d^3*e + (b^2*c*d^2 + 14*a*b*d^3)*f)*x^2 - 7*(2*b^2*c^2*d - 10*a*b*c*d^2 - 15*a^2*d^3)*e + (8*b^2*c^3 - 28*a*b*c^2*d + 35*a^2*c*d^2)*f + (7*(b^2*c*d^2 + 10*a*b*d^3)*e - (4*b^2*c^2*d - 14*a*b*c*d^2 - 35*a^2*d^3)*f)*x)*sqrt(d*x + c))/d^3]","A",0
10,1,219,0,0.900718," ","integrate((b*x+a)*(f*x+e)*(d*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, a \sqrt{c} d^{2} e \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(3 \, b d^{2} f x^{2} + 5 \, {\left(b c d + 3 \, a d^{2}\right)} e - {\left(2 \, b c^{2} - 5 \, a c d\right)} f + {\left(5 \, b d^{2} e + {\left(b c d + 5 \, a d^{2}\right)} f\right)} x\right)} \sqrt{d x + c}}{15 \, d^{2}}, \frac{2 \, {\left(15 \, a \sqrt{-c} d^{2} e \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(3 \, b d^{2} f x^{2} + 5 \, {\left(b c d + 3 \, a d^{2}\right)} e - {\left(2 \, b c^{2} - 5 \, a c d\right)} f + {\left(5 \, b d^{2} e + {\left(b c d + 5 \, a d^{2}\right)} f\right)} x\right)} \sqrt{d x + c}\right)}}{15 \, d^{2}}\right]"," ",0,"[1/15*(15*a*sqrt(c)*d^2*e*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(3*b*d^2*f*x^2 + 5*(b*c*d + 3*a*d^2)*e - (2*b*c^2 - 5*a*c*d)*f + (5*b*d^2*e + (b*c*d + 5*a*d^2)*f)*x)*sqrt(d*x + c))/d^2, 2/15*(15*a*sqrt(-c)*d^2*e*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (3*b*d^2*f*x^2 + 5*(b*c*d + 3*a*d^2)*e - (2*b*c^2 - 5*a*c*d)*f + (5*b*d^2*e + (b*c*d + 5*a*d^2)*f)*x)*sqrt(d*x + c))/d^2]","A",0
11,1,111,0,0.865638," ","integrate((f*x+e)*(d*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{c} d e \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left(d f x + 3 \, d e + c f\right)} \sqrt{d x + c}}{3 \, d}, \frac{2 \, {\left(3 \, \sqrt{-c} d e \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(d f x + 3 \, d e + c f\right)} \sqrt{d x + c}\right)}}{3 \, d}\right]"," ",0,"[1/3*(3*sqrt(c)*d*e*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*(d*f*x + 3*d*e + c*f)*sqrt(d*x + c))/d, 2/3*(3*sqrt(-c)*d*e*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (d*f*x + 3*d*e + c*f)*sqrt(d*x + c))/d]","A",0
12,1,449,0,1.216850," ","integrate((f*x+e)*(d*x+c)^(1/2)/x/(b*x+a),x, algorithm=""fricas"")","\left[\frac{b \sqrt{c} e \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, \sqrt{d x + c} a f - {\left(b e - a f\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right)}{a b}, \frac{b \sqrt{c} e \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, \sqrt{d x + c} a f + 2 \, {\left(b e - a f\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right)}{a b}, \frac{2 \, b \sqrt{-c} e \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + 2 \, \sqrt{d x + c} a f - {\left(b e - a f\right)} \sqrt{\frac{b c - a d}{b}} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{d x + c} b \sqrt{\frac{b c - a d}{b}}}{b x + a}\right)}{a b}, \frac{2 \, {\left(b \sqrt{-c} e \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + \sqrt{d x + c} a f + {\left(b e - a f\right)} \sqrt{-\frac{b c - a d}{b}} \arctan\left(-\frac{\sqrt{d x + c} b \sqrt{-\frac{b c - a d}{b}}}{b c - a d}\right)\right)}}{a b}\right]"," ",0,"[(b*sqrt(c)*e*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*sqrt(d*x + c)*a*f - (b*e - a*f)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)))/(a*b), (b*sqrt(c)*e*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*sqrt(d*x + c)*a*f + 2*(b*e - a*f)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)))/(a*b), (2*b*sqrt(-c)*e*arctan(sqrt(d*x + c)*sqrt(-c)/c) + 2*sqrt(d*x + c)*a*f - (b*e - a*f)*sqrt((b*c - a*d)/b)*log((b*d*x + 2*b*c - a*d - 2*sqrt(d*x + c)*b*sqrt((b*c - a*d)/b))/(b*x + a)))/(a*b), 2*(b*sqrt(-c)*e*arctan(sqrt(d*x + c)*sqrt(-c)/c) + sqrt(d*x + c)*a*f + (b*e - a*f)*sqrt(-(b*c - a*d)/b)*arctan(-sqrt(d*x + c)*b*sqrt(-(b*c - a*d)/b)/(b*c - a*d)))/(a*b)]","A",0
13,1,1018,0,1.345145," ","integrate((f*x+e)*(d*x+c)^(1/2)/x/(b*x+a)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{3} d f - {\left(2 \, a b^{2} c - a^{2} b d\right)} e + {\left(a^{2} b d f - {\left(2 \, b^{3} c - a b^{2} d\right)} e\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left({\left(b^{4} c - a b^{3} d\right)} e x + {\left(a b^{3} c - a^{2} b^{2} d\right)} e\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + 2 \, {\left({\left(a b^{3} c - a^{2} b^{2} d\right)} e - {\left(a^{2} b^{2} c - a^{3} b d\right)} f\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b^{3} c - a^{4} b^{2} d + {\left(a^{2} b^{4} c - a^{3} b^{3} d\right)} x\right)}}, \frac{{\left(a^{3} d f - {\left(2 \, a b^{2} c - a^{2} b d\right)} e + {\left(a^{2} b d f - {\left(2 \, b^{3} c - a b^{2} d\right)} e\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + {\left({\left(b^{4} c - a b^{3} d\right)} e x + {\left(a b^{3} c - a^{2} b^{2} d\right)} e\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) + {\left({\left(a b^{3} c - a^{2} b^{2} d\right)} e - {\left(a^{2} b^{2} c - a^{3} b d\right)} f\right)} \sqrt{d x + c}}{a^{3} b^{3} c - a^{4} b^{2} d + {\left(a^{2} b^{4} c - a^{3} b^{3} d\right)} x}, \frac{4 \, {\left({\left(b^{4} c - a b^{3} d\right)} e x + {\left(a b^{3} c - a^{2} b^{2} d\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left(a^{3} d f - {\left(2 \, a b^{2} c - a^{2} b d\right)} e + {\left(a^{2} b d f - {\left(2 \, b^{3} c - a b^{2} d\right)} e\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left({\left(a b^{3} c - a^{2} b^{2} d\right)} e - {\left(a^{2} b^{2} c - a^{3} b d\right)} f\right)} \sqrt{d x + c}}{2 \, {\left(a^{3} b^{3} c - a^{4} b^{2} d + {\left(a^{2} b^{4} c - a^{3} b^{3} d\right)} x\right)}}, \frac{{\left(a^{3} d f - {\left(2 \, a b^{2} c - a^{2} b d\right)} e + {\left(a^{2} b d f - {\left(2 \, b^{3} c - a b^{2} d\right)} e\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) + 2 \, {\left({\left(b^{4} c - a b^{3} d\right)} e x + {\left(a b^{3} c - a^{2} b^{2} d\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) + {\left({\left(a b^{3} c - a^{2} b^{2} d\right)} e - {\left(a^{2} b^{2} c - a^{3} b d\right)} f\right)} \sqrt{d x + c}}{a^{3} b^{3} c - a^{4} b^{2} d + {\left(a^{2} b^{4} c - a^{3} b^{3} d\right)} x}\right]"," ",0,"[1/2*((a^3*d*f - (2*a*b^2*c - a^2*b*d)*e + (a^2*b*d*f - (2*b^3*c - a*b^2*d)*e)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*((b^4*c - a*b^3*d)*e*x + (a*b^3*c - a^2*b^2*d)*e)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + 2*((a*b^3*c - a^2*b^2*d)*e - (a^2*b^2*c - a^3*b*d)*f)*sqrt(d*x + c))/(a^3*b^3*c - a^4*b^2*d + (a^2*b^4*c - a^3*b^3*d)*x), ((a^3*d*f - (2*a*b^2*c - a^2*b*d)*e + (a^2*b*d*f - (2*b^3*c - a*b^2*d)*e)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + ((b^4*c - a*b^3*d)*e*x + (a*b^3*c - a^2*b^2*d)*e)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) + ((a*b^3*c - a^2*b^2*d)*e - (a^2*b^2*c - a^3*b*d)*f)*sqrt(d*x + c))/(a^3*b^3*c - a^4*b^2*d + (a^2*b^4*c - a^3*b^3*d)*x), 1/2*(4*((b^4*c - a*b^3*d)*e*x + (a*b^3*c - a^2*b^2*d)*e)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + (a^3*d*f - (2*a*b^2*c - a^2*b*d)*e + (a^2*b*d*f - (2*b^3*c - a*b^2*d)*e)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*((a*b^3*c - a^2*b^2*d)*e - (a^2*b^2*c - a^3*b*d)*f)*sqrt(d*x + c))/(a^3*b^3*c - a^4*b^2*d + (a^2*b^4*c - a^3*b^3*d)*x), ((a^3*d*f - (2*a*b^2*c - a^2*b*d)*e + (a^2*b*d*f - (2*b^3*c - a*b^2*d)*e)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) + 2*((b^4*c - a*b^3*d)*e*x + (a*b^3*c - a^2*b^2*d)*e)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) + ((a*b^3*c - a^2*b^2*d)*e - (a^2*b^2*c - a^3*b*d)*f)*sqrt(d*x + c))/(a^3*b^3*c - a^4*b^2*d + (a^2*b^4*c - a^3*b^3*d)*x)]","B",0
14,1,2216,0,3.163802," ","integrate((f*x+e)*(d*x+c)^(1/2)/x/(b*x+a)^3,x, algorithm=""fricas"")","\left[-\frac{{\left(a^{5} d^{2} f + {\left(a^{3} b^{2} d^{2} f + {\left(8 \, b^{5} c^{2} - 12 \, a b^{4} c d + 3 \, a^{2} b^{3} d^{2}\right)} e\right)} x^{2} + {\left(8 \, a^{2} b^{3} c^{2} - 12 \, a^{3} b^{2} c d + 3 \, a^{4} b d^{2}\right)} e + 2 \, {\left(a^{4} b d^{2} f + {\left(8 \, a b^{4} c^{2} - 12 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} e\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) - 8 \, {\left({\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} e x^{2} + 2 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} e x + {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} e\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - 2 \, {\left({\left(6 \, a^{2} b^{4} c^{2} - 11 \, a^{3} b^{3} c d + 5 \, a^{4} b^{2} d^{2}\right)} e - {\left(2 \, a^{3} b^{3} c^{2} - 3 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} f + {\left({\left(4 \, a b^{5} c^{2} - 7 \, a^{2} b^{4} c d + 3 \, a^{3} b^{3} d^{2}\right)} e - {\left(a^{3} b^{3} c d - a^{4} b^{2} d^{2}\right)} f\right)} x\right)} \sqrt{d x + c}}{8 \, {\left(a^{5} b^{4} c^{2} - 2 \, a^{6} b^{3} c d + a^{7} b^{2} d^{2} + {\left(a^{3} b^{6} c^{2} - 2 \, a^{4} b^{5} c d + a^{5} b^{4} d^{2}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} x\right)}}, -\frac{{\left(a^{5} d^{2} f + {\left(a^{3} b^{2} d^{2} f + {\left(8 \, b^{5} c^{2} - 12 \, a b^{4} c d + 3 \, a^{2} b^{3} d^{2}\right)} e\right)} x^{2} + {\left(8 \, a^{2} b^{3} c^{2} - 12 \, a^{3} b^{2} c d + 3 \, a^{4} b d^{2}\right)} e + 2 \, {\left(a^{4} b d^{2} f + {\left(8 \, a b^{4} c^{2} - 12 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} e\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - 4 \, {\left({\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} e x^{2} + 2 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} e x + {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} e\right)} \sqrt{c} \log\left(\frac{d x - 2 \, \sqrt{d x + c} \sqrt{c} + 2 \, c}{x}\right) - {\left({\left(6 \, a^{2} b^{4} c^{2} - 11 \, a^{3} b^{3} c d + 5 \, a^{4} b^{2} d^{2}\right)} e - {\left(2 \, a^{3} b^{3} c^{2} - 3 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} f + {\left({\left(4 \, a b^{5} c^{2} - 7 \, a^{2} b^{4} c d + 3 \, a^{3} b^{3} d^{2}\right)} e - {\left(a^{3} b^{3} c d - a^{4} b^{2} d^{2}\right)} f\right)} x\right)} \sqrt{d x + c}}{4 \, {\left(a^{5} b^{4} c^{2} - 2 \, a^{6} b^{3} c d + a^{7} b^{2} d^{2} + {\left(a^{3} b^{6} c^{2} - 2 \, a^{4} b^{5} c d + a^{5} b^{4} d^{2}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} x\right)}}, \frac{16 \, {\left({\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} e x^{2} + 2 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} e x + {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left(a^{5} d^{2} f + {\left(a^{3} b^{2} d^{2} f + {\left(8 \, b^{5} c^{2} - 12 \, a b^{4} c d + 3 \, a^{2} b^{3} d^{2}\right)} e\right)} x^{2} + {\left(8 \, a^{2} b^{3} c^{2} - 12 \, a^{3} b^{2} c d + 3 \, a^{4} b d^{2}\right)} e + 2 \, {\left(a^{4} b d^{2} f + {\left(8 \, a b^{4} c^{2} - 12 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} e\right)} x\right)} \sqrt{b^{2} c - a b d} \log\left(\frac{b d x + 2 \, b c - a d - 2 \, \sqrt{b^{2} c - a b d} \sqrt{d x + c}}{b x + a}\right) + 2 \, {\left({\left(6 \, a^{2} b^{4} c^{2} - 11 \, a^{3} b^{3} c d + 5 \, a^{4} b^{2} d^{2}\right)} e - {\left(2 \, a^{3} b^{3} c^{2} - 3 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} f + {\left({\left(4 \, a b^{5} c^{2} - 7 \, a^{2} b^{4} c d + 3 \, a^{3} b^{3} d^{2}\right)} e - {\left(a^{3} b^{3} c d - a^{4} b^{2} d^{2}\right)} f\right)} x\right)} \sqrt{d x + c}}{8 \, {\left(a^{5} b^{4} c^{2} - 2 \, a^{6} b^{3} c d + a^{7} b^{2} d^{2} + {\left(a^{3} b^{6} c^{2} - 2 \, a^{4} b^{5} c d + a^{5} b^{4} d^{2}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} x\right)}}, -\frac{{\left(a^{5} d^{2} f + {\left(a^{3} b^{2} d^{2} f + {\left(8 \, b^{5} c^{2} - 12 \, a b^{4} c d + 3 \, a^{2} b^{3} d^{2}\right)} e\right)} x^{2} + {\left(8 \, a^{2} b^{3} c^{2} - 12 \, a^{3} b^{2} c d + 3 \, a^{4} b d^{2}\right)} e + 2 \, {\left(a^{4} b d^{2} f + {\left(8 \, a b^{4} c^{2} - 12 \, a^{2} b^{3} c d + 3 \, a^{3} b^{2} d^{2}\right)} e\right)} x\right)} \sqrt{-b^{2} c + a b d} \arctan\left(\frac{\sqrt{-b^{2} c + a b d} \sqrt{d x + c}}{b d x + b c}\right) - 8 \, {\left({\left(b^{6} c^{2} - 2 \, a b^{5} c d + a^{2} b^{4} d^{2}\right)} e x^{2} + 2 \, {\left(a b^{5} c^{2} - 2 \, a^{2} b^{4} c d + a^{3} b^{3} d^{2}\right)} e x + {\left(a^{2} b^{4} c^{2} - 2 \, a^{3} b^{3} c d + a^{4} b^{2} d^{2}\right)} e\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{d x + c} \sqrt{-c}}{c}\right) - {\left({\left(6 \, a^{2} b^{4} c^{2} - 11 \, a^{3} b^{3} c d + 5 \, a^{4} b^{2} d^{2}\right)} e - {\left(2 \, a^{3} b^{3} c^{2} - 3 \, a^{4} b^{2} c d + a^{5} b d^{2}\right)} f + {\left({\left(4 \, a b^{5} c^{2} - 7 \, a^{2} b^{4} c d + 3 \, a^{3} b^{3} d^{2}\right)} e - {\left(a^{3} b^{3} c d - a^{4} b^{2} d^{2}\right)} f\right)} x\right)} \sqrt{d x + c}}{4 \, {\left(a^{5} b^{4} c^{2} - 2 \, a^{6} b^{3} c d + a^{7} b^{2} d^{2} + {\left(a^{3} b^{6} c^{2} - 2 \, a^{4} b^{5} c d + a^{5} b^{4} d^{2}\right)} x^{2} + 2 \, {\left(a^{4} b^{5} c^{2} - 2 \, a^{5} b^{4} c d + a^{6} b^{3} d^{2}\right)} x\right)}}\right]"," ",0,"[-1/8*((a^5*d^2*f + (a^3*b^2*d^2*f + (8*b^5*c^2 - 12*a*b^4*c*d + 3*a^2*b^3*d^2)*e)*x^2 + (8*a^2*b^3*c^2 - 12*a^3*b^2*c*d + 3*a^4*b*d^2)*e + 2*(a^4*b*d^2*f + (8*a*b^4*c^2 - 12*a^2*b^3*c*d + 3*a^3*b^2*d^2)*e)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) - 8*((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*e*x^2 + 2*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*e*x + (a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*e)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - 2*((6*a^2*b^4*c^2 - 11*a^3*b^3*c*d + 5*a^4*b^2*d^2)*e - (2*a^3*b^3*c^2 - 3*a^4*b^2*c*d + a^5*b*d^2)*f + ((4*a*b^5*c^2 - 7*a^2*b^4*c*d + 3*a^3*b^3*d^2)*e - (a^3*b^3*c*d - a^4*b^2*d^2)*f)*x)*sqrt(d*x + c))/(a^5*b^4*c^2 - 2*a^6*b^3*c*d + a^7*b^2*d^2 + (a^3*b^6*c^2 - 2*a^4*b^5*c*d + a^5*b^4*d^2)*x^2 + 2*(a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*x), -1/4*((a^5*d^2*f + (a^3*b^2*d^2*f + (8*b^5*c^2 - 12*a*b^4*c*d + 3*a^2*b^3*d^2)*e)*x^2 + (8*a^2*b^3*c^2 - 12*a^3*b^2*c*d + 3*a^4*b*d^2)*e + 2*(a^4*b*d^2*f + (8*a*b^4*c^2 - 12*a^2*b^3*c*d + 3*a^3*b^2*d^2)*e)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - 4*((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*e*x^2 + 2*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*e*x + (a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*e)*sqrt(c)*log((d*x - 2*sqrt(d*x + c)*sqrt(c) + 2*c)/x) - ((6*a^2*b^4*c^2 - 11*a^3*b^3*c*d + 5*a^4*b^2*d^2)*e - (2*a^3*b^3*c^2 - 3*a^4*b^2*c*d + a^5*b*d^2)*f + ((4*a*b^5*c^2 - 7*a^2*b^4*c*d + 3*a^3*b^3*d^2)*e - (a^3*b^3*c*d - a^4*b^2*d^2)*f)*x)*sqrt(d*x + c))/(a^5*b^4*c^2 - 2*a^6*b^3*c*d + a^7*b^2*d^2 + (a^3*b^6*c^2 - 2*a^4*b^5*c*d + a^5*b^4*d^2)*x^2 + 2*(a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*x), 1/8*(16*((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*e*x^2 + 2*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*e*x + (a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*e)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - (a^5*d^2*f + (a^3*b^2*d^2*f + (8*b^5*c^2 - 12*a*b^4*c*d + 3*a^2*b^3*d^2)*e)*x^2 + (8*a^2*b^3*c^2 - 12*a^3*b^2*c*d + 3*a^4*b*d^2)*e + 2*(a^4*b*d^2*f + (8*a*b^4*c^2 - 12*a^2*b^3*c*d + 3*a^3*b^2*d^2)*e)*x)*sqrt(b^2*c - a*b*d)*log((b*d*x + 2*b*c - a*d - 2*sqrt(b^2*c - a*b*d)*sqrt(d*x + c))/(b*x + a)) + 2*((6*a^2*b^4*c^2 - 11*a^3*b^3*c*d + 5*a^4*b^2*d^2)*e - (2*a^3*b^3*c^2 - 3*a^4*b^2*c*d + a^5*b*d^2)*f + ((4*a*b^5*c^2 - 7*a^2*b^4*c*d + 3*a^3*b^3*d^2)*e - (a^3*b^3*c*d - a^4*b^2*d^2)*f)*x)*sqrt(d*x + c))/(a^5*b^4*c^2 - 2*a^6*b^3*c*d + a^7*b^2*d^2 + (a^3*b^6*c^2 - 2*a^4*b^5*c*d + a^5*b^4*d^2)*x^2 + 2*(a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*x), -1/4*((a^5*d^2*f + (a^3*b^2*d^2*f + (8*b^5*c^2 - 12*a*b^4*c*d + 3*a^2*b^3*d^2)*e)*x^2 + (8*a^2*b^3*c^2 - 12*a^3*b^2*c*d + 3*a^4*b*d^2)*e + 2*(a^4*b*d^2*f + (8*a*b^4*c^2 - 12*a^2*b^3*c*d + 3*a^3*b^2*d^2)*e)*x)*sqrt(-b^2*c + a*b*d)*arctan(sqrt(-b^2*c + a*b*d)*sqrt(d*x + c)/(b*d*x + b*c)) - 8*((b^6*c^2 - 2*a*b^5*c*d + a^2*b^4*d^2)*e*x^2 + 2*(a*b^5*c^2 - 2*a^2*b^4*c*d + a^3*b^3*d^2)*e*x + (a^2*b^4*c^2 - 2*a^3*b^3*c*d + a^4*b^2*d^2)*e)*sqrt(-c)*arctan(sqrt(d*x + c)*sqrt(-c)/c) - ((6*a^2*b^4*c^2 - 11*a^3*b^3*c*d + 5*a^4*b^2*d^2)*e - (2*a^3*b^3*c^2 - 3*a^4*b^2*c*d + a^5*b*d^2)*f + ((4*a*b^5*c^2 - 7*a^2*b^4*c*d + 3*a^3*b^3*d^2)*e - (a^3*b^3*c*d - a^4*b^2*d^2)*f)*x)*sqrt(d*x + c))/(a^5*b^4*c^2 - 2*a^6*b^3*c*d + a^7*b^2*d^2 + (a^3*b^6*c^2 - 2*a^4*b^5*c*d + a^5*b^4*d^2)*x^2 + 2*(a^4*b^5*c^2 - 2*a^5*b^4*c*d + a^6*b^3*d^2)*x)]","B",0
15,1,641,0,1.403370," ","integrate((d*x+c)^3*(f*x+e)*(b*x+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{315 \, \sqrt{a} b^{4} c^{3} e \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(35 \, b^{4} d^{3} f x^{4} + 5 \, {\left(9 \, b^{4} d^{3} e + {\left(27 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} f\right)} x^{3} + 3 \, {\left(3 \, {\left(21 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} e + {\left(63 \, b^{4} c^{2} d + 9 \, a b^{3} c d^{2} - 2 \, a^{2} b^{2} d^{3}\right)} f\right)} x^{2} + 3 \, {\left(105 \, b^{4} c^{3} + 105 \, a b^{3} c^{2} d - 42 \, a^{2} b^{2} c d^{2} + 8 \, a^{3} b d^{3}\right)} e + {\left(105 \, a b^{3} c^{3} - 126 \, a^{2} b^{2} c^{2} d + 72 \, a^{3} b c d^{2} - 16 \, a^{4} d^{3}\right)} f + {\left(3 \, {\left(105 \, b^{4} c^{2} d + 21 \, a b^{3} c d^{2} - 4 \, a^{2} b^{2} d^{3}\right)} e + {\left(105 \, b^{4} c^{3} + 63 \, a b^{3} c^{2} d - 36 \, a^{2} b^{2} c d^{2} + 8 \, a^{3} b d^{3}\right)} f\right)} x\right)} \sqrt{b x + a}}{315 \, b^{4}}, \frac{2 \, {\left(315 \, \sqrt{-a} b^{4} c^{3} e \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(35 \, b^{4} d^{3} f x^{4} + 5 \, {\left(9 \, b^{4} d^{3} e + {\left(27 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} f\right)} x^{3} + 3 \, {\left(3 \, {\left(21 \, b^{4} c d^{2} + a b^{3} d^{3}\right)} e + {\left(63 \, b^{4} c^{2} d + 9 \, a b^{3} c d^{2} - 2 \, a^{2} b^{2} d^{3}\right)} f\right)} x^{2} + 3 \, {\left(105 \, b^{4} c^{3} + 105 \, a b^{3} c^{2} d - 42 \, a^{2} b^{2} c d^{2} + 8 \, a^{3} b d^{3}\right)} e + {\left(105 \, a b^{3} c^{3} - 126 \, a^{2} b^{2} c^{2} d + 72 \, a^{3} b c d^{2} - 16 \, a^{4} d^{3}\right)} f + {\left(3 \, {\left(105 \, b^{4} c^{2} d + 21 \, a b^{3} c d^{2} - 4 \, a^{2} b^{2} d^{3}\right)} e + {\left(105 \, b^{4} c^{3} + 63 \, a b^{3} c^{2} d - 36 \, a^{2} b^{2} c d^{2} + 8 \, a^{3} b d^{3}\right)} f\right)} x\right)} \sqrt{b x + a}\right)}}{315 \, b^{4}}\right]"," ",0,"[1/315*(315*sqrt(a)*b^4*c^3*e*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(35*b^4*d^3*f*x^4 + 5*(9*b^4*d^3*e + (27*b^4*c*d^2 + a*b^3*d^3)*f)*x^3 + 3*(3*(21*b^4*c*d^2 + a*b^3*d^3)*e + (63*b^4*c^2*d + 9*a*b^3*c*d^2 - 2*a^2*b^2*d^3)*f)*x^2 + 3*(105*b^4*c^3 + 105*a*b^3*c^2*d - 42*a^2*b^2*c*d^2 + 8*a^3*b*d^3)*e + (105*a*b^3*c^3 - 126*a^2*b^2*c^2*d + 72*a^3*b*c*d^2 - 16*a^4*d^3)*f + (3*(105*b^4*c^2*d + 21*a*b^3*c*d^2 - 4*a^2*b^2*d^3)*e + (105*b^4*c^3 + 63*a*b^3*c^2*d - 36*a^2*b^2*c*d^2 + 8*a^3*b*d^3)*f)*x)*sqrt(b*x + a))/b^4, 2/315*(315*sqrt(-a)*b^4*c^3*e*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (35*b^4*d^3*f*x^4 + 5*(9*b^4*d^3*e + (27*b^4*c*d^2 + a*b^3*d^3)*f)*x^3 + 3*(3*(21*b^4*c*d^2 + a*b^3*d^3)*e + (63*b^4*c^2*d + 9*a*b^3*c*d^2 - 2*a^2*b^2*d^3)*f)*x^2 + 3*(105*b^4*c^3 + 105*a*b^3*c^2*d - 42*a^2*b^2*c*d^2 + 8*a^3*b*d^3)*e + (105*a*b^3*c^3 - 126*a^2*b^2*c^2*d + 72*a^3*b*c*d^2 - 16*a^4*d^3)*f + (3*(105*b^4*c^2*d + 21*a*b^3*c*d^2 - 4*a^2*b^2*d^3)*e + (105*b^4*c^3 + 63*a*b^3*c^2*d - 36*a^2*b^2*c*d^2 + 8*a^3*b*d^3)*f)*x)*sqrt(b*x + a))/b^4]","A",0
16,1,403,0,1.071257," ","integrate((d*x+c)^2*(f*x+e)*(b*x+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{105 \, \sqrt{a} b^{3} c^{2} e \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(15 \, b^{3} d^{2} f x^{3} + 3 \, {\left(7 \, b^{3} d^{2} e + {\left(14 \, b^{3} c d + a b^{2} d^{2}\right)} f\right)} x^{2} + 7 \, {\left(15 \, b^{3} c^{2} + 10 \, a b^{2} c d - 2 \, a^{2} b d^{2}\right)} e + {\left(35 \, a b^{2} c^{2} - 28 \, a^{2} b c d + 8 \, a^{3} d^{2}\right)} f + {\left(7 \, {\left(10 \, b^{3} c d + a b^{2} d^{2}\right)} e + {\left(35 \, b^{3} c^{2} + 14 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} f\right)} x\right)} \sqrt{b x + a}}{105 \, b^{3}}, \frac{2 \, {\left(105 \, \sqrt{-a} b^{3} c^{2} e \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(15 \, b^{3} d^{2} f x^{3} + 3 \, {\left(7 \, b^{3} d^{2} e + {\left(14 \, b^{3} c d + a b^{2} d^{2}\right)} f\right)} x^{2} + 7 \, {\left(15 \, b^{3} c^{2} + 10 \, a b^{2} c d - 2 \, a^{2} b d^{2}\right)} e + {\left(35 \, a b^{2} c^{2} - 28 \, a^{2} b c d + 8 \, a^{3} d^{2}\right)} f + {\left(7 \, {\left(10 \, b^{3} c d + a b^{2} d^{2}\right)} e + {\left(35 \, b^{3} c^{2} + 14 \, a b^{2} c d - 4 \, a^{2} b d^{2}\right)} f\right)} x\right)} \sqrt{b x + a}\right)}}{105 \, b^{3}}\right]"," ",0,"[1/105*(105*sqrt(a)*b^3*c^2*e*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(15*b^3*d^2*f*x^3 + 3*(7*b^3*d^2*e + (14*b^3*c*d + a*b^2*d^2)*f)*x^2 + 7*(15*b^3*c^2 + 10*a*b^2*c*d - 2*a^2*b*d^2)*e + (35*a*b^2*c^2 - 28*a^2*b*c*d + 8*a^3*d^2)*f + (7*(10*b^3*c*d + a*b^2*d^2)*e + (35*b^3*c^2 + 14*a*b^2*c*d - 4*a^2*b*d^2)*f)*x)*sqrt(b*x + a))/b^3, 2/105*(105*sqrt(-a)*b^3*c^2*e*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (15*b^3*d^2*f*x^3 + 3*(7*b^3*d^2*e + (14*b^3*c*d + a*b^2*d^2)*f)*x^2 + 7*(15*b^3*c^2 + 10*a*b^2*c*d - 2*a^2*b*d^2)*e + (35*a*b^2*c^2 - 28*a^2*b*c*d + 8*a^3*d^2)*f + (7*(10*b^3*c*d + a*b^2*d^2)*e + (35*b^3*c^2 + 14*a*b^2*c*d - 4*a^2*b*d^2)*f)*x)*sqrt(b*x + a))/b^3]","A",0
17,1,217,0,0.925174," ","integrate((d*x+c)*(f*x+e)*(b*x+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{15 \, \sqrt{a} b^{2} c e \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(3 \, b^{2} d f x^{2} + 5 \, {\left(3 \, b^{2} c + a b d\right)} e + {\left(5 \, a b c - 2 \, a^{2} d\right)} f + {\left(5 \, b^{2} d e + {\left(5 \, b^{2} c + a b d\right)} f\right)} x\right)} \sqrt{b x + a}}{15 \, b^{2}}, \frac{2 \, {\left(15 \, \sqrt{-a} b^{2} c e \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(3 \, b^{2} d f x^{2} + 5 \, {\left(3 \, b^{2} c + a b d\right)} e + {\left(5 \, a b c - 2 \, a^{2} d\right)} f + {\left(5 \, b^{2} d e + {\left(5 \, b^{2} c + a b d\right)} f\right)} x\right)} \sqrt{b x + a}\right)}}{15 \, b^{2}}\right]"," ",0,"[1/15*(15*sqrt(a)*b^2*c*e*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(3*b^2*d*f*x^2 + 5*(3*b^2*c + a*b*d)*e + (5*a*b*c - 2*a^2*d)*f + (5*b^2*d*e + (5*b^2*c + a*b*d)*f)*x)*sqrt(b*x + a))/b^2, 2/15*(15*sqrt(-a)*b^2*c*e*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (3*b^2*d*f*x^2 + 5*(3*b^2*c + a*b*d)*e + (5*a*b*c - 2*a^2*d)*f + (5*b^2*d*e + (5*b^2*c + a*b*d)*f)*x)*sqrt(b*x + a))/b^2]","A",0
18,1,111,0,0.781900," ","integrate((f*x+e)*(b*x+a)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a} b e \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left(b f x + 3 \, b e + a f\right)} \sqrt{b x + a}}{3 \, b}, \frac{2 \, {\left(3 \, \sqrt{-a} b e \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(b f x + 3 \, b e + a f\right)} \sqrt{b x + a}\right)}}{3 \, b}\right]"," ",0,"[1/3*(3*sqrt(a)*b*e*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*(b*f*x + 3*b*e + a*f)*sqrt(b*x + a))/b, 2/3*(3*sqrt(-a)*b*e*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (b*f*x + 3*b*e + a*f)*sqrt(b*x + a))/b]","A",0
19,1,450,0,1.473270," ","integrate((f*x+e)*(b*x+a)^(1/2)/x/(d*x+c),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} d e \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, \sqrt{b x + a} c f - {\left(d e - c f\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{b d x - b c + 2 \, a d - 2 \, \sqrt{b x + a} d \sqrt{-\frac{b c - a d}{d}}}{d x + c}\right)}{c d}, \frac{2 \, \sqrt{-a} d e \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + 2 \, \sqrt{b x + a} c f - {\left(d e - c f\right)} \sqrt{-\frac{b c - a d}{d}} \log\left(\frac{b d x - b c + 2 \, a d - 2 \, \sqrt{b x + a} d \sqrt{-\frac{b c - a d}{d}}}{d x + c}\right)}{c d}, \frac{\sqrt{a} d e \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, \sqrt{b x + a} c f - 2 \, {\left(d e - c f\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{\sqrt{b x + a} d \sqrt{\frac{b c - a d}{d}}}{b c - a d}\right)}{c d}, \frac{2 \, {\left(\sqrt{-a} d e \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + \sqrt{b x + a} c f - {\left(d e - c f\right)} \sqrt{\frac{b c - a d}{d}} \arctan\left(-\frac{\sqrt{b x + a} d \sqrt{\frac{b c - a d}{d}}}{b c - a d}\right)\right)}}{c d}\right]"," ",0,"[(sqrt(a)*d*e*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*sqrt(b*x + a)*c*f - (d*e - c*f)*sqrt(-(b*c - a*d)/d)*log((b*d*x - b*c + 2*a*d - 2*sqrt(b*x + a)*d*sqrt(-(b*c - a*d)/d))/(d*x + c)))/(c*d), (2*sqrt(-a)*d*e*arctan(sqrt(b*x + a)*sqrt(-a)/a) + 2*sqrt(b*x + a)*c*f - (d*e - c*f)*sqrt(-(b*c - a*d)/d)*log((b*d*x - b*c + 2*a*d - 2*sqrt(b*x + a)*d*sqrt(-(b*c - a*d)/d))/(d*x + c)))/(c*d), (sqrt(a)*d*e*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*sqrt(b*x + a)*c*f - 2*(d*e - c*f)*sqrt((b*c - a*d)/d)*arctan(-sqrt(b*x + a)*d*sqrt((b*c - a*d)/d)/(b*c - a*d)))/(c*d), 2*(sqrt(-a)*d*e*arctan(sqrt(b*x + a)*sqrt(-a)/a) + sqrt(b*x + a)*c*f - (d*e - c*f)*sqrt((b*c - a*d)/d)*arctan(-sqrt(b*x + a)*d*sqrt((b*c - a*d)/d)/(b*c - a*d)))/(c*d)]","A",0
20,1,1008,0,1.355245," ","integrate((f*x+e)*(b*x+a)^(1/2)/x/(d*x+c)^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b c^{3} f + {\left(b c^{2} d - 2 \, a c d^{2}\right)} e + {\left(b c^{2} d f + {\left(b c d^{2} - 2 \, a d^{3}\right)} e\right)} x\right)} \sqrt{-b c d + a d^{2}} \log\left(\frac{b d x - b c + 2 \, a d - 2 \, \sqrt{-b c d + a d^{2}} \sqrt{b x + a}}{d x + c}\right) - 2 \, {\left({\left(b c d^{3} - a d^{4}\right)} e x + {\left(b c^{2} d^{2} - a c d^{3}\right)} e\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - 2 \, {\left({\left(b c^{2} d^{2} - a c d^{3}\right)} e - {\left(b c^{3} d - a c^{2} d^{2}\right)} f\right)} \sqrt{b x + a}}{2 \, {\left(b c^{4} d^{2} - a c^{3} d^{3} + {\left(b c^{3} d^{3} - a c^{2} d^{4}\right)} x\right)}}, \frac{4 \, {\left({\left(b c d^{3} - a d^{4}\right)} e x + {\left(b c^{2} d^{2} - a c d^{3}\right)} e\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left(b c^{3} f + {\left(b c^{2} d - 2 \, a c d^{2}\right)} e + {\left(b c^{2} d f + {\left(b c d^{2} - 2 \, a d^{3}\right)} e\right)} x\right)} \sqrt{-b c d + a d^{2}} \log\left(\frac{b d x - b c + 2 \, a d - 2 \, \sqrt{-b c d + a d^{2}} \sqrt{b x + a}}{d x + c}\right) + 2 \, {\left({\left(b c^{2} d^{2} - a c d^{3}\right)} e - {\left(b c^{3} d - a c^{2} d^{2}\right)} f\right)} \sqrt{b x + a}}{2 \, {\left(b c^{4} d^{2} - a c^{3} d^{3} + {\left(b c^{3} d^{3} - a c^{2} d^{4}\right)} x\right)}}, -\frac{{\left(b c^{3} f + {\left(b c^{2} d - 2 \, a c d^{2}\right)} e + {\left(b c^{2} d f + {\left(b c d^{2} - 2 \, a d^{3}\right)} e\right)} x\right)} \sqrt{b c d - a d^{2}} \arctan\left(\frac{\sqrt{b c d - a d^{2}} \sqrt{b x + a}}{b d x + a d}\right) - {\left({\left(b c d^{3} - a d^{4}\right)} e x + {\left(b c^{2} d^{2} - a c d^{3}\right)} e\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - {\left({\left(b c^{2} d^{2} - a c d^{3}\right)} e - {\left(b c^{3} d - a c^{2} d^{2}\right)} f\right)} \sqrt{b x + a}}{b c^{4} d^{2} - a c^{3} d^{3} + {\left(b c^{3} d^{3} - a c^{2} d^{4}\right)} x}, -\frac{{\left(b c^{3} f + {\left(b c^{2} d - 2 \, a c d^{2}\right)} e + {\left(b c^{2} d f + {\left(b c d^{2} - 2 \, a d^{3}\right)} e\right)} x\right)} \sqrt{b c d - a d^{2}} \arctan\left(\frac{\sqrt{b c d - a d^{2}} \sqrt{b x + a}}{b d x + a d}\right) - 2 \, {\left({\left(b c d^{3} - a d^{4}\right)} e x + {\left(b c^{2} d^{2} - a c d^{3}\right)} e\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left({\left(b c^{2} d^{2} - a c d^{3}\right)} e - {\left(b c^{3} d - a c^{2} d^{2}\right)} f\right)} \sqrt{b x + a}}{b c^{4} d^{2} - a c^{3} d^{3} + {\left(b c^{3} d^{3} - a c^{2} d^{4}\right)} x}\right]"," ",0,"[-1/2*((b*c^3*f + (b*c^2*d - 2*a*c*d^2)*e + (b*c^2*d*f + (b*c*d^2 - 2*a*d^3)*e)*x)*sqrt(-b*c*d + a*d^2)*log((b*d*x - b*c + 2*a*d - 2*sqrt(-b*c*d + a*d^2)*sqrt(b*x + a))/(d*x + c)) - 2*((b*c*d^3 - a*d^4)*e*x + (b*c^2*d^2 - a*c*d^3)*e)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - 2*((b*c^2*d^2 - a*c*d^3)*e - (b*c^3*d - a*c^2*d^2)*f)*sqrt(b*x + a))/(b*c^4*d^2 - a*c^3*d^3 + (b*c^3*d^3 - a*c^2*d^4)*x), 1/2*(4*((b*c*d^3 - a*d^4)*e*x + (b*c^2*d^2 - a*c*d^3)*e)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - (b*c^3*f + (b*c^2*d - 2*a*c*d^2)*e + (b*c^2*d*f + (b*c*d^2 - 2*a*d^3)*e)*x)*sqrt(-b*c*d + a*d^2)*log((b*d*x - b*c + 2*a*d - 2*sqrt(-b*c*d + a*d^2)*sqrt(b*x + a))/(d*x + c)) + 2*((b*c^2*d^2 - a*c*d^3)*e - (b*c^3*d - a*c^2*d^2)*f)*sqrt(b*x + a))/(b*c^4*d^2 - a*c^3*d^3 + (b*c^3*d^3 - a*c^2*d^4)*x), -((b*c^3*f + (b*c^2*d - 2*a*c*d^2)*e + (b*c^2*d*f + (b*c*d^2 - 2*a*d^3)*e)*x)*sqrt(b*c*d - a*d^2)*arctan(sqrt(b*c*d - a*d^2)*sqrt(b*x + a)/(b*d*x + a*d)) - ((b*c*d^3 - a*d^4)*e*x + (b*c^2*d^2 - a*c*d^3)*e)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - ((b*c^2*d^2 - a*c*d^3)*e - (b*c^3*d - a*c^2*d^2)*f)*sqrt(b*x + a))/(b*c^4*d^2 - a*c^3*d^3 + (b*c^3*d^3 - a*c^2*d^4)*x), -((b*c^3*f + (b*c^2*d - 2*a*c*d^2)*e + (b*c^2*d*f + (b*c*d^2 - 2*a*d^3)*e)*x)*sqrt(b*c*d - a*d^2)*arctan(sqrt(b*c*d - a*d^2)*sqrt(b*x + a)/(b*d*x + a*d)) - 2*((b*c*d^3 - a*d^4)*e*x + (b*c^2*d^2 - a*c*d^3)*e)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - ((b*c^2*d^2 - a*c*d^3)*e - (b*c^3*d - a*c^2*d^2)*f)*sqrt(b*x + a))/(b*c^4*d^2 - a*c^3*d^3 + (b*c^3*d^3 - a*c^2*d^4)*x)]","B",0
21,1,2211,0,3.638164," ","integrate((f*x+e)*(b*x+a)^(1/2)/x/(d*x+c)^3,x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{5} f + {\left(b^{2} c^{3} d^{2} f + {\left(3 \, b^{2} c^{2} d^{3} - 12 \, a b c d^{4} + 8 \, a^{2} d^{5}\right)} e\right)} x^{2} + {\left(3 \, b^{2} c^{4} d - 12 \, a b c^{3} d^{2} + 8 \, a^{2} c^{2} d^{3}\right)} e + 2 \, {\left(b^{2} c^{4} d f + {\left(3 \, b^{2} c^{3} d^{2} - 12 \, a b c^{2} d^{3} + 8 \, a^{2} c d^{4}\right)} e\right)} x\right)} \sqrt{-b c d + a d^{2}} \log\left(\frac{b d x - b c + 2 \, a d + 2 \, \sqrt{-b c d + a d^{2}} \sqrt{b x + a}}{d x + c}\right) + 8 \, {\left({\left(b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} e x^{2} + 2 \, {\left(b^{2} c^{3} d^{3} - 2 \, a b c^{2} d^{4} + a^{2} c d^{5}\right)} e x + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} e\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) + 2 \, {\left({\left(5 \, b^{2} c^{4} d^{2} - 11 \, a b c^{3} d^{3} + 6 \, a^{2} c^{2} d^{4}\right)} e - {\left(b^{2} c^{5} d - 3 \, a b c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3}\right)} f + {\left({\left(3 \, b^{2} c^{3} d^{3} - 7 \, a b c^{2} d^{4} + 4 \, a^{2} c d^{5}\right)} e + {\left(b^{2} c^{4} d^{2} - a b c^{3} d^{3}\right)} f\right)} x\right)} \sqrt{b x + a}}{8 \, {\left(b^{2} c^{7} d^{2} - 2 \, a b c^{6} d^{3} + a^{2} c^{5} d^{4} + {\left(b^{2} c^{5} d^{4} - 2 \, a b c^{4} d^{5} + a^{2} c^{3} d^{6}\right)} x^{2} + 2 \, {\left(b^{2} c^{6} d^{3} - 2 \, a b c^{5} d^{4} + a^{2} c^{4} d^{5}\right)} x\right)}}, \frac{16 \, {\left({\left(b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} e x^{2} + 2 \, {\left(b^{2} c^{3} d^{3} - 2 \, a b c^{2} d^{4} + a^{2} c d^{5}\right)} e x + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} e\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) + {\left(b^{2} c^{5} f + {\left(b^{2} c^{3} d^{2} f + {\left(3 \, b^{2} c^{2} d^{3} - 12 \, a b c d^{4} + 8 \, a^{2} d^{5}\right)} e\right)} x^{2} + {\left(3 \, b^{2} c^{4} d - 12 \, a b c^{3} d^{2} + 8 \, a^{2} c^{2} d^{3}\right)} e + 2 \, {\left(b^{2} c^{4} d f + {\left(3 \, b^{2} c^{3} d^{2} - 12 \, a b c^{2} d^{3} + 8 \, a^{2} c d^{4}\right)} e\right)} x\right)} \sqrt{-b c d + a d^{2}} \log\left(\frac{b d x - b c + 2 \, a d + 2 \, \sqrt{-b c d + a d^{2}} \sqrt{b x + a}}{d x + c}\right) + 2 \, {\left({\left(5 \, b^{2} c^{4} d^{2} - 11 \, a b c^{3} d^{3} + 6 \, a^{2} c^{2} d^{4}\right)} e - {\left(b^{2} c^{5} d - 3 \, a b c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3}\right)} f + {\left({\left(3 \, b^{2} c^{3} d^{3} - 7 \, a b c^{2} d^{4} + 4 \, a^{2} c d^{5}\right)} e + {\left(b^{2} c^{4} d^{2} - a b c^{3} d^{3}\right)} f\right)} x\right)} \sqrt{b x + a}}{8 \, {\left(b^{2} c^{7} d^{2} - 2 \, a b c^{6} d^{3} + a^{2} c^{5} d^{4} + {\left(b^{2} c^{5} d^{4} - 2 \, a b c^{4} d^{5} + a^{2} c^{3} d^{6}\right)} x^{2} + 2 \, {\left(b^{2} c^{6} d^{3} - 2 \, a b c^{5} d^{4} + a^{2} c^{4} d^{5}\right)} x\right)}}, -\frac{{\left(b^{2} c^{5} f + {\left(b^{2} c^{3} d^{2} f + {\left(3 \, b^{2} c^{2} d^{3} - 12 \, a b c d^{4} + 8 \, a^{2} d^{5}\right)} e\right)} x^{2} + {\left(3 \, b^{2} c^{4} d - 12 \, a b c^{3} d^{2} + 8 \, a^{2} c^{2} d^{3}\right)} e + 2 \, {\left(b^{2} c^{4} d f + {\left(3 \, b^{2} c^{3} d^{2} - 12 \, a b c^{2} d^{3} + 8 \, a^{2} c d^{4}\right)} e\right)} x\right)} \sqrt{b c d - a d^{2}} \arctan\left(\frac{\sqrt{b c d - a d^{2}} \sqrt{b x + a}}{b d x + a d}\right) - 4 \, {\left({\left(b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} e x^{2} + 2 \, {\left(b^{2} c^{3} d^{3} - 2 \, a b c^{2} d^{4} + a^{2} c d^{5}\right)} e x + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} e\right)} \sqrt{a} \log\left(\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right) - {\left({\left(5 \, b^{2} c^{4} d^{2} - 11 \, a b c^{3} d^{3} + 6 \, a^{2} c^{2} d^{4}\right)} e - {\left(b^{2} c^{5} d - 3 \, a b c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3}\right)} f + {\left({\left(3 \, b^{2} c^{3} d^{3} - 7 \, a b c^{2} d^{4} + 4 \, a^{2} c d^{5}\right)} e + {\left(b^{2} c^{4} d^{2} - a b c^{3} d^{3}\right)} f\right)} x\right)} \sqrt{b x + a}}{4 \, {\left(b^{2} c^{7} d^{2} - 2 \, a b c^{6} d^{3} + a^{2} c^{5} d^{4} + {\left(b^{2} c^{5} d^{4} - 2 \, a b c^{4} d^{5} + a^{2} c^{3} d^{6}\right)} x^{2} + 2 \, {\left(b^{2} c^{6} d^{3} - 2 \, a b c^{5} d^{4} + a^{2} c^{4} d^{5}\right)} x\right)}}, -\frac{{\left(b^{2} c^{5} f + {\left(b^{2} c^{3} d^{2} f + {\left(3 \, b^{2} c^{2} d^{3} - 12 \, a b c d^{4} + 8 \, a^{2} d^{5}\right)} e\right)} x^{2} + {\left(3 \, b^{2} c^{4} d - 12 \, a b c^{3} d^{2} + 8 \, a^{2} c^{2} d^{3}\right)} e + 2 \, {\left(b^{2} c^{4} d f + {\left(3 \, b^{2} c^{3} d^{2} - 12 \, a b c^{2} d^{3} + 8 \, a^{2} c d^{4}\right)} e\right)} x\right)} \sqrt{b c d - a d^{2}} \arctan\left(\frac{\sqrt{b c d - a d^{2}} \sqrt{b x + a}}{b d x + a d}\right) - 8 \, {\left({\left(b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} e x^{2} + 2 \, {\left(b^{2} c^{3} d^{3} - 2 \, a b c^{2} d^{4} + a^{2} c d^{5}\right)} e x + {\left(b^{2} c^{4} d^{2} - 2 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4}\right)} e\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{b x + a} \sqrt{-a}}{a}\right) - {\left({\left(5 \, b^{2} c^{4} d^{2} - 11 \, a b c^{3} d^{3} + 6 \, a^{2} c^{2} d^{4}\right)} e - {\left(b^{2} c^{5} d - 3 \, a b c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3}\right)} f + {\left({\left(3 \, b^{2} c^{3} d^{3} - 7 \, a b c^{2} d^{4} + 4 \, a^{2} c d^{5}\right)} e + {\left(b^{2} c^{4} d^{2} - a b c^{3} d^{3}\right)} f\right)} x\right)} \sqrt{b x + a}}{4 \, {\left(b^{2} c^{7} d^{2} - 2 \, a b c^{6} d^{3} + a^{2} c^{5} d^{4} + {\left(b^{2} c^{5} d^{4} - 2 \, a b c^{4} d^{5} + a^{2} c^{3} d^{6}\right)} x^{2} + 2 \, {\left(b^{2} c^{6} d^{3} - 2 \, a b c^{5} d^{4} + a^{2} c^{4} d^{5}\right)} x\right)}}\right]"," ",0,"[1/8*((b^2*c^5*f + (b^2*c^3*d^2*f + (3*b^2*c^2*d^3 - 12*a*b*c*d^4 + 8*a^2*d^5)*e)*x^2 + (3*b^2*c^4*d - 12*a*b*c^3*d^2 + 8*a^2*c^2*d^3)*e + 2*(b^2*c^4*d*f + (3*b^2*c^3*d^2 - 12*a*b*c^2*d^3 + 8*a^2*c*d^4)*e)*x)*sqrt(-b*c*d + a*d^2)*log((b*d*x - b*c + 2*a*d + 2*sqrt(-b*c*d + a*d^2)*sqrt(b*x + a))/(d*x + c)) + 8*((b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*e*x^2 + 2*(b^2*c^3*d^3 - 2*a*b*c^2*d^4 + a^2*c*d^5)*e*x + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*e)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) + 2*((5*b^2*c^4*d^2 - 11*a*b*c^3*d^3 + 6*a^2*c^2*d^4)*e - (b^2*c^5*d - 3*a*b*c^4*d^2 + 2*a^2*c^3*d^3)*f + ((3*b^2*c^3*d^3 - 7*a*b*c^2*d^4 + 4*a^2*c*d^5)*e + (b^2*c^4*d^2 - a*b*c^3*d^3)*f)*x)*sqrt(b*x + a))/(b^2*c^7*d^2 - 2*a*b*c^6*d^3 + a^2*c^5*d^4 + (b^2*c^5*d^4 - 2*a*b*c^4*d^5 + a^2*c^3*d^6)*x^2 + 2*(b^2*c^6*d^3 - 2*a*b*c^5*d^4 + a^2*c^4*d^5)*x), 1/8*(16*((b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*e*x^2 + 2*(b^2*c^3*d^3 - 2*a*b*c^2*d^4 + a^2*c*d^5)*e*x + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*e)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) + (b^2*c^5*f + (b^2*c^3*d^2*f + (3*b^2*c^2*d^3 - 12*a*b*c*d^4 + 8*a^2*d^5)*e)*x^2 + (3*b^2*c^4*d - 12*a*b*c^3*d^2 + 8*a^2*c^2*d^3)*e + 2*(b^2*c^4*d*f + (3*b^2*c^3*d^2 - 12*a*b*c^2*d^3 + 8*a^2*c*d^4)*e)*x)*sqrt(-b*c*d + a*d^2)*log((b*d*x - b*c + 2*a*d + 2*sqrt(-b*c*d + a*d^2)*sqrt(b*x + a))/(d*x + c)) + 2*((5*b^2*c^4*d^2 - 11*a*b*c^3*d^3 + 6*a^2*c^2*d^4)*e - (b^2*c^5*d - 3*a*b*c^4*d^2 + 2*a^2*c^3*d^3)*f + ((3*b^2*c^3*d^3 - 7*a*b*c^2*d^4 + 4*a^2*c*d^5)*e + (b^2*c^4*d^2 - a*b*c^3*d^3)*f)*x)*sqrt(b*x + a))/(b^2*c^7*d^2 - 2*a*b*c^6*d^3 + a^2*c^5*d^4 + (b^2*c^5*d^4 - 2*a*b*c^4*d^5 + a^2*c^3*d^6)*x^2 + 2*(b^2*c^6*d^3 - 2*a*b*c^5*d^4 + a^2*c^4*d^5)*x), -1/4*((b^2*c^5*f + (b^2*c^3*d^2*f + (3*b^2*c^2*d^3 - 12*a*b*c*d^4 + 8*a^2*d^5)*e)*x^2 + (3*b^2*c^4*d - 12*a*b*c^3*d^2 + 8*a^2*c^2*d^3)*e + 2*(b^2*c^4*d*f + (3*b^2*c^3*d^2 - 12*a*b*c^2*d^3 + 8*a^2*c*d^4)*e)*x)*sqrt(b*c*d - a*d^2)*arctan(sqrt(b*c*d - a*d^2)*sqrt(b*x + a)/(b*d*x + a*d)) - 4*((b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*e*x^2 + 2*(b^2*c^3*d^3 - 2*a*b*c^2*d^4 + a^2*c*d^5)*e*x + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*e)*sqrt(a)*log((b*x - 2*sqrt(b*x + a)*sqrt(a) + 2*a)/x) - ((5*b^2*c^4*d^2 - 11*a*b*c^3*d^3 + 6*a^2*c^2*d^4)*e - (b^2*c^5*d - 3*a*b*c^4*d^2 + 2*a^2*c^3*d^3)*f + ((3*b^2*c^3*d^3 - 7*a*b*c^2*d^4 + 4*a^2*c*d^5)*e + (b^2*c^4*d^2 - a*b*c^3*d^3)*f)*x)*sqrt(b*x + a))/(b^2*c^7*d^2 - 2*a*b*c^6*d^3 + a^2*c^5*d^4 + (b^2*c^5*d^4 - 2*a*b*c^4*d^5 + a^2*c^3*d^6)*x^2 + 2*(b^2*c^6*d^3 - 2*a*b*c^5*d^4 + a^2*c^4*d^5)*x), -1/4*((b^2*c^5*f + (b^2*c^3*d^2*f + (3*b^2*c^2*d^3 - 12*a*b*c*d^4 + 8*a^2*d^5)*e)*x^2 + (3*b^2*c^4*d - 12*a*b*c^3*d^2 + 8*a^2*c^2*d^3)*e + 2*(b^2*c^4*d*f + (3*b^2*c^3*d^2 - 12*a*b*c^2*d^3 + 8*a^2*c*d^4)*e)*x)*sqrt(b*c*d - a*d^2)*arctan(sqrt(b*c*d - a*d^2)*sqrt(b*x + a)/(b*d*x + a*d)) - 8*((b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*e*x^2 + 2*(b^2*c^3*d^3 - 2*a*b*c^2*d^4 + a^2*c*d^5)*e*x + (b^2*c^4*d^2 - 2*a*b*c^3*d^3 + a^2*c^2*d^4)*e)*sqrt(-a)*arctan(sqrt(b*x + a)*sqrt(-a)/a) - ((5*b^2*c^4*d^2 - 11*a*b*c^3*d^3 + 6*a^2*c^2*d^4)*e - (b^2*c^5*d - 3*a*b*c^4*d^2 + 2*a^2*c^3*d^3)*f + ((3*b^2*c^3*d^3 - 7*a*b*c^2*d^4 + 4*a^2*c*d^5)*e + (b^2*c^4*d^2 - a*b*c^3*d^3)*f)*x)*sqrt(b*x + a))/(b^2*c^7*d^2 - 2*a*b*c^6*d^3 + a^2*c^5*d^4 + (b^2*c^5*d^4 - 2*a*b*c^4*d^5 + a^2*c^3*d^6)*x^2 + 2*(b^2*c^6*d^3 - 2*a*b*c^5*d^4 + a^2*c^4*d^5)*x)]","B",0
22,1,65,0,1.317639," ","integrate(x^3*(a*x+1)/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(16 \, a^{3} x^{3} + 40 \, a^{2} x^{2} + 50 \, a x + 75\right)} \sqrt{a x} \sqrt{-a x + 1} + 75 \, \arctan\left(\frac{\sqrt{a x} \sqrt{-a x + 1}}{a x}\right)}{64 \, a^{4}}"," ",0,"-1/64*((16*a^3*x^3 + 40*a^2*x^2 + 50*a*x + 75)*sqrt(a*x)*sqrt(-a*x + 1) + 75*arctan(sqrt(a*x)*sqrt(-a*x + 1)/(a*x)))/a^4","A",0
23,1,57,0,1.289182," ","integrate(x^2*(a*x+1)/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, a^{2} x^{2} + 22 \, a x + 33\right)} \sqrt{a x} \sqrt{-a x + 1} + 33 \, \arctan\left(\frac{\sqrt{a x} \sqrt{-a x + 1}}{a x}\right)}{24 \, a^{3}}"," ",0,"-1/24*((8*a^2*x^2 + 22*a*x + 33)*sqrt(a*x)*sqrt(-a*x + 1) + 33*arctan(sqrt(a*x)*sqrt(-a*x + 1)/(a*x)))/a^3","A",0
24,1,49,0,1.312161," ","integrate(x*(a*x+1)/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, a x + 7\right)} \sqrt{a x} \sqrt{-a x + 1} + 7 \, \arctan\left(\frac{\sqrt{a x} \sqrt{-a x + 1}}{a x}\right)}{4 \, a^{2}}"," ",0,"-1/4*((2*a*x + 7)*sqrt(a*x)*sqrt(-a*x + 1) + 7*arctan(sqrt(a*x)*sqrt(-a*x + 1)/(a*x)))/a^2","A",0
25,1,43,0,1.307268," ","integrate((a*x+1)/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{a x} \sqrt{-a x + 1} + 3 \, \arctan\left(\frac{\sqrt{a x} \sqrt{-a x + 1}}{a x}\right)}{a}"," ",0,"-(sqrt(a*x)*sqrt(-a*x + 1) + 3*arctan(sqrt(a*x)*sqrt(-a*x + 1)/(a*x)))/a","A",0
26,1,47,0,0.807691," ","integrate((a*x+1)/x/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a x \arctan\left(\frac{\sqrt{a x} \sqrt{-a x + 1}}{a x}\right) + \sqrt{a x} \sqrt{-a x + 1}\right)}}{a x}"," ",0,"-2*(a*x*arctan(sqrt(a*x)*sqrt(-a*x + 1)/(a*x)) + sqrt(a*x)*sqrt(-a*x + 1))/(a*x)","B",0
27,1,27,0,0.803486," ","integrate((a*x+1)/x^2/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, a x + 1\right)} \sqrt{a x} \sqrt{-a x + 1}}{3 \, a x^{2}}"," ",0,"-2/3*(5*a*x + 1)*sqrt(a*x)*sqrt(-a*x + 1)/(a*x^2)","A",0
28,1,35,0,1.325560," ","integrate((a*x+1)/x^3/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, a^{2} x^{2} + 3 \, a x + 1\right)} \sqrt{a x} \sqrt{-a x + 1}}{5 \, a x^{3}}"," ",0,"-2/5*(6*a^2*x^2 + 3*a*x + 1)*sqrt(a*x)*sqrt(-a*x + 1)/(a*x^3)","A",0
29,1,43,0,0.833411," ","integrate((a*x+1)/x^4/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(104 \, a^{3} x^{3} + 52 \, a^{2} x^{2} + 39 \, a x + 15\right)} \sqrt{a x} \sqrt{-a x + 1}}{105 \, a x^{4}}"," ",0,"-2/105*(104*a^3*x^3 + 52*a^2*x^2 + 39*a*x + 15)*sqrt(a*x)*sqrt(-a*x + 1)/(a*x^4)","A",0
30,1,51,0,0.906482," ","integrate((a*x+1)/x^5/(a*x)^(1/2)/(-a*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(272 \, a^{4} x^{4} + 136 \, a^{3} x^{3} + 102 \, a^{2} x^{2} + 85 \, a x + 35\right)} \sqrt{a x} \sqrt{-a x + 1}}{315 \, a x^{5}}"," ",0,"-2/315*(272*a^4*x^4 + 136*a^3*x^3 + 102*a^2*x^2 + 85*a*x + 35)*sqrt(a*x)*sqrt(-a*x + 1)/(a*x^5)","A",0
31,1,40,0,0.810287," ","integrate((2*a*x-1)/x^2/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{4 \, a x \arctan\left(\sqrt{x + 1} \sqrt{x - 1} - x\right) - \sqrt{x + 1} \sqrt{x - 1} - x}{x}"," ",0,"(4*a*x*arctan(sqrt(x + 1)*sqrt(x - 1) - x) - sqrt(x + 1)*sqrt(x - 1) - x)/x","A",0
32,1,40,0,1.075873," ","integrate((a^2*x^2-(-a*x+1)^2)/x^2/(-1+x)^(1/2)/(1+x)^(1/2),x, algorithm=""fricas"")","\frac{4 \, a x \arctan\left(\sqrt{x + 1} \sqrt{x - 1} - x\right) - \sqrt{x + 1} \sqrt{x - 1} - x}{x}"," ",0,"(4*a*x*arctan(sqrt(x + 1)*sqrt(x - 1) - x) - sqrt(x + 1)*sqrt(x - 1) - x)/x","A",0
33,0,0,0,1.565667," ","integrate((B*x+A)/(b*x+a)^(1/2)/(c+b*(-1+c)*x/a)^(1/2)/(e+b*(-1+e)*x/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B a^{2} x + A a^{2}\right)} \sqrt{b x + a} \sqrt{\frac{a c + {\left(b c - b\right)} x}{a}} \sqrt{\frac{a e + {\left(b e - b\right)} x}{a}}}{a^{3} c e - {\left(b^{3} c - b^{3} - {\left(b^{3} c - b^{3}\right)} e\right)} x^{3} - {\left(2 \, a b^{2} c - a b^{2} - {\left(3 \, a b^{2} c - 2 \, a b^{2}\right)} e\right)} x^{2} - {\left(a^{2} b c - {\left(3 \, a^{2} b c - a^{2} b\right)} e\right)} x}, x\right)"," ",0,"integral((B*a^2*x + A*a^2)*sqrt(b*x + a)*sqrt((a*c + (b*c - b)*x)/a)*sqrt((a*e + (b*e - b)*x)/a)/(a^3*c*e - (b^3*c - b^3 - (b^3*c - b^3)*e)*x^3 - (2*a*b^2*c - a*b^2 - (3*a*b^2*c - 2*a*b^2)*e)*x^2 - (a^2*b*c - (3*a^2*b*c - a^2*b)*e)*x), x)","F",0
34,0,0,0,1.658588," ","integrate((B*x+A)/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(e+b*(-1+e)*x/a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B a x + A a\right)} \sqrt{b x + a} \sqrt{d x + c} \sqrt{\frac{a e + {\left(b e - b\right)} x}{a}}}{a^{2} c e + {\left(b^{2} d e - b^{2} d\right)} x^{3} - {\left(b^{2} c + a b d - {\left(b^{2} c + 2 \, a b d\right)} e\right)} x^{2} - {\left(a b c - {\left(2 \, a b c + a^{2} d\right)} e\right)} x}, x\right)"," ",0,"integral((B*a*x + A*a)*sqrt(b*x + a)*sqrt(d*x + c)*sqrt((a*e + (b*e - b)*x)/a)/(a^2*c*e + (b^2*d*e - b^2*d)*x^3 - (b^2*c + a*b*d - (b^2*c + 2*a*b*d)*e)*x^2 - (a*b*c - (2*a*b*c + a^2*d)*e)*x), x)","F",0
35,0,0,0,1.443884," ","integrate((7+5*x)^3*(2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(125 \, x^{3} + 525 \, x^{2} + 735 \, x + 343\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}, x\right)"," ",0,"integral((125*x^3 + 525*x^2 + 735*x + 343)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2), x)","F",0
36,0,0,0,1.393541," ","integrate((7+5*x)^2*(2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(25 \, x^{2} + 70 \, x + 49\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}, x\right)"," ",0,"integral((25*x^2 + 70*x + 49)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2), x)","F",0
37,0,0,0,1.372072," ","integrate((7+5*x)*(2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(5 \, x + 7\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}, x\right)"," ",0,"integral((5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2), x)","F",0
38,0,0,0,1.286699," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2), x)","F",0
39,0,0,0,1.006880," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{5 \, x + 7}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(5*x + 7), x)","F",0
40,0,0,0,1.406589," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{25 \, x^{2} + 70 \, x + 49}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(25*x^2 + 70*x + 49), x)","F",0
41,0,0,0,1.378489," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{125 \, x^{3} + 525 \, x^{2} + 735 \, x + 343}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(125*x^3 + 525*x^2 + 735*x + 343), x)","F",0
42,0,0,0,1.184834," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{625 \, x^{4} + 3500 \, x^{3} + 7350 \, x^{2} + 6860 \, x + 2401}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(625*x^4 + 3500*x^3 + 7350*x^2 + 6860*x + 2401), x)","F",0
43,-1,0,0,0.000000," ","integrate((d*x+c)^(1/2)*(f*x+e)^(1/2)*(h*x+g)^(1/2)/(b*x+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,0,0,0,1.543855," ","integrate((7+5*x)^3*(2-3*x)^(1/2)*(1+4*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(125 \, x^{3} + 525 \, x^{2} + 735 \, x + 343\right)} \sqrt{4 \, x + 1} \sqrt{-3 \, x + 2}}{\sqrt{2 \, x - 5}}, x\right)"," ",0,"integral((125*x^3 + 525*x^2 + 735*x + 343)*sqrt(4*x + 1)*sqrt(-3*x + 2)/sqrt(2*x - 5), x)","F",0
45,0,0,0,1.197875," ","integrate((7+5*x)^2*(2-3*x)^(1/2)*(1+4*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 70 \, x + 49\right)} \sqrt{4 \, x + 1} \sqrt{-3 \, x + 2}}{\sqrt{2 \, x - 5}}, x\right)"," ",0,"integral((25*x^2 + 70*x + 49)*sqrt(4*x + 1)*sqrt(-3*x + 2)/sqrt(2*x - 5), x)","F",0
46,0,0,0,1.200645," ","integrate((7+5*x)*(2-3*x)^(1/2)*(1+4*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 7\right)} \sqrt{4 \, x + 1} \sqrt{-3 \, x + 2}}{\sqrt{2 \, x - 5}}, x\right)"," ",0,"integral((5*x + 7)*sqrt(4*x + 1)*sqrt(-3*x + 2)/sqrt(2*x - 5), x)","F",0
47,0,0,0,1.492620," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{-3 \, x + 2}}{\sqrt{2 \, x - 5}}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(-3*x + 2)/sqrt(2*x - 5), x)","F",0
48,0,0,0,1.449891," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{10 \, x^{2} - 11 \, x - 35}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(10*x^2 - 11*x - 35), x)","F",0
49,0,0,0,1.374110," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^2/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{50 \, x^{3} + 15 \, x^{2} - 252 \, x - 245}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(50*x^3 + 15*x^2 - 252*x - 245), x)","F",0
50,0,0,0,1.485844," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^3/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{250 \, x^{4} + 425 \, x^{3} - 1155 \, x^{2} - 2989 \, x - 1715}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(250*x^4 + 425*x^3 - 1155*x^2 - 2989*x - 1715), x)","F",0
51,0,0,0,1.306309," ","integrate((7+5*x)^3*(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(125 \, x^{3} + 525 \, x^{2} + 735 \, x + 343\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{8 \, x^{2} - 18 \, x - 5}, x\right)"," ",0,"integral((125*x^3 + 525*x^2 + 735*x + 343)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(8*x^2 - 18*x - 5), x)","F",0
52,0,0,0,1.344945," ","integrate((7+5*x)^2*(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 70 \, x + 49\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{8 \, x^{2} - 18 \, x - 5}, x\right)"," ",0,"integral((25*x^2 + 70*x + 49)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(8*x^2 - 18*x - 5), x)","F",0
53,0,0,0,1.324196," ","integrate((7+5*x)*(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 7\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{8 \, x^{2} - 18 \, x - 5}, x\right)"," ",0,"integral((5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(8*x^2 - 18*x - 5), x)","F",0
54,0,0,0,1.126786," ","integrate((2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{8 \, x^{2} - 18 \, x - 5}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(8*x^2 - 18*x - 5), x)","F",0
55,0,0,0,1.450122," ","integrate((2-3*x)^(1/2)/(7+5*x)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{40 \, x^{3} - 34 \, x^{2} - 151 \, x - 35}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(40*x^3 - 34*x^2 - 151*x - 35), x)","F",0
56,0,0,0,1.484052," ","integrate((2-3*x)^(1/2)/(7+5*x)^2/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{200 \, x^{4} + 110 \, x^{3} - 993 \, x^{2} - 1232 \, x - 245}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(200*x^4 + 110*x^3 - 993*x^2 - 1232*x - 245), x)","F",0
57,0,0,0,1.279070," ","integrate((2-3*x)^(1/2)/(7+5*x)^3/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{1000 \, x^{5} + 1950 \, x^{4} - 4195 \, x^{3} - 13111 \, x^{2} - 9849 \, x - 1715}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(1000*x^5 + 1950*x^4 - 4195*x^3 - 13111*x^2 - 9849*x - 1715), x)","F",0
58,-1,0,0,0.000000," ","integrate((d*x+c)^(1/2)/(b*x+a)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate((d*x+c)^(3/2)/(b*x+a)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,0,0,0,1.488832," ","integrate((7+5*x)^4/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(625 \, x^{4} + 3500 \, x^{3} + 7350 \, x^{2} + 6860 \, x + 2401\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right)"," ",0,"integral(-(625*x^4 + 3500*x^3 + 7350*x^2 + 6860*x + 2401)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(24*x^3 - 70*x^2 + 21*x + 10), x)","F",0
61,0,0,0,1.452603," ","integrate((7+5*x)^3/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(125 \, x^{3} + 525 \, x^{2} + 735 \, x + 343\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right)"," ",0,"integral(-(125*x^3 + 525*x^2 + 735*x + 343)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(24*x^3 - 70*x^2 + 21*x + 10), x)","F",0
62,0,0,0,1.666255," ","integrate((7+5*x)^2/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 70 \, x + 49\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right)"," ",0,"integral(-(25*x^2 + 70*x + 49)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(24*x^3 - 70*x^2 + 21*x + 10), x)","F",0
63,0,0,0,1.683078," ","integrate((7+5*x)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 7\right)} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right)"," ",0,"integral(-(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(24*x^3 - 70*x^2 + 21*x + 10), x)","F",0
64,0,0,0,0.792835," ","integrate(1/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right)"," ",0,"integral(-sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(24*x^3 - 70*x^2 + 21*x + 10), x)","F",0
65,0,0,0,1.453460," ","integrate(1/(7+5*x)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{120 \, x^{4} - 182 \, x^{3} - 385 \, x^{2} + 197 \, x + 70}, x\right)"," ",0,"integral(-sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(120*x^4 - 182*x^3 - 385*x^2 + 197*x + 70), x)","F",0
66,0,0,0,1.366176," ","integrate(1/(7+5*x)^2/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{600 \, x^{5} - 70 \, x^{4} - 3199 \, x^{3} - 1710 \, x^{2} + 1729 \, x + 490}, x\right)"," ",0,"integral(-sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(600*x^5 - 70*x^4 - 3199*x^3 - 1710*x^2 + 1729*x + 490), x)","F",0
67,0,0,0,1.679395," ","integrate(1/(7+5*x)^3/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{3000 \, x^{6} + 3850 \, x^{5} - 16485 \, x^{4} - 30943 \, x^{3} - 3325 \, x^{2} + 14553 \, x + 3430}, x\right)"," ",0,"integral(-sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(3000*x^6 + 3850*x^5 - 16485*x^4 - 30943*x^3 - 3325*x^2 + 14553*x + 3430), x)","F",0
68,0,0,0,1.362814," ","integrate((d*i*x+c*i)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x + c} \sqrt{f x + e} \sqrt{h x + g} i}{f h x^{2} + e g + {\left(f g + e h\right)} x}, x\right)"," ",0,"integral(sqrt(d*x + c)*sqrt(f*x + e)*sqrt(h*x + g)*i/(f*h*x^2 + e*g + (f*g + e*h)*x), x)","F",0
69,0,0,0,1.834154," ","integrate((b*x+a)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)} \sqrt{d x + c} \sqrt{f x + e} \sqrt{h x + g}}{d f h x^{3} + c e g + {\left(d f g + {\left(d e + c f\right)} h\right)} x^{2} + {\left(c e h + {\left(d e + c f\right)} g\right)} x}, x\right)"," ",0,"integral((b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)*sqrt(h*x + g)/(d*f*h*x^3 + c*e*g + (d*f*g + (d*e + c*f)*h)*x^2 + (c*e*h + (d*e + c*f)*g)*x), x)","F",0
70,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(3/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(5/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(1/2)/(-f*x+1)^(1/2)/(f*x+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(1/2)/(-f^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(1/2)/(-f^2*x+1)^(1/2)/(f^2*x+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate(1/(b*x+a)/(d*x+c)^(1/2)/(-f^4*x^2+1)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,0,0,0,1.266945," ","integrate((7+5*x)^(5/2)*(2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(25 \, x^{2} + 70 \, x + 49\right)} \sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}, x\right)"," ",0,"integral((25*x^2 + 70*x + 49)*sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2), x)","F",0
78,0,0,0,1.414530," ","integrate((7+5*x)^(3/2)*(2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(5 \, x + 7\right)}^{\frac{3}{2}} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}, x\right)"," ",0,"integral((5*x + 7)^(3/2)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2), x)","F",0
79,0,0,0,1.407690," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)*(7+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2), x)","F",0
80,0,0,0,1.144459," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{\sqrt{5 \, x + 7}}, x\right)"," ",0,"integral(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/sqrt(5*x + 7), x)","F",0
81,0,0,0,1.148902," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{25 \, x^{2} + 70 \, x + 49}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(25*x^2 + 70*x + 49), x)","F",0
82,0,0,0,1.030871," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{125 \, x^{3} + 525 \, x^{2} + 735 \, x + 343}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(125*x^3 + 525*x^2 + 735*x + 343), x)","F",0
83,0,0,0,1.137135," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{625 \, x^{4} + 3500 \, x^{3} + 7350 \, x^{2} + 6860 \, x + 2401}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(625*x^4 + 3500*x^3 + 7350*x^2 + 6860*x + 2401), x)","F",0
84,0,0,0,1.024690," ","integrate((2-3*x)^(1/2)*(-5+2*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{3125 \, x^{5} + 21875 \, x^{4} + 61250 \, x^{3} + 85750 \, x^{2} + 60025 \, x + 16807}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(3125*x^5 + 21875*x^4 + 61250*x^3 + 85750*x^2 + 60025*x + 16807), x)","F",0
85,0,0,0,1.270947," ","integrate((7+5*x)^(5/2)*(2-3*x)^(1/2)*(1+4*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 70 \, x + 49\right)} \sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{-3 \, x + 2}}{\sqrt{2 \, x - 5}}, x\right)"," ",0,"integral((25*x^2 + 70*x + 49)*sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(-3*x + 2)/sqrt(2*x - 5), x)","F",0
86,0,0,0,1.014837," ","integrate((7+5*x)^(3/2)*(2-3*x)^(1/2)*(1+4*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 7\right)}^{\frac{3}{2}} \sqrt{4 \, x + 1} \sqrt{-3 \, x + 2}}{\sqrt{2 \, x - 5}}, x\right)"," ",0,"integral((5*x + 7)^(3/2)*sqrt(4*x + 1)*sqrt(-3*x + 2)/sqrt(2*x - 5), x)","F",0
87,0,0,0,0.932375," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)*(7+5*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{-3 \, x + 2}}{\sqrt{2 \, x - 5}}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(-3*x + 2)/sqrt(2*x - 5), x)","F",0
88,0,0,0,0.965401," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(1/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{10 \, x^{2} - 11 \, x - 35}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(10*x^2 - 11*x - 35), x)","F",0
89,0,0,0,1.043868," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(3/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{50 \, x^{3} + 15 \, x^{2} - 252 \, x - 245}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(50*x^3 + 15*x^2 - 252*x - 245), x)","F",0
90,0,0,0,0.974044," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(5/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{250 \, x^{4} + 425 \, x^{3} - 1155 \, x^{2} - 2989 \, x - 1715}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(250*x^4 + 425*x^3 - 1155*x^2 - 2989*x - 1715), x)","F",0
91,0,0,0,0.997613," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(7/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{1250 \, x^{5} + 3875 \, x^{4} - 2800 \, x^{3} - 23030 \, x^{2} - 29498 \, x - 12005}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(1250*x^5 + 3875*x^4 - 2800*x^3 - 23030*x^2 - 29498*x - 12005), x)","F",0
92,0,0,0,0.963297," ","integrate((2-3*x)^(1/2)*(1+4*x)^(1/2)/(7+5*x)^(9/2)/(-5+2*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{6250 \, x^{6} + 28125 \, x^{5} + 13125 \, x^{4} - 134750 \, x^{3} - 308700 \, x^{2} - 266511 \, x - 84035}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(6250*x^6 + 28125*x^5 + 13125*x^4 - 134750*x^3 - 308700*x^2 - 266511*x - 84035), x)","F",0
93,0,0,0,1.294868," ","integrate((7+5*x)^(5/2)*(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{2} + 70 \, x + 49\right)} \sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{8 \, x^{2} - 18 \, x - 5}, x\right)"," ",0,"integral((25*x^2 + 70*x + 49)*sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(8*x^2 - 18*x - 5), x)","F",0
94,0,0,0,0.917129," ","integrate((7+5*x)^(3/2)*(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(5 \, x + 7\right)}^{\frac{3}{2}} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{8 \, x^{2} - 18 \, x - 5}, x\right)"," ",0,"integral((5*x + 7)^(3/2)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(8*x^2 - 18*x - 5), x)","F",0
95,0,0,0,1.122327," ","integrate((7+5*x)^(1/2)*(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{8 \, x^{2} - 18 \, x - 5}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(8*x^2 - 18*x - 5), x)","F",0
96,0,0,0,1.029007," ","integrate((2-3*x)^(1/2)/(7+5*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{40 \, x^{3} - 34 \, x^{2} - 151 \, x - 35}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(40*x^3 - 34*x^2 - 151*x - 35), x)","F",0
97,0,0,0,0.697683," ","integrate((2-3*x)^(1/2)/(7+5*x)^(3/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{200 \, x^{4} + 110 \, x^{3} - 993 \, x^{2} - 1232 \, x - 245}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(200*x^4 + 110*x^3 - 993*x^2 - 1232*x - 245), x)","F",0
98,0,0,0,0.936417," ","integrate((2-3*x)^(1/2)/(7+5*x)^(5/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{1000 \, x^{5} + 1950 \, x^{4} - 4195 \, x^{3} - 13111 \, x^{2} - 9849 \, x - 1715}, x\right)"," ",0,"integral(sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(1000*x^5 + 1950*x^4 - 4195*x^3 - 13111*x^2 - 9849*x - 1715), x)","F",0
99,-1,0,0,0.000000," ","integrate((b*x+a)^(1/2)*(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,0,0,0,5.716403," ","integrate((d*x+c)^(1/2)/(b*x+a)^(3/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e} \sqrt{h x + g}}{b^{2} f h x^{4} + a^{2} e g + {\left(b^{2} f g + {\left(b^{2} e + 2 \, a b f\right)} h\right)} x^{3} + {\left({\left(b^{2} e + 2 \, a b f\right)} g + {\left(2 \, a b e + a^{2} f\right)} h\right)} x^{2} + {\left(a^{2} e h + {\left(2 \, a b e + a^{2} f\right)} g\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)*sqrt(h*x + g)/(b^2*f*h*x^4 + a^2*e*g + (b^2*f*g + (b^2*e + 2*a*b*f)*h)*x^3 + ((b^2*e + 2*a*b*f)*g + (2*a*b*e + a^2*f)*h)*x^2 + (a^2*e*h + (2*a*b*e + a^2*f)*g)*x), x)","F",0
101,0,0,0,1.184012," ","integrate((7+5*x)^(5/2)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{2} + 70 \, x + 49\right)} \sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right)"," ",0,"integral(-(25*x^2 + 70*x + 49)*sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(24*x^3 - 70*x^2 + 21*x + 10), x)","F",0
102,0,0,0,1.138648," ","integrate((7+5*x)^(3/2)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(5 \, x + 7\right)}^{\frac{3}{2}} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right)"," ",0,"integral(-(5*x + 7)^(3/2)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(24*x^3 - 70*x^2 + 21*x + 10), x)","F",0
103,0,0,0,1.012827," ","integrate((7+5*x)^(1/2)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{24 \, x^{3} - 70 \, x^{2} + 21 \, x + 10}, x\right)"," ",0,"integral(-sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(24*x^3 - 70*x^2 + 21*x + 10), x)","F",0
104,0,0,0,1.097024," ","integrate(1/(7+5*x)^(1/2)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{120 \, x^{4} - 182 \, x^{3} - 385 \, x^{2} + 197 \, x + 70}, x\right)"," ",0,"integral(-sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(120*x^4 - 182*x^3 - 385*x^2 + 197*x + 70), x)","F",0
105,0,0,0,0.752095," ","integrate(1/(7+5*x)^(3/2)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{600 \, x^{5} - 70 \, x^{4} - 3199 \, x^{3} - 1710 \, x^{2} + 1729 \, x + 490}, x\right)"," ",0,"integral(-sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(600*x^5 - 70*x^4 - 3199*x^3 - 1710*x^2 + 1729*x + 490), x)","F",0
106,0,0,0,1.010861," ","integrate(1/(7+5*x)^(5/2)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{5 \, x + 7} \sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}{3000 \, x^{6} + 3850 \, x^{5} - 16485 \, x^{4} - 30943 \, x^{3} - 3325 \, x^{2} + 14553 \, x + 3430}, x\right)"," ",0,"integral(-sqrt(5*x + 7)*sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)/(3000*x^6 + 3850*x^5 - 16485*x^4 - 30943*x^3 - 3325*x^2 + 14553*x + 3430), x)","F",0
107,-1,0,0,0.000000," ","integrate((b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,0,0,0,4.491620," ","integrate(1/(b*x+a)^(1/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e} \sqrt{h x + g}}{b d f h x^{4} + a c e g + {\left(b d f g + {\left(b d e + {\left(b c + a d\right)} f\right)} h\right)} x^{3} + {\left({\left(b d e + {\left(b c + a d\right)} f\right)} g + {\left(a c f + {\left(b c + a d\right)} e\right)} h\right)} x^{2} + {\left(a c e h + {\left(a c f + {\left(b c + a d\right)} e\right)} g\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)*sqrt(h*x + g)/(b*d*f*h*x^4 + a*c*e*g + (b*d*f*g + (b*d*e + (b*c + a*d)*f)*h)*x^3 + ((b*d*e + (b*c + a*d)*f)*g + (a*c*f + (b*c + a*d)*e)*h)*x^2 + (a*c*e*h + (a*c*f + (b*c + a*d)*e)*g)*x), x)","F",0
110,0,0,0,1.150183," ","integrate(1/(b*x+a)^(3/2)/(d*x+c)^(1/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e} \sqrt{h x + g}}{b^{2} d f h x^{5} + a^{2} c e g + {\left(b^{2} d f g + {\left(b^{2} d e + {\left(b^{2} c + 2 \, a b d\right)} f\right)} h\right)} x^{4} + {\left({\left(b^{2} d e + {\left(b^{2} c + 2 \, a b d\right)} f\right)} g + {\left({\left(b^{2} c + 2 \, a b d\right)} e + {\left(2 \, a b c + a^{2} d\right)} f\right)} h\right)} x^{3} + {\left({\left({\left(b^{2} c + 2 \, a b d\right)} e + {\left(2 \, a b c + a^{2} d\right)} f\right)} g + {\left(a^{2} c f + {\left(2 \, a b c + a^{2} d\right)} e\right)} h\right)} x^{2} + {\left(a^{2} c e h + {\left(a^{2} c f + {\left(2 \, a b c + a^{2} d\right)} e\right)} g\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)*sqrt(h*x + g)/(b^2*d*f*h*x^5 + a^2*c*e*g + (b^2*d*f*g + (b^2*d*e + (b^2*c + 2*a*b*d)*f)*h)*x^4 + ((b^2*d*e + (b^2*c + 2*a*b*d)*f)*g + ((b^2*c + 2*a*b*d)*e + (2*a*b*c + a^2*d)*f)*h)*x^3 + (((b^2*c + 2*a*b*d)*e + (2*a*b*c + a^2*d)*f)*g + (a^2*c*f + (2*a*b*c + a^2*d)*e)*h)*x^2 + (a^2*c*e*h + (a^2*c*f + (2*a*b*c + a^2*d)*e)*g)*x), x)","F",0
111,0,0,0,5.186995," ","integrate(1/(b*x+a)^(3/2)/(d*x+c)^(3/2)/(f*x+e)^(1/2)/(h*x+g)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b x + a} \sqrt{d x + c} \sqrt{f x + e} \sqrt{h x + g}}{b^{2} d^{2} f h x^{6} + a^{2} c^{2} e g + {\left(b^{2} d^{2} f g + {\left(b^{2} d^{2} e + 2 \, {\left(b^{2} c d + a b d^{2}\right)} f\right)} h\right)} x^{5} + {\left({\left(b^{2} d^{2} e + 2 \, {\left(b^{2} c d + a b d^{2}\right)} f\right)} g + {\left(2 \, {\left(b^{2} c d + a b d^{2}\right)} e + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f\right)} h\right)} x^{4} + {\left({\left(2 \, {\left(b^{2} c d + a b d^{2}\right)} e + {\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} f\right)} g + {\left({\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} e + 2 \, {\left(a b c^{2} + a^{2} c d\right)} f\right)} h\right)} x^{3} + {\left({\left({\left(b^{2} c^{2} + 4 \, a b c d + a^{2} d^{2}\right)} e + 2 \, {\left(a b c^{2} + a^{2} c d\right)} f\right)} g + {\left(a^{2} c^{2} f + 2 \, {\left(a b c^{2} + a^{2} c d\right)} e\right)} h\right)} x^{2} + {\left(a^{2} c^{2} e h + {\left(a^{2} c^{2} f + 2 \, {\left(a b c^{2} + a^{2} c d\right)} e\right)} g\right)} x}, x\right)"," ",0,"integral(sqrt(b*x + a)*sqrt(d*x + c)*sqrt(f*x + e)*sqrt(h*x + g)/(b^2*d^2*f*h*x^6 + a^2*c^2*e*g + (b^2*d^2*f*g + (b^2*d^2*e + 2*(b^2*c*d + a*b*d^2)*f)*h)*x^5 + ((b^2*d^2*e + 2*(b^2*c*d + a*b*d^2)*f)*g + (2*(b^2*c*d + a*b*d^2)*e + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f)*h)*x^4 + ((2*(b^2*c*d + a*b*d^2)*e + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*f)*g + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e + 2*(a*b*c^2 + a^2*c*d)*f)*h)*x^3 + (((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*e + 2*(a*b*c^2 + a^2*c*d)*f)*g + (a^2*c^2*f + 2*(a*b*c^2 + a^2*c*d)*e)*h)*x^2 + (a^2*c^2*e*h + (a^2*c^2*f + 2*(a*b*c^2 + a^2*c*d)*e)*g)*x), x)","F",0
112,0,0,0,1.111562," ","integrate(x^4*(f*x+e)^n/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{4}}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral((f*x + e)^n*x^4/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
113,0,0,0,0.990051," ","integrate(x^3*(f*x+e)^n/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{3}}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral((f*x + e)^n*x^3/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
114,0,0,0,0.619685," ","integrate(x^2*(f*x+e)^n/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{2}}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral((f*x + e)^n*x^2/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
115,0,0,0,0.805768," ","integrate(x*(f*x+e)^n/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral((f*x + e)^n*x/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
116,0,0,0,0.648198," ","integrate((f*x+e)^n/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral((f*x + e)^n/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
117,0,0,0,0.641888," ","integrate((f*x+e)^n/x/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{b d x^{3} + a c x + {\left(b c + a d\right)} x^{2}}, x\right)"," ",0,"integral((f*x + e)^n/(b*d*x^3 + a*c*x + (b*c + a*d)*x^2), x)","F",0
118,0,0,0,0.870743," ","integrate((f*x+e)^n/x^2/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n}}{b d x^{4} + a c x^{2} + {\left(b c + a d\right)} x^{3}}, x\right)"," ",0,"integral((f*x + e)^n/(b*d*x^4 + a*c*x^2 + (b*c + a*d)*x^3), x)","F",0
119,1,877,0,0.864678," ","integrate((b*x+a)^m*(d*x+c)*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","\frac{{\left(a b^{3} c e g m^{3} + {\left(b^{4} d f h m^{3} + 6 \, b^{4} d f h m^{2} + 11 \, b^{4} d f h m + 6 \, b^{4} d f h\right)} x^{4} + {\left(8 \, b^{4} d f g + {\left(b^{4} d f g + {\left(b^{4} d e + {\left(b^{4} c + a b^{3} d\right)} f\right)} h\right)} m^{3} + {\left(7 \, b^{4} d f g + {\left(7 \, b^{4} d e + {\left(7 \, b^{4} c + 3 \, a b^{3} d\right)} f\right)} h\right)} m^{2} + 8 \, {\left(b^{4} d e + b^{4} c f\right)} h + 2 \, {\left(7 \, b^{4} d f g + {\left(7 \, b^{4} d e + {\left(7 \, b^{4} c + a b^{3} d\right)} f\right)} h\right)} m\right)} x^{3} - {\left(a^{2} b^{2} c e h + {\left(a^{2} b^{2} c f - {\left(9 \, a b^{3} c - a^{2} b^{2} d\right)} e\right)} g\right)} m^{2} + {\left(12 \, b^{4} c e h + {\left({\left(b^{4} d e + {\left(b^{4} c + a b^{3} d\right)} f\right)} g + {\left(a b^{3} c f + {\left(b^{4} c + a b^{3} d\right)} e\right)} h\right)} m^{3} + {\left({\left(8 \, b^{4} d e + {\left(8 \, b^{4} c + 5 \, a b^{3} d\right)} f\right)} g + {\left({\left(8 \, b^{4} c + 5 \, a b^{3} d\right)} e + {\left(5 \, a b^{3} c - 3 \, a^{2} b^{2} d\right)} f\right)} h\right)} m^{2} + 12 \, {\left(b^{4} d e + b^{4} c f\right)} g + {\left({\left(19 \, b^{4} d e + {\left(19 \, b^{4} c + 4 \, a b^{3} d\right)} f\right)} g + {\left({\left(19 \, b^{4} c + 4 \, a b^{3} d\right)} e + {\left(4 \, a b^{3} c - 3 \, a^{2} b^{2} d\right)} f\right)} h\right)} m\right)} x^{2} + 4 \, {\left(3 \, {\left(2 \, a b^{3} c - a^{2} b^{2} d\right)} e - {\left(3 \, a^{2} b^{2} c - 2 \, a^{3} b d\right)} f\right)} g - 2 \, {\left(2 \, {\left(3 \, a^{2} b^{2} c - 2 \, a^{3} b d\right)} e - {\left(4 \, a^{3} b c - 3 \, a^{4} d\right)} f\right)} h + {\left({\left({\left(26 \, a b^{3} c - 7 \, a^{2} b^{2} d\right)} e - {\left(7 \, a^{2} b^{2} c - 2 \, a^{3} b d\right)} f\right)} g + {\left(2 \, a^{3} b c f - {\left(7 \, a^{2} b^{2} c - 2 \, a^{3} b d\right)} e\right)} h\right)} m + {\left(24 \, b^{4} c e g + {\left(a b^{3} c e h + {\left(a b^{3} c f + {\left(b^{4} c + a b^{3} d\right)} e\right)} g\right)} m^{3} + {\left({\left({\left(9 \, b^{4} c + 7 \, a b^{3} d\right)} e + {\left(7 \, a b^{3} c - 2 \, a^{2} b^{2} d\right)} f\right)} g - {\left(2 \, a^{2} b^{2} c f - {\left(7 \, a b^{3} c - 2 \, a^{2} b^{2} d\right)} e\right)} h\right)} m^{2} + 2 \, {\left({\left({\left(13 \, b^{4} c + 6 \, a b^{3} d\right)} e + 2 \, {\left(3 \, a b^{3} c - 2 \, a^{2} b^{2} d\right)} f\right)} g + {\left(2 \, {\left(3 \, a b^{3} c - 2 \, a^{2} b^{2} d\right)} e - {\left(4 \, a^{2} b^{2} c - 3 \, a^{3} b d\right)} f\right)} h\right)} m\right)} x\right)} {\left(b x + a\right)}^{m}}{b^{4} m^{4} + 10 \, b^{4} m^{3} + 35 \, b^{4} m^{2} + 50 \, b^{4} m + 24 \, b^{4}}"," ",0,"(a*b^3*c*e*g*m^3 + (b^4*d*f*h*m^3 + 6*b^4*d*f*h*m^2 + 11*b^4*d*f*h*m + 6*b^4*d*f*h)*x^4 + (8*b^4*d*f*g + (b^4*d*f*g + (b^4*d*e + (b^4*c + a*b^3*d)*f)*h)*m^3 + (7*b^4*d*f*g + (7*b^4*d*e + (7*b^4*c + 3*a*b^3*d)*f)*h)*m^2 + 8*(b^4*d*e + b^4*c*f)*h + 2*(7*b^4*d*f*g + (7*b^4*d*e + (7*b^4*c + a*b^3*d)*f)*h)*m)*x^3 - (a^2*b^2*c*e*h + (a^2*b^2*c*f - (9*a*b^3*c - a^2*b^2*d)*e)*g)*m^2 + (12*b^4*c*e*h + ((b^4*d*e + (b^4*c + a*b^3*d)*f)*g + (a*b^3*c*f + (b^4*c + a*b^3*d)*e)*h)*m^3 + ((8*b^4*d*e + (8*b^4*c + 5*a*b^3*d)*f)*g + ((8*b^4*c + 5*a*b^3*d)*e + (5*a*b^3*c - 3*a^2*b^2*d)*f)*h)*m^2 + 12*(b^4*d*e + b^4*c*f)*g + ((19*b^4*d*e + (19*b^4*c + 4*a*b^3*d)*f)*g + ((19*b^4*c + 4*a*b^3*d)*e + (4*a*b^3*c - 3*a^2*b^2*d)*f)*h)*m)*x^2 + 4*(3*(2*a*b^3*c - a^2*b^2*d)*e - (3*a^2*b^2*c - 2*a^3*b*d)*f)*g - 2*(2*(3*a^2*b^2*c - 2*a^3*b*d)*e - (4*a^3*b*c - 3*a^4*d)*f)*h + (((26*a*b^3*c - 7*a^2*b^2*d)*e - (7*a^2*b^2*c - 2*a^3*b*d)*f)*g + (2*a^3*b*c*f - (7*a^2*b^2*c - 2*a^3*b*d)*e)*h)*m + (24*b^4*c*e*g + (a*b^3*c*e*h + (a*b^3*c*f + (b^4*c + a*b^3*d)*e)*g)*m^3 + (((9*b^4*c + 7*a*b^3*d)*e + (7*a*b^3*c - 2*a^2*b^2*d)*f)*g - (2*a^2*b^2*c*f - (7*a*b^3*c - 2*a^2*b^2*d)*e)*h)*m^2 + 2*(((13*b^4*c + 6*a*b^3*d)*e + 2*(3*a*b^3*c - 2*a^2*b^2*d)*f)*g + (2*(3*a*b^3*c - 2*a^2*b^2*d)*e - (4*a^2*b^2*c - 3*a^3*b*d)*f)*h)*m)*x)*(b*x + a)^m/(b^4*m^4 + 10*b^4*m^3 + 35*b^4*m^2 + 50*b^4*m + 24*b^4)","B",0
120,0,0,0,0.800580," ","integrate((b*x+a)^m*(d*x+c)*(f*x+e)/(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d f x^{2} + c e + {\left(d e + c f\right)} x\right)} {\left(b x + a\right)}^{m}}{h x + g}, x\right)"," ",0,"integral((d*f*x^2 + c*e + (d*e + c*f)*x)*(b*x + a)^m/(h*x + g), x)","F",0
121,0,0,0,0.696807," ","integrate((b*x+a)^m*(d*x+c)/(f*x+e)/(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)} {\left(b x + a\right)}^{m}}{f h x^{2} + e g + {\left(f g + e h\right)} x}, x\right)"," ",0,"integral((d*x + c)*(b*x + a)^m/(f*h*x^2 + e*g + (f*g + e*h)*x), x)","F",0
122,0,0,0,0.985415," ","integrate((b*x+a)^m/(d*x+c)/(f*x+e)/(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m}}{d f h x^{3} + c e g + {\left(d f g + {\left(d e + c f\right)} h\right)} x^{2} + {\left(c e h + {\left(d e + c f\right)} g\right)} x}, x\right)"," ",0,"integral((b*x + a)^m/(d*f*h*x^3 + c*e*g + (d*f*g + (d*e + c*f)*h)*x^2 + (c*e*h + (d*e + c*f)*g)*x), x)","F",0
123,0,0,0,0.736492," ","integrate(x^m*(f*x+e)^n/(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{n} x^{m}}{b d x^{2} + a c + {\left(b c + a d\right)} x}, x\right)"," ",0,"integral((f*x + e)^n*x^m/(b*d*x^2 + a*c + (b*c + a*d)*x), x)","F",0
124,0,0,0,1.039236," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left({\left(f h x^{2} + e g + {\left(f g + e h\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n}, x\right)"," ",0,"integral((f*h*x^2 + e*g + (f*g + e*h)*x)*(b*x + a)^m*(d*x + c)^n, x)","F",0
125,0,0,0,1.019664," ","integrate((b*x+a)^m*(d*x+c)^(1-m)*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left({\left(f h x^{2} + e g + {\left(f g + e h\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m + 1}, x\right)"," ",0,"integral((f*h*x^2 + e*g + (f*g + e*h)*x)*(b*x + a)^m*(d*x + c)^(-m + 1), x)","F",0
126,0,0,0,1.075041," ","integrate((b*x+a)^m*(f*x+e)*(h*x+g)/((d*x+c)^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f h x^{2} + e g + {\left(f g + e h\right)} x\right)} {\left(b x + a\right)}^{m}}{{\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((f*h*x^2 + e*g + (f*g + e*h)*x)*(b*x + a)^m/(d*x + c)^m, x)","F",0
127,0,0,0,0.899759," ","integrate((b*x+a)^m*(d*x+c)^(-1-m)*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left({\left(f h x^{2} + e g + {\left(f g + e h\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 1}, x\right)"," ",0,"integral((f*h*x^2 + e*g + (f*g + e*h)*x)*(b*x + a)^m*(d*x + c)^(-m - 1), x)","F",0
128,0,0,0,1.125257," ","integrate((b*x+a)^m*(d*x+c)^(-2-m)*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left({\left(f h x^{2} + e g + {\left(f g + e h\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 2}, x\right)"," ",0,"integral((f*h*x^2 + e*g + (f*g + e*h)*x)*(b*x + a)^m*(d*x + c)^(-m - 2), x)","F",0
129,0,0,0,1.192392," ","integrate((b*x+a)^m*(d*x+c)^(-3-m)*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left({\left(f h x^{2} + e g + {\left(f g + e h\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 3}, x\right)"," ",0,"integral((f*h*x^2 + e*g + (f*g + e*h)*x)*(b*x + a)^m*(d*x + c)^(-m - 3), x)","F",0
130,1,1659,0,0.927464," ","integrate((b*x+a)^m*(d*x+c)^(-4-m)*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","\frac{{\left({\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e g m^{2} + {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f h m^{2} + {\left(2 \, b^{3} d^{3} e + {\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} f\right)} g + {\left({\left(b^{3} c d^{2} - 3 \, a b^{2} d^{3}\right)} e + 2 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} f\right)} h + {\left({\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} f g + {\left({\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e + {\left(3 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 5 \, a^{2} b d^{3}\right)} f\right)} h\right)} m\right)} x^{4} + {\left({\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} f g + {\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} f\right)} h\right)} m^{2} + 4 \, {\left(2 \, b^{3} c d^{2} e + {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2}\right)} f\right)} g + 2 \, {\left(2 \, {\left(b^{3} c^{2} d - 3 \, a b^{2} c d^{2}\right)} e + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} f\right)} h + {\left({\left(2 \, {\left(b^{3} c d^{2} - a b^{2} d^{3}\right)} e + {\left(5 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} f\right)} g + {\left({\left(5 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + 3 \, a^{2} b d^{3}\right)} e + {\left(3 \, b^{3} c^{3} - 7 \, a b^{2} c^{2} d - a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} f\right)} h\right)} m\right)} x^{3} + {\left({\left({\left({\left(b^{3} c^{2} d - 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e + {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} f\right)} g + {\left({\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f\right)} h\right)} m^{2} + 3 \, {\left(4 \, b^{3} c^{2} d e + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} f\right)} g + 3 \, {\left(4 \, a^{3} c d^{2} f + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e\right)} h + {\left({\left({\left(7 \, b^{3} c^{2} d - 8 \, a b^{2} c d^{2} + a^{2} b d^{3}\right)} e + 4 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} f\right)} g + {\left(4 \, {\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e + {\left(a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 7 \, a^{3} c d^{2}\right)} f\right)} h\right)} m\right)} x^{2} + {\left(2 \, {\left(3 \, a b^{2} c^{3} - 3 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e - {\left(3 \, a^{2} b c^{3} - a^{3} c^{2} d\right)} f\right)} g + {\left(2 \, a^{3} c^{3} f - {\left(3 \, a^{2} b c^{3} - a^{3} c^{2} d\right)} e\right)} h - {\left({\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} e h - {\left({\left(5 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 3 \, a^{3} c d^{2}\right)} e - {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} f\right)} g\right)} m + {\left({\left({\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} e h + {\left({\left(b^{3} c^{3} - a b^{2} c^{2} d - a^{2} b c d^{2} + a^{3} d^{3}\right)} e + {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} f\right)} g\right)} m^{2} + 2 \, {\left({\left(3 \, b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} e - 2 \, {\left(3 \, a^{2} b c^{2} d - a^{3} c d^{2}\right)} f\right)} g + 4 \, {\left(2 \, a^{3} c^{2} d f - {\left(3 \, a^{2} b c^{2} d - a^{3} c d^{2}\right)} e\right)} h + {\left({\left({\left(5 \, b^{3} c^{3} - a b^{2} c^{2} d - 7 \, a^{2} b c d^{2} + 3 \, a^{3} d^{3}\right)} e + {\left(3 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} f\right)} g + {\left({\left(3 \, a b^{2} c^{3} - 8 \, a^{2} b c^{2} d + 5 \, a^{3} c d^{2}\right)} e - 2 \, {\left(a^{2} b c^{3} - a^{3} c^{2} d\right)} f\right)} h\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 4}}{6 \, b^{3} c^{3} - 18 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} - 6 \, a^{3} d^{3} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m^{3} + 6 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m^{2} + 11 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} m}"," ",0,"((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e*g*m^2 + ((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*f*h*m^2 + (2*b^3*d^3*e + (b^3*c*d^2 - 3*a*b^2*d^3)*f)*g + ((b^3*c*d^2 - 3*a*b^2*d^3)*e + 2*(b^3*c^2*d - 3*a*b^2*c*d^2 + 3*a^2*b*d^3)*f)*h + ((b^3*c*d^2 - a*b^2*d^3)*f*g + ((b^3*c*d^2 - a*b^2*d^3)*e + (3*b^3*c^2*d - 8*a*b^2*c*d^2 + 5*a^2*b*d^3)*f)*h)*m)*x^4 + (((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*f*g + ((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*f)*h)*m^2 + 4*(2*b^3*c*d^2*e + (b^3*c^2*d - 3*a*b^2*c*d^2)*f)*g + 2*(2*(b^3*c^2*d - 3*a*b^2*c*d^2)*e + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 + 3*a^3*d^3)*f)*h + ((2*(b^3*c*d^2 - a*b^2*d^3)*e + (5*b^3*c^2*d - 8*a*b^2*c*d^2 + 3*a^2*b*d^3)*f)*g + ((5*b^3*c^2*d - 8*a*b^2*c*d^2 + 3*a^2*b*d^3)*e + (3*b^3*c^3 - 7*a*b^2*c^2*d - a^2*b*c*d^2 + 5*a^3*d^3)*f)*h)*m)*x^3 + ((((b^3*c^2*d - 2*a*b^2*c*d^2 + a^2*b*d^3)*e + (b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*f)*g + ((b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*f)*h)*m^2 + 3*(4*b^3*c^2*d*e + (b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*f)*g + 3*(4*a^3*c*d^2*f + (b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*e)*h + (((7*b^3*c^2*d - 8*a*b^2*c*d^2 + a^2*b*d^3)*e + 4*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*f)*g + (4*(b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e + (a*b^2*c^3 - 8*a^2*b*c^2*d + 7*a^3*c*d^2)*f)*h)*m)*x^2 + (2*(3*a*b^2*c^3 - 3*a^2*b*c^2*d + a^3*c*d^2)*e - (3*a^2*b*c^3 - a^3*c^2*d)*f)*g + (2*a^3*c^3*f - (3*a^2*b*c^3 - a^3*c^2*d)*e)*h - ((a^2*b*c^3 - a^3*c^2*d)*e*h - ((5*a*b^2*c^3 - 8*a^2*b*c^2*d + 3*a^3*c*d^2)*e - (a^2*b*c^3 - a^3*c^2*d)*f)*g)*m + (((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*e*h + ((b^3*c^3 - a*b^2*c^2*d - a^2*b*c*d^2 + a^3*d^3)*e + (a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*f)*g)*m^2 + 2*((3*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*e - 2*(3*a^2*b*c^2*d - a^3*c*d^2)*f)*g + 4*(2*a^3*c^2*d*f - (3*a^2*b*c^2*d - a^3*c*d^2)*e)*h + (((5*b^3*c^3 - a*b^2*c^2*d - 7*a^2*b*c*d^2 + 3*a^3*d^3)*e + (3*a*b^2*c^3 - 8*a^2*b*c^2*d + 5*a^3*c*d^2)*f)*g + ((3*a*b^2*c^3 - 8*a^2*b*c^2*d + 5*a^3*c*d^2)*e - 2*(a^2*b*c^3 - a^3*c^2*d)*f)*h)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 4)/(6*b^3*c^3 - 18*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 6*a^3*d^3 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m^3 + 6*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m^2 + 11*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*m)","B",0
131,1,3441,0,1.180148," ","integrate((b*x+a)^m*(d*x+c)^(-5-m)*(f*x+e)*(h*x+g),x, algorithm=""fricas"")","\frac{{\left({\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)} e g m^{3} + {\left({\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} f h m^{2} + 2 \, {\left(3 \, b^{4} d^{4} e + {\left(b^{4} c d^{3} - 4 \, a b^{3} d^{4}\right)} f\right)} g + 2 \, {\left({\left(b^{4} c d^{3} - 4 \, a b^{3} d^{4}\right)} e + {\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3} + 6 \, a^{2} b^{2} d^{4}\right)} f\right)} h + {\left(2 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} f g + {\left(2 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e + {\left(3 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} + 7 \, a^{2} b^{2} d^{4}\right)} f\right)} h\right)} m\right)} x^{5} + {\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)} f h m^{3} + {\left(2 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} f g + {\left(2 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e + {\left(8 \, b^{4} c^{3} d - 23 \, a b^{3} c^{2} d^{2} + 22 \, a^{2} b^{2} c d^{3} - 7 \, a^{3} b d^{4}\right)} f\right)} h\right)} m^{2} + 10 \, {\left(3 \, b^{4} c d^{3} e + {\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3}\right)} f\right)} g + 10 \, {\left({\left(b^{4} c^{2} d^{2} - 4 \, a b^{3} c d^{3}\right)} e + {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3}\right)} f\right)} h + {\left(2 \, {\left(3 \, {\left(b^{4} c d^{3} - a b^{3} d^{4}\right)} e + 2 \, {\left(3 \, b^{4} c^{2} d^{2} - 5 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} f\right)} g + {\left(4 \, {\left(3 \, b^{4} c^{2} d^{2} - 5 \, a b^{3} c d^{3} + 2 \, a^{2} b^{2} d^{4}\right)} e + {\left(17 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 55 \, a^{2} b^{2} c d^{3} - 12 \, a^{3} b d^{4}\right)} f\right)} h\right)} m\right)} x^{4} + {\left({\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)} f g + {\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)} e + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} f\right)} h\right)} m^{3} + {\left({\left(3 \, {\left(b^{4} c^{2} d^{2} - 2 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e + 5 \, {\left(2 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} + 4 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} f\right)} g + {\left(5 \, {\left(2 \, b^{4} c^{3} d - 5 \, a b^{3} c^{2} d^{2} + 4 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e + {\left(7 \, b^{4} c^{4} - 16 \, a b^{3} c^{3} d + 3 \, a^{2} b^{2} c^{2} d^{2} + 14 \, a^{3} b c d^{3} - 8 \, a^{4} d^{4}\right)} f\right)} h\right)} m^{2} + 20 \, {\left(3 \, b^{4} c^{2} d^{2} e + {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2}\right)} f\right)} g + 4 \, {\left(5 \, {\left(b^{4} c^{3} d - 4 \, a b^{3} c^{2} d^{2}\right)} e + {\left(2 \, b^{4} c^{4} - 8 \, a b^{3} c^{3} d + 12 \, a^{2} b^{2} c^{2} d^{2} + 12 \, a^{3} b c d^{3} - 3 \, a^{4} d^{4}\right)} f\right)} h + {\left({\left(3 \, {\left(9 \, b^{4} c^{2} d^{2} - 10 \, a b^{3} c d^{3} + a^{2} b^{2} d^{4}\right)} e + {\left(29 \, b^{4} c^{3} d - 66 \, a b^{3} c^{2} d^{2} + 41 \, a^{2} b^{2} c d^{3} - 4 \, a^{3} b d^{4}\right)} f\right)} g + {\left({\left(29 \, b^{4} c^{3} d - 66 \, a b^{3} c^{2} d^{2} + 41 \, a^{2} b^{2} c d^{3} - 4 \, a^{3} b d^{4}\right)} e + {\left(14 \, b^{4} c^{4} - 46 \, a b^{3} c^{3} d + 15 \, a^{2} b^{2} c^{2} d^{2} + 36 \, a^{3} b c d^{3} - 19 \, a^{4} d^{4}\right)} f\right)} h\right)} m\right)} x^{3} - {\left({\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} e h - {\left(3 \, {\left(3 \, a b^{3} c^{4} - 8 \, a^{2} b^{2} c^{3} d + 7 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3}\right)} e - {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} f\right)} g\right)} m^{2} + {\left({\left({\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)} e + {\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} f\right)} g + {\left({\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e + {\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)} f\right)} h\right)} m^{3} + {\left({\left(3 \, {\left(4 \, b^{4} c^{3} d - 9 \, a b^{3} c^{2} d^{2} + 6 \, a^{2} b^{2} c d^{3} - a^{3} b d^{4}\right)} e + {\left(8 \, b^{4} c^{4} - 14 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} f\right)} g + {\left({\left(8 \, b^{4} c^{4} - 14 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 16 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} e + 5 \, {\left(a b^{3} c^{4} - 4 \, a^{2} b^{2} c^{3} d + 5 \, a^{3} b c^{2} d^{2} - 2 \, a^{4} c d^{3}\right)} f\right)} h\right)} m^{2} + 4 \, {\left(15 \, b^{4} c^{3} d e + {\left(3 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 8 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} f\right)} g + 4 \, {\left({\left(3 \, b^{4} c^{4} - 12 \, a b^{3} c^{3} d - 12 \, a^{2} b^{2} c^{2} d^{2} + 8 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} e + 5 \, {\left(4 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} f\right)} h + {\left({\left({\left(47 \, b^{4} c^{3} d - 60 \, a b^{3} c^{2} d^{2} + 15 \, a^{2} b^{2} c d^{3} - 2 \, a^{3} b d^{4}\right)} e + {\left(19 \, b^{4} c^{4} - 36 \, a b^{3} c^{3} d - 15 \, a^{2} b^{2} c^{2} d^{2} + 46 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} f\right)} g + {\left({\left(19 \, b^{4} c^{4} - 36 \, a b^{3} c^{3} d - 15 \, a^{2} b^{2} c^{2} d^{2} + 46 \, a^{3} b c d^{3} - 14 \, a^{4} d^{4}\right)} e + {\left(4 \, a b^{3} c^{4} - 41 \, a^{2} b^{2} c^{3} d + 66 \, a^{3} b c^{2} d^{2} - 29 \, a^{4} c d^{3}\right)} f\right)} h\right)} m\right)} x^{2} + 2 \, {\left(3 \, {\left(4 \, a b^{3} c^{4} - 6 \, a^{2} b^{2} c^{3} d + 4 \, a^{3} b c^{2} d^{2} - a^{4} c d^{3}\right)} e - {\left(6 \, a^{2} b^{2} c^{4} - 4 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} f\right)} g - 2 \, {\left({\left(6 \, a^{2} b^{2} c^{4} - 4 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} e - {\left(4 \, a^{3} b c^{4} - a^{4} c^{3} d\right)} f\right)} h + {\left({\left({\left(26 \, a b^{3} c^{4} - 57 \, a^{2} b^{2} c^{3} d + 42 \, a^{3} b c^{2} d^{2} - 11 \, a^{4} c d^{3}\right)} e - {\left(7 \, a^{2} b^{2} c^{4} - 10 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f\right)} g - {\left({\left(7 \, a^{2} b^{2} c^{4} - 10 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} e - 2 \, {\left(a^{3} b c^{4} - a^{4} c^{3} d\right)} f\right)} h\right)} m + {\left({\left({\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)} e h + {\left({\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + 2 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e + {\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)} f\right)} g\right)} m^{3} + {\left({\left(3 \, {\left(3 \, b^{4} c^{4} - 4 \, a b^{3} c^{3} d - 3 \, a^{2} b^{2} c^{2} d^{2} + 6 \, a^{3} b c d^{3} - 2 \, a^{4} d^{4}\right)} e + {\left(7 \, a b^{3} c^{4} - 22 \, a^{2} b^{2} c^{3} d + 23 \, a^{3} b c^{2} d^{2} - 8 \, a^{4} c d^{3}\right)} f\right)} g + {\left({\left(7 \, a b^{3} c^{4} - 22 \, a^{2} b^{2} c^{3} d + 23 \, a^{3} b c^{2} d^{2} - 8 \, a^{4} c d^{3}\right)} e - 2 \, {\left(a^{2} b^{2} c^{4} - 2 \, a^{3} b c^{3} d + a^{4} c^{2} d^{2}\right)} f\right)} h\right)} m^{2} + 2 \, {\left(3 \, {\left(4 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} e - 5 \, {\left(6 \, a^{2} b^{2} c^{3} d - 4 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} f\right)} g - 10 \, {\left({\left(6 \, a^{2} b^{2} c^{3} d - 4 \, a^{3} b c^{2} d^{2} + a^{4} c d^{3}\right)} e - {\left(4 \, a^{3} b c^{3} d - a^{4} c^{2} d^{2}\right)} f\right)} h + {\left({\left({\left(26 \, b^{4} c^{4} - 10 \, a b^{3} c^{3} d - 45 \, a^{2} b^{2} c^{2} d^{2} + 40 \, a^{3} b c d^{3} - 11 \, a^{4} d^{4}\right)} e + {\left(12 \, a b^{3} c^{4} - 55 \, a^{2} b^{2} c^{3} d + 60 \, a^{3} b c^{2} d^{2} - 17 \, a^{4} c d^{3}\right)} f\right)} g + {\left({\left(12 \, a b^{3} c^{4} - 55 \, a^{2} b^{2} c^{3} d + 60 \, a^{3} b c^{2} d^{2} - 17 \, a^{4} c d^{3}\right)} e - 4 \, {\left(2 \, a^{2} b^{2} c^{4} - 5 \, a^{3} b c^{3} d + 3 \, a^{4} c^{2} d^{2}\right)} f\right)} h\right)} m\right)} x\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{-m - 5}}{24 \, b^{4} c^{4} - 96 \, a b^{3} c^{3} d + 144 \, a^{2} b^{2} c^{2} d^{2} - 96 \, a^{3} b c d^{3} + 24 \, a^{4} d^{4} + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{4} + 10 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{3} + 35 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m^{2} + 50 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} m}"," ",0,"((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)*e*g*m^3 + ((b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*f*h*m^2 + 2*(3*b^4*d^4*e + (b^4*c*d^3 - 4*a*b^3*d^4)*f)*g + 2*((b^4*c*d^3 - 4*a*b^3*d^4)*e + (b^4*c^2*d^2 - 4*a*b^3*c*d^3 + 6*a^2*b^2*d^4)*f)*h + (2*(b^4*c*d^3 - a*b^3*d^4)*f*g + (2*(b^4*c*d^3 - a*b^3*d^4)*e + (3*b^4*c^2*d^2 - 10*a*b^3*c*d^3 + 7*a^2*b^2*d^4)*f)*h)*m)*x^5 + ((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)*f*h*m^3 + (2*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*f*g + (2*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e + (8*b^4*c^3*d - 23*a*b^3*c^2*d^2 + 22*a^2*b^2*c*d^3 - 7*a^3*b*d^4)*f)*h)*m^2 + 10*(3*b^4*c*d^3*e + (b^4*c^2*d^2 - 4*a*b^3*c*d^3)*f)*g + 10*((b^4*c^2*d^2 - 4*a*b^3*c*d^3)*e + (b^4*c^3*d - 4*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3)*f)*h + (2*(3*(b^4*c*d^3 - a*b^3*d^4)*e + 2*(3*b^4*c^2*d^2 - 5*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*f)*g + (4*(3*b^4*c^2*d^2 - 5*a*b^3*c*d^3 + 2*a^2*b^2*d^4)*e + (17*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 55*a^2*b^2*c*d^3 - 12*a^3*b*d^4)*f)*h)*m)*x^4 + (((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)*f*g + ((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)*e + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*f)*h)*m^3 + ((3*(b^4*c^2*d^2 - 2*a*b^3*c*d^3 + a^2*b^2*d^4)*e + 5*(2*b^4*c^3*d - 5*a*b^3*c^2*d^2 + 4*a^2*b^2*c*d^3 - a^3*b*d^4)*f)*g + (5*(2*b^4*c^3*d - 5*a*b^3*c^2*d^2 + 4*a^2*b^2*c*d^3 - a^3*b*d^4)*e + (7*b^4*c^4 - 16*a*b^3*c^3*d + 3*a^2*b^2*c^2*d^2 + 14*a^3*b*c*d^3 - 8*a^4*d^4)*f)*h)*m^2 + 20*(3*b^4*c^2*d^2*e + (b^4*c^3*d - 4*a*b^3*c^2*d^2)*f)*g + 4*(5*(b^4*c^3*d - 4*a*b^3*c^2*d^2)*e + (2*b^4*c^4 - 8*a*b^3*c^3*d + 12*a^2*b^2*c^2*d^2 + 12*a^3*b*c*d^3 - 3*a^4*d^4)*f)*h + ((3*(9*b^4*c^2*d^2 - 10*a*b^3*c*d^3 + a^2*b^2*d^4)*e + (29*b^4*c^3*d - 66*a*b^3*c^2*d^2 + 41*a^2*b^2*c*d^3 - 4*a^3*b*d^4)*f)*g + ((29*b^4*c^3*d - 66*a*b^3*c^2*d^2 + 41*a^2*b^2*c*d^3 - 4*a^3*b*d^4)*e + (14*b^4*c^4 - 46*a*b^3*c^3*d + 15*a^2*b^2*c^2*d^2 + 36*a^3*b*c*d^3 - 19*a^4*d^4)*f)*h)*m)*x^3 - ((a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*e*h - (3*(3*a*b^3*c^4 - 8*a^2*b^2*c^3*d + 7*a^3*b*c^2*d^2 - 2*a^4*c*d^3)*e - (a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*f)*g)*m^2 + ((((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)*e + (b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*f)*g + ((b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*e + (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)*f)*h)*m^3 + ((3*(4*b^4*c^3*d - 9*a*b^3*c^2*d^2 + 6*a^2*b^2*c*d^3 - a^3*b*d^4)*e + (8*b^4*c^4 - 14*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 - 7*a^4*d^4)*f)*g + ((8*b^4*c^4 - 14*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 16*a^3*b*c*d^3 - 7*a^4*d^4)*e + 5*(a*b^3*c^4 - 4*a^2*b^2*c^3*d + 5*a^3*b*c^2*d^2 - 2*a^4*c*d^3)*f)*h)*m^2 + 4*(15*b^4*c^3*d*e + (3*b^4*c^4 - 12*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 8*a^3*b*c*d^3 - 2*a^4*d^4)*f)*g + 4*((3*b^4*c^4 - 12*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 8*a^3*b*c*d^3 - 2*a^4*d^4)*e + 5*(4*a^3*b*c^2*d^2 - a^4*c*d^3)*f)*h + (((47*b^4*c^3*d - 60*a*b^3*c^2*d^2 + 15*a^2*b^2*c*d^3 - 2*a^3*b*d^4)*e + (19*b^4*c^4 - 36*a*b^3*c^3*d - 15*a^2*b^2*c^2*d^2 + 46*a^3*b*c*d^3 - 14*a^4*d^4)*f)*g + ((19*b^4*c^4 - 36*a*b^3*c^3*d - 15*a^2*b^2*c^2*d^2 + 46*a^3*b*c*d^3 - 14*a^4*d^4)*e + (4*a*b^3*c^4 - 41*a^2*b^2*c^3*d + 66*a^3*b*c^2*d^2 - 29*a^4*c*d^3)*f)*h)*m)*x^2 + 2*(3*(4*a*b^3*c^4 - 6*a^2*b^2*c^3*d + 4*a^3*b*c^2*d^2 - a^4*c*d^3)*e - (6*a^2*b^2*c^4 - 4*a^3*b*c^3*d + a^4*c^2*d^2)*f)*g - 2*((6*a^2*b^2*c^4 - 4*a^3*b*c^3*d + a^4*c^2*d^2)*e - (4*a^3*b*c^4 - a^4*c^3*d)*f)*h + (((26*a*b^3*c^4 - 57*a^2*b^2*c^3*d + 42*a^3*b*c^2*d^2 - 11*a^4*c*d^3)*e - (7*a^2*b^2*c^4 - 10*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f)*g - ((7*a^2*b^2*c^4 - 10*a^3*b*c^3*d + 3*a^4*c^2*d^2)*e - 2*(a^3*b*c^4 - a^4*c^3*d)*f)*h)*m + (((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)*e*h + ((b^4*c^4 - 2*a*b^3*c^3*d + 2*a^3*b*c*d^3 - a^4*d^4)*e + (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)*f)*g)*m^3 + ((3*(3*b^4*c^4 - 4*a*b^3*c^3*d - 3*a^2*b^2*c^2*d^2 + 6*a^3*b*c*d^3 - 2*a^4*d^4)*e + (7*a*b^3*c^4 - 22*a^2*b^2*c^3*d + 23*a^3*b*c^2*d^2 - 8*a^4*c*d^3)*f)*g + ((7*a*b^3*c^4 - 22*a^2*b^2*c^3*d + 23*a^3*b*c^2*d^2 - 8*a^4*c*d^3)*e - 2*(a^2*b^2*c^4 - 2*a^3*b*c^3*d + a^4*c^2*d^2)*f)*h)*m^2 + 2*(3*(4*b^4*c^4 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*e - 5*(6*a^2*b^2*c^3*d - 4*a^3*b*c^2*d^2 + a^4*c*d^3)*f)*g - 10*((6*a^2*b^2*c^3*d - 4*a^3*b*c^2*d^2 + a^4*c*d^3)*e - (4*a^3*b*c^3*d - a^4*c^2*d^2)*f)*h + (((26*b^4*c^4 - 10*a*b^3*c^3*d - 45*a^2*b^2*c^2*d^2 + 40*a^3*b*c*d^3 - 11*a^4*d^4)*e + (12*a*b^3*c^4 - 55*a^2*b^2*c^3*d + 60*a^3*b*c^2*d^2 - 17*a^4*c*d^3)*f)*g + ((12*a*b^3*c^4 - 55*a^2*b^2*c^3*d + 60*a^3*b*c^2*d^2 - 17*a^4*c*d^3)*e - 4*(2*a^2*b^2*c^4 - 5*a^3*b*c^3*d + 3*a^4*c^2*d^2)*f)*h)*m)*x)*(b*x + a)^m*(d*x + c)^(-m - 5)/(24*b^4*c^4 - 96*a*b^3*c^3*d + 144*a^2*b^2*c^2*d^2 - 96*a^3*b*c*d^3 + 24*a^4*d^4 + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^4 + 10*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^3 + 35*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m^2 + 50*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*m)","B",0
132,0,0,0,0.952779," ","integrate((b*x+a)^3*(d*x+c)^(-4-m)*(f*x+e)^m*(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} h x^{4} + a^{3} g + {\left(b^{3} g + 3 \, a b^{2} h\right)} x^{3} + 3 \, {\left(a b^{2} g + a^{2} b h\right)} x^{2} + {\left(3 \, a^{2} b g + a^{3} h\right)} x\right)} {\left(d x + c\right)}^{-m - 4} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b^3*h*x^4 + a^3*g + (b^3*g + 3*a*b^2*h)*x^3 + 3*(a*b^2*g + a^2*b*h)*x^2 + (3*a^2*b*g + a^3*h)*x)*(d*x + c)^(-m - 4)*(f*x + e)^m, x)","F",0
133,0,0,0,0.758610," ","integrate((b*x+a)^2*(d*x+c)^(-4-m)*(f*x+e)^m*(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} h x^{3} + a^{2} g + {\left(b^{2} g + 2 \, a b h\right)} x^{2} + {\left(2 \, a b g + a^{2} h\right)} x\right)} {\left(d x + c\right)}^{-m - 4} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b^2*h*x^3 + a^2*g + (b^2*g + 2*a*b*h)*x^2 + (2*a*b*g + a^2*h)*x)*(d*x + c)^(-m - 4)*(f*x + e)^m, x)","F",0
134,1,1608,0,0.705092," ","integrate((b*x+a)*(d*x+c)^(-4-m)*(f*x+e)^m*(h*x+g),x, algorithm=""fricas"")","-\frac{{\left({\left({\left(b d^{3} e^{2} f - 2 \, b c d^{2} e f^{2} + b c^{2} d f^{3}\right)} h m^{2} - {\left(3 \, b d^{3} e f^{2} - {\left(b c d^{2} + 2 \, a d^{3}\right)} f^{3}\right)} g + {\left(6 \, b d^{3} e^{2} f - 3 \, {\left(2 \, b c d^{2} + a d^{3}\right)} e f^{2} + {\left(2 \, b c^{2} d + a c d^{2}\right)} f^{3}\right)} h - {\left({\left(b d^{3} e f^{2} - b c d^{2} f^{3}\right)} g - {\left(5 \, b d^{3} e^{2} f - {\left(8 \, b c d^{2} + a d^{3}\right)} e f^{2} + {\left(3 \, b c^{2} d + a c d^{2}\right)} f^{3}\right)} h\right)} m\right)} x^{4} + {\left(a c d^{2} e^{3} - 2 \, a c^{2} d e^{2} f + a c^{3} e f^{2}\right)} g m^{2} + {\left({\left({\left(b d^{3} e^{2} f - 2 \, b c d^{2} e f^{2} + b c^{2} d f^{3}\right)} g + {\left(b d^{3} e^{3} - {\left(b c d^{2} - a d^{3}\right)} e^{2} f - {\left(b c^{2} d + 2 \, a c d^{2}\right)} e f^{2} + {\left(b c^{3} + a c^{2} d\right)} f^{3}\right)} h\right)} m^{2} - 4 \, {\left(3 \, b c d^{2} e f^{2} - {\left(b c^{2} d + 2 \, a c d^{2}\right)} f^{3}\right)} g + 2 \, {\left(3 \, b d^{3} e^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} d + 2 \, a c d^{2}\right)} e f^{2} + {\left(b c^{3} + 2 \, a c^{2} d\right)} f^{3}\right)} h + {\left({\left(3 \, b d^{3} e^{2} f - 2 \, {\left(4 \, b c d^{2} + a d^{3}\right)} e f^{2} + {\left(5 \, b c^{2} d + 2 \, a c d^{2}\right)} f^{3}\right)} g + {\left(5 \, b d^{3} e^{3} - {\left(b c d^{2} - 3 \, a d^{3}\right)} e^{2} f - {\left(7 \, b c^{2} d + 8 \, a c d^{2}\right)} e f^{2} + {\left(3 \, b c^{3} + 5 \, a c^{2} d\right)} f^{3}\right)} h\right)} m\right)} x^{3} + {\left({\left({\left(b d^{3} e^{3} - {\left(b c d^{2} - a d^{3}\right)} e^{2} f - {\left(b c^{2} d + 2 \, a c d^{2}\right)} e f^{2} + {\left(b c^{3} + a c^{2} d\right)} f^{3}\right)} g + {\left(a c^{3} f^{3} + {\left(b c d^{2} + a d^{3}\right)} e^{3} - {\left(2 \, b c^{2} d + a c d^{2}\right)} e^{2} f + {\left(b c^{3} - a c^{2} d\right)} e f^{2}\right)} h\right)} m^{2} + 3 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + {\left(b c^{3} + 4 \, a c^{2} d\right)} f^{3}\right)} g - 3 \, {\left(3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3} - {\left(4 \, b c d^{2} + a d^{3}\right)} e^{3}\right)} h + {\left({\left(4 \, b d^{3} e^{3} - {\left(4 \, b c d^{2} - a d^{3}\right)} e^{2} f - 4 \, {\left(b c^{2} d + 2 \, a c d^{2}\right)} e f^{2} + {\left(4 \, b c^{3} + 7 \, a c^{2} d\right)} f^{3}\right)} g + {\left(4 \, a c^{3} f^{3} + {\left(7 \, b c d^{2} + 4 \, a d^{3}\right)} e^{3} - 4 \, {\left(2 \, b c^{2} d + a c d^{2}\right)} e^{2} f + {\left(b c^{3} - 4 \, a c^{2} d\right)} e f^{2}\right)} h\right)} m\right)} x^{2} + {\left(6 \, a c^{3} e f^{2} + {\left(b c^{2} d + 2 \, a c d^{2}\right)} e^{3} - 3 \, {\left(b c^{3} + 2 \, a c^{2} d\right)} e^{2} f\right)} g - {\left(3 \, a c^{3} e^{2} f - {\left(2 \, b c^{3} + a c^{2} d\right)} e^{3}\right)} h + {\left({\left(5 \, a c^{3} e f^{2} + {\left(b c^{2} d + 3 \, a c d^{2}\right)} e^{3} - {\left(b c^{3} + 8 \, a c^{2} d\right)} e^{2} f\right)} g + {\left(a c^{2} d e^{3} - a c^{3} e^{2} f\right)} h\right)} m + {\left({\left({\left(a c^{3} f^{3} + {\left(b c d^{2} + a d^{3}\right)} e^{3} - {\left(2 \, b c^{2} d + a c d^{2}\right)} e^{2} f + {\left(b c^{3} - a c^{2} d\right)} e f^{2}\right)} g + {\left(a c d^{2} e^{3} - 2 \, a c^{2} d e^{2} f + a c^{3} e f^{2}\right)} h\right)} m^{2} + 2 \, {\left(3 \, a c^{2} d e f^{2} + 3 \, a c^{3} f^{3} + {\left(2 \, b c d^{2} + a d^{3}\right)} e^{3} - 3 \, {\left(2 \, b c^{2} d + a c d^{2}\right)} e^{2} f\right)} g - 4 \, {\left(3 \, a c^{2} d e^{2} f - {\left(2 \, b c^{2} d + a c d^{2}\right)} e^{3}\right)} h + {\left({\left(5 \, a c^{3} f^{3} + {\left(5 \, b c d^{2} + 3 \, a d^{3}\right)} e^{3} - {\left(8 \, b c^{2} d + 7 \, a c d^{2}\right)} e^{2} f + {\left(3 \, b c^{3} - a c^{2} d\right)} e f^{2}\right)} g + {\left(3 \, a c^{3} e f^{2} + {\left(2 \, b c^{2} d + 5 \, a c d^{2}\right)} e^{3} - 2 \, {\left(b c^{3} + 4 \, a c^{2} d\right)} e^{2} f\right)} h\right)} m\right)} x\right)} {\left(d x + c\right)}^{-m - 4} {\left(f x + e\right)}^{m}}{6 \, d^{3} e^{3} - 18 \, c d^{2} e^{2} f + 18 \, c^{2} d e f^{2} - 6 \, c^{3} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} m^{3} + 6 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} m^{2} + 11 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} m}"," ",0,"-(((b*d^3*e^2*f - 2*b*c*d^2*e*f^2 + b*c^2*d*f^3)*h*m^2 - (3*b*d^3*e*f^2 - (b*c*d^2 + 2*a*d^3)*f^3)*g + (6*b*d^3*e^2*f - 3*(2*b*c*d^2 + a*d^3)*e*f^2 + (2*b*c^2*d + a*c*d^2)*f^3)*h - ((b*d^3*e*f^2 - b*c*d^2*f^3)*g - (5*b*d^3*e^2*f - (8*b*c*d^2 + a*d^3)*e*f^2 + (3*b*c^2*d + a*c*d^2)*f^3)*h)*m)*x^4 + (a*c*d^2*e^3 - 2*a*c^2*d*e^2*f + a*c^3*e*f^2)*g*m^2 + (((b*d^3*e^2*f - 2*b*c*d^2*e*f^2 + b*c^2*d*f^3)*g + (b*d^3*e^3 - (b*c*d^2 - a*d^3)*e^2*f - (b*c^2*d + 2*a*c*d^2)*e*f^2 + (b*c^3 + a*c^2*d)*f^3)*h)*m^2 - 4*(3*b*c*d^2*e*f^2 - (b*c^2*d + 2*a*c*d^2)*f^3)*g + 2*(3*b*d^3*e^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2*d + 2*a*c*d^2)*e*f^2 + (b*c^3 + 2*a*c^2*d)*f^3)*h + ((3*b*d^3*e^2*f - 2*(4*b*c*d^2 + a*d^3)*e*f^2 + (5*b*c^2*d + 2*a*c*d^2)*f^3)*g + (5*b*d^3*e^3 - (b*c*d^2 - 3*a*d^3)*e^2*f - (7*b*c^2*d + 8*a*c*d^2)*e*f^2 + (3*b*c^3 + 5*a*c^2*d)*f^3)*h)*m)*x^3 + (((b*d^3*e^3 - (b*c*d^2 - a*d^3)*e^2*f - (b*c^2*d + 2*a*c*d^2)*e*f^2 + (b*c^3 + a*c^2*d)*f^3)*g + (a*c^3*f^3 + (b*c*d^2 + a*d^3)*e^3 - (2*b*c^2*d + a*c*d^2)*e^2*f + (b*c^3 - a*c^2*d)*e*f^2)*h)*m^2 + 3*(b*d^3*e^3 - 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + (b*c^3 + 4*a*c^2*d)*f^3)*g - 3*(3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3 - (4*b*c*d^2 + a*d^3)*e^3)*h + ((4*b*d^3*e^3 - (4*b*c*d^2 - a*d^3)*e^2*f - 4*(b*c^2*d + 2*a*c*d^2)*e*f^2 + (4*b*c^3 + 7*a*c^2*d)*f^3)*g + (4*a*c^3*f^3 + (7*b*c*d^2 + 4*a*d^3)*e^3 - 4*(2*b*c^2*d + a*c*d^2)*e^2*f + (b*c^3 - 4*a*c^2*d)*e*f^2)*h)*m)*x^2 + (6*a*c^3*e*f^2 + (b*c^2*d + 2*a*c*d^2)*e^3 - 3*(b*c^3 + 2*a*c^2*d)*e^2*f)*g - (3*a*c^3*e^2*f - (2*b*c^3 + a*c^2*d)*e^3)*h + ((5*a*c^3*e*f^2 + (b*c^2*d + 3*a*c*d^2)*e^3 - (b*c^3 + 8*a*c^2*d)*e^2*f)*g + (a*c^2*d*e^3 - a*c^3*e^2*f)*h)*m + (((a*c^3*f^3 + (b*c*d^2 + a*d^3)*e^3 - (2*b*c^2*d + a*c*d^2)*e^2*f + (b*c^3 - a*c^2*d)*e*f^2)*g + (a*c*d^2*e^3 - 2*a*c^2*d*e^2*f + a*c^3*e*f^2)*h)*m^2 + 2*(3*a*c^2*d*e*f^2 + 3*a*c^3*f^3 + (2*b*c*d^2 + a*d^3)*e^3 - 3*(2*b*c^2*d + a*c*d^2)*e^2*f)*g - 4*(3*a*c^2*d*e^2*f - (2*b*c^2*d + a*c*d^2)*e^3)*h + ((5*a*c^3*f^3 + (5*b*c*d^2 + 3*a*d^3)*e^3 - (8*b*c^2*d + 7*a*c*d^2)*e^2*f + (3*b*c^3 - a*c^2*d)*e*f^2)*g + (3*a*c^3*e*f^2 + (2*b*c^2*d + 5*a*c*d^2)*e^3 - 2*(b*c^3 + 4*a*c^2*d)*e^2*f)*h)*m)*x)*(d*x + c)^(-m - 4)*(f*x + e)^m/(6*d^3*e^3 - 18*c*d^2*e^2*f + 18*c^2*d*e*f^2 - 6*c^3*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*m^3 + 6*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*m^2 + 11*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*m)","B",0
135,1,905,0,0.842001," ","integrate((d*x+c)^(-4-m)*(f*x+e)^m*(h*x+g),x, algorithm=""fricas"")","-\frac{{\left({\left(2 \, d^{3} f^{3} g - {\left(d^{3} e f^{2} - c d^{2} f^{3}\right)} h m - {\left(3 \, d^{3} e f^{2} - c d^{2} f^{3}\right)} h\right)} x^{4} + {\left(c d^{2} e^{3} - 2 \, c^{2} d e^{2} f + c^{3} e f^{2}\right)} g m^{2} + {\left(8 \, c d^{2} f^{3} g + {\left(d^{3} e^{2} f - 2 \, c d^{2} e f^{2} + c^{2} d f^{3}\right)} h m^{2} - 4 \, {\left(3 \, c d^{2} e f^{2} - c^{2} d f^{3}\right)} h - {\left(2 \, {\left(d^{3} e f^{2} - c d^{2} f^{3}\right)} g - {\left(3 \, d^{3} e^{2} f - 8 \, c d^{2} e f^{2} + 5 \, c^{2} d f^{3}\right)} h\right)} m\right)} x^{3} + {\left(12 \, c^{2} d f^{3} g + {\left({\left(d^{3} e^{2} f - 2 \, c d^{2} e f^{2} + c^{2} d f^{3}\right)} g + {\left(d^{3} e^{3} - c d^{2} e^{2} f - c^{2} d e f^{2} + c^{3} f^{3}\right)} h\right)} m^{2} + 3 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} h + {\left({\left(d^{3} e^{2} f - 8 \, c d^{2} e f^{2} + 7 \, c^{2} d f^{3}\right)} g + 4 \, {\left(d^{3} e^{3} - c d^{2} e^{2} f - c^{2} d e f^{2} + c^{3} f^{3}\right)} h\right)} m\right)} x^{2} + 2 \, {\left(c d^{2} e^{3} - 3 \, c^{2} d e^{2} f + 3 \, c^{3} e f^{2}\right)} g + {\left(c^{2} d e^{3} - 3 \, c^{3} e^{2} f\right)} h + {\left({\left(3 \, c d^{2} e^{3} - 8 \, c^{2} d e^{2} f + 5 \, c^{3} e f^{2}\right)} g + {\left(c^{2} d e^{3} - c^{3} e^{2} f\right)} h\right)} m + {\left({\left({\left(d^{3} e^{3} - c d^{2} e^{2} f - c^{2} d e f^{2} + c^{3} f^{3}\right)} g + {\left(c d^{2} e^{3} - 2 \, c^{2} d e^{2} f + c^{3} e f^{2}\right)} h\right)} m^{2} + 2 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} + 3 \, c^{3} f^{3}\right)} g + 4 \, {\left(c d^{2} e^{3} - 3 \, c^{2} d e^{2} f\right)} h + {\left({\left(3 \, d^{3} e^{3} - 7 \, c d^{2} e^{2} f - c^{2} d e f^{2} + 5 \, c^{3} f^{3}\right)} g + {\left(5 \, c d^{2} e^{3} - 8 \, c^{2} d e^{2} f + 3 \, c^{3} e f^{2}\right)} h\right)} m\right)} x\right)} {\left(d x + c\right)}^{-m - 4} {\left(f x + e\right)}^{m}}{6 \, d^{3} e^{3} - 18 \, c d^{2} e^{2} f + 18 \, c^{2} d e f^{2} - 6 \, c^{3} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} m^{3} + 6 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} m^{2} + 11 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} m}"," ",0,"-((2*d^3*f^3*g - (d^3*e*f^2 - c*d^2*f^3)*h*m - (3*d^3*e*f^2 - c*d^2*f^3)*h)*x^4 + (c*d^2*e^3 - 2*c^2*d*e^2*f + c^3*e*f^2)*g*m^2 + (8*c*d^2*f^3*g + (d^3*e^2*f - 2*c*d^2*e*f^2 + c^2*d*f^3)*h*m^2 - 4*(3*c*d^2*e*f^2 - c^2*d*f^3)*h - (2*(d^3*e*f^2 - c*d^2*f^3)*g - (3*d^3*e^2*f - 8*c*d^2*e*f^2 + 5*c^2*d*f^3)*h)*m)*x^3 + (12*c^2*d*f^3*g + ((d^3*e^2*f - 2*c*d^2*e*f^2 + c^2*d*f^3)*g + (d^3*e^3 - c*d^2*e^2*f - c^2*d*e*f^2 + c^3*f^3)*h)*m^2 + 3*(d^3*e^3 - 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*h + ((d^3*e^2*f - 8*c*d^2*e*f^2 + 7*c^2*d*f^3)*g + 4*(d^3*e^3 - c*d^2*e^2*f - c^2*d*e*f^2 + c^3*f^3)*h)*m)*x^2 + 2*(c*d^2*e^3 - 3*c^2*d*e^2*f + 3*c^3*e*f^2)*g + (c^2*d*e^3 - 3*c^3*e^2*f)*h + ((3*c*d^2*e^3 - 8*c^2*d*e^2*f + 5*c^3*e*f^2)*g + (c^2*d*e^3 - c^3*e^2*f)*h)*m + (((d^3*e^3 - c*d^2*e^2*f - c^2*d*e*f^2 + c^3*f^3)*g + (c*d^2*e^3 - 2*c^2*d*e^2*f + c^3*e*f^2)*h)*m^2 + 2*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 + 3*c^3*f^3)*g + 4*(c*d^2*e^3 - 3*c^2*d*e^2*f)*h + ((3*d^3*e^3 - 7*c*d^2*e^2*f - c^2*d*e*f^2 + 5*c^3*f^3)*g + (5*c*d^2*e^3 - 8*c^2*d*e^2*f + 3*c^3*e*f^2)*h)*m)*x)*(d*x + c)^(-m - 4)*(f*x + e)^m/(6*d^3*e^3 - 18*c*d^2*e^2*f + 18*c^2*d*e*f^2 - 6*c^3*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*m^3 + 6*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*m^2 + 11*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*m)","B",0
136,0,0,0,0.879381," ","integrate((B*x+A)*(d*x+c)^n*(f*x+e)^p/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}}{b x + a}, x\right)"," ",0,"integral((B*x + A)*(d*x + c)^n*(f*x + e)^p/(b*x + a), x)","F",0
137,0,0,0,0.829664," ","integrate((b*x+a)^m*(B*x+A)/((d*x+c)^m)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(b x + a\right)}^{m}}{{\left(f x + e\right)} {\left(d x + c\right)}^{m}}, x\right)"," ",0,"integral((B*x + A)*(b*x + a)^m/((f*x + e)*(d*x + c)^m), x)","F",0
138,0,0,0,0.839881," ","integrate((B*x+A)*(d*x+c)^n*(f*x+e)^p/(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x + A\right)} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}}{\sqrt{b x + a}}, x\right)"," ",0,"integral((B*x + A)*(d*x + c)^n*(f*x + e)^p/sqrt(b*x + a), x)","F",0
139,0,0,0,2.945787," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p*(h*x+g)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(h^{3} x^{3} + 3 \, g h^{2} x^{2} + 3 \, g^{2} h x + g^{3}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((h^3*x^3 + 3*g*h^2*x^2 + 3*g^2*h*x + g^3)*(b*x + a)^m*(d*x + c)^n*(f*x + e)^p, x)","F",0
140,0,0,0,2.456318," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p*(h*x+g)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(h^{2} x^{2} + 2 \, g h x + g^{2}\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((h^2*x^2 + 2*g*h*x + g^2)*(b*x + a)^m*(d*x + c)^n*(f*x + e)^p, x)","F",0
141,0,0,0,1.171802," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p*(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left({\left(h x + g\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((h*x + g)*(b*x + a)^m*(d*x + c)^n*(f*x + e)^p, x)","F",0
142,0,0,0,0.971398," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^p, x)","F",0
143,0,0,0,0.817130," ","integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p/(h*x+g),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{p}}{h x + g}, x\right)"," ",0,"integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^p/(h*x + g), x)","F",0
144,0,0,0,1.691746," ","integrate((b*x+a)^m*(B*x+A)*(d*x+c)^n*(f*x+e)^(-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n}, x\right)"," ",0,"integral((B*x + A)*(b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n), x)","F",0
145,0,0,0,1.760761," ","integrate((b*x+a)^m*(B*x+A)*(d*x+c)^n*(f*x+e)^(-1-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n - 1}, x\right)"," ",0,"integral((B*x + A)*(b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n - 1), x)","F",0
146,0,0,0,1.863029," ","integrate((b*x+a)^m*(B*x+A)*(d*x+c)^n*(f*x+e)^(-2-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n - 2}, x\right)"," ",0,"integral((B*x + A)*(b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n - 2), x)","F",0
147,0,0,0,2.463935," ","integrate((b*x+a)^m*(B*x+A)*(d*x+c)^n*(f*x+e)^(-3-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n - 3}, x\right)"," ",0,"integral((B*x + A)*(b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n - 3), x)","F",0
148,0,0,0,3.164294," ","integrate((b*x+a)^m*(B*x+A)*(d*x+c)^n*(f*x+e)^(-4-m-n),x, algorithm=""fricas"")","{\rm integral}\left({\left(B x + A\right)} {\left(b x + a\right)}^{m} {\left(d x + c\right)}^{n} {\left(f x + e\right)}^{-m - n - 4}, x\right)"," ",0,"integral((B*x + A)*(b*x + a)^m*(d*x + c)^n*(f*x + e)^(-m - n - 4), x)","F",0
149,1,78,0,0.884083," ","integrate(x*(c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{6 \, b d \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right) + {\left(2 \, c d^{2} x^{2} + 3 \, b d^{2} x + 6 \, a d^{2} + 4 \, c\right)} \sqrt{d x + 1} \sqrt{-d x + 1}}{6 \, d^{4}}"," ",0,"-1/6*(6*b*d*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)) + (2*c*d^2*x^2 + 3*b*d^2*x + 6*a*d^2 + 4*c)*sqrt(d*x + 1)*sqrt(-d*x + 1))/d^4","A",0
150,1,67,0,0.939602," ","integrate((c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(c d x + 2 \, b d\right)} \sqrt{d x + 1} \sqrt{-d x + 1} + 2 \, {\left(2 \, a d^{2} + c\right)} \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{2 \, d^{3}}"," ",0,"-1/2*((c*d*x + 2*b*d)*sqrt(d*x + 1)*sqrt(-d*x + 1) + 2*(2*a*d^2 + c)*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/d^3","A",0
151,1,81,0,0.936412," ","integrate((c*x^2+b*x+a)/x/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{a d^{2} \log\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{x}\right) - 2 \, b d \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right) - \sqrt{d x + 1} \sqrt{-d x + 1} c}{d^{2}}"," ",0,"(a*d^2*log((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/x) - 2*b*d*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)) - sqrt(d*x + 1)*sqrt(-d*x + 1)*c)/d^2","A",0
152,1,84,0,0.871855," ","integrate((c*x^2+b*x+a)/x^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{b d x \log\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{x}\right) - \sqrt{d x + 1} \sqrt{-d x + 1} a d - 2 \, c x \arctan\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{d x}\right)}{d x}"," ",0,"(b*d*x*log((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/x) - sqrt(d*x + 1)*sqrt(-d*x + 1)*a*d - 2*c*x*arctan((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/(d*x)))/(d*x)","A",0
153,1,65,0,0.657071," ","integrate((c*x^2+b*x+a)/x^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(a d^{2} + 2 \, c\right)} x^{2} \log\left(\frac{\sqrt{d x + 1} \sqrt{-d x + 1} - 1}{x}\right) - {\left(2 \, b x + a\right)} \sqrt{d x + 1} \sqrt{-d x + 1}}{2 \, x^{2}}"," ",0,"1/2*((a*d^2 + 2*c)*x^2*log((sqrt(d*x + 1)*sqrt(-d*x + 1) - 1)/x) - (2*b*x + a)*sqrt(d*x + 1)*sqrt(-d*x + 1))/x^2","A",0
154,1,73,0,0.907174," ","integrate(x*(c*x^2+b*x+a)/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","-\frac{3 \, b d \log\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) - {\left(2 \, c d^{2} x^{2} + 3 \, b d^{2} x + 6 \, a d^{2} + 4 \, c\right)} \sqrt{d x + 1} \sqrt{d x - 1}}{6 \, d^{4}}"," ",0,"-1/6*(3*b*d*log(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) - (2*c*d^2*x^2 + 3*b*d^2*x + 6*a*d^2 + 4*c)*sqrt(d*x + 1)*sqrt(d*x - 1))/d^4","A",0
155,1,61,0,0.923338," ","integrate((c*x^2+b*x+a)/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(c d x + 2 \, b d\right)} \sqrt{d x + 1} \sqrt{d x - 1} - {\left(2 \, a d^{2} + c\right)} \log\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right)}{2 \, d^{3}}"," ",0,"1/2*((c*d*x + 2*b*d)*sqrt(d*x + 1)*sqrt(d*x - 1) - (2*a*d^2 + c)*log(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)))/d^3","A",0
156,1,73,0,0.743971," ","integrate((c*x^2+b*x+a)/x/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a d^{2} \arctan\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) - b d \log\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) + \sqrt{d x + 1} \sqrt{d x - 1} c}{d^{2}}"," ",0,"(2*a*d^2*arctan(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) - b*d*log(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) + sqrt(d*x + 1)*sqrt(d*x - 1)*c)/d^2","A",0
157,1,82,0,1.025223," ","integrate((c*x^2+b*x+a)/x^2/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{a d^{2} x + 2 \, b d x \arctan\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) + \sqrt{d x + 1} \sqrt{d x - 1} a d - c x \log\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right)}{d x}"," ",0,"(a*d^2*x + 2*b*d*x*arctan(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) + sqrt(d*x + 1)*sqrt(d*x - 1)*a*d - c*x*log(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)))/(d*x)","A",0
158,1,69,0,0.880843," ","integrate((c*x^2+b*x+a)/x^3/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, b d x^{2} + 2 \, {\left(a d^{2} + 2 \, c\right)} x^{2} \arctan\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) + {\left(2 \, b x + a\right)} \sqrt{d x + 1} \sqrt{d x - 1}}{2 \, x^{2}}"," ",0,"1/2*(2*b*d*x^2 + 2*(a*d^2 + 2*c)*x^2*arctan(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) + (2*b*x + a)*sqrt(d*x + 1)*sqrt(d*x - 1))/x^2","A",0
159,1,90,0,0.945413," ","integrate((c*x^2+b*x+a)/x^4/(d*x-1)^(1/2)/(d*x+1)^(1/2),x, algorithm=""fricas"")","\frac{6 \, b d^{2} x^{3} \arctan\left(-d x + \sqrt{d x + 1} \sqrt{d x - 1}\right) + 2 \, {\left(2 \, a d^{3} + 3 \, c d\right)} x^{3} + {\left(2 \, {\left(2 \, a d^{2} + 3 \, c\right)} x^{2} + 3 \, b x + 2 \, a\right)} \sqrt{d x + 1} \sqrt{d x - 1}}{6 \, x^{3}}"," ",0,"1/6*(6*b*d^2*x^3*arctan(-d*x + sqrt(d*x + 1)*sqrt(d*x - 1)) + 2*(2*a*d^3 + 3*c*d)*x^3 + (2*(2*a*d^2 + 3*c)*x^2 + 3*b*x + 2*a)*sqrt(d*x + 1)*sqrt(d*x - 1))/x^3","A",0
