1,1,87,0,0.150939," ","integrate((B*x+A)*(c*x^2+b*x+a)/(f*x^2+d),x, algorithm=""giac"")","-\frac{{\left(B b d + A c d - A a f\right)} \arctan\left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f} f} - \frac{{\left(B c d - B a f - A b f\right)} \log\left(f x^{2} + d\right)}{2 \, f^{2}} + \frac{B c f x^{2} + 2 \, B b f x + 2 \, A c f x}{2 \, f^{2}}"," ",0,"-(B*b*d + A*c*d - A*a*f)*arctan(f*x/sqrt(d*f))/(sqrt(d*f)*f) - 1/2*(B*c*d - B*a*f - A*b*f)*log(f*x^2 + d)/f^2 + 1/2*(B*c*f*x^2 + 2*B*b*f*x + 2*A*c*f*x)/f^2","A",0
2,1,263,0,0.159284," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(f*x^2+d),x, algorithm=""giac"")","\frac{{\left(2 \, B b c d^{2} + A c^{2} d^{2} - 2 \, B a b d f - A b^{2} d f - 2 \, A a c d f + A a^{2} f^{2}\right)} \arctan\left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f} f^{2}} + \frac{{\left(B c^{2} d^{2} - B b^{2} d f - 2 \, B a c d f - 2 \, A b c d f + B a^{2} f^{2} + 2 \, A a b f^{2}\right)} \log\left(f x^{2} + d\right)}{2 \, f^{3}} + \frac{3 \, B c^{2} f^{3} x^{4} + 8 \, B b c f^{3} x^{3} + 4 \, A c^{2} f^{3} x^{3} - 6 \, B c^{2} d f^{2} x^{2} + 6 \, B b^{2} f^{3} x^{2} + 12 \, B a c f^{3} x^{2} + 12 \, A b c f^{3} x^{2} - 24 \, B b c d f^{2} x - 12 \, A c^{2} d f^{2} x + 24 \, B a b f^{3} x + 12 \, A b^{2} f^{3} x + 24 \, A a c f^{3} x}{12 \, f^{4}}"," ",0,"(2*B*b*c*d^2 + A*c^2*d^2 - 2*B*a*b*d*f - A*b^2*d*f - 2*A*a*c*d*f + A*a^2*f^2)*arctan(f*x/sqrt(d*f))/(sqrt(d*f)*f^2) + 1/2*(B*c^2*d^2 - B*b^2*d*f - 2*B*a*c*d*f - 2*A*b*c*d*f + B*a^2*f^2 + 2*A*a*b*f^2)*log(f*x^2 + d)/f^3 + 1/12*(3*B*c^2*f^3*x^4 + 8*B*b*c*f^3*x^3 + 4*A*c^2*f^3*x^3 - 6*B*c^2*d*f^2*x^2 + 6*B*b^2*f^3*x^2 + 12*B*a*c*f^3*x^2 + 12*A*b*c*f^3*x^2 - 24*B*b*c*d*f^2*x - 12*A*c^2*d*f^2*x + 24*B*a*b*f^3*x + 12*A*b^2*f^3*x + 24*A*a*c*f^3*x)/f^4","A",0
3,1,623,0,0.163819," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(f*x^2+d),x, algorithm=""giac"")","-\frac{{\left(3 \, B b c^{2} d^{3} + A c^{3} d^{3} - B b^{3} d^{2} f - 6 \, B a b c d^{2} f - 3 \, A b^{2} c d^{2} f - 3 \, A a c^{2} d^{2} f + 3 \, B a^{2} b d f^{2} + 3 \, A a b^{2} d f^{2} + 3 \, A a^{2} c d f^{2} - A a^{3} f^{3}\right)} \arctan\left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f} f^{3}} - \frac{{\left(B c^{3} d^{3} - 3 \, B b^{2} c d^{2} f - 3 \, B a c^{2} d^{2} f - 3 \, A b c^{2} d^{2} f + 3 \, B a b^{2} d f^{2} + A b^{3} d f^{2} + 3 \, B a^{2} c d f^{2} + 6 \, A a b c d f^{2} - B a^{3} f^{3} - 3 \, A a^{2} b f^{3}\right)} \log\left(f x^{2} + d\right)}{2 \, f^{4}} + \frac{10 \, B c^{3} f^{5} x^{6} + 36 \, B b c^{2} f^{5} x^{5} + 12 \, A c^{3} f^{5} x^{5} - 15 \, B c^{3} d f^{4} x^{4} + 45 \, B b^{2} c f^{5} x^{4} + 45 \, B a c^{2} f^{5} x^{4} + 45 \, A b c^{2} f^{5} x^{4} - 60 \, B b c^{2} d f^{4} x^{3} - 20 \, A c^{3} d f^{4} x^{3} + 20 \, B b^{3} f^{5} x^{3} + 120 \, B a b c f^{5} x^{3} + 60 \, A b^{2} c f^{5} x^{3} + 60 \, A a c^{2} f^{5} x^{3} + 30 \, B c^{3} d^{2} f^{3} x^{2} - 90 \, B b^{2} c d f^{4} x^{2} - 90 \, B a c^{2} d f^{4} x^{2} - 90 \, A b c^{2} d f^{4} x^{2} + 90 \, B a b^{2} f^{5} x^{2} + 30 \, A b^{3} f^{5} x^{2} + 90 \, B a^{2} c f^{5} x^{2} + 180 \, A a b c f^{5} x^{2} + 180 \, B b c^{2} d^{2} f^{3} x + 60 \, A c^{3} d^{2} f^{3} x - 60 \, B b^{3} d f^{4} x - 360 \, B a b c d f^{4} x - 180 \, A b^{2} c d f^{4} x - 180 \, A a c^{2} d f^{4} x + 180 \, B a^{2} b f^{5} x + 180 \, A a b^{2} f^{5} x + 180 \, A a^{2} c f^{5} x}{60 \, f^{6}}"," ",0,"-(3*B*b*c^2*d^3 + A*c^3*d^3 - B*b^3*d^2*f - 6*B*a*b*c*d^2*f - 3*A*b^2*c*d^2*f - 3*A*a*c^2*d^2*f + 3*B*a^2*b*d*f^2 + 3*A*a*b^2*d*f^2 + 3*A*a^2*c*d*f^2 - A*a^3*f^3)*arctan(f*x/sqrt(d*f))/(sqrt(d*f)*f^3) - 1/2*(B*c^3*d^3 - 3*B*b^2*c*d^2*f - 3*B*a*c^2*d^2*f - 3*A*b*c^2*d^2*f + 3*B*a*b^2*d*f^2 + A*b^3*d*f^2 + 3*B*a^2*c*d*f^2 + 6*A*a*b*c*d*f^2 - B*a^3*f^3 - 3*A*a^2*b*f^3)*log(f*x^2 + d)/f^4 + 1/60*(10*B*c^3*f^5*x^6 + 36*B*b*c^2*f^5*x^5 + 12*A*c^3*f^5*x^5 - 15*B*c^3*d*f^4*x^4 + 45*B*b^2*c*f^5*x^4 + 45*B*a*c^2*f^5*x^4 + 45*A*b*c^2*f^5*x^4 - 60*B*b*c^2*d*f^4*x^3 - 20*A*c^3*d*f^4*x^3 + 20*B*b^3*f^5*x^3 + 120*B*a*b*c*f^5*x^3 + 60*A*b^2*c*f^5*x^3 + 60*A*a*c^2*f^5*x^3 + 30*B*c^3*d^2*f^3*x^2 - 90*B*b^2*c*d*f^4*x^2 - 90*B*a*c^2*d*f^4*x^2 - 90*A*b*c^2*d*f^4*x^2 + 90*B*a*b^2*f^5*x^2 + 30*A*b^3*f^5*x^2 + 90*B*a^2*c*f^5*x^2 + 180*A*a*b*c*f^5*x^2 + 180*B*b*c^2*d^2*f^3*x + 60*A*c^3*d^2*f^3*x - 60*B*b^3*d*f^4*x - 360*B*a*b*c*d*f^4*x - 180*A*b^2*c*d*f^4*x - 180*A*a*c^2*d*f^4*x + 180*B*a^2*b*f^5*x + 180*A*a*b^2*f^5*x + 180*A*a^2*c*f^5*x)/f^6","A",0
4,1,266,0,0.168463," ","integrate((B*x+A)/(c*x^2+b*x+a)/(f*x^2+d),x, algorithm=""giac"")","\frac{{\left(B c d - B a f + A b f\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2}\right)}} - \frac{{\left(B c d - B a f + A b f\right)} \log\left(f x^{2} + d\right)}{2 \, {\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2}\right)}} + \frac{{\left(B b d f - A c d f + A a f^{2}\right)} \arctan\left(\frac{f x}{\sqrt{d f}}\right)}{{\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2}\right)} \sqrt{d f}} - \frac{{\left(B b c d - 2 \, A c^{2} d + B a b f - A b^{2} f + 2 \, A a c f\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2}\right)} \sqrt{-b^{2} + 4 \, a c}}"," ",0,"1/2*(B*c*d - B*a*f + A*b*f)*log(c*x^2 + b*x + a)/(c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2) - 1/2*(B*c*d - B*a*f + A*b*f)*log(f*x^2 + d)/(c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2) + (B*b*d*f - A*c*d*f + A*a*f^2)*arctan(f*x/sqrt(d*f))/((c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2)*sqrt(d*f)) - (B*b*c*d - 2*A*c^2*d + B*a*b*f - A*b^2*f + 2*A*a*c*f)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2)*sqrt(-b^2 + 4*a*c))","A",0
5,1,1313,0,0.205459," ","integrate((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+d),x, algorithm=""giac"")","-\frac{{\left(B c^{2} d^{2} f - B b^{2} d f^{2} - 2 \, B a c d f^{2} + 2 \, A b c d f^{2} + B a^{2} f^{3} - 2 \, A a b f^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{4} d^{4} + 2 \, b^{2} c^{2} d^{3} f - 4 \, a c^{3} d^{3} f + b^{4} d^{2} f^{2} - 4 \, a b^{2} c d^{2} f^{2} + 6 \, a^{2} c^{2} d^{2} f^{2} + 2 \, a^{2} b^{2} d f^{3} - 4 \, a^{3} c d f^{3} + a^{4} f^{4}\right)}} + \frac{{\left(B c^{2} d^{2} f - B b^{2} d f^{2} - 2 \, B a c d f^{2} + 2 \, A b c d f^{2} + B a^{2} f^{3} - 2 \, A a b f^{3}\right)} \log\left(f x^{2} + d\right)}{2 \, {\left(c^{4} d^{4} + 2 \, b^{2} c^{2} d^{3} f - 4 \, a c^{3} d^{3} f + b^{4} d^{2} f^{2} - 4 \, a b^{2} c d^{2} f^{2} + 6 \, a^{2} c^{2} d^{2} f^{2} + 2 \, a^{2} b^{2} d f^{3} - 4 \, a^{3} c d f^{3} + a^{4} f^{4}\right)}} - \frac{{\left(2 \, B b c d^{2} f^{2} - A c^{2} d^{2} f^{2} - 2 \, B a b d f^{3} + A b^{2} d f^{3} + 2 \, A a c d f^{3} - A a^{2} f^{4}\right)} \arctan\left(\frac{f x}{\sqrt{d f}}\right)}{{\left(c^{4} d^{4} + 2 \, b^{2} c^{2} d^{3} f - 4 \, a c^{3} d^{3} f + b^{4} d^{2} f^{2} - 4 \, a b^{2} c d^{2} f^{2} + 6 \, a^{2} c^{2} d^{2} f^{2} + 2 \, a^{2} b^{2} d f^{3} - 4 \, a^{3} c d f^{3} + a^{4} f^{4}\right)} \sqrt{d f}} + \frac{{\left(2 \, B b c^{4} d^{3} - 4 \, A c^{5} d^{3} + 5 \, B b^{3} c^{2} d^{2} f - 14 \, B a b c^{3} d^{2} f - 8 \, A b^{2} c^{3} d^{2} f + 20 \, A a c^{4} d^{2} f + B b^{5} d f^{2} - 4 \, B a b^{3} c d f^{2} - 2 \, A b^{4} c d f^{2} + 6 \, B a^{2} b c^{2} d f^{2} + 12 \, A a b^{2} c^{2} d f^{2} - 28 \, A a^{2} c^{3} d f^{2} - B a^{2} b^{3} f^{3} + 2 \, A a b^{4} f^{3} + 6 \, B a^{3} b c f^{3} - 12 \, A a^{2} b^{2} c f^{3} + 12 \, A a^{3} c^{2} f^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{4} d^{4} - 4 \, a c^{5} d^{4} + 2 \, b^{4} c^{2} d^{3} f - 12 \, a b^{2} c^{3} d^{3} f + 16 \, a^{2} c^{4} d^{3} f + b^{6} d^{2} f^{2} - 8 \, a b^{4} c d^{2} f^{2} + 22 \, a^{2} b^{2} c^{2} d^{2} f^{2} - 24 \, a^{3} c^{3} d^{2} f^{2} + 2 \, a^{2} b^{4} d f^{3} - 12 \, a^{3} b^{2} c d f^{3} + 16 \, a^{4} c^{2} d f^{3} + a^{4} b^{2} f^{4} - 4 \, a^{5} c f^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{2 \, B a c^{4} d^{3} - A b c^{4} d^{3} + 3 \, B a b^{2} c^{2} d^{2} f - 2 \, A b^{3} c^{2} d^{2} f - 6 \, B a^{2} c^{3} d^{2} f + 5 \, A a b c^{3} d^{2} f + B a b^{4} d f^{2} - A b^{5} d f^{2} - 4 \, B a^{2} b^{2} c d f^{2} + 5 \, A a b^{3} c d f^{2} + 6 \, B a^{3} c^{2} d f^{2} - 7 \, A a^{2} b c^{2} d f^{2} + B a^{3} b^{2} f^{3} - A a^{2} b^{3} f^{3} - 2 \, B a^{4} c f^{3} + 3 \, A a^{3} b c f^{3} + {\left(B b c^{4} d^{3} - 2 \, A c^{5} d^{3} + B b^{3} c^{2} d^{2} f - B a b c^{3} d^{2} f - 3 \, A b^{2} c^{3} d^{2} f + 6 \, A a c^{4} d^{2} f + B a b^{3} c d f^{2} - A b^{4} c d f^{2} - B a^{2} b c^{2} d f^{2} + 4 \, A a b^{2} c^{2} d f^{2} - 6 \, A a^{2} c^{3} d f^{2} + B a^{3} b c f^{3} - A a^{2} b^{2} c f^{3} + 2 \, A a^{3} c^{2} f^{3}\right)} x}{{\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2}\right)}^{2} {\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-1/2*(B*c^2*d^2*f - B*b^2*d*f^2 - 2*B*a*c*d*f^2 + 2*A*b*c*d*f^2 + B*a^2*f^3 - 2*A*a*b*f^3)*log(c*x^2 + b*x + a)/(c^4*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^3*d^3*f + b^4*d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3 - 4*a^3*c*d*f^3 + a^4*f^4) + 1/2*(B*c^2*d^2*f - B*b^2*d*f^2 - 2*B*a*c*d*f^2 + 2*A*b*c*d*f^2 + B*a^2*f^3 - 2*A*a*b*f^3)*log(f*x^2 + d)/(c^4*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^3*d^3*f + b^4*d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3 - 4*a^3*c*d*f^3 + a^4*f^4) - (2*B*b*c*d^2*f^2 - A*c^2*d^2*f^2 - 2*B*a*b*d*f^3 + A*b^2*d*f^3 + 2*A*a*c*d*f^3 - A*a^2*f^4)*arctan(f*x/sqrt(d*f))/((c^4*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^3*d^3*f + b^4*d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3 - 4*a^3*c*d*f^3 + a^4*f^4)*sqrt(d*f)) + (2*B*b*c^4*d^3 - 4*A*c^5*d^3 + 5*B*b^3*c^2*d^2*f - 14*B*a*b*c^3*d^2*f - 8*A*b^2*c^3*d^2*f + 20*A*a*c^4*d^2*f + B*b^5*d*f^2 - 4*B*a*b^3*c*d*f^2 - 2*A*b^4*c*d*f^2 + 6*B*a^2*b*c^2*d*f^2 + 12*A*a*b^2*c^2*d*f^2 - 28*A*a^2*c^3*d*f^2 - B*a^2*b^3*f^3 + 2*A*a*b^4*f^3 + 6*B*a^3*b*c*f^3 - 12*A*a^2*b^2*c*f^3 + 12*A*a^3*c^2*f^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^4*d^4 - 4*a*c^5*d^4 + 2*b^4*c^2*d^3*f - 12*a*b^2*c^3*d^3*f + 16*a^2*c^4*d^3*f + b^6*d^2*f^2 - 8*a*b^4*c*d^2*f^2 + 22*a^2*b^2*c^2*d^2*f^2 - 24*a^3*c^3*d^2*f^2 + 2*a^2*b^4*d*f^3 - 12*a^3*b^2*c*d*f^3 + 16*a^4*c^2*d*f^3 + a^4*b^2*f^4 - 4*a^5*c*f^4)*sqrt(-b^2 + 4*a*c)) + (2*B*a*c^4*d^3 - A*b*c^4*d^3 + 3*B*a*b^2*c^2*d^2*f - 2*A*b^3*c^2*d^2*f - 6*B*a^2*c^3*d^2*f + 5*A*a*b*c^3*d^2*f + B*a*b^4*d*f^2 - A*b^5*d*f^2 - 4*B*a^2*b^2*c*d*f^2 + 5*A*a*b^3*c*d*f^2 + 6*B*a^3*c^2*d*f^2 - 7*A*a^2*b*c^2*d*f^2 + B*a^3*b^2*f^3 - A*a^2*b^3*f^3 - 2*B*a^4*c*f^3 + 3*A*a^3*b*c*f^3 + (B*b*c^4*d^3 - 2*A*c^5*d^3 + B*b^3*c^2*d^2*f - B*a*b*c^3*d^2*f - 3*A*b^2*c^3*d^2*f + 6*A*a*c^4*d^2*f + B*a*b^3*c*d*f^2 - A*b^4*c*d*f^2 - B*a^2*b*c^2*d*f^2 + 4*A*a*b^2*c^2*d*f^2 - 6*A*a^2*c^3*d*f^2 + B*a^3*b*c*f^3 - A*a^2*b^2*c*f^3 + 2*A*a^3*c^2*f^3)*x)/((c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2)^2*(c*x^2 + b*x + a)*(b^2 - 4*a*c))","B",0
6,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
7,-2,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueConj Error: Bad Argument Type","F(-2)",0
8,-2,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 10.66Conj Error: Bad Argument Type","F(-2)",0
9,-2,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)^(5/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 5.84Conj Error: Bad Argument Type","F(-2)",0
10,1,48,0,0.245916," ","integrate((1+2*x)/(x^2-1)/(x^2+x-1)^(1/2),x, algorithm=""giac"")","\arctan\left(-x + \sqrt{x^{2} + x - 1} - 1\right) - \frac{3}{2} \, \log\left({\left| -x + \sqrt{x^{2} + x - 1} + 2 \right|}\right) + \frac{3}{2} \, \log\left({\left| -x + \sqrt{x^{2} + x - 1} \right|}\right)"," ",0,"arctan(-x + sqrt(x^2 + x - 1) - 1) - 3/2*log(abs(-x + sqrt(x^2 + x - 1) + 2)) + 3/2*log(abs(-x + sqrt(x^2 + x - 1)))","A",0
11,1,457,0,0.375735," ","integrate((1+2*x)/(x^2+1)/(x^2+x-1)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 4} \log\left(16 \, {\left(15 \, \sqrt{5} {\left(x - \sqrt{x^{2} + x - 1}\right)} + 33 \, x + 5 \, \sqrt{5} - 33 \, \sqrt{x^{2} + x - 1} + 2 \, \sqrt{5 \, \sqrt{5} + 11} + 11\right)}^{2} + 16 \, {\left(5 \, \sqrt{5} {\left(x - \sqrt{x^{2} + x - 1}\right)} + 11 \, x - 5 \, \sqrt{5} \sqrt{5 \, \sqrt{5} + 11} - 15 \, \sqrt{5} - 11 \, \sqrt{x^{2} + x - 1} - 11 \, \sqrt{5 \, \sqrt{5} + 11} - 33\right)}^{2}\right) - \frac{1}{4} \, \sqrt{2 \, \sqrt{5} - 4} \log\left(16 \, {\left(15 \, \sqrt{5} {\left(x - \sqrt{x^{2} + x - 1}\right)} + 33 \, x + 5 \, \sqrt{5} - 33 \, \sqrt{x^{2} + x - 1} - 2 \, \sqrt{5 \, \sqrt{5} + 11} + 11\right)}^{2} + 16 \, {\left(5 \, \sqrt{5} {\left(x - \sqrt{x^{2} + x - 1}\right)} + 11 \, x + 5 \, \sqrt{5} \sqrt{5 \, \sqrt{5} + 11} - 15 \, \sqrt{5} - 11 \, \sqrt{x^{2} + x - 1} + 11 \, \sqrt{5 \, \sqrt{5} + 11} - 33\right)}^{2}\right) + \frac{\sqrt{2 \, \sqrt{5} - 4} {\left(\arctan\left(3\right) + \arctan\left(\frac{1}{10} \, {\left(x - \sqrt{x^{2} + x - 1}\right)} {\left(\sqrt{5} \sqrt{5 \, \sqrt{5} + 11} + 4 \, \sqrt{5} - 5 \, \sqrt{5 \, \sqrt{5} + 11}\right)} - \frac{7}{10} \, \sqrt{5} \sqrt{5 \, \sqrt{5} + 11} + \frac{1}{5} \, \sqrt{5} + \frac{3}{2} \, \sqrt{5 \, \sqrt{5} + 11}\right)\right)}}{2 \, {\left(\sqrt{5} - 2\right)}} - \frac{\sqrt{2 \, \sqrt{5} - 4} {\left(\arctan\left(3\right) + \arctan\left(-\frac{1}{10} \, {\left(x - \sqrt{x^{2} + x - 1}\right)} {\left(\sqrt{5} \sqrt{5 \, \sqrt{5} + 11} - 4 \, \sqrt{5} - 5 \, \sqrt{5 \, \sqrt{5} + 11}\right)} + \frac{7}{10} \, \sqrt{5} \sqrt{5 \, \sqrt{5} + 11} + \frac{1}{5} \, \sqrt{5} - \frac{3}{2} \, \sqrt{5 \, \sqrt{5} + 11}\right)\right)}}{2 \, {\left(\sqrt{5} - 2\right)}}"," ",0,"1/4*sqrt(2*sqrt(5) - 4)*log(16*(15*sqrt(5)*(x - sqrt(x^2 + x - 1)) + 33*x + 5*sqrt(5) - 33*sqrt(x^2 + x - 1) + 2*sqrt(5*sqrt(5) + 11) + 11)^2 + 16*(5*sqrt(5)*(x - sqrt(x^2 + x - 1)) + 11*x - 5*sqrt(5)*sqrt(5*sqrt(5) + 11) - 15*sqrt(5) - 11*sqrt(x^2 + x - 1) - 11*sqrt(5*sqrt(5) + 11) - 33)^2) - 1/4*sqrt(2*sqrt(5) - 4)*log(16*(15*sqrt(5)*(x - sqrt(x^2 + x - 1)) + 33*x + 5*sqrt(5) - 33*sqrt(x^2 + x - 1) - 2*sqrt(5*sqrt(5) + 11) + 11)^2 + 16*(5*sqrt(5)*(x - sqrt(x^2 + x - 1)) + 11*x + 5*sqrt(5)*sqrt(5*sqrt(5) + 11) - 15*sqrt(5) - 11*sqrt(x^2 + x - 1) + 11*sqrt(5*sqrt(5) + 11) - 33)^2) + 1/2*sqrt(2*sqrt(5) - 4)*(arctan(3) + arctan(1/10*(x - sqrt(x^2 + x - 1))*(sqrt(5)*sqrt(5*sqrt(5) + 11) + 4*sqrt(5) - 5*sqrt(5*sqrt(5) + 11)) - 7/10*sqrt(5)*sqrt(5*sqrt(5) + 11) + 1/5*sqrt(5) + 3/2*sqrt(5*sqrt(5) + 11)))/(sqrt(5) - 2) - 1/2*sqrt(2*sqrt(5) - 4)*(arctan(3) + arctan(-1/10*(x - sqrt(x^2 + x - 1))*(sqrt(5)*sqrt(5*sqrt(5) + 11) - 4*sqrt(5) - 5*sqrt(5*sqrt(5) + 11)) + 7/10*sqrt(5)*sqrt(5*sqrt(5) + 11) + 1/5*sqrt(5) - 3/2*sqrt(5*sqrt(5) + 11)))/(sqrt(5) - 2)","B",0
12,-2,0,0,0.000000," ","integrate((b*x+a-c)/(x^2+1)/(c*x^2+b*x+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c]=[42,62,91]Warning, choosing root of [1,0,%%%{-2,[2,0,0]%%%}+%%%{4,[1,0,1]%%%}+%%%{4,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%}+%%%{-2,[0,0,2]%%%}+%%%{-4,[0,0,1]%%%},%%%{-8,[2,0,0]%%%}+%%%{16,[1,0,1]%%%}+%%%{-8,[0,2,0]%%%}+%%%{-8,[0,0,2]%%%},%%%{1,[4,0,0]%%%}+%%%{-4,[3,0,1]%%%}+%%%{4,[3,0,0]%%%}+%%%{2,[2,2,0]%%%}+%%%{6,[2,0,2]%%%}+%%%{-12,[2,0,1]%%%}+%%%{-4,[1,2,1]%%%}+%%%{4,[1,2,0]%%%}+%%%{-4,[1,0,3]%%%}+%%%{12,[1,0,2]%%%}+%%%{1,[0,4,0]%%%}+%%%{2,[0,2,2]%%%}+%%%{-4,[0,2,1]%%%}+%%%{-4,[0,2,0]%%%}+%%%{1,[0,0,4]%%%}+%%%{-4,[0,0,3]%%%}] at parameters values [-27,26,-89]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[-66,-52]Evaluation time: 7.83Unable to convert to real %%%{1.0,[2]%%%}+%%%{132.0,[1]%%%}+%%%{7060.0,[0]%%%} Error: Bad Argument Value","F(-2)",0
13,1,191,0,0.168905," ","integrate((B*x+A)*(c*x^2+b*x+a)/(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{B c f x^{2} + 2 \, B b f x + 2 \, A c f x - 2 \, B c x e}{2 \, f^{2}} - \frac{{\left(B c d f - B a f^{2} - A b f^{2} + B b f e + A c f e - B c e^{2}\right)} \log\left(f x^{2} + x e + d\right)}{2 \, f^{3}} - \frac{{\left(2 \, B b d f^{2} + 2 \, A c d f^{2} - 2 \, A a f^{3} - 3 \, B c d f e + B a f^{2} e + A b f^{2} e - B b f e^{2} - A c f e^{2} + B c e^{3}\right)} \arctan\left(\frac{2 \, f x + e}{\sqrt{4 \, d f - e^{2}}}\right)}{\sqrt{4 \, d f - e^{2}} f^{3}}"," ",0,"1/2*(B*c*f*x^2 + 2*B*b*f*x + 2*A*c*f*x - 2*B*c*x*e)/f^2 - 1/2*(B*c*d*f - B*a*f^2 - A*b*f^2 + B*b*f*e + A*c*f*e - B*c*e^2)*log(f*x^2 + x*e + d)/f^3 - (2*B*b*d*f^2 + 2*A*c*d*f^2 - 2*A*a*f^3 - 3*B*c*d*f*e + B*a*f^2*e + A*b*f^2*e - B*b*f*e^2 - A*c*f*e^2 + B*c*e^3)*arctan((2*f*x + e)/sqrt(4*d*f - e^2))/(sqrt(4*d*f - e^2)*f^3)","A",0
14,1,738,0,0.245770," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{3 \, B c^{2} f^{3} x^{4} + 8 \, B b c f^{3} x^{3} + 4 \, A c^{2} f^{3} x^{3} - 4 \, B c^{2} f^{2} x^{3} e - 6 \, B c^{2} d f^{2} x^{2} + 6 \, B b^{2} f^{3} x^{2} + 12 \, B a c f^{3} x^{2} + 12 \, A b c f^{3} x^{2} - 12 \, B b c f^{2} x^{2} e - 6 \, A c^{2} f^{2} x^{2} e - 24 \, B b c d f^{2} x - 12 \, A c^{2} d f^{2} x + 24 \, B a b f^{3} x + 12 \, A b^{2} f^{3} x + 24 \, A a c f^{3} x + 6 \, B c^{2} f x^{2} e^{2} + 24 \, B c^{2} d f x e - 12 \, B b^{2} f^{2} x e - 24 \, B a c f^{2} x e - 24 \, A b c f^{2} x e + 24 \, B b c f x e^{2} + 12 \, A c^{2} f x e^{2} - 12 \, B c^{2} x e^{3}}{12 \, f^{4}} + \frac{{\left(B c^{2} d^{2} f^{2} - B b^{2} d f^{3} - 2 \, B a c d f^{3} - 2 \, A b c d f^{3} + B a^{2} f^{4} + 2 \, A a b f^{4} + 4 \, B b c d f^{2} e + 2 \, A c^{2} d f^{2} e - 2 \, B a b f^{3} e - A b^{2} f^{3} e - 2 \, A a c f^{3} e - 3 \, B c^{2} d f e^{2} + B b^{2} f^{2} e^{2} + 2 \, B a c f^{2} e^{2} + 2 \, A b c f^{2} e^{2} - 2 \, B b c f e^{3} - A c^{2} f e^{3} + B c^{2} e^{4}\right)} \log\left(f x^{2} + x e + d\right)}{2 \, f^{5}} + \frac{{\left(4 \, B b c d^{2} f^{3} + 2 \, A c^{2} d^{2} f^{3} - 4 \, B a b d f^{4} - 2 \, A b^{2} d f^{4} - 4 \, A a c d f^{4} + 2 \, A a^{2} f^{5} - 5 \, B c^{2} d^{2} f^{2} e + 3 \, B b^{2} d f^{3} e + 6 \, B a c d f^{3} e + 6 \, A b c d f^{3} e - B a^{2} f^{4} e - 2 \, A a b f^{4} e - 8 \, B b c d f^{2} e^{2} - 4 \, A c^{2} d f^{2} e^{2} + 2 \, B a b f^{3} e^{2} + A b^{2} f^{3} e^{2} + 2 \, A a c f^{3} e^{2} + 5 \, B c^{2} d f e^{3} - B b^{2} f^{2} e^{3} - 2 \, B a c f^{2} e^{3} - 2 \, A b c f^{2} e^{3} + 2 \, B b c f e^{4} + A c^{2} f e^{4} - B c^{2} e^{5}\right)} \arctan\left(\frac{2 \, f x + e}{\sqrt{4 \, d f - e^{2}}}\right)}{\sqrt{4 \, d f - e^{2}} f^{5}}"," ",0,"1/12*(3*B*c^2*f^3*x^4 + 8*B*b*c*f^3*x^3 + 4*A*c^2*f^3*x^3 - 4*B*c^2*f^2*x^3*e - 6*B*c^2*d*f^2*x^2 + 6*B*b^2*f^3*x^2 + 12*B*a*c*f^3*x^2 + 12*A*b*c*f^3*x^2 - 12*B*b*c*f^2*x^2*e - 6*A*c^2*f^2*x^2*e - 24*B*b*c*d*f^2*x - 12*A*c^2*d*f^2*x + 24*B*a*b*f^3*x + 12*A*b^2*f^3*x + 24*A*a*c*f^3*x + 6*B*c^2*f*x^2*e^2 + 24*B*c^2*d*f*x*e - 12*B*b^2*f^2*x*e - 24*B*a*c*f^2*x*e - 24*A*b*c*f^2*x*e + 24*B*b*c*f*x*e^2 + 12*A*c^2*f*x*e^2 - 12*B*c^2*x*e^3)/f^4 + 1/2*(B*c^2*d^2*f^2 - B*b^2*d*f^3 - 2*B*a*c*d*f^3 - 2*A*b*c*d*f^3 + B*a^2*f^4 + 2*A*a*b*f^4 + 4*B*b*c*d*f^2*e + 2*A*c^2*d*f^2*e - 2*B*a*b*f^3*e - A*b^2*f^3*e - 2*A*a*c*f^3*e - 3*B*c^2*d*f*e^2 + B*b^2*f^2*e^2 + 2*B*a*c*f^2*e^2 + 2*A*b*c*f^2*e^2 - 2*B*b*c*f*e^3 - A*c^2*f*e^3 + B*c^2*e^4)*log(f*x^2 + x*e + d)/f^5 + (4*B*b*c*d^2*f^3 + 2*A*c^2*d^2*f^3 - 4*B*a*b*d*f^4 - 2*A*b^2*d*f^4 - 4*A*a*c*d*f^4 + 2*A*a^2*f^5 - 5*B*c^2*d^2*f^2*e + 3*B*b^2*d*f^3*e + 6*B*a*c*d*f^3*e + 6*A*b*c*d*f^3*e - B*a^2*f^4*e - 2*A*a*b*f^4*e - 8*B*b*c*d*f^2*e^2 - 4*A*c^2*d*f^2*e^2 + 2*B*a*b*f^3*e^2 + A*b^2*f^3*e^2 + 2*A*a*c*f^3*e^2 + 5*B*c^2*d*f*e^3 - B*b^2*f^2*e^3 - 2*B*a*c*f^2*e^3 - 2*A*b*c*f^2*e^3 + 2*B*b*c*f*e^4 + A*c^2*f*e^4 - B*c^2*e^5)*arctan((2*f*x + e)/sqrt(4*d*f - e^2))/(sqrt(4*d*f - e^2)*f^5)","A",0
15,1,416,0,0.169429," ","integrate((B*x+A)/(c*x^2+b*x+a)/(f*x^2+e*x+d),x, algorithm=""giac"")","\frac{{\left(B c d - B a f + A b f - A c e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2} - b c d e - a b f e + a c e^{2}\right)}} - \frac{{\left(B c d - B a f + A b f - A c e\right)} \log\left(f x^{2} + x e + d\right)}{2 \, {\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2} - b c d e - a b f e + a c e^{2}\right)}} - \frac{{\left(B b c d - 2 \, A c^{2} d + B a b f - A b^{2} f + 2 \, A a c f - 2 \, B a c e + A b c e\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2} - b c d e - a b f e + a c e^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{{\left(2 \, B b d f - 2 \, A c d f + 2 \, A a f^{2} - B c d e - B a f e - A b f e + A c e^{2}\right)} \arctan\left(\frac{2 \, f x + e}{\sqrt{4 \, d f - e^{2}}}\right)}{{\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2} - b c d e - a b f e + a c e^{2}\right)} \sqrt{4 \, d f - e^{2}}}"," ",0,"1/2*(B*c*d - B*a*f + A*b*f - A*c*e)*log(c*x^2 + b*x + a)/(c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2 - b*c*d*e - a*b*f*e + a*c*e^2) - 1/2*(B*c*d - B*a*f + A*b*f - A*c*e)*log(f*x^2 + x*e + d)/(c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2 - b*c*d*e - a*b*f*e + a*c*e^2) - (B*b*c*d - 2*A*c^2*d + B*a*b*f - A*b^2*f + 2*A*a*c*f - 2*B*a*c*e + A*b*c*e)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2 - b*c*d*e - a*b*f*e + a*c*e^2)*sqrt(-b^2 + 4*a*c)) + (2*B*b*d*f - 2*A*c*d*f + 2*A*a*f^2 - B*c*d*e - B*a*f*e - A*b*f*e + A*c*e^2)*arctan((2*f*x + e)/sqrt(4*d*f - e^2))/((c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2 - b*c*d*e - a*b*f*e + a*c*e^2)*sqrt(4*d*f - e^2))","A",0
16,1,3226,0,0.450965," ","integrate((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x, algorithm=""giac"")","-\frac{{\left(B c^{2} d^{2} f - B b^{2} d f^{2} - 2 \, B a c d f^{2} + 2 \, A b c d f^{2} + B a^{2} f^{3} - 2 \, A a b f^{3} + 2 \, B b c d f e - 2 \, A c^{2} d f e + A b^{2} f^{2} e + 2 \, A a c f^{2} e - B c^{2} d e^{2} - 2 \, A b c f e^{2} + A c^{2} e^{3}\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(c^{4} d^{4} + 2 \, b^{2} c^{2} d^{3} f - 4 \, a c^{3} d^{3} f + b^{4} d^{2} f^{2} - 4 \, a b^{2} c d^{2} f^{2} + 6 \, a^{2} c^{2} d^{2} f^{2} + 2 \, a^{2} b^{2} d f^{3} - 4 \, a^{3} c d f^{3} + a^{4} f^{4} - 2 \, b c^{3} d^{3} e - 2 \, b^{3} c d^{2} f e + 2 \, a b c^{2} d^{2} f e - 2 \, a b^{3} d f^{2} e + 2 \, a^{2} b c d f^{2} e - 2 \, a^{3} b f^{3} e + b^{2} c^{2} d^{2} e^{2} + 2 \, a c^{3} d^{2} e^{2} + 4 \, a b^{2} c d f e^{2} - 4 \, a^{2} c^{2} d f e^{2} + a^{2} b^{2} f^{2} e^{2} + 2 \, a^{3} c f^{2} e^{2} - 2 \, a b c^{2} d e^{3} - 2 \, a^{2} b c f e^{3} + a^{2} c^{2} e^{4}\right)}} + \frac{{\left(B c^{2} d^{2} f - B b^{2} d f^{2} - 2 \, B a c d f^{2} + 2 \, A b c d f^{2} + B a^{2} f^{3} - 2 \, A a b f^{3} + 2 \, B b c d f e - 2 \, A c^{2} d f e + A b^{2} f^{2} e + 2 \, A a c f^{2} e - B c^{2} d e^{2} - 2 \, A b c f e^{2} + A c^{2} e^{3}\right)} \log\left(f x^{2} + x e + d\right)}{2 \, {\left(c^{4} d^{4} + 2 \, b^{2} c^{2} d^{3} f - 4 \, a c^{3} d^{3} f + b^{4} d^{2} f^{2} - 4 \, a b^{2} c d^{2} f^{2} + 6 \, a^{2} c^{2} d^{2} f^{2} + 2 \, a^{2} b^{2} d f^{3} - 4 \, a^{3} c d f^{3} + a^{4} f^{4} - 2 \, b c^{3} d^{3} e - 2 \, b^{3} c d^{2} f e + 2 \, a b c^{2} d^{2} f e - 2 \, a b^{3} d f^{2} e + 2 \, a^{2} b c d f^{2} e - 2 \, a^{3} b f^{3} e + b^{2} c^{2} d^{2} e^{2} + 2 \, a c^{3} d^{2} e^{2} + 4 \, a b^{2} c d f e^{2} - 4 \, a^{2} c^{2} d f e^{2} + a^{2} b^{2} f^{2} e^{2} + 2 \, a^{3} c f^{2} e^{2} - 2 \, a b c^{2} d e^{3} - 2 \, a^{2} b c f e^{3} + a^{2} c^{2} e^{4}\right)}} + \frac{{\left(2 \, B b c^{4} d^{3} - 4 \, A c^{5} d^{3} + 5 \, B b^{3} c^{2} d^{2} f - 14 \, B a b c^{3} d^{2} f - 8 \, A b^{2} c^{3} d^{2} f + 20 \, A a c^{4} d^{2} f + B b^{5} d f^{2} - 4 \, B a b^{3} c d f^{2} - 2 \, A b^{4} c d f^{2} + 6 \, B a^{2} b c^{2} d f^{2} + 12 \, A a b^{2} c^{2} d f^{2} - 28 \, A a^{2} c^{3} d f^{2} - B a^{2} b^{3} f^{3} + 2 \, A a b^{4} f^{3} + 6 \, B a^{3} b c f^{3} - 12 \, A a^{2} b^{2} c f^{3} + 12 \, A a^{3} c^{2} f^{3} - 4 \, B b^{2} c^{3} d^{2} e + 4 \, B a c^{4} d^{2} e + 6 \, A b c^{4} d^{2} e - 2 \, B b^{4} c d f e + 2 \, A b^{3} c^{2} d f e + 8 \, B a^{2} c^{3} d f e + 4 \, A a b c^{3} d f e - A b^{5} f^{2} e + 4 \, A a b^{3} c f^{2} e - 12 \, B a^{3} c^{2} f^{2} e + 6 \, A a^{2} b c^{2} f^{2} e + B b^{3} c^{2} d e^{2} + 2 \, B a b c^{3} d e^{2} - 12 \, A a c^{4} d e^{2} + 2 \, A b^{4} c f e^{2} + 6 \, B a^{2} b c^{2} f e^{2} - 12 \, A a b^{2} c^{2} f e^{2} + 4 \, A a^{2} c^{3} f e^{2} - A b^{3} c^{2} e^{3} - 4 \, B a^{2} c^{3} e^{3} + 6 \, A a b c^{3} e^{3}\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{2} c^{4} d^{4} - 4 \, a c^{5} d^{4} + 2 \, b^{4} c^{2} d^{3} f - 12 \, a b^{2} c^{3} d^{3} f + 16 \, a^{2} c^{4} d^{3} f + b^{6} d^{2} f^{2} - 8 \, a b^{4} c d^{2} f^{2} + 22 \, a^{2} b^{2} c^{2} d^{2} f^{2} - 24 \, a^{3} c^{3} d^{2} f^{2} + 2 \, a^{2} b^{4} d f^{3} - 12 \, a^{3} b^{2} c d f^{3} + 16 \, a^{4} c^{2} d f^{3} + a^{4} b^{2} f^{4} - 4 \, a^{5} c f^{4} - 2 \, b^{3} c^{3} d^{3} e + 8 \, a b c^{4} d^{3} e - 2 \, b^{5} c d^{2} f e + 10 \, a b^{3} c^{2} d^{2} f e - 8 \, a^{2} b c^{3} d^{2} f e - 2 \, a b^{5} d f^{2} e + 10 \, a^{2} b^{3} c d f^{2} e - 8 \, a^{3} b c^{2} d f^{2} e - 2 \, a^{3} b^{3} f^{3} e + 8 \, a^{4} b c f^{3} e + b^{4} c^{2} d^{2} e^{2} - 2 \, a b^{2} c^{3} d^{2} e^{2} - 8 \, a^{2} c^{4} d^{2} e^{2} + 4 \, a b^{4} c d f e^{2} - 20 \, a^{2} b^{2} c^{2} d f e^{2} + 16 \, a^{3} c^{3} d f e^{2} + a^{2} b^{4} f^{2} e^{2} - 2 \, a^{3} b^{2} c f^{2} e^{2} - 8 \, a^{4} c^{2} f^{2} e^{2} - 2 \, a b^{3} c^{2} d e^{3} + 8 \, a^{2} b c^{3} d e^{3} - 2 \, a^{2} b^{3} c f e^{3} + 8 \, a^{3} b c^{2} f e^{3} + a^{2} b^{2} c^{2} e^{4} - 4 \, a^{3} c^{3} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c}} - \frac{{\left(4 \, B b c d^{2} f^{2} - 2 \, A c^{2} d^{2} f^{2} - 4 \, B a b d f^{3} + 2 \, A b^{2} d f^{3} + 4 \, A a c d f^{3} - 2 \, A a^{2} f^{4} - 3 \, B c^{2} d^{2} f e + B b^{2} d f^{2} e + 2 \, B a c d f^{2} e - 6 \, A b c d f^{2} e + B a^{2} f^{3} e + 2 \, A a b f^{3} e - 2 \, B b c d f e^{2} + 4 \, A c^{2} d f e^{2} - A b^{2} f^{2} e^{2} - 2 \, A a c f^{2} e^{2} + B c^{2} d e^{3} + 2 \, A b c f e^{3} - A c^{2} e^{4}\right)} \arctan\left(\frac{2 \, f x + e}{\sqrt{4 \, d f - e^{2}}}\right)}{{\left(c^{4} d^{4} + 2 \, b^{2} c^{2} d^{3} f - 4 \, a c^{3} d^{3} f + b^{4} d^{2} f^{2} - 4 \, a b^{2} c d^{2} f^{2} + 6 \, a^{2} c^{2} d^{2} f^{2} + 2 \, a^{2} b^{2} d f^{3} - 4 \, a^{3} c d f^{3} + a^{4} f^{4} - 2 \, b c^{3} d^{3} e - 2 \, b^{3} c d^{2} f e + 2 \, a b c^{2} d^{2} f e - 2 \, a b^{3} d f^{2} e + 2 \, a^{2} b c d f^{2} e - 2 \, a^{3} b f^{3} e + b^{2} c^{2} d^{2} e^{2} + 2 \, a c^{3} d^{2} e^{2} + 4 \, a b^{2} c d f e^{2} - 4 \, a^{2} c^{2} d f e^{2} + a^{2} b^{2} f^{2} e^{2} + 2 \, a^{3} c f^{2} e^{2} - 2 \, a b c^{2} d e^{3} - 2 \, a^{2} b c f e^{3} + a^{2} c^{2} e^{4}\right)} \sqrt{4 \, d f - e^{2}}} + \frac{2 \, B a c^{4} d^{3} - A b c^{4} d^{3} + 3 \, B a b^{2} c^{2} d^{2} f - 2 \, A b^{3} c^{2} d^{2} f - 6 \, B a^{2} c^{3} d^{2} f + 5 \, A a b c^{3} d^{2} f + B a b^{4} d f^{2} - A b^{5} d f^{2} - 4 \, B a^{2} b^{2} c d f^{2} + 5 \, A a b^{3} c d f^{2} + 6 \, B a^{3} c^{2} d f^{2} - 7 \, A a^{2} b c^{2} d f^{2} + B a^{3} b^{2} f^{3} - A a^{2} b^{3} f^{3} - 2 \, B a^{4} c f^{3} + 3 \, A a^{3} b c f^{3} - 3 \, B a b c^{3} d^{2} e + 2 \, A b^{2} c^{3} d^{2} e - 2 \, A a c^{4} d^{2} e - 2 \, B a b^{3} c d f e + 2 \, A b^{4} c d f e + 2 \, B a^{2} b c^{2} d f e - 6 \, A a b^{2} c^{2} d f e + 4 \, A a^{2} c^{3} d f e - B a^{2} b^{3} f^{2} e + A a b^{4} f^{2} e + B a^{3} b c f^{2} e - 2 \, A a^{2} b^{2} c f^{2} e - 2 \, A a^{3} c^{2} f^{2} e + B a b^{2} c^{2} d e^{2} - A b^{3} c^{2} d e^{2} + 2 \, B a^{2} c^{3} d e^{2} + A a b c^{3} d e^{2} + 2 \, B a^{2} b^{2} c f e^{2} - 2 \, A a b^{3} c f e^{2} - 2 \, B a^{3} c^{2} f e^{2} + 5 \, A a^{2} b c^{2} f e^{2} - B a^{2} b c^{2} e^{3} + A a b^{2} c^{2} e^{3} - 2 \, A a^{2} c^{3} e^{3} + {\left(B b c^{4} d^{3} - 2 \, A c^{5} d^{3} + B b^{3} c^{2} d^{2} f - B a b c^{3} d^{2} f - 3 \, A b^{2} c^{3} d^{2} f + 6 \, A a c^{4} d^{2} f + B a b^{3} c d f^{2} - A b^{4} c d f^{2} - B a^{2} b c^{2} d f^{2} + 4 \, A a b^{2} c^{2} d f^{2} - 6 \, A a^{2} c^{3} d f^{2} + B a^{3} b c f^{3} - A a^{2} b^{2} c f^{3} + 2 \, A a^{3} c^{2} f^{3} - B b^{2} c^{3} d^{2} e - 2 \, B a c^{4} d^{2} e + 3 \, A b c^{4} d^{2} e - 4 \, B a b^{2} c^{2} d f e + 2 \, A b^{3} c^{2} d f e + 4 \, B a^{2} c^{3} d f e - 2 \, A a b c^{3} d f e - B a^{2} b^{2} c f^{2} e + A a b^{3} c f^{2} e - 2 \, B a^{3} c^{2} f^{2} e - A a^{2} b c^{2} f^{2} e + 3 \, B a b c^{3} d e^{2} - A b^{2} c^{3} d e^{2} - 2 \, A a c^{4} d e^{2} + 3 \, B a^{2} b c^{2} f e^{2} - 2 \, A a b^{2} c^{2} f e^{2} + 2 \, A a^{2} c^{3} f e^{2} - 2 \, B a^{2} c^{3} e^{3} + A a b c^{3} e^{3}\right)} x}{{\left(c^{2} d^{2} + b^{2} d f - 2 \, a c d f + a^{2} f^{2} - b c d e - a b f e + a c e^{2}\right)}^{2} {\left(c x^{2} + b x + a\right)} {\left(b^{2} - 4 \, a c\right)}}"," ",0,"-1/2*(B*c^2*d^2*f - B*b^2*d*f^2 - 2*B*a*c*d*f^2 + 2*A*b*c*d*f^2 + B*a^2*f^3 - 2*A*a*b*f^3 + 2*B*b*c*d*f*e - 2*A*c^2*d*f*e + A*b^2*f^2*e + 2*A*a*c*f^2*e - B*c^2*d*e^2 - 2*A*b*c*f*e^2 + A*c^2*e^3)*log(c*x^2 + b*x + a)/(c^4*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^3*d^3*f + b^4*d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3 - 4*a^3*c*d*f^3 + a^4*f^4 - 2*b*c^3*d^3*e - 2*b^3*c*d^2*f*e + 2*a*b*c^2*d^2*f*e - 2*a*b^3*d*f^2*e + 2*a^2*b*c*d*f^2*e - 2*a^3*b*f^3*e + b^2*c^2*d^2*e^2 + 2*a*c^3*d^2*e^2 + 4*a*b^2*c*d*f*e^2 - 4*a^2*c^2*d*f*e^2 + a^2*b^2*f^2*e^2 + 2*a^3*c*f^2*e^2 - 2*a*b*c^2*d*e^3 - 2*a^2*b*c*f*e^3 + a^2*c^2*e^4) + 1/2*(B*c^2*d^2*f - B*b^2*d*f^2 - 2*B*a*c*d*f^2 + 2*A*b*c*d*f^2 + B*a^2*f^3 - 2*A*a*b*f^3 + 2*B*b*c*d*f*e - 2*A*c^2*d*f*e + A*b^2*f^2*e + 2*A*a*c*f^2*e - B*c^2*d*e^2 - 2*A*b*c*f*e^2 + A*c^2*e^3)*log(f*x^2 + x*e + d)/(c^4*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^3*d^3*f + b^4*d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3 - 4*a^3*c*d*f^3 + a^4*f^4 - 2*b*c^3*d^3*e - 2*b^3*c*d^2*f*e + 2*a*b*c^2*d^2*f*e - 2*a*b^3*d*f^2*e + 2*a^2*b*c*d*f^2*e - 2*a^3*b*f^3*e + b^2*c^2*d^2*e^2 + 2*a*c^3*d^2*e^2 + 4*a*b^2*c*d*f*e^2 - 4*a^2*c^2*d*f*e^2 + a^2*b^2*f^2*e^2 + 2*a^3*c*f^2*e^2 - 2*a*b*c^2*d*e^3 - 2*a^2*b*c*f*e^3 + a^2*c^2*e^4) + (2*B*b*c^4*d^3 - 4*A*c^5*d^3 + 5*B*b^3*c^2*d^2*f - 14*B*a*b*c^3*d^2*f - 8*A*b^2*c^3*d^2*f + 20*A*a*c^4*d^2*f + B*b^5*d*f^2 - 4*B*a*b^3*c*d*f^2 - 2*A*b^4*c*d*f^2 + 6*B*a^2*b*c^2*d*f^2 + 12*A*a*b^2*c^2*d*f^2 - 28*A*a^2*c^3*d*f^2 - B*a^2*b^3*f^3 + 2*A*a*b^4*f^3 + 6*B*a^3*b*c*f^3 - 12*A*a^2*b^2*c*f^3 + 12*A*a^3*c^2*f^3 - 4*B*b^2*c^3*d^2*e + 4*B*a*c^4*d^2*e + 6*A*b*c^4*d^2*e - 2*B*b^4*c*d*f*e + 2*A*b^3*c^2*d*f*e + 8*B*a^2*c^3*d*f*e + 4*A*a*b*c^3*d*f*e - A*b^5*f^2*e + 4*A*a*b^3*c*f^2*e - 12*B*a^3*c^2*f^2*e + 6*A*a^2*b*c^2*f^2*e + B*b^3*c^2*d*e^2 + 2*B*a*b*c^3*d*e^2 - 12*A*a*c^4*d*e^2 + 2*A*b^4*c*f*e^2 + 6*B*a^2*b*c^2*f*e^2 - 12*A*a*b^2*c^2*f*e^2 + 4*A*a^2*c^3*f*e^2 - A*b^3*c^2*e^3 - 4*B*a^2*c^3*e^3 + 6*A*a*b*c^3*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^4*d^4 - 4*a*c^5*d^4 + 2*b^4*c^2*d^3*f - 12*a*b^2*c^3*d^3*f + 16*a^2*c^4*d^3*f + b^6*d^2*f^2 - 8*a*b^4*c*d^2*f^2 + 22*a^2*b^2*c^2*d^2*f^2 - 24*a^3*c^3*d^2*f^2 + 2*a^2*b^4*d*f^3 - 12*a^3*b^2*c*d*f^3 + 16*a^4*c^2*d*f^3 + a^4*b^2*f^4 - 4*a^5*c*f^4 - 2*b^3*c^3*d^3*e + 8*a*b*c^4*d^3*e - 2*b^5*c*d^2*f*e + 10*a*b^3*c^2*d^2*f*e - 8*a^2*b*c^3*d^2*f*e - 2*a*b^5*d*f^2*e + 10*a^2*b^3*c*d*f^2*e - 8*a^3*b*c^2*d*f^2*e - 2*a^3*b^3*f^3*e + 8*a^4*b*c*f^3*e + b^4*c^2*d^2*e^2 - 2*a*b^2*c^3*d^2*e^2 - 8*a^2*c^4*d^2*e^2 + 4*a*b^4*c*d*f*e^2 - 20*a^2*b^2*c^2*d*f*e^2 + 16*a^3*c^3*d*f*e^2 + a^2*b^4*f^2*e^2 - 2*a^3*b^2*c*f^2*e^2 - 8*a^4*c^2*f^2*e^2 - 2*a*b^3*c^2*d*e^3 + 8*a^2*b*c^3*d*e^3 - 2*a^2*b^3*c*f*e^3 + 8*a^3*b*c^2*f*e^3 + a^2*b^2*c^2*e^4 - 4*a^3*c^3*e^4)*sqrt(-b^2 + 4*a*c)) - (4*B*b*c*d^2*f^2 - 2*A*c^2*d^2*f^2 - 4*B*a*b*d*f^3 + 2*A*b^2*d*f^3 + 4*A*a*c*d*f^3 - 2*A*a^2*f^4 - 3*B*c^2*d^2*f*e + B*b^2*d*f^2*e + 2*B*a*c*d*f^2*e - 6*A*b*c*d*f^2*e + B*a^2*f^3*e + 2*A*a*b*f^3*e - 2*B*b*c*d*f*e^2 + 4*A*c^2*d*f*e^2 - A*b^2*f^2*e^2 - 2*A*a*c*f^2*e^2 + B*c^2*d*e^3 + 2*A*b*c*f*e^3 - A*c^2*e^4)*arctan((2*f*x + e)/sqrt(4*d*f - e^2))/((c^4*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^3*d^3*f + b^4*d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3 - 4*a^3*c*d*f^3 + a^4*f^4 - 2*b*c^3*d^3*e - 2*b^3*c*d^2*f*e + 2*a*b*c^2*d^2*f*e - 2*a*b^3*d*f^2*e + 2*a^2*b*c*d*f^2*e - 2*a^3*b*f^3*e + b^2*c^2*d^2*e^2 + 2*a*c^3*d^2*e^2 + 4*a*b^2*c*d*f*e^2 - 4*a^2*c^2*d*f*e^2 + a^2*b^2*f^2*e^2 + 2*a^3*c*f^2*e^2 - 2*a*b*c^2*d*e^3 - 2*a^2*b*c*f*e^3 + a^2*c^2*e^4)*sqrt(4*d*f - e^2)) + (2*B*a*c^4*d^3 - A*b*c^4*d^3 + 3*B*a*b^2*c^2*d^2*f - 2*A*b^3*c^2*d^2*f - 6*B*a^2*c^3*d^2*f + 5*A*a*b*c^3*d^2*f + B*a*b^4*d*f^2 - A*b^5*d*f^2 - 4*B*a^2*b^2*c*d*f^2 + 5*A*a*b^3*c*d*f^2 + 6*B*a^3*c^2*d*f^2 - 7*A*a^2*b*c^2*d*f^2 + B*a^3*b^2*f^3 - A*a^2*b^3*f^3 - 2*B*a^4*c*f^3 + 3*A*a^3*b*c*f^3 - 3*B*a*b*c^3*d^2*e + 2*A*b^2*c^3*d^2*e - 2*A*a*c^4*d^2*e - 2*B*a*b^3*c*d*f*e + 2*A*b^4*c*d*f*e + 2*B*a^2*b*c^2*d*f*e - 6*A*a*b^2*c^2*d*f*e + 4*A*a^2*c^3*d*f*e - B*a^2*b^3*f^2*e + A*a*b^4*f^2*e + B*a^3*b*c*f^2*e - 2*A*a^2*b^2*c*f^2*e - 2*A*a^3*c^2*f^2*e + B*a*b^2*c^2*d*e^2 - A*b^3*c^2*d*e^2 + 2*B*a^2*c^3*d*e^2 + A*a*b*c^3*d*e^2 + 2*B*a^2*b^2*c*f*e^2 - 2*A*a*b^3*c*f*e^2 - 2*B*a^3*c^2*f*e^2 + 5*A*a^2*b*c^2*f*e^2 - B*a^2*b*c^2*e^3 + A*a*b^2*c^2*e^3 - 2*A*a^2*c^3*e^3 + (B*b*c^4*d^3 - 2*A*c^5*d^3 + B*b^3*c^2*d^2*f - B*a*b*c^3*d^2*f - 3*A*b^2*c^3*d^2*f + 6*A*a*c^4*d^2*f + B*a*b^3*c*d*f^2 - A*b^4*c*d*f^2 - B*a^2*b*c^2*d*f^2 + 4*A*a*b^2*c^2*d*f^2 - 6*A*a^2*c^3*d*f^2 + B*a^3*b*c*f^3 - A*a^2*b^2*c*f^3 + 2*A*a^3*c^2*f^3 - B*b^2*c^3*d^2*e - 2*B*a*c^4*d^2*e + 3*A*b*c^4*d^2*e - 4*B*a*b^2*c^2*d*f*e + 2*A*b^3*c^2*d*f*e + 4*B*a^2*c^3*d*f*e - 2*A*a*b*c^3*d*f*e - B*a^2*b^2*c*f^2*e + A*a*b^3*c*f^2*e - 2*B*a^3*c^2*f^2*e - A*a^2*b*c^2*f^2*e + 3*B*a*b*c^3*d*e^2 - A*b^2*c^3*d*e^2 - 2*A*a*c^4*d*e^2 + 3*B*a^2*b*c^2*f*e^2 - 2*A*a*b^2*c^2*f*e^2 + 2*A*a^2*c^3*f*e^2 - 2*B*a^2*c^3*e^3 + A*a*b*c^3*e^3)*x)/((c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2 - b*c*d*e - a*b*f*e + a*c*e^2)^2*(c*x^2 + b*x + a)*(b^2 - 4*a*c))","B",0
17,1,219,0,0.172266," ","integrate((h*x+g)/(c*x^2+b*x+a)/(c*d*x^2+b*d*x+a*d)^2,x, algorithm=""giac"")","\frac{6 \, {\left(2 \, c^{2} g - b c h\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} d^{2} - 8 \, a b^{2} c d^{2} + 16 \, a^{2} c^{2} d^{2}\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} g x^{3} - 6 \, b c^{2} h x^{3} + 18 \, b c^{2} g x^{2} - 9 \, b^{2} c h x^{2} + 4 \, b^{2} c g x + 20 \, a c^{2} g x - 2 \, b^{3} h x - 10 \, a b c h x - b^{3} g + 10 \, a b c g - a b^{2} h - 8 \, a^{2} c h}{2 \, {\left(b^{4} d^{2} - 8 \, a b^{2} c d^{2} + 16 \, a^{2} c^{2} d^{2}\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"6*(2*c^2*g - b*c*h)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*d^2 - 8*a*b^2*c*d^2 + 16*a^2*c^2*d^2)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^3*g*x^3 - 6*b*c^2*h*x^3 + 18*b*c^2*g*x^2 - 9*b^2*c*h*x^2 + 4*b^2*c*g*x + 20*a*c^2*g*x - 2*b^3*h*x - 10*a*b*c*h*x - b^3*g + 10*a*b*c*g - a*b^2*h - 8*a^2*c*h)/((b^4*d^2 - 8*a*b^2*c*d^2 + 16*a^2*c^2*d^2)*(c*x^2 + b*x + a)^2)","A",0
18,1,207,0,0.170301," ","integrate((h*x+g)/(c*x^2+b*x+a)^2/(c*d*x^2+b*d*x+a*d),x, algorithm=""giac"")","\frac{6 \, {\left(2 \, c^{2} g - b c h\right)} \arctan\left(\frac{2 \, c x + b}{\sqrt{-b^{2} + 4 \, a c}}\right)}{{\left(b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d\right)} \sqrt{-b^{2} + 4 \, a c}} + \frac{12 \, c^{3} g x^{3} - 6 \, b c^{2} h x^{3} + 18 \, b c^{2} g x^{2} - 9 \, b^{2} c h x^{2} + 4 \, b^{2} c g x + 20 \, a c^{2} g x - 2 \, b^{3} h x - 10 \, a b c h x - b^{3} g + 10 \, a b c g - a b^{2} h - 8 \, a^{2} c h}{2 \, {\left(b^{4} d - 8 \, a b^{2} c d + 16 \, a^{2} c^{2} d\right)} {\left(c x^{2} + b x + a\right)}^{2}}"," ",0,"6*(2*c^2*g - b*c*h)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d)*sqrt(-b^2 + 4*a*c)) + 1/2*(12*c^3*g*x^3 - 6*b*c^2*h*x^3 + 18*b*c^2*g*x^2 - 9*b^2*c*h*x^2 + 4*b^2*c*g*x + 20*a*c^2*g*x - 2*b^3*h*x - 10*a*b*c*h*x - b^3*g + 10*a*b*c*g - a*b^2*h - 8*a^2*c*h)/((b^4*d - 8*a*b^2*c*d + 16*a^2*c^2*d)*(c*x^2 + b*x + a)^2)","A",0
19,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
20,-2,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
21,-2,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)/(f*x^2+e*x+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{poly1[%%%{-4,[3,2,0]%%%}+%%%{16,[1,3,1]%%%},%%%{4,[4,2,0]%%%}+%%%{-24,[2,3,1]%%%}+%%%{32,[0,4,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[2,1,0,0,0]%%%}+%%%{%%{[%%%{-4,[5,0,0]%%%}+%%%{24,[3,1,1]%%%}+%%%{-32,[1,2,2]%%%},%%%{4,[6,0,0]%%%}+%%%{-32,[4,1,1]%%%}+%%%{72,[2,2,2]%%%}+%%%{-32,[0,3,3]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[2,0,0,1,0]%%%}+%%%{%%{[%%%{4,[4,1,0]%%%}+%%%{-20,[2,2,1]%%%}+%%%{16,[0,3,2]%%%},%%%{-4,[5,1,0]%%%}+%%%{28,[3,2,1]%%%}+%%%{-48,[1,3,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[2,0,0,0,1]%%%}+%%%{%%{poly1[%%%{8,[2,3,0]%%%}+%%%{-32,[0,4,1]%%%},%%%{-8,[3,3,0]%%%}+%%%{32,[1,4,1]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[1,1,1,0,0]%%%}+%%%{%%{[%%%{8,[4,1,0]%%%}+%%%{-40,[2,2,1]%%%}+%%%{32,[0,3,2]%%%},%%%{-8,[5,1,0]%%%}+%%%{56,[3,2,1]%%%}+%%%{-96,[1,3,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[1,0,1,1,0]%%%}+%%%{%%{[%%%{-8,[3,2,0]%%%}+%%%{32,[1,3,1]%%%},%%%{8,[4,2,0]%%%}+%%%{-48,[2,3,1]%%%}+%%%{64,[0,4,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[1,0,1,0,1]%%%}+%%%{%%%{8,[2,4,0]%%%}+%%%{-32,[0,5,1]%%%},[0,1,2,0,0]%%%}+%%%{%%{poly1[%%%{-4,[3,2,0]%%%}+%%%{16,[1,3,1]%%%},%%%{4,[4,2,0]%%%}+%%%{-24,[2,3,1]%%%}+%%%{32,[0,4,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[0,0,2,1,0]%%%}+%%%{%%{poly1[%%%{4,[2,3,0]%%%}+%%%{-16,[0,4,1]%%%},%%%{-4,[3,3,0]%%%}+%%%{16,[1,4,1]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[0,0,2,0,1]%%%} / %%%{%%{[%%%{4,[3,2,0]%%%}+%%%{-16,[1,3,1]%%%},%%%{-4,[4,2,0]%%%}+%%%{24,[2,3,1]%%%}+%%%{-32,[0,4,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[0,1,0,0,0]%%%}+%%%{%%{[%%%{4,[5,0,0]%%%}+%%%{-24,[3,1,1]%%%}+%%%{32,[1,2,2]%%%},%%%{-4,[6,0,0]%%%}+%%%{32,[4,1,1]%%%}+%%%{-72,[2,2,2]%%%}+%%%{32,[0,3,3]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[0,0,0,1,0]%%%}+%%%{%%{[%%%{-4,[4,1,0]%%%}+%%%{20,[2,2,1]%%%}+%%%{-16,[0,3,2]%%%},%%%{4,[5,1,0]%%%}+%%%{-28,[3,2,1]%%%}+%%%{48,[1,3,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[0,0,0,0,1]%%%} Error: Bad Argument ValueEvaluation time: 0.92Unable to divide, perhaps due to rounding error%%%{%%{[%%%{1,[3,0,0]%%%}+%%%{-4,[1,1,1]%%%},%%%{1,[4,0,0]%%%}+%%%{-6,[2,1,1]%%%}+%%%{8,[0,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,2]%%%},[2,1,0,0,0]%%%}+%%%{%%%{1,[2,0,0]%%%}+%%%{-4,[0,1,1]%%%}/2,[2,0,0,1,0]%%%}+%%%{%%{[%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%},%%%{-1,[3,0,0]%%%}+%%%{4,[1,1,1]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,1]%%%},[2,0,0,0,1]%%%}+%%%{%%{[%%%{-1,[4,0,0]%%%}+%%%{5,[2,1,1]%%%}+%%%{-4,[0,2,2]%%%},%%%{-1,[5,0,0]%%%}+%%%{7,[3,1,1]%%%}+%%%{-12,[1,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{2,[0,0,3]%%%},[1,1,1,0,0]%%%}+%%%{%%{[%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%},%%%{-1,[3,0,0]%%%}+%%%{4,[1,1,1]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{2,[0,0,1]%%%},[1,0,1,1,0]%%%}+%%%{%%{[%%%{1,[3,0,0]%%%}+%%%{-4,[1,1,1]%%%},%%%{1,[4,0,0]%%%}+%%%{-6,[2,1,1]%%%}+%%%{8,[0,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{2,[0,0,2]%%%},[1,0,1,0,1]%%%}+%%%{%%{[%%%{1,[5,0,0]%%%}+%%%{-6,[3,1,1]%%%}+%%%{8,[1,2,2]%%%},%%%{1,[6,0,0]%%%}+%%%{-8,[4,1,1]%%%}+%%%{18,[2,2,2]%%%}+%%%{-8,[0,3,3]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,4]%%%},[0,1,2,0,0]%%%}+%%%{%%{[%%%{1,[3,0,0]%%%}+%%%{-4,[1,1,1]%%%},%%%{1,[4,0,0]%%%}+%%%{-6,[2,1,1]%%%}+%%%{8,[0,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,2]%%%},[0,0,2,1,0]%%%}+%%%{%%{[%%%{-1,[4,0,0]%%%}+%%%{5,[2,1,1]%%%}+%%%{-4,[0,2,2]%%%},%%%{-1,[5,0,0]%%%}+%%%{7,[3,1,1]%%%}+%%%{-12,[1,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,3]%%%},[0,0,2,0,1]%%%} / %%%{%%{[%%%{-1,[3,0,0]%%%}+%%%{4,[1,1,1]%%%},%%%{-1,[4,0,0]%%%}+%%%{6,[2,1,1]%%%}+%%%{-8,[0,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,4]%%%},[0,1,0,0,0]%%%}+%%%{%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}/%%%{2,[0,0,2]%%%},[0,0,0,1,0]%%%}+%%%{%%{[%%%{1,[2,0,0]%%%}+%%%{-4,[0,1,1]%%%},%%%{1,[3,0,0]%%%}+%%%{-4,[1,1,1]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,3]%%%},[0,0,0,0,1]%%%} Error: Bad Argument Value","F(-2)",0
22,-2,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+a)/(f*x^2+e*x+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueConj Error: Bad Argument Type","F(-2)",0
23,-2,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)/(f*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{poly1[%%%{-4,[3,2,0]%%%}+%%%{16,[1,3,1]%%%},%%%{4,[4,2,0]%%%}+%%%{-24,[2,3,1]%%%}+%%%{32,[0,4,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[2,1,0,0]%%%}+%%%{%%{[%%%{-4,[5,0,0]%%%}+%%%{24,[3,1,1]%%%}+%%%{-32,[1,2,2]%%%},%%%{4,[6,0,0]%%%}+%%%{-32,[4,1,1]%%%}+%%%{72,[2,2,2]%%%}+%%%{-32,[0,3,3]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[2,0,0,1]%%%}+%%%{%%{poly1[%%%{8,[2,3,0]%%%}+%%%{-32,[0,4,1]%%%},%%%{-8,[3,3,0]%%%}+%%%{32,[1,4,1]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[1,1,1,0]%%%}+%%%{%%{[%%%{8,[4,1,0]%%%}+%%%{-40,[2,2,1]%%%}+%%%{32,[0,3,2]%%%},%%%{-8,[5,1,0]%%%}+%%%{56,[3,2,1]%%%}+%%%{-96,[1,3,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[1,0,1,1]%%%}+%%%{%%%{8,[2,4,0]%%%}+%%%{-32,[0,5,1]%%%},[0,1,2,0]%%%}+%%%{%%{poly1[%%%{-4,[3,2,0]%%%}+%%%{16,[1,3,1]%%%},%%%{4,[4,2,0]%%%}+%%%{-24,[2,3,1]%%%}+%%%{32,[0,4,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[0,0,2,1]%%%} / %%%{%%{[%%%{-4,[3,2,0]%%%}+%%%{16,[1,3,1]%%%},%%%{4,[4,2,0]%%%}+%%%{-24,[2,3,1]%%%}+%%%{32,[0,4,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[0,1,0,0]%%%}+%%%{%%{[%%%{-4,[5,0,0]%%%}+%%%{24,[3,1,1]%%%}+%%%{-32,[1,2,2]%%%},%%%{4,[6,0,0]%%%}+%%%{-32,[4,1,1]%%%}+%%%{72,[2,2,2]%%%}+%%%{-32,[0,3,3]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%},[0,0,0,1]%%%} Error: Bad Argument ValueUnable to divide, perhaps due to rounding error%%%{%%{[%%%{1,[3,0,0]%%%}+%%%{-4,[1,1,1]%%%},%%%{1,[4,0,0]%%%}+%%%{-6,[2,1,1]%%%}+%%%{8,[0,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,2]%%%},[2,1,0,0]%%%}+%%%{%%%{1,[2,0,0]%%%}+%%%{-4,[0,1,1]%%%}/2,[2,0,0,1]%%%}+%%%{%%{[%%%{-1,[4,0,0]%%%}+%%%{5,[2,1,1]%%%}+%%%{-4,[0,2,2]%%%},%%%{-1,[5,0,0]%%%}+%%%{7,[3,1,1]%%%}+%%%{-12,[1,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{2,[0,0,3]%%%},[1,1,1,0]%%%}+%%%{%%{[%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%},%%%{-1,[3,0,0]%%%}+%%%{4,[1,1,1]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{2,[0,0,1]%%%},[1,0,1,1]%%%}+%%%{%%{[%%%{1,[5,0,0]%%%}+%%%{-6,[3,1,1]%%%}+%%%{8,[1,2,2]%%%},%%%{1,[6,0,0]%%%}+%%%{-8,[4,1,1]%%%}+%%%{18,[2,2,2]%%%}+%%%{-8,[0,3,3]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,4]%%%},[0,1,2,0]%%%}+%%%{%%{[%%%{1,[3,0,0]%%%}+%%%{-4,[1,1,1]%%%},%%%{1,[4,0,0]%%%}+%%%{-6,[2,1,1]%%%}+%%%{8,[0,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,2]%%%},[0,0,2,1]%%%} / %%%{%%{[%%%{1,[3,0,0]%%%}+%%%{-4,[1,1,1]%%%},%%%{1,[4,0,0]%%%}+%%%{-6,[2,1,1]%%%}+%%%{8,[0,2,2]%%%}]:[1,0,%%%{-1,[2,0,0]%%%}+%%%{4,[0,1,1]%%%}]%%}/%%%{4,[0,0,4]%%%},[0,1,0,0]%%%}+%%%{%%%{1,[2,0,0]%%%}+%%%{-4,[0,1,1]%%%}/%%%{2,[0,0,2]%%%},[0,0,0,1]%%%} Error: Bad Argument Value","F(-2)",0
24,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+a)/(f*x^2+d)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,1,93,0,0.476663," ","integrate((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(1/2),x, algorithm=""giac"")","0.169235232112667 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} + 5.90976932712000\right) - 0.686556214893333 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 0.176527156327000\right) + 0.686556214893333 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 0.919278730509000\right) - 0.169235232112667 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 1.04272727395000\right)"," ",0,"0.169235232112667*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) + 5.90976932712000) - 0.686556214893333*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 0.176527156327000) + 0.686556214893333*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 0.919278730509000) - 0.169235232112667*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 1.04272727395000)","A",0
29,1,112,0,0.498716," ","integrate((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(22 \, x + 21\right)}}{5 \, \sqrt{2 \, x^{2} + 3 \, x + 1}} + 0.0140045514133333 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} + 5.90976932712000\right) - 4.97793168620000 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 0.176527156327000\right) + 4.97793168620000 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 0.919278730509000\right) - 0.0140045514125333 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 1.04272727395000\right)"," ",0,"2/5*(22*x + 21)/sqrt(2*x^2 + 3*x + 1) + 0.0140045514133333*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) + 5.90976932712000) - 4.97793168620000*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 0.176527156327000) + 4.97793168620000*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 0.919278730509000) - 0.0140045514125333*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 1.04272727395000)","A",0
30,1,121,0,0.540844," ","integrate((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left({\left(4 \, {\left(115 \, x + 309\right)} x + 1071\right)} x + 294\right)}}{15 \, {\left(2 \, x^{2} + 3 \, x + 1\right)}^{\frac{3}{2}}} + 0.00115890443050800 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} + 5.90976932712000\right) - 36.0928986365333 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 0.176527156327000\right) + 36.0928986365333 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 0.919278730509000\right) - 0.00115890442528267 \, \log\left(-\sqrt{2} x + \sqrt{2 \, x^{2} + 3 \, x + 1} - 1.04272727395000\right)"," ",0,"2/15*((4*(115*x + 309)*x + 1071)*x + 294)/(2*x^2 + 3*x + 1)^(3/2) + 0.00115890443050800*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) + 5.90976932712000) - 36.0928986365333*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 0.176527156327000) + 36.0928986365333*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 0.919278730509000) - 0.00115890442528267*log(-sqrt(2)*x + sqrt(2*x^2 + 3*x + 1) - 1.04272727395000)","A",0
31,1,31,0,0.347499," ","integrate((1+x)/(x^2+2*x+4)/(x^2+2*x+5)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\sqrt{x^{2} + 2 \, x + 5} + 1\right) + \frac{1}{2} \, \log\left(\sqrt{x^{2} + 2 \, x + 5} - 1\right)"," ",0,"-1/2*log(sqrt(x^2 + 2*x + 5) + 1) + 1/2*log(sqrt(x^2 + 2*x + 5) - 1)","B",0
32,1,108,0,0.373631," ","integrate((4+x)/(x^2+2*x+4)/(x^2+2*x+5)^(1/2),x, algorithm=""giac"")","-\sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(x - \sqrt{x^{2} + 2 \, x + 5} + 2\right)}\right) + \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(x - \sqrt{x^{2} + 2 \, x + 5}\right)}\right) + \frac{1}{2} \, \log\left({\left(x - \sqrt{x^{2} + 2 \, x + 5}\right)}^{2} + 4 \, x - 4 \, \sqrt{x^{2} + 2 \, x + 5} + 7\right) - \frac{1}{2} \, \log\left({\left(x - \sqrt{x^{2} + 2 \, x + 5}\right)}^{2} + 3\right)"," ",0,"-sqrt(3)*arctan(-1/3*sqrt(3)*(x - sqrt(x^2 + 2*x + 5) + 2)) + sqrt(3)*arctan(-1/3*sqrt(3)*(x - sqrt(x^2 + 2*x + 5))) + 1/2*log((x - sqrt(x^2 + 2*x + 5))^2 + 4*x - 4*sqrt(x^2 + 2*x + 5) + 7) - 1/2*log((x - sqrt(x^2 + 2*x + 5))^2 + 3)","B",0
33,1,39,0,0.355077," ","integrate((1+2*x)/(x^2+x+3)/(x^2+x+5)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\sqrt{2} + \sqrt{x^{2} + x + 5}\right) + \frac{1}{2} \, \sqrt{2} \log\left(-\sqrt{2} + \sqrt{x^{2} + x + 5}\right)"," ",0,"-1/2*sqrt(2)*log(sqrt(2) + sqrt(x^2 + x + 5)) + 1/2*sqrt(2)*log(-sqrt(2) + sqrt(x^2 + x + 5))","B",0
34,1,133,0,0.319483," ","integrate(x/(x^2+x+3)/(x^2+x+5)^(1/2),x, algorithm=""giac"")","\frac{1}{22} \, \sqrt{11} \sqrt{2} \arctan\left(-\frac{1}{11} \, \sqrt{11} {\left(2 \, x + 2 \, \sqrt{2} - 2 \, \sqrt{x^{2} + x + 5} + 1\right)}\right) - \frac{1}{22} \, \sqrt{11} \sqrt{2} \arctan\left(-\frac{1}{11} \, \sqrt{11} {\left(2 \, x - 2 \, \sqrt{2} - 2 \, \sqrt{x^{2} + x + 5} + 1\right)}\right) + \frac{1}{4} \, \sqrt{2} \log\left(324 \, {\left(2 \, x + 2 \, \sqrt{2} - 2 \, \sqrt{x^{2} + x + 5} + 1\right)}^{2} + 3564\right) - \frac{1}{4} \, \sqrt{2} \log\left(324 \, {\left(2 \, x - 2 \, \sqrt{2} - 2 \, \sqrt{x^{2} + x + 5} + 1\right)}^{2} + 3564\right)"," ",0,"1/22*sqrt(11)*sqrt(2)*arctan(-1/11*sqrt(11)*(2*x + 2*sqrt(2) - 2*sqrt(x^2 + x + 5) + 1)) - 1/22*sqrt(11)*sqrt(2)*arctan(-1/11*sqrt(11)*(2*x - 2*sqrt(2) - 2*sqrt(x^2 + x + 5) + 1)) + 1/4*sqrt(2)*log(324*(2*x + 2*sqrt(2) - 2*sqrt(x^2 + x + 5) + 1)^2 + 3564) - 1/4*sqrt(2)*log(324*(2*x - 2*sqrt(2) - 2*sqrt(x^2 + x + 5) + 1)^2 + 3564)","B",0
35,-2,0,0,0.000000," ","integrate((B*x+A)/(b*f*x^2+b*e*x+a*e)^2/(f*x^2+e*x+d)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%%{1,[2]%%%},[8,2,0,0,0]%%%}+%%%{%%{[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,2,1,0,0]%%%}+%%%{%%%{6,[1]%%%},[6,2,2,0,0]%%%}+%%%{%%%{-4,[2]%%%},[6,2,0,0,1]%%%}+%%%{%%%{8,[2]%%%},[6,1,1,1,0]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[5,2,3,0,0]%%%}+%%%{%%{[%%%{12,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,2,1,0,1]%%%}+%%%{%%{[%%%{-24,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,2,1,0]%%%}+%%%{1,[4,2,4,0,0]%%%}+%%%{%%%{-14,[1]%%%},[4,2,2,0,1]%%%}+%%%{%%%{6,[2]%%%},[4,2,0,0,2]%%%}+%%%{%%%{26,[1]%%%},[4,1,3,1,0]%%%}+%%%{%%%{-16,[2]%%%},[4,1,1,1,1]%%%}+%%%{%%%{16,[2]%%%},[4,0,2,2,0]%%%}+%%%{%%{[8,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,3,0,1]%%%}+%%%{%%{[%%%{-12,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,1,0,2]%%%}+%%%{%%{[-12,0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,4,1,0]%%%}+%%%{%%{[%%%{32,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,2,1,1]%%%}+%%%{%%{[%%%{-32,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,3,2,0]%%%}+%%%{-2,[2,2,4,0,1]%%%}+%%%{%%%{10,[1]%%%},[2,2,2,0,2]%%%}+%%%{%%%{-4,[2]%%%},[2,2,0,0,3]%%%}+%%%{2,[2,1,5,1,0]%%%}+%%%{%%%{-28,[1]%%%},[2,1,3,1,1]%%%}+%%%{%%%{8,[2]%%%},[2,1,1,1,2]%%%}+%%%{%%%{24,[1]%%%},[2,0,4,2,0]%%%}+%%%{%%{[-4,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,3,0,2]%%%}+%%%{%%{[%%%{4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,1,0,3]%%%}+%%%{%%{[12,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,4,1,1]%%%}+%%%{%%{[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,2,1,2]%%%}+%%%{%%{[-8,0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,5,2,0]%%%}+%%%{1,[0,2,4,0,2]%%%}+%%%{%%%{-2,[1]%%%},[0,2,2,0,3]%%%}+%%%{%%%{1,[2]%%%},[0,2,0,0,4]%%%}+%%%{-2,[0,1,5,1,1]%%%}+%%%{%%%{2,[1]%%%},[0,1,3,1,2]%%%}+%%%{1,[0,0,6,2,0]%%%} / %%%{%%%{1,[3]%%%},[8,2,0,0,0]%%%}+%%%{%%{poly1[%%%{-4,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[7,2,1,0,0]%%%}+%%%{%%%{6,[2]%%%},[6,2,2,0,0]%%%}+%%%{%%%{-4,[3]%%%},[6,2,0,0,1]%%%}+%%%{%%%{8,[3]%%%},[6,1,1,1,0]%%%}+%%%{%%{poly1[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,2,3,0,0]%%%}+%%%{%%{poly1[%%%{12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,2,1,0,1]%%%}+%%%{%%{poly1[%%%{-24,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[5,1,2,1,0]%%%}+%%%{%%%{1,[1]%%%},[4,2,4,0,0]%%%}+%%%{%%%{-14,[2]%%%},[4,2,2,0,1]%%%}+%%%{%%%{6,[3]%%%},[4,2,0,0,2]%%%}+%%%{%%%{26,[2]%%%},[4,1,3,1,0]%%%}+%%%{%%%{-16,[3]%%%},[4,1,1,1,1]%%%}+%%%{%%%{16,[3]%%%},[4,0,2,2,0]%%%}+%%%{%%{poly1[%%%{8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,3,0,1]%%%}+%%%{%%{poly1[%%%{-12,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,2,1,0,2]%%%}+%%%{%%{poly1[%%%{-12,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,4,1,0]%%%}+%%%{%%{poly1[%%%{32,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,1,2,1,1]%%%}+%%%{%%{poly1[%%%{-32,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[3,0,3,2,0]%%%}+%%%{%%%{-2,[1]%%%},[2,2,4,0,1]%%%}+%%%{%%%{10,[2]%%%},[2,2,2,0,2]%%%}+%%%{%%%{-4,[3]%%%},[2,2,0,0,3]%%%}+%%%{%%%{2,[1]%%%},[2,1,5,1,0]%%%}+%%%{%%%{-28,[2]%%%},[2,1,3,1,1]%%%}+%%%{%%%{8,[3]%%%},[2,1,1,1,2]%%%}+%%%{%%%{24,[2]%%%},[2,0,4,2,0]%%%}+%%%{%%{poly1[%%%{-4,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,3,0,2]%%%}+%%%{%%{poly1[%%%{4,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,2,1,0,3]%%%}+%%%{%%{poly1[%%%{12,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,4,1,1]%%%}+%%%{%%{poly1[%%%{-8,[2]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,1,2,1,2]%%%}+%%%{%%{poly1[%%%{-8,[1]%%%},0]:[1,0,%%%{-1,[1]%%%}]%%},[1,0,5,2,0]%%%}+%%%{%%%{1,[1]%%%},[0,2,4,0,2]%%%}+%%%{%%%{-2,[2]%%%},[0,2,2,0,3]%%%}+%%%{%%%{1,[3]%%%},[0,2,0,0,4]%%%}+%%%{%%%{-2,[1]%%%},[0,1,5,1,1]%%%}+%%%{%%%{2,[2]%%%},[0,1,3,1,2]%%%}+%%%{%%%{1,[1]%%%},[0,0,6,2,0]%%%} Error: Bad Argument Value","F(-2)",0
36,1,81,0,0.265925," ","integrate((h*x+g)*(c*x^2+b*x+a)^(1/2)/(c*d*x^2+b*d*x+a*d)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c d^{2} g - b d^{2} h\right)} x}{b^{2} d^{4} - 4 \, a c d^{4}} + \frac{b d^{2} g - 2 \, a d^{2} h}{b^{2} d^{4} - 4 \, a c d^{4}}\right)}}{\sqrt{c x^{2} + b x + a}}"," ",0,"-2*((2*c*d^2*g - b*d^2*h)*x/(b^2*d^4 - 4*a*c*d^4) + (b*d^2*g - 2*a*d^2*h)/(b^2*d^4 - 4*a*c*d^4))/sqrt(c*x^2 + b*x + a)","A",0
37,1,98,0,0.230631," ","integrate((3+2*x)/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) - \frac{1}{2} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"1/2*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) - 1/2*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","B",0
38,1,163,0,0.274996," ","integrate((3+4*x)/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) + \frac{1}{2} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) - \frac{1}{2} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/2*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) - 1/2*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","B",0
39,0,0,0,0.000000," ","integrate((h*x+g)*(c*x^2+b*x+a)^(1/2)/(c*d*x^2+b*d*x+a*d)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{c x^{2} + b x + a} {\left(h x + g\right)}}{{\left(c d x^{2} + b d x + a d\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(c*x^2 + b*x + a)*(h*x + g)/(c*d*x^2 + b*d*x + a*d)^(3/2), x)","F",0
40,1,117,0,0.252735," ","integrate(x^2*((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{a c^{2} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right) \mathrm{sgn}\left(b x + a\right)}{8 \, d^{\frac{3}{2}}} + \frac{1}{120} \, \sqrt{d x^{2} + c} {\left({\left(2 \, {\left(3 \, {\left(4 \, b x \mathrm{sgn}\left(b x + a\right) + 5 \, a \mathrm{sgn}\left(b x + a\right)\right)} x + \frac{4 \, b c \mathrm{sgn}\left(b x + a\right)}{d}\right)} x + \frac{15 \, a c \mathrm{sgn}\left(b x + a\right)}{d}\right)} x - \frac{16 \, b c^{2} \mathrm{sgn}\left(b x + a\right)}{d^{2}}\right)}"," ",0,"1/8*a*c^2*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))*sgn(b*x + a)/d^(3/2) + 1/120*sqrt(d*x^2 + c)*((2*(3*(4*b*x*sgn(b*x + a) + 5*a*sgn(b*x + a))*x + 4*b*c*sgn(b*x + a)/d)*x + 15*a*c*sgn(b*x + a)/d)*x - 16*b*c^2*sgn(b*x + a)/d^2)","A",0
41,1,98,0,0.212625," ","integrate(x*((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{b c^{2} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right) \mathrm{sgn}\left(b x + a\right)}{8 \, d^{\frac{3}{2}}} + \frac{1}{24} \, \sqrt{d x^{2} + c} {\left({\left(2 \, {\left(3 \, b x \mathrm{sgn}\left(b x + a\right) + 4 \, a \mathrm{sgn}\left(b x + a\right)\right)} x + \frac{3 \, b c \mathrm{sgn}\left(b x + a\right)}{d}\right)} x + \frac{8 \, a c \mathrm{sgn}\left(b x + a\right)}{d}\right)}"," ",0,"1/8*b*c^2*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))*sgn(b*x + a)/d^(3/2) + 1/24*sqrt(d*x^2 + c)*((2*(3*b*x*sgn(b*x + a) + 4*a*sgn(b*x + a))*x + 3*b*c*sgn(b*x + a)/d)*x + 8*a*c*sgn(b*x + a)/d)","A",0
42,1,79,0,0.270522," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{a c \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right) \mathrm{sgn}\left(b x + a\right)}{2 \, \sqrt{d}} + \frac{1}{6} \, \sqrt{d x^{2} + c} {\left({\left(2 \, b x \mathrm{sgn}\left(b x + a\right) + 3 \, a \mathrm{sgn}\left(b x + a\right)\right)} x + \frac{2 \, b c \mathrm{sgn}\left(b x + a\right)}{d}\right)}"," ",0,"-1/2*a*c*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))*sgn(b*x + a)/sqrt(d) + 1/6*sqrt(d*x^2 + c)*((2*b*x*sgn(b*x + a) + 3*a*sgn(b*x + a))*x + 2*b*c*sgn(b*x + a)/d)","A",0
43,1,102,0,0.247210," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x,x, algorithm=""giac"")","\frac{2 \, a c \arctan\left(-\frac{\sqrt{d} x - \sqrt{d x^{2} + c}}{\sqrt{-c}}\right) \mathrm{sgn}\left(b x + a\right)}{\sqrt{-c}} - \frac{b c \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right) \mathrm{sgn}\left(b x + a\right)}{2 \, \sqrt{d}} + \frac{1}{2} \, \sqrt{d x^{2} + c} {\left(b x \mathrm{sgn}\left(b x + a\right) + 2 \, a \mathrm{sgn}\left(b x + a\right)\right)}"," ",0,"2*a*c*arctan(-(sqrt(d)*x - sqrt(d*x^2 + c))/sqrt(-c))*sgn(b*x + a)/sqrt(-c) - 1/2*b*c*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))*sgn(b*x + a)/sqrt(d) + 1/2*sqrt(d*x^2 + c)*(b*x*sgn(b*x + a) + 2*a*sgn(b*x + a))","A",0
44,1,126,0,0.260468," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x^2,x, algorithm=""giac"")","\frac{2 \, b c \arctan\left(-\frac{\sqrt{d} x - \sqrt{d x^{2} + c}}{\sqrt{-c}}\right) \mathrm{sgn}\left(b x + a\right)}{\sqrt{-c}} - a \sqrt{d} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right) \mathrm{sgn}\left(b x + a\right) + \sqrt{d x^{2} + c} b \mathrm{sgn}\left(b x + a\right) + \frac{2 \, a c \sqrt{d} \mathrm{sgn}\left(b x + a\right)}{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c}"," ",0,"2*b*c*arctan(-(sqrt(d)*x - sqrt(d*x^2 + c))/sqrt(-c))*sgn(b*x + a)/sqrt(-c) - a*sqrt(d)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))*sgn(b*x + a) + sqrt(d*x^2 + c)*b*sgn(b*x + a) + 2*a*c*sqrt(d)*sgn(b*x + a)/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)","A",0
45,1,199,0,0.275211," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x^3,x, algorithm=""giac"")","\frac{a d \arctan\left(-\frac{\sqrt{d} x - \sqrt{d x^{2} + c}}{\sqrt{-c}}\right) \mathrm{sgn}\left(b x + a\right)}{\sqrt{-c}} - b \sqrt{d} \log\left({\left| -\sqrt{d} x + \sqrt{d x^{2} + c} \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{3} a d \mathrm{sgn}\left(b x + a\right) + 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c \sqrt{d} \mathrm{sgn}\left(b x + a\right) + {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)} a c d \mathrm{sgn}\left(b x + a\right) - 2 \, b c^{2} \sqrt{d} \mathrm{sgn}\left(b x + a\right)}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} - c\right)}^{2}}"," ",0,"a*d*arctan(-(sqrt(d)*x - sqrt(d*x^2 + c))/sqrt(-c))*sgn(b*x + a)/sqrt(-c) - b*sqrt(d)*log(abs(-sqrt(d)*x + sqrt(d*x^2 + c)))*sgn(b*x + a) + ((sqrt(d)*x - sqrt(d*x^2 + c))^3*a*d*sgn(b*x + a) + 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c*sqrt(d)*sgn(b*x + a) + (sqrt(d)*x - sqrt(d*x^2 + c))*a*c*d*sgn(b*x + a) - 2*b*c^2*sqrt(d)*sgn(b*x + a))/((sqrt(d)*x - sqrt(d*x^2 + c))^2 - c)^2","A",0
46,1,368,0,0.310561," ","integrate(x^2*((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x, algorithm=""giac"")","\frac{1}{1920} \, \sqrt{d x^{2} + x e + c} {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, b x \mathrm{sgn}\left(b x + a\right) + \frac{10 \, a d^{4} \mathrm{sgn}\left(b x + a\right) + b d^{3} e \mathrm{sgn}\left(b x + a\right)}{d^{4}}\right)} x + \frac{16 \, b c d^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a d^{3} e \mathrm{sgn}\left(b x + a\right) - 7 \, b d^{2} e^{2} \mathrm{sgn}\left(b x + a\right)}{d^{4}}\right)} x + \frac{120 \, a c d^{3} \mathrm{sgn}\left(b x + a\right) - 116 \, b c d^{2} e \mathrm{sgn}\left(b x + a\right) - 50 \, a d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 35 \, b d e^{3} \mathrm{sgn}\left(b x + a\right)}{d^{4}}\right)} x - \frac{256 \, b c^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 520 \, a c d^{2} e \mathrm{sgn}\left(b x + a\right) - 460 \, b c d e^{2} \mathrm{sgn}\left(b x + a\right) - 150 \, a d e^{3} \mathrm{sgn}\left(b x + a\right) + 105 \, b e^{4} \mathrm{sgn}\left(b x + a\right)}{d^{4}}\right)} + \frac{{\left(32 \, a c^{2} d^{3} \mathrm{sgn}\left(b x + a\right) - 48 \, b c^{2} d^{2} e \mathrm{sgn}\left(b x + a\right) - 48 \, a c d^{2} e^{2} \mathrm{sgn}\left(b x + a\right) + 40 \, b c d e^{3} \mathrm{sgn}\left(b x + a\right) + 10 \, a d e^{4} \mathrm{sgn}\left(b x + a\right) - 7 \, b e^{5} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| -2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)} \sqrt{d} - e \right|}\right)}{256 \, d^{\frac{9}{2}}}"," ",0,"1/1920*sqrt(d*x^2 + x*e + c)*(2*(4*(6*(8*b*x*sgn(b*x + a) + (10*a*d^4*sgn(b*x + a) + b*d^3*e*sgn(b*x + a))/d^4)*x + (16*b*c*d^3*sgn(b*x + a) + 10*a*d^3*e*sgn(b*x + a) - 7*b*d^2*e^2*sgn(b*x + a))/d^4)*x + (120*a*c*d^3*sgn(b*x + a) - 116*b*c*d^2*e*sgn(b*x + a) - 50*a*d^2*e^2*sgn(b*x + a) + 35*b*d*e^3*sgn(b*x + a))/d^4)*x - (256*b*c^2*d^2*sgn(b*x + a) + 520*a*c*d^2*e*sgn(b*x + a) - 460*b*c*d*e^2*sgn(b*x + a) - 150*a*d*e^3*sgn(b*x + a) + 105*b*e^4*sgn(b*x + a))/d^4) + 1/256*(32*a*c^2*d^3*sgn(b*x + a) - 48*b*c^2*d^2*e*sgn(b*x + a) - 48*a*c*d^2*e^2*sgn(b*x + a) + 40*b*c*d*e^3*sgn(b*x + a) + 10*a*d*e^4*sgn(b*x + a) - 7*b*e^5*sgn(b*x + a))*log(abs(-2*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))*sqrt(d) - e))/d^(9/2)","A",0
47,1,268,0,0.283189," ","integrate(x*((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x, algorithm=""giac"")","\frac{1}{192} \, \sqrt{d x^{2} + x e + c} {\left(2 \, {\left(4 \, {\left(6 \, b x \mathrm{sgn}\left(b x + a\right) + \frac{8 \, a d^{3} \mathrm{sgn}\left(b x + a\right) + b d^{2} e \mathrm{sgn}\left(b x + a\right)}{d^{3}}\right)} x + \frac{12 \, b c d^{2} \mathrm{sgn}\left(b x + a\right) + 8 \, a d^{2} e \mathrm{sgn}\left(b x + a\right) - 5 \, b d e^{2} \mathrm{sgn}\left(b x + a\right)}{d^{3}}\right)} x + \frac{64 \, a c d^{2} \mathrm{sgn}\left(b x + a\right) - 52 \, b c d e \mathrm{sgn}\left(b x + a\right) - 24 \, a d e^{2} \mathrm{sgn}\left(b x + a\right) + 15 \, b e^{3} \mathrm{sgn}\left(b x + a\right)}{d^{3}}\right)} + \frac{{\left(16 \, b c^{2} d^{2} \mathrm{sgn}\left(b x + a\right) + 32 \, a c d^{2} e \mathrm{sgn}\left(b x + a\right) - 24 \, b c d e^{2} \mathrm{sgn}\left(b x + a\right) - 8 \, a d e^{3} \mathrm{sgn}\left(b x + a\right) + 5 \, b e^{4} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| -2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)} \sqrt{d} - e \right|}\right)}{128 \, d^{\frac{7}{2}}}"," ",0,"1/192*sqrt(d*x^2 + x*e + c)*(2*(4*(6*b*x*sgn(b*x + a) + (8*a*d^3*sgn(b*x + a) + b*d^2*e*sgn(b*x + a))/d^3)*x + (12*b*c*d^2*sgn(b*x + a) + 8*a*d^2*e*sgn(b*x + a) - 5*b*d*e^2*sgn(b*x + a))/d^3)*x + (64*a*c*d^2*sgn(b*x + a) - 52*b*c*d*e*sgn(b*x + a) - 24*a*d*e^2*sgn(b*x + a) + 15*b*e^3*sgn(b*x + a))/d^3) + 1/128*(16*b*c^2*d^2*sgn(b*x + a) + 32*a*c*d^2*e*sgn(b*x + a) - 24*b*c*d*e^2*sgn(b*x + a) - 8*a*d*e^3*sgn(b*x + a) + 5*b*e^4*sgn(b*x + a))*log(abs(-2*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))*sqrt(d) - e))/d^(7/2)","A",0
48,1,185,0,0.301717," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x, algorithm=""giac"")","\frac{1}{24} \, \sqrt{d x^{2} + x e + c} {\left(2 \, {\left(4 \, b x \mathrm{sgn}\left(b x + a\right) + \frac{6 \, a d^{2} \mathrm{sgn}\left(b x + a\right) + b d e \mathrm{sgn}\left(b x + a\right)}{d^{2}}\right)} x + \frac{8 \, b c d \mathrm{sgn}\left(b x + a\right) + 6 \, a d e \mathrm{sgn}\left(b x + a\right) - 3 \, b e^{2} \mathrm{sgn}\left(b x + a\right)}{d^{2}}\right)} - \frac{{\left(8 \, a c d^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, b c d e \mathrm{sgn}\left(b x + a\right) - 2 \, a d e^{2} \mathrm{sgn}\left(b x + a\right) + b e^{3} \mathrm{sgn}\left(b x + a\right)\right)} \log\left({\left| -2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)} \sqrt{d} - e \right|}\right)}{16 \, d^{\frac{5}{2}}}"," ",0,"1/24*sqrt(d*x^2 + x*e + c)*(2*(4*b*x*sgn(b*x + a) + (6*a*d^2*sgn(b*x + a) + b*d*e*sgn(b*x + a))/d^2)*x + (8*b*c*d*sgn(b*x + a) + 6*a*d*e*sgn(b*x + a) - 3*b*e^2*sgn(b*x + a))/d^2) - 1/16*(8*a*c*d^2*sgn(b*x + a) - 4*b*c*d*e*sgn(b*x + a) - 2*a*d*e^2*sgn(b*x + a) + b*e^3*sgn(b*x + a))*log(abs(-2*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))*sqrt(d) - e))/d^(5/2)","A",0
49,-2,0,0,0.000000," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(b*x+a)]Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
50,-2,0,0,0.000000," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(b*x+a)]Unable to divide, perhaps due to rounding error%%%{2,[4,4,0]%%%}+%%%{%%%{-16,[1]%%%},[4,2,1]%%%}+%%%{%%%{32,[2]%%%},[4,0,2]%%%}+%%%{-4,[2,4,1]%%%}+%%%{%%%{32,[1]%%%},[2,2,2]%%%}+%%%{%%%{-64,[2]%%%},[2,0,3]%%%}+%%%{2,[0,4,2]%%%}+%%%{%%%{-16,[1]%%%},[0,2,3]%%%}+%%%{%%%{32,[2]%%%},[0,0,4]%%%} / %%%{4,[4,0,0]%%%}+%%%{-8,[2,0,1]%%%}+%%%{4,[0,0,2]%%%} Error: Bad Argument Value","F(-2)",0
51,1,450,0,0.412876," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x^3,x, algorithm=""giac"")","-b \sqrt{d} \log\left({\left| -2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)} d - \sqrt{d} e \right|}\right) \mathrm{sgn}\left(b x + a\right) + \frac{{\left(4 \, a c d \mathrm{sgn}\left(b x + a\right) + 4 \, b c e \mathrm{sgn}\left(b x + a\right) - a e^{2} \mathrm{sgn}\left(b x + a\right)\right)} \arctan\left(-\frac{\sqrt{d} x - \sqrt{d x^{2} + x e + c}}{\sqrt{-c}}\right)}{4 \, \sqrt{-c} c} + \frac{4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)}^{3} a c d \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)}^{3} b c e \mathrm{sgn}\left(b x + a\right) + 8 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)}^{2} b c^{2} \sqrt{d} \mathrm{sgn}\left(b x + a\right) + 8 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)}^{2} a c \sqrt{d} e \mathrm{sgn}\left(b x + a\right) + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)} a c^{2} d \mathrm{sgn}\left(b x + a\right) + {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)}^{3} a e^{2} \mathrm{sgn}\left(b x + a\right) - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)} b c^{2} e \mathrm{sgn}\left(b x + a\right) - 8 \, b c^{3} \sqrt{d} \mathrm{sgn}\left(b x + a\right) + {\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)} a c e^{2} \mathrm{sgn}\left(b x + a\right)}{4 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + x e + c}\right)}^{2} - c\right)}^{2} c}"," ",0,"-b*sqrt(d)*log(abs(-2*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))*d - sqrt(d)*e))*sgn(b*x + a) + 1/4*(4*a*c*d*sgn(b*x + a) + 4*b*c*e*sgn(b*x + a) - a*e^2*sgn(b*x + a))*arctan(-(sqrt(d)*x - sqrt(d*x^2 + x*e + c))/sqrt(-c))/(sqrt(-c)*c) + 1/4*(4*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))^3*a*c*d*sgn(b*x + a) + 4*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))^3*b*c*e*sgn(b*x + a) + 8*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))^2*b*c^2*sqrt(d)*sgn(b*x + a) + 8*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))^2*a*c*sqrt(d)*e*sgn(b*x + a) + 4*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))*a*c^2*d*sgn(b*x + a) + (sqrt(d)*x - sqrt(d*x^2 + x*e + c))^3*a*e^2*sgn(b*x + a) - 4*(sqrt(d)*x - sqrt(d*x^2 + x*e + c))*b*c^2*e*sgn(b*x + a) - 8*b*c^3*sqrt(d)*sgn(b*x + a) + (sqrt(d)*x - sqrt(d*x^2 + x*e + c))*a*c*e^2*sgn(b*x + a))/(((sqrt(d)*x - sqrt(d*x^2 + x*e + c))^2 - c)^2*c)","B",0
52,-1,0,0,0.000000," ","integrate(x^2*(c*x^2+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate(x*(c*x^2+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,-1,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-2,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/x/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 2Error index.cc index_gcd Error: Bad Argument Value","F(-2)",0
56,-2,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/x^2/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 5.11Error index.cc index_gcd Error: Bad Argument Value","F(-2)",0
57,-2,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/x^3/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
58,0,0,0,0.000000," ","integrate(x^2*(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
59,0,0,0,0.000000," ","integrate(x*(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
60,0,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
61,-2,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/x/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
62,0,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/x^2/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
63,0,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/x^3/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
64,-2,0,0,0.000000," ","integrate(x^3/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 11.34sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
65,-2,0,0,0.000000," ","integrate(x^2/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 6.03Error index.cc index_gcd Error: Bad Argument Value","F(-2)",0
66,-2,0,0,0.000000," ","integrate(x/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.77index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
67,-2,0,0,0.000000," ","integrate(1/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.45Error index.cc index_gcd Error: Bad Argument Value","F(-2)",0
68,-1,0,0,0.000000," ","integrate(1/x/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-2,0,0,0.000000," ","integrate(1/x^2/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 9.45Error index.cc index_gcd Error: Bad Argument Value","F(-2)",0
70,-1,0,0,0.000000," ","integrate(1/x^3/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,0,0,0,0.000000," ","integrate(x^3/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
72,0,0,0,0.000000," ","integrate(x^2/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
73,0,0,0,0.000000," ","integrate(x/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
74,0,0,0,0.000000," ","integrate(1/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
75,-1,0,0,0.000000," ","integrate(1/x/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,0,0,0,0.000000," ","integrate(1/x^2/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
77,-2,0,0,0.000000," ","integrate(x^3*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
78,-2,0,0,0.000000," ","integrate(x^2*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
79,-2,0,0,0.000000," ","integrate(x*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
80,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
81,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/x/(-f*x^2+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
82,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/x^2/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.87sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
83,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/x^3/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 1.36sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
84,-2,0,0,0.000000," ","integrate(x^3*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
85,-2,0,0,0.000000," ","integrate(x^2*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
86,-2,0,0,0.000000," ","integrate(x*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
87,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
88,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/x/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
89,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/x^2/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
90,0,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/x^3/(-f*x^2+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
91,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(-x^2+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
92,1,73,0,0.195366," ","integrate((x^2-x-1)^(1/2)/(-x^2+1),x, algorithm=""giac"")","\arctan\left(-x + \sqrt{x^{2} - x - 1} + 1\right) - \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} - x - 1} \right|}\right) + \frac{1}{2} \, \log\left({\left| -x + \sqrt{x^{2} - x - 1} - 2 \right|}\right) + \log\left({\left| -2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1 \right|}\right)"," ",0,"arctan(-x + sqrt(x^2 - x - 1) + 1) - 1/2*log(abs(-x + sqrt(x^2 - x - 1))) + 1/2*log(abs(-x + sqrt(x^2 - x - 1) - 2)) + log(abs(-2*x + 2*sqrt(x^2 - x - 1) + 1))","A",0
93,-2,0,0,0.000000," ","integrate((x^2+x)^(3/2)/(x^2+1),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{poly1[293782586339316530197997184853348485491135961433723696543014566614744867108514065050877682658325195312500,-1819836231078896246311493561574067193374841713101201438235703732895037079303690375957661805226995422363281250,-4570375695680747260290242204763542388785602152024439547119677612825585897607153309996504109115565063476562500,56570880284365138950603682381140450875287062211863720342792049323742216450449018769549097192324681377441406250000]:[1,0,-31106,-99112,-65203241]%%},[6]%%%}+%%%{%%{poly1[56321484668680812198933307201849014223494499885125012071486954344416211288878769544268525719225646972656250,-6967146305649204279403284456902850546760915601336158133975389261008891579718157298328760901400260223388671875,-1850163930169118917187666861102755522009505443939328592128060577266969896374212292165333079361994541992187500000,211543560165990204169085849967411852854582551443377700410708031605115841400857697288402456445542251729797363281250]:[1,0,-31106,-99112,-65203241]%%},[5]%%%}+%%%{%%{poly1[249752783489288169448537286816821893432606364903446504002320498492700674161652642483438265732405822753906250,1028994152554895293120249414987124107117628894418263717921826093710373154539467963565591544030347656250000000,-8295331102783948196018736424875839613569744462926182727988533904129604785618275766584587664596969303680419921875,-62131498289770782417925650416698560088355013579825493623515403867274663312677694266518451768241345782073974609375]:[1,0,-31106,-99112,-65203241]%%},[4]%%%}+%%%{%%{poly1[134061679438690600698329033958374395472346927695250329215956874109101434753056577258503485208281677246093750,14482236354700157104111054005212626608902674674742541683251127446785370439987875476208796249161474060058593750,-4507439462283168458345037220805969239709706183771049286983714907113445787303583904941659518660699478698730468750,-501259088879939665231933655971301952587189466470689047006275328975844492780545187141383181367765715754302978515625]:[1,0,-31106,-99112,-65203241]%%},[3]%%%}+%%%{%%{poly1[-381381386714161407348746082633738466949446345681605193953880120440269250489670513355644056050692291259765625,-928090484018458467281328667589231013642654084462078716361857082560926680726081331041009281187046966552734375,12575476280638925266580991997598805853444942419824788143547130961660366332269561014277652901709172789611816406250,16358037436900106479732840612571178737540638352696122276658871622820423281266441048684041183868245192871093750000]:[1,0,-31106,-99112,-65203241]%%},[2]%%%}+%%%{%%{poly1[-282916504651425899151886477092387517185612250847482022493155387806666315512821307401148679503541625976562500,-11047522024183640405812419383946846813110461930170928876192826646859750070859837003681504660562347747802734375,9262241057362042200139028328026660341302166093506300746660069939833383152346374953014297625933910590026855468750,379944404413115369887516401121805461986384147356195938788669206085547964391733575642579455121057385054046630859375]:[1,0,-31106,-99112,-65203241]%%},[1]%%%}+%%%{%%{poly1[145744257028158078272793741263638276606104729476650851683626206635230909249444607603805733373105438232421875,4515159924667733682618710569206479554327942753854919836504993991415145829367574203658363698710825103759765625,-4949952822251924970018385488181468617511266061169463951678445919411830447649751834787235187730954876190185546875,-118464124267461539474328024609355477174113903628048164370055623880000124338618560214721618505583680160430908203125]:[1,0,-31106,-99112,-65203241]%%},[0]%%%} / %%%{%%{poly1[-44900316662769750,278135011567527216375,698514226322709000750,1028664866672275019250]:[1,0,-31106,-99112,-65203241]%%},[1]%%%}+%%%{%%{[2929989585103994875,368557731538442832750,907666859350191995250,-45807860415265619064625]:[1,0,-31106,-99112,-65203241]%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
94,-2,0,0,0.000000," ","integrate(x^4/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
95,-2,0,0,0.000000," ","integrate(x^3/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
96,-2,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
97,-2,0,0,0.000000," ","integrate(x/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.52sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
98,-2,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 0.58sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
99,0,0,0,0.000000," ","integrate(1/x/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
100,-2,0,0,0.000000," ","integrate(1/x^2/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 1.11sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
101,-2,0,0,0.000000," ","integrate(1/x^3/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 1.43sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
102,-2,0,0,0.000000," ","integrate(x^4/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
103,-2,0,0,0.000000," ","integrate(x^3/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valueint()  Bad Argument Type","F(-2)",0
104,-2,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valueint()  Bad Argument Type","F(-2)",0
105,-2,0,0,0.000000," ","integrate(x/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valueint()  Bad Argument Type","F(-2)",0
106,-2,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valueint()  Bad Argument Type","F(-2)",0
107,0,0,0,0.000000," ","integrate(1/x/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
108,-2,0,0,0.000000," ","integrate(1/x^2/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 1.84int()  Bad Argument Type","F(-2)",0
109,-2,0,0,0.000000," ","integrate(x^2*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
110,-2,0,0,0.000000," ","integrate(x*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
111,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
112,-2,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/x/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 7.77sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
113,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/x^2/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-2,0,0,0.000000," ","integrate(x^3/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Error: Bad Argument Type","F(-2)",0
115,-2,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
116,-1,0,0,0.000000," ","integrate(x/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate(1/x/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate(1/x^2/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate(1/x^3/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(x^3/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,0,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
123,0,0,0,0.000000," ","integrate(x/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
124,0,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{2}"," ",0,"sage2","F",0
125,0,0,0,0.000000," ","integrate(1/x/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
126,1,188,0,0.202818," ","integrate(x^4/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{-x^{2} - 4 \, x - 3} {\left(x - 10\right)} + \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) + \frac{11}{2} \, \arcsin\left(x + 2\right) - \frac{5}{8} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) + \frac{5}{8} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"-1/4*sqrt(-x^2 - 4*x - 3)*(x - 10) + 1/4*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/4*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 11/2*arcsin(x + 2) - 5/8*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) + 5/8*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","A",0
127,1,185,0,0.247472," ","integrate(x^3/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) - \frac{1}{2} \, \sqrt{-x^{2} - 4 \, x - 3} - 2 \, \arcsin\left(x + 2\right) + \frac{1}{2} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) - \frac{1}{2} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"1/4*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/4*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) - 1/2*sqrt(-x^2 - 4*x - 3) - 2*arcsin(x + 2) + 1/2*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) - 1/2*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","A",0
128,1,171,0,0.225910," ","integrate(x^2/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) - \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) + \frac{1}{2} \, \arcsin\left(x + 2\right) - \frac{1}{4} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) + \frac{1}{4} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"-1/2*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) - 1/2*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/2*arcsin(x + 2) - 1/4*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) + 1/4*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","B",0
129,1,68,0,0.184692," ","integrate(x/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1))","A",0
130,1,165,0,0.188449," ","integrate(1/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) - \frac{1}{3} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) + \frac{1}{6} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) - \frac{1}{6} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"-1/3*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) - 1/3*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/6*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) - 1/6*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","B",0
131,1,199,0,0.200948," ","integrate(1/x/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \frac{1}{9} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) - \frac{2}{9} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) + \frac{2}{9} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"1/9*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 1/9*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) - 2/9*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) + 2/9*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","A",0
132,1,269,0,0.482637," ","integrate(1/x^2/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""giac"")","\frac{2}{27} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) - \frac{4}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + 1\right)}\right) + \frac{2}{27} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 1\right)}\right) - \frac{\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + 2}{18 \, {\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} - 1}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right)}} + \frac{5}{27} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{3 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 1\right) - \frac{5}{27} \, \log\left(\frac{2 \, {\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}}{x + 2} + \frac{{\left(\sqrt{-x^{2} - 4 \, x - 3} - 1\right)}^{2}}{{\left(x + 2\right)}^{2}} + 3\right)"," ",0,"2/27*sqrt(2)*arctan(1/2*sqrt(2)*(3*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) - 4/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) + 2/27*sqrt(2)*arctan(1/2*sqrt(2)*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 1)) - 1/18*((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 2)/((sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) + 5/27*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + 3*(sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 1) - 5/27*log(2*(sqrt(-x^2 - 4*x - 3) - 1)/(x + 2) + (sqrt(-x^2 - 4*x - 3) - 1)^2/(x + 2)^2 + 3)","B",0
133,1,85,0,0.296782," ","integrate((2+3*x)^2*(-12*x^2+31*x+30)^2*(12*x^2+17*x+6)^(1/2),x, algorithm=""giac"")","\frac{1}{1056964608} \, {\left(8 \, {\left(48 \, {\left(24 \, {\left(96 \, {\left(24 \, {\left(48 \, {\left(168 \, x - 719\right)} x - 56047\right)} x + 3886417\right)} x + 973832951\right)} x + 20570842213\right)} x + 391519660247\right)} x + 474999091769\right)} \sqrt{12 \, x^{2} + 17 \, x + 6} + \frac{125455}{1811939328} \, \sqrt{3} \log\left({\left| -4 \, \sqrt{3} {\left(2 \, \sqrt{3} x - \sqrt{12 \, x^{2} + 17 \, x + 6}\right)} - 17 \right|}\right)"," ",0,"1/1056964608*(8*(48*(24*(96*(24*(48*(168*x - 719)*x - 56047)*x + 3886417)*x + 973832951)*x + 20570842213)*x + 391519660247)*x + 474999091769)*sqrt(12*x^2 + 17*x + 6) + 125455/1811939328*sqrt(3)*log(abs(-4*sqrt(3)*(2*sqrt(3)*x - sqrt(12*x^2 + 17*x + 6)) - 17))","A",0
134,1,70,0,0.203968," ","integrate((2+3*x)*(-12*x^2+31*x+30)*(12*x^2+17*x+6)^(1/2),x, algorithm=""giac"")","-\frac{1}{122880} \, {\left(8 \, {\left(48 \, {\left(72 \, {\left(32 \, x - 71\right)} x - 17807\right)} x - 681893\right)} x - 1353611\right)} \sqrt{12 \, x^{2} + 17 \, x + 6} - \frac{97}{294912} \, \sqrt{3} \log\left({\left| -4 \, \sqrt{3} {\left(2 \, \sqrt{3} x - \sqrt{12 \, x^{2} + 17 \, x + 6}\right)} - 17 \right|}\right)"," ",0,"-1/122880*(8*(48*(72*(32*x - 71)*x - 17807)*x - 681893)*x - 1353611)*sqrt(12*x^2 + 17*x + 6) - 97/294912*sqrt(3)*log(abs(-4*sqrt(3)*(2*sqrt(3)*x - sqrt(12*x^2 + 17*x + 6)) - 17))","A",0
135,1,63,0,0.272177," ","integrate((12*x^2+17*x+6)^(1/2)/(2+3*x)/(-12*x^2+31*x+30),x, algorithm=""giac"")","\frac{1}{42} \, \log\left({\left| -6 \, \sqrt{3} x + 20 \, \sqrt{3} + 3 \, \sqrt{12 \, x^{2} + 17 \, x + 6} + 42 \right|}\right) - \frac{1}{42} \, \log\left({\left| -6 \, \sqrt{3} x + 20 \, \sqrt{3} + 3 \, \sqrt{12 \, x^{2} + 17 \, x + 6} - 42 \right|}\right)"," ",0,"1/42*log(abs(-6*sqrt(3)*x + 20*sqrt(3) + 3*sqrt(12*x^2 + 17*x + 6) + 42)) - 1/42*log(abs(-6*sqrt(3)*x + 20*sqrt(3) + 3*sqrt(12*x^2 + 17*x + 6) - 42))","B",0
136,1,159,0,0.271553," ","integrate((12*x^2+17*x+6)^(1/2)/(2+3*x)^2/(-12*x^2+31*x+30)^2,x, algorithm=""giac"")","\frac{1}{9680832} \, \sqrt{3} {\left(\sqrt{3} {\left(175672 \, \sqrt{3} + 97 \, \log\left(\frac{7 \, \sqrt{3} - 12}{7 \, \sqrt{3} + 12}\right)\right)} \mathrm{sgn}\left(\frac{1}{3 \, x + 2}\right) - {\left(97 \, \sqrt{3} \log\left(\frac{{\left| -28 \, \sqrt{3} + 24 \, \sqrt{\frac{1}{3 \, x + 2} + 4} \right|}}{4 \, {\left(7 \, \sqrt{3} + 6 \, \sqrt{\frac{1}{3 \, x + 2} + 4}\right)}}\right) + 134456 \, \sqrt{\frac{1}{3 \, x + 2} + 4} + \frac{28 \, {\left(\frac{221183}{3 \, x + 2} - 18436\right)}}{12 \, {\left(\frac{1}{3 \, x + 2} + 4\right)}^{\frac{3}{2}} - 49 \, \sqrt{\frac{1}{3 \, x + 2} + 4}}\right)} \mathrm{sgn}\left(\frac{1}{3 \, x + 2}\right)\right)}"," ",0,"1/9680832*sqrt(3)*(sqrt(3)*(175672*sqrt(3) + 97*log((7*sqrt(3) - 12)/(7*sqrt(3) + 12)))*sgn(1/(3*x + 2)) - (97*sqrt(3)*log(1/4*abs(-28*sqrt(3) + 24*sqrt(1/(3*x + 2) + 4))/(7*sqrt(3) + 6*sqrt(1/(3*x + 2) + 4))) + 134456*sqrt(1/(3*x + 2) + 4) + 28*(221183/(3*x + 2) - 18436)/(12*(1/(3*x + 2) + 4)^(3/2) - 49*sqrt(1/(3*x + 2) + 4)))*sgn(1/(3*x + 2)))","B",0
137,1,232,0,0.260155," ","integrate((12*x^2+17*x+6)^(1/2)/(2+3*x)^3/(-12*x^2+31*x+30)^3,x, algorithm=""giac"")","\frac{\sqrt{3} {\left(282273 \, \sqrt{3} {\left(2 \, \sqrt{3} x - \sqrt{12 \, x^{2} + 17 \, x + 6}\right)}^{3} - 11460924 \, {\left(2 \, \sqrt{3} x - \sqrt{12 \, x^{2} + 17 \, x + 6}\right)}^{2} - 37551180 \, \sqrt{3} {\left(2 \, \sqrt{3} x - \sqrt{12 \, x^{2} + 17 \, x + 6}\right)} - 83365264\right)}}{159385218048 \, {\left(3 \, {\left(2 \, \sqrt{3} x - \sqrt{12 \, x^{2} + 17 \, x + 6}\right)}^{2} - 40 \, \sqrt{3} {\left(2 \, \sqrt{3} x - \sqrt{12 \, x^{2} + 17 \, x + 6}\right)} - 188\right)}^{2}} + \frac{{\left(8 \, {\left(2860316794 \, x + 6078171227\right)} x + 34383350229\right)} x + 8090114146}{2213683584 \, {\left(12 \, x^{2} + 17 \, x + 6\right)}^{\frac{3}{2}}} + \frac{40325}{637540872192} \, \log\left({\left| -6 \, \sqrt{3} x + 20 \, \sqrt{3} + 3 \, \sqrt{12 \, x^{2} + 17 \, x + 6} + 42 \right|}\right) - \frac{40325}{637540872192} \, \log\left({\left| -6 \, \sqrt{3} x + 20 \, \sqrt{3} + 3 \, \sqrt{12 \, x^{2} + 17 \, x + 6} - 42 \right|}\right)"," ",0,"1/159385218048*sqrt(3)*(282273*sqrt(3)*(2*sqrt(3)*x - sqrt(12*x^2 + 17*x + 6))^3 - 11460924*(2*sqrt(3)*x - sqrt(12*x^2 + 17*x + 6))^2 - 37551180*sqrt(3)*(2*sqrt(3)*x - sqrt(12*x^2 + 17*x + 6)) - 83365264)/(3*(2*sqrt(3)*x - sqrt(12*x^2 + 17*x + 6))^2 - 40*sqrt(3)*(2*sqrt(3)*x - sqrt(12*x^2 + 17*x + 6)) - 188)^2 + 1/2213683584*((8*(2860316794*x + 6078171227)*x + 34383350229)*x + 8090114146)/(12*x^2 + 17*x + 6)^(3/2) + 40325/637540872192*log(abs(-6*sqrt(3)*x + 20*sqrt(3) + 3*sqrt(12*x^2 + 17*x + 6) + 42)) - 40325/637540872192*log(abs(-6*sqrt(3)*x + 20*sqrt(3) + 3*sqrt(12*x^2 + 17*x + 6) - 42))","A",0
138,1,11,0,0.152744," ","integrate((-3+2*x)*(x^2-3*x)^(2/3),x, algorithm=""giac"")","\frac{3}{5} \, {\left(x^{2} - 3 \, x\right)}^{\frac{5}{3}}"," ",0,"3/5*(x^2 - 3*x)^(5/3)","A",0
139,1,11,0,0.150267," ","integrate(((-3+x)*x)^(2/3)*(-3+2*x),x, algorithm=""giac"")","\frac{3}{5} \, {\left(x^{2} - 3 \, x\right)}^{\frac{5}{3}}"," ",0,"3/5*(x^2 - 3*x)^(5/3)","A",0
140,1,11,0,0.159528," ","integrate(x*(2*x^2-9*x+9)/(x^2-3*x)^(1/3),x, algorithm=""giac"")","\frac{3}{5} \, {\left(x^{2} - 3 \, x\right)}^{\frac{5}{3}}"," ",0,"3/5*(x^2 - 3*x)^(5/3)","A",0
141,1,11,0,0.200909," ","integrate(x*(2*x^2-9*x+9)/((-3+x)*x)^(1/3),x, algorithm=""giac"")","\frac{3}{5} \, {\left(x^{2} - 3 \, x\right)}^{\frac{5}{3}}"," ",0,"3/5*(x^2 - 3*x)^(5/3)","A",0
142,0,0,0,0.000000," ","integrate((h*x+g)/(-c*g^2/h^2+9*c*x^2)^(1/3)/(3*h^2*x^2+g^2),x, algorithm=""giac"")","\int \frac{h x + g}{{\left(3 \, h^{2} x^{2} + g^{2}\right)} {\left(9 \, c x^{2} - \frac{c g^{2}}{h^{2}}\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((h*x + g)/((3*h^2*x^2 + g^2)*(9*c*x^2 - c*g^2/h^2)^(1/3)), x)","F",0
143,0,0,0,0.000000," ","integrate((h*x+g)/(1/9*(2*b^2*h^2+b*c*g*h-c^2*g^2)/c/h^2+b*x+c*x^2)^(1/3)/(f*(b^2+1/3*(-2*b^2*h^2-b*c*g*h+c^2*g^2)/h^2)/c^2+b*f*x/c+f*x^2),x, algorithm=""giac"")","\int \frac{3 \, {\left(h x + g\right)}}{{\left(c x^{2} + b x - \frac{c^{2} g^{2} - b c g h - 2 \, b^{2} h^{2}}{9 \, c h^{2}}\right)}^{\frac{1}{3}} {\left(3 \, f x^{2} + \frac{3 \, b f x}{c} + \frac{{\left(3 \, b^{2} + \frac{c^{2} g^{2} - b c g h - 2 \, b^{2} h^{2}}{h^{2}}\right)} f}{c^{2}}\right)}}\,{d x}"," ",0,"integrate(3*(h*x + g)/((c*x^2 + b*x - 1/9*(c^2*g^2 - b*c*g*h - 2*b^2*h^2)/(c*h^2))^(1/3)*(3*f*x^2 + 3*b*f*x/c + (3*b^2 + (c^2*g^2 - b*c*g*h - 2*b^2*h^2)/h^2)*f/c^2)), x)","F",0
