1,1,133,82,0.031000," ","int((B*x+A)*(c*x^2+b*x+a)/(f*x^2+d),x)","\frac{A a \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}}-\frac{A c d \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f}-\frac{B b d \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f}+\frac{B c \,x^{2}}{2 f}+\frac{A b \ln \left(f \,x^{2}+d \right)}{2 f}+\frac{A c x}{f}+\frac{B a \ln \left(f \,x^{2}+d \right)}{2 f}+\frac{B b x}{f}-\frac{B c d \ln \left(f \,x^{2}+d \right)}{2 f^{2}}"," ",0,"1/2*B*c*x^2/f+1/f*A*c*x+1/f*b*B*x+1/2/f*ln(f*x^2+d)*A*b+1/2/f*ln(f*x^2+d)*B*a-1/2/f^2*ln(f*x^2+d)*B*c*d+1/(d*f)^(1/2)*arctan(x*f/(d*f)^(1/2))*A*a-1/f/(d*f)^(1/2)*arctan(x*f/(d*f)^(1/2))*A*c*d-1/f/(d*f)^(1/2)*arctan(x*f/(d*f)^(1/2))*B*b*d","A"
2,1,373,212,0.012000," ","int((B*x+A)*(c*x^2+b*x+a)^2/(f*x^2+d),x)","\frac{B \,c^{2} x^{4}}{4 f}+\frac{A \,c^{2} x^{3}}{3 f}+\frac{2 B b c \,x^{3}}{3 f}+\frac{A \,a^{2} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}}-\frac{2 A a c d \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f}-\frac{A \,b^{2} d \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f}+\frac{A b c \,x^{2}}{f}+\frac{A \,c^{2} d^{2} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f^{2}}-\frac{2 B a b d \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f}+\frac{B a c \,x^{2}}{f}+\frac{B \,b^{2} x^{2}}{2 f}+\frac{2 B b c \,d^{2} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f^{2}}-\frac{B \,c^{2} d \,x^{2}}{2 f^{2}}+\frac{A a b \ln \left(f \,x^{2}+d \right)}{f}+\frac{2 A a c x}{f}+\frac{A \,b^{2} x}{f}-\frac{A b c d \ln \left(f \,x^{2}+d \right)}{f^{2}}-\frac{A \,c^{2} d x}{f^{2}}+\frac{B \,a^{2} \ln \left(f \,x^{2}+d \right)}{2 f}+\frac{2 B a b x}{f}-\frac{B a c d \ln \left(f \,x^{2}+d \right)}{f^{2}}-\frac{B \,b^{2} d \ln \left(f \,x^{2}+d \right)}{2 f^{2}}-\frac{2 B b c d x}{f^{2}}+\frac{B \,c^{2} d^{2} \ln \left(f \,x^{2}+d \right)}{2 f^{3}}"," ",0,"1/4*B*c^2*x^4/f+1/3/f*A*x^3*c^2+2/3/f*B*x^3*b*c+1/f*A*x^2*b*c+1/f*B*x^2*a*c+1/2/f*B*x^2*b^2-1/2/f^2*B*x^2*c^2*d+2/f*A*a*c*x+1/f*A*b^2*x-1/f^2*A*c^2*d*x+2/f*B*a*b*x-2/f^2*B*b*c*d*x+1/f*ln(f*x^2+d)*A*a*b-1/f^2*ln(f*x^2+d)*A*b*c*d+1/2/f*ln(f*x^2+d)*B*a^2-1/f^2*ln(f*x^2+d)*B*a*c*d-1/2/f^2*ln(f*x^2+d)*B*b^2*d+1/2/f^3*ln(f*x^2+d)*B*c^2*d^2+1/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*a^2-2/f/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*a*c*d-1/f/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*b^2*d+1/f^2/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*c^2*d^2-2/f/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*B*a*b*d+2/f^2/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*B*b*c*d^2","A"
3,1,822,421,0.008000," ","int((B*x+A)*(c*x^2+b*x+a)^3/(f*x^2+d),x)","\frac{B \,c^{3} x^{6}}{6 f}+\frac{A \,c^{3} x^{5}}{5 f}+\frac{3 B b \,c^{2} x^{5}}{5 f}+\frac{3 A b \,c^{2} x^{4}}{4 f}+\frac{3 B a \,c^{2} x^{4}}{4 f}+\frac{3 B \,b^{2} c \,x^{4}}{4 f}-\frac{B \,c^{3} d \,x^{4}}{4 f^{2}}+\frac{A a \,c^{2} x^{3}}{f}+\frac{A \,b^{2} c \,x^{3}}{f}-\frac{A \,c^{3} d \,x^{3}}{3 f^{2}}+\frac{2 B a b c \,x^{3}}{f}+\frac{B \,b^{3} x^{3}}{3 f}-\frac{B b \,c^{2} d \,x^{3}}{f^{2}}+\frac{A \,a^{3} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}}-\frac{3 A \,a^{2} c d \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f}-\frac{3 A a \,b^{2} d \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f}+\frac{3 A a b c \,x^{2}}{f}+\frac{3 A a \,c^{2} d^{2} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f^{2}}+\frac{A \,b^{3} x^{2}}{2 f}+\frac{3 A \,b^{2} c \,d^{2} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f^{2}}-\frac{3 A b \,c^{2} d \,x^{2}}{2 f^{2}}-\frac{A \,c^{3} d^{3} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f^{3}}-\frac{3 B \,a^{2} b d \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f}+\frac{3 B \,a^{2} c \,x^{2}}{2 f}+\frac{3 B a \,b^{2} x^{2}}{2 f}+\frac{6 B a b c \,d^{2} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f^{2}}-\frac{3 B a \,c^{2} d \,x^{2}}{2 f^{2}}+\frac{B \,b^{3} d^{2} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f^{2}}-\frac{3 B \,b^{2} c d \,x^{2}}{2 f^{2}}-\frac{3 B b \,c^{2} d^{3} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\sqrt{d f}\, f^{3}}+\frac{B \,c^{3} d^{2} x^{2}}{2 f^{3}}+\frac{3 A \,a^{2} b \ln \left(f \,x^{2}+d \right)}{2 f}+\frac{3 A \,a^{2} c x}{f}+\frac{3 A a \,b^{2} x}{f}-\frac{3 A a b c d \ln \left(f \,x^{2}+d \right)}{f^{2}}-\frac{3 A a \,c^{2} d x}{f^{2}}-\frac{A \,b^{3} d \ln \left(f \,x^{2}+d \right)}{2 f^{2}}-\frac{3 A \,b^{2} c d x}{f^{2}}+\frac{3 A b \,c^{2} d^{2} \ln \left(f \,x^{2}+d \right)}{2 f^{3}}+\frac{A \,c^{3} d^{2} x}{f^{3}}+\frac{B \,a^{3} \ln \left(f \,x^{2}+d \right)}{2 f}+\frac{3 B \,a^{2} b x}{f}-\frac{3 B \,a^{2} c d \ln \left(f \,x^{2}+d \right)}{2 f^{2}}-\frac{3 B a \,b^{2} d \ln \left(f \,x^{2}+d \right)}{2 f^{2}}-\frac{6 B a b c d x}{f^{2}}+\frac{3 B a \,c^{2} d^{2} \ln \left(f \,x^{2}+d \right)}{2 f^{3}}-\frac{B \,b^{3} d x}{f^{2}}+\frac{3 B \,b^{2} c \,d^{2} \ln \left(f \,x^{2}+d \right)}{2 f^{3}}+\frac{3 B b \,c^{2} d^{2} x}{f^{3}}-\frac{B \,c^{3} d^{3} \ln \left(f \,x^{2}+d \right)}{2 f^{4}}"," ",0,"6/f^2/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*B*a*b*c*d^2-1/f^2*b^3*B*d*x+3/f*A*a*b^2*x+1/6*B*c^3*x^6/f-3/2/f^2*ln(f*x^2+d)*B*a^2*c*d-3/2/f^2*ln(f*x^2+d)*B*a*b^2*d+3/2/f^3*ln(f*x^2+d)*B*a*c^2*d^2+3/2/f^3*ln(f*x^2+d)*B*b^2*c*d^2-1/f^3/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*c^3*d^3+1/f^2/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*b^3*B*d^2+3/f^3*B*b*c^2*d^2*x+2/f*B*x^3*a*b*c-1/f^2*B*x^3*b*c^2*d+3/f*A*x^2*a*b*c-3/2/f^2*A*x^2*b*c^2*d-3/2/f^2*B*x^2*a*c^2*d-3/2/f^2*B*x^2*b^2*c*d-3/f^2*A*a*c^2*d*x-3/f^2*A*b^2*c*d*x+3/2/f^3*ln(f*x^2+d)*A*b*c^2*d^2+1/2/f*ln(f*x^2+d)*B*a^3+1/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*a^3+1/3/f*B*x^3*b^3+1/2/f*A*x^2*b^3+1/5/f*A*x^5*c^3-3/f^2*ln(f*x^2+d)*A*a*b*c*d-3/f/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*a^2*c*d-3/f/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*a*b^2*d+3/f^2/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*a*c^2*d^2+3/f^2/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*b^2*c*d^2-3/f/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*B*a^2*b*d-3/f^3/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*B*b*c^2*d^3-6/f^2*B*a*b*c*d*x+3/5/f*B*x^5*b*c^2+3/4/f*A*x^4*b*c^2+1/f*A*x^3*a*c^2+3/2/f*ln(f*x^2+d)*A*a^2*b-1/2/f^2*ln(f*x^2+d)*A*b^3*d-1/2/f^4*ln(f*x^2+d)*B*c^3*d^3+1/f*A*x^3*b^2*c+1/2/f^3*B*x^2*c^3*d^2+1/f^3*A*c^3*d^2*x+3/f*B*a^2*b*x-1/3/f^2*A*x^3*c^3*d+3/2/f*B*x^2*a^2*c+3/2/f*B*x^2*a*b^2+3/f*A*a^2*c*x+3/4/f*B*x^4*a*c^2+3/4/f*B*x^4*b^2*c-1/4/f^2*B*x^4*c^3*d","A"
4,1,745,258,0.016000," ","int((B*x+A)/(c*x^2+b*x+a)/(f*x^2+d),x)","-\frac{2 A a c f \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{A a \,f^{2} \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right) \sqrt{d f}}+\frac{A \,b^{2} f \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{2 A \,c^{2} d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{A c d f \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right) \sqrt{d f}}-\frac{B a b f \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{B b c d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{B b d f \arctan \left(\frac{f x}{\sqrt{d f}}\right)}{\left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right) \sqrt{d f}}-\frac{A b f \ln \left(f \,x^{2}+d \right)}{2 \left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right)}+\frac{A b f \ln \left(c \,x^{2}+b x +a \right)}{2 a^{2} f^{2}-4 a c d f +2 b^{2} d f +2 c^{2} d^{2}}+\frac{B a f \ln \left(f \,x^{2}+d \right)}{2 a^{2} f^{2}-4 a c d f +2 b^{2} d f +2 c^{2} d^{2}}-\frac{B a f \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right)}-\frac{B c d \ln \left(f \,x^{2}+d \right)}{2 \left(a^{2} f^{2}-2 a c d f +b^{2} d f +c^{2} d^{2}\right)}+\frac{B c d \ln \left(c \,x^{2}+b x +a \right)}{2 a^{2} f^{2}-4 a c d f +2 b^{2} d f +2 c^{2} d^{2}}"," ",0,"-1/2*f/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)*ln(f*x^2+d)*A*b+1/2*f/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)*ln(f*x^2+d)*B*a-1/2/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)*ln(f*x^2+d)*B*c*d+f^2/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*a-f/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*A*c*d+f/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)/(d*f)^(1/2)*arctan(1/(d*f)^(1/2)*f*x)*B*b*d+1/2/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)*ln(c*x^2+b*x+a)*A*b*f-1/2/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)*ln(c*x^2+b*x+a)*B*a*f+1/2/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)*c*ln(c*x^2+b*x+a)*B*d-2/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*A*a*c*f+1/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*A*b^2*f+2/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*A*c^2*d-1/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*B*a*b*f-1/(a^2*f^2-2*a*c*d*f+b^2*d*f+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*B*b*c*d","B"
5,1,9311,580,0.055000," ","int((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
6,1,3358,251,0.085000," ","int((B*x+A)*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"1/2/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*A-1/2/f*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*B-1/2/f*ln((1/2/f*(-2*c*(d*f)^(1/2)+b*f)+c*(x+(d*f)^(1/2)/f))/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))*c^(1/2)*A+1/2*(d*f)^(1/2)/f^2*ln((1/2/f*(-2*c*(d*f)^(1/2)+b*f)+c*(x+(d*f)^(1/2)/f))/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))*c^(1/2)*B+1/4/(d*f)^(1/2)*ln((1/2/f*(-2*c*(d*f)^(1/2)+b*f)+c*(x+(d*f)^(1/2)/f))/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/c^(1/2)*b*A-1/4/f*ln((1/2/f*(-2*c*(d*f)^(1/2)+b*f)+c*(x+(d*f)^(1/2)/f))/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/c^(1/2)*b*B+1/2/f/(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*ln((2/f*(-b*(d*f)^(1/2)+a*f+c*d)+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+2*(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/(x+(d*f)^(1/2)/f))*b*A-1/2*(d*f)^(1/2)/f^2/(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*ln((2/f*(-b*(d*f)^(1/2)+a*f+c*d)+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+2*(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/(x+(d*f)^(1/2)/f))*b*B-1/2/(d*f)^(1/2)/(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*ln((2/f*(-b*(d*f)^(1/2)+a*f+c*d)+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+2*(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/(x+(d*f)^(1/2)/f))*a*A+1/2/f/(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*ln((2/f*(-b*(d*f)^(1/2)+a*f+c*d)+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+2*(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/(x+(d*f)^(1/2)/f))*a*B-1/2/(d*f)^(1/2)/f/(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*ln((2/f*(-b*(d*f)^(1/2)+a*f+c*d)+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+2*(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/(x+(d*f)^(1/2)/f))*c*d*A+1/2/f^2/(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*ln((2/f*(-b*(d*f)^(1/2)+a*f+c*d)+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+2*(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/(x+(d*f)^(1/2)/f))*c*d*B-1/2/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*A-1/2/f*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*B-1/2/f*ln((1/2*(2*c*(d*f)^(1/2)+b*f)/f+c*(x-(d*f)^(1/2)/f))/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))*c^(1/2)*A-1/2*(d*f)^(1/2)/f^2*ln((1/2*(2*c*(d*f)^(1/2)+b*f)/f+c*(x-(d*f)^(1/2)/f))/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))*c^(1/2)*B-1/4/(d*f)^(1/2)*ln((1/2*(2*c*(d*f)^(1/2)+b*f)/f+c*(x-(d*f)^(1/2)/f))/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/c^(1/2)*b*A-1/4/f*ln((1/2*(2*c*(d*f)^(1/2)+b*f)/f+c*(x-(d*f)^(1/2)/f))/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/c^(1/2)*b*B+1/2/f/((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*ln((2*(b*(d*f)^(1/2)+a*f+c*d)/f+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+2*((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*A+1/2*(d*f)^(1/2)/f^2/((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*ln((2*(b*(d*f)^(1/2)+a*f+c*d)/f+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+2*((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*B+1/2/(d*f)^(1/2)/((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*ln((2*(b*(d*f)^(1/2)+a*f+c*d)/f+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+2*((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a*A+1/2/f/((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*ln((2*(b*(d*f)^(1/2)+a*f+c*d)/f+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+2*((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a*B+1/2/(d*f)^(1/2)/f/((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*ln((2*(b*(d*f)^(1/2)+a*f+c*d)/f+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+2*((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c*d*A+1/2/f^2/((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*ln((2*(b*(d*f)^(1/2)+a*f+c*d)/f+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+2*((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c*d*B","B"
7,1,714,185,0.024000," ","int((B*x+A)/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","-\frac{A \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{A \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{B \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{B \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}"," ",0,"-1/2/(d*f)^(1/2)/(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*ln((2/f*(-b*(d*f)^(1/2)+a*f+c*d)+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+2*(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/(x+(d*f)^(1/2)/f))*A+1/2/f/(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*ln((2/f*(-b*(d*f)^(1/2)+a*f+c*d)+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+2*(1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2)*((x+(d*f)^(1/2)/f)^2*c+1/f*(-2*c*(d*f)^(1/2)+b*f)*(x+(d*f)^(1/2)/f)+1/f*(-b*(d*f)^(1/2)+a*f+c*d))^(1/2))/(x+(d*f)^(1/2)/f))*B+1/2/(d*f)^(1/2)/((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*ln((2*(b*(d*f)^(1/2)+a*f+c*d)/f+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+2*((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/(x-(d*f)^(1/2)/f))*A+1/2/f/((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*ln((2*(b*(d*f)^(1/2)+a*f+c*d)/f+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+2*((b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(2*c*(d*f)^(1/2)+b*f)/f*(x-(d*f)^(1/2)/f)+(b*(d*f)^(1/2)+a*f+c*d)/f)^(1/2))/(x-(d*f)^(1/2)/f))*B","B"
8,1,2758,311,0.026000," ","int((B*x+A)/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","-\frac{A b c f x}{\sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{A b c f x}{\sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{A \,b^{2} f}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{A \,b^{2} f}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{2 A \,c^{2} x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{2 A \,c^{2} x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{B b c x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{B b c x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{A b c}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{A b c}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{A f \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{A f \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{B \,b^{2}}{2 \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{B \,b^{2}}{2 \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{2 \sqrt{d f}\, B \,c^{2} x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{2 \sqrt{d f}\, B \,c^{2} x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{A f}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}-\frac{A f}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{\sqrt{d f}\, B b c}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{\sqrt{d f}\, B b c}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{B \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{B \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{B}{2 \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}-\frac{B}{2 \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}"," ",0,"1/2/(d*f)^(1/2)*f/(a*f+c*d-(d*f)^(1/2)*b)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*A-1/2/(a*f+c*d-(d*f)^(1/2)*b)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*B+2/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c^2*A-2*(d*f)^(1/2)/f/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c^2*B-1/(d*f)^(1/2)*f/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c*A+1/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c*B+1/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*c*A-(d*f)^(1/2)/f/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*c*B-1/2/(d*f)^(1/2)*f/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2*A+1/2/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2*B-1/2/(d*f)^(1/2)*f/(a*f+c*d-(d*f)^(1/2)*b)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*A+1/2/(a*f+c*d-(d*f)^(1/2)*b)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*B-1/2/(d*f)^(1/2)*f/(a*f+c*d+(d*f)^(1/2)*b)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*A-1/2/(a*f+c*d+(d*f)^(1/2)*b)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*B+2/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c^2*A+2*(d*f)^(1/2)/f/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c^2*B+1/(d*f)^(1/2)*f/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c*A+1/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c*B+1/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*c*A+(d*f)^(1/2)/f/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*c*B+1/2/(d*f)^(1/2)*f/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2*A+1/2/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2*B+1/2/(d*f)^(1/2)*f/(a*f+c*d+(d*f)^(1/2)*b)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*A+1/2/(a*f+c*d+(d*f)^(1/2)*b)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*B","B"
9,1,6422,721,0.031000," ","int((B*x+A)/(c*x^2+b*x+a)^(5/2)/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
10,1,46,35,0.018000," ","int((1+2*x)/(x^2-1)/(x^2+x-1)^(1/2),x)","-\frac{3 \arctanh \left(\frac{3 x -1}{2 \sqrt{3 x +\left(x -1\right)^{2}-2}}\right)}{2}+\frac{\arctan \left(\frac{-x -3}{2 \sqrt{-x +\left(x +1\right)^{2}-2}}\right)}{2}"," ",0,"-3/2*arctanh(1/2*(-1+3*x)/((x-1)^2+3*x-2)^(1/2))+1/2*arctan(1/2*(-3-x)/((1+x)^2-x-2)^(1/2))","A"
11,1,637,86,0.176000," ","int((1+2*x)/(x^2+1)/(x^2+x-1)^(1/2),x)","\frac{\sqrt{\frac{10 \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}-\frac{5 \sqrt{5}\, \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}+10+5 \sqrt{5}}\, \sqrt{5}\, \left(\arctanh \left(\frac{\sqrt{\frac{10 \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}-\frac{5 \sqrt{5}\, \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}+10+5 \sqrt{5}}}{\sqrt{20+10 \sqrt{5}}}\right)+\sqrt{5}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{\left(\sqrt{5}-2\right) \left(-\frac{\left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}+4 \sqrt{5}+9\right)}\, \sqrt{20+10 \sqrt{5}}\, \left(\frac{\sqrt{5}\, \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}+\frac{2 \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}-\sqrt{5}+2\right) \left(x -\sqrt{5}-2\right) \left(\sqrt{5}-2\right)}{5 \left(-x -\sqrt{5}+2\right) \left(\frac{\left(x -\sqrt{5}-2\right)^{4}}{\left(-x -\sqrt{5}+2\right)^{4}}-\frac{18 \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}+1\right)}\right)+2 \arctan \left(\frac{\sqrt{5}\, \sqrt{\left(\sqrt{5}-2\right) \left(-\frac{\left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}+4 \sqrt{5}+9\right)}\, \sqrt{20+10 \sqrt{5}}\, \left(\frac{\sqrt{5}\, \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}+\frac{2 \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}-\sqrt{5}+2\right) \left(x -\sqrt{5}-2\right) \left(\sqrt{5}-2\right)}{5 \left(-x -\sqrt{5}+2\right) \left(\frac{\left(x -\sqrt{5}-2\right)^{4}}{\left(-x -\sqrt{5}+2\right)^{4}}-\frac{18 \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}+1\right)}\right)\right)}{\sqrt{-\frac{5 \left(\frac{\sqrt{5}\, \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}-\frac{2 \left(x -\sqrt{5}-2\right)^{2}}{\left(-x -\sqrt{5}+2\right)^{2}}-\sqrt{5}-2\right)}{\left(\frac{x -\sqrt{5}-2}{-x -\sqrt{5}+2}+1\right)^{2}}}\, \left(\frac{x -\sqrt{5}-2}{-x -\sqrt{5}+2}+1\right) \sqrt{20+10 \sqrt{5}}}"," ",0,"(10*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2-5*5^(1/2)*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2+10+5*5^(1/2))^(1/2)*5^(1/2)*(arctan(1/5*5^(1/2)*((5^(1/2)-2)*(-(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2+4*5^(1/2)+9))^(1/2)*(20+10*5^(1/2))^(1/2)*(5^(1/2)*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2+2*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2-5^(1/2)+2)*(-5^(1/2)-2+x)/(-5^(1/2)+2-x)*(5^(1/2)-2)/((-5^(1/2)-2+x)^4/(-5^(1/2)+2-x)^4-18*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2+1))*5^(1/2)+arctanh((10*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2-5*5^(1/2)*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2+10+5*5^(1/2))^(1/2)/(20+10*5^(1/2))^(1/2))+2*arctan(1/5*5^(1/2)*((5^(1/2)-2)*(-(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2+4*5^(1/2)+9))^(1/2)*(20+10*5^(1/2))^(1/2)*(5^(1/2)*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2+2*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2-5^(1/2)+2)*(-5^(1/2)-2+x)/(-5^(1/2)+2-x)*(5^(1/2)-2)/((-5^(1/2)-2+x)^4/(-5^(1/2)+2-x)^4-18*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2+1)))/(-5*(5^(1/2)*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2-2*(-5^(1/2)-2+x)^2/(-5^(1/2)+2-x)^2-5^(1/2)-2)/((-5^(1/2)-2+x)/(-5^(1/2)+2-x)+1)^2)^(1/2)/((-5^(1/2)-2+x)/(-5^(1/2)+2-x)+1)/(20+10*5^(1/2))^(1/2)","B"
12,1,6871419,434,0.515000," ","int((b*x+a-c)/(x^2+1)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
13,1,510,176,0.008000," ","int((B*x+A)*(c*x^2+b*x+a)/(f*x^2+e*x+d),x)","\frac{2 A a \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}}-\frac{A b e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}-\frac{2 A c d \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}+\frac{A c \,e^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}-\frac{B a e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}-\frac{2 B b d \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}+\frac{B b \,e^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}+\frac{3 B c d e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}-\frac{B c \,e^{3} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{3}}+\frac{B c \,x^{2}}{2 f}+\frac{A b \ln \left(f \,x^{2}+e x +d \right)}{2 f}-\frac{A c e \ln \left(f \,x^{2}+e x +d \right)}{2 f^{2}}+\frac{A c x}{f}+\frac{B a \ln \left(f \,x^{2}+e x +d \right)}{2 f}-\frac{B b e \ln \left(f \,x^{2}+e x +d \right)}{2 f^{2}}+\frac{B b x}{f}-\frac{B c d \ln \left(f \,x^{2}+e x +d \right)}{2 f^{2}}+\frac{B c \,e^{2} \ln \left(f \,x^{2}+e x +d \right)}{2 f^{3}}-\frac{B c e x}{f^{2}}"," ",0,"1/2*B*c/f*x^2+A*c/f*x+B*b/f*x-1/f^2*B*c*e*x+1/2/f*ln(f*x^2+e*x+d)*A*b-1/2/f^2*ln(f*x^2+e*x+d)*A*c*e+1/2/f*ln(f*x^2+e*x+d)*B*a-1/2/f^2*ln(f*x^2+e*x+d)*B*b*e-1/2/f^2*ln(f*x^2+e*x+d)*B*c*d+1/2/f^3*ln(f*x^2+e*x+d)*B*c*e^2+2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*a-2/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*c*d-2/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*b*d+3/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*c*d*e-1/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e*A*b+1/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^2*A*c-1/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e*B*a+1/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^2*B*b-1/f^3/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^3*B*c","B"
14,1,1672,530,0.012000," ","int((B*x+A)*(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x)","\frac{B \,c^{2} x^{4}}{4 f}+\frac{A \,c^{2} x^{3}}{3 f}+\frac{2 B b c \,x^{3}}{3 f}-\frac{B \,c^{2} e \,x^{3}}{3 f^{2}}+\frac{2 A \,a^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}}-\frac{2 A a b e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}-\frac{4 A a c d \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}+\frac{2 A a c \,e^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}-\frac{2 A \,b^{2} d \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}+\frac{A \,b^{2} e^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}+\frac{6 A b c d e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}-\frac{2 A b c \,e^{3} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{3}}+\frac{A b c \,x^{2}}{f}+\frac{2 A \,c^{2} d^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}-\frac{4 A \,c^{2} d \,e^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{3}}+\frac{A \,c^{2} e^{4} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{4}}-\frac{A \,c^{2} e \,x^{2}}{2 f^{2}}-\frac{B \,a^{2} e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}-\frac{4 B a b d \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f}+\frac{2 B a b \,e^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}+\frac{6 B a c d e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}-\frac{2 B a c \,e^{3} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{3}}+\frac{B a c \,x^{2}}{f}+\frac{3 B \,b^{2} d e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}-\frac{B \,b^{2} e^{3} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{3}}+\frac{B \,b^{2} x^{2}}{2 f}+\frac{4 B b c \,d^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{2}}-\frac{8 B b c d \,e^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{3}}+\frac{2 B b c \,e^{4} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{4}}-\frac{B b c e \,x^{2}}{f^{2}}-\frac{5 B \,c^{2} d^{2} e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{3}}+\frac{5 B \,c^{2} d \,e^{3} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{4}}-\frac{B \,c^{2} d \,x^{2}}{2 f^{2}}-\frac{B \,c^{2} e^{5} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\sqrt{4 d f -e^{2}}\, f^{5}}+\frac{B \,c^{2} e^{2} x^{2}}{2 f^{3}}+\frac{A a b \ln \left(f \,x^{2}+e x +d \right)}{f}-\frac{A a c e \ln \left(f \,x^{2}+e x +d \right)}{f^{2}}+\frac{2 A a c x}{f}-\frac{A \,b^{2} e \ln \left(f \,x^{2}+e x +d \right)}{2 f^{2}}+\frac{A \,b^{2} x}{f}-\frac{A b c d \ln \left(f \,x^{2}+e x +d \right)}{f^{2}}+\frac{A b c \,e^{2} \ln \left(f \,x^{2}+e x +d \right)}{f^{3}}-\frac{2 A b c e x}{f^{2}}+\frac{A \,c^{2} d e \ln \left(f \,x^{2}+e x +d \right)}{f^{3}}-\frac{A \,c^{2} d x}{f^{2}}-\frac{A \,c^{2} e^{3} \ln \left(f \,x^{2}+e x +d \right)}{2 f^{4}}+\frac{A \,c^{2} e^{2} x}{f^{3}}+\frac{B \,a^{2} \ln \left(f \,x^{2}+e x +d \right)}{2 f}-\frac{B a b e \ln \left(f \,x^{2}+e x +d \right)}{f^{2}}+\frac{2 B a b x}{f}-\frac{B a c d \ln \left(f \,x^{2}+e x +d \right)}{f^{2}}+\frac{B a c \,e^{2} \ln \left(f \,x^{2}+e x +d \right)}{f^{3}}-\frac{2 B a c e x}{f^{2}}-\frac{B \,b^{2} d \ln \left(f \,x^{2}+e x +d \right)}{2 f^{2}}+\frac{B \,b^{2} e^{2} \ln \left(f \,x^{2}+e x +d \right)}{2 f^{3}}-\frac{B \,b^{2} e x}{f^{2}}+\frac{2 B b c d e \ln \left(f \,x^{2}+e x +d \right)}{f^{3}}-\frac{2 B b c d x}{f^{2}}-\frac{B b c \,e^{3} \ln \left(f \,x^{2}+e x +d \right)}{f^{4}}+\frac{2 B b c \,e^{2} x}{f^{3}}+\frac{B \,c^{2} d^{2} \ln \left(f \,x^{2}+e x +d \right)}{2 f^{3}}-\frac{3 B \,c^{2} d \,e^{2} \ln \left(f \,x^{2}+e x +d \right)}{2 f^{4}}+\frac{2 B \,c^{2} d e x}{f^{3}}+\frac{B \,c^{2} e^{4} \ln \left(f \,x^{2}+e x +d \right)}{2 f^{5}}-\frac{B \,c^{2} e^{3} x}{f^{4}}"," ",0,"1/4*B*c^2/f*x^4-2*B*b*c*d/f^2*x+1/2/f*ln(f*x^2+e*x+d)*B*a^2+2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*a^2+1/3*A*c^2/f*x^3+1/2*B*b^2/f*x^2+A*b^2/f*x-A*c^2*d/f^2*x+2*B*a*b/f*x+B*a*c/f*x^2-1/2*B*c^2*d/f^2*x^2+2*A*a*c/f*x+2/3*B*b*c/f*x^3+A*b*c/f*x^2-8/f^3/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*b*c*d*e^2+6/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*b*c*d*e+6/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*a*c*d*e+1/f^3*A*c^2*e^2*x-1/f^2*B*b^2*e*x-1/f^4*B*c^2*e^3*x-1/2/f^2*A*x^2*c^2*e+1/2/f^3*B*x^2*c^2*e^2-1/3/f^2*B*x^3*c^2*e-1/2/f^2*ln(f*x^2+e*x+d)*A*b^2*e-1/2/f^4*ln(f*x^2+e*x+d)*A*c^2*e^3-1/2/f^2*ln(f*x^2+e*x+d)*B*b^2*d+1/2/f^3*ln(f*x^2+e*x+d)*B*b^2*e^2+1/2/f^3*ln(f*x^2+e*x+d)*B*c^2*d^2+1/2/f^5*ln(f*x^2+e*x+d)*B*c^2*e^4+1/f*ln(f*x^2+e*x+d)*A*a*b-1/f^2*B*x^2*b*c*e-2/f^2*A*b*c*e*x-2/f^2*B*a*c*e*x+2/f^3*B*b*c*e^2*x+2/f^3*B*c^2*d*e*x+1/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^2*A*b^2-1/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e*B*a^2-1/f^3/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^3*B*b^2-1/f^5/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^5*B*c^2-2/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*b^2*d+2/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*c^2*d^2-1/f^2*ln(f*x^2+e*x+d)*A*a*c*e-1/f^2*ln(f*x^2+e*x+d)*A*b*c*d+1/f^3*ln(f*x^2+e*x+d)*A*b*c*e^2+1/f^3*ln(f*x^2+e*x+d)*A*c^2*d*e-1/f^2*ln(f*x^2+e*x+d)*B*a*b*e-1/f^2*ln(f*x^2+e*x+d)*B*a*c*d+1/f^3*ln(f*x^2+e*x+d)*B*a*c*e^2-1/f^4*ln(f*x^2+e*x+d)*B*b*c*e^3-3/2/f^4*ln(f*x^2+e*x+d)*B*c^2*d*e^2+1/f^4/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^4*A*c^2-2/f^3/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^3*A*b*c+2/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^2*B*a*b-2/f^3/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^3*B*a*c+2/f^3*ln(f*x^2+e*x+d)*B*b*c*d*e-4/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*a*c*d-4/f^3/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*c^2*d*e^2-4/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*a*b*d+3/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*b^2*d*e+4/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*b*c*d^2-5/f^3/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*c^2*d^2*e-2/f/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e*A*a*b+5/f^4/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*c^2*d*e^3+2/f^4/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^4*B*b*c+2/f^2/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*e^2*A*a*c","B"
15,1,1698,394,0.013000," ","int((B*x+A)/(c*x^2+b*x+a)/(f*x^2+e*x+d),x)","-\frac{2 A a c f \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{2 A a \,f^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 d f -e^{2}}}+\frac{A \,b^{2} f \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{A b c e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{A b e f \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 d f -e^{2}}}+\frac{2 A \,c^{2} d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{2 A c d f \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 d f -e^{2}}}+\frac{A c \,e^{2} \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 d f -e^{2}}}-\frac{B a b f \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{2 B a c e \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{B a e f \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 d f -e^{2}}}-\frac{B b c d \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{2 B b d f \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 d f -e^{2}}}-\frac{B c d e \arctan \left(\frac{2 f x +e}{\sqrt{4 d f -e^{2}}}\right)}{\left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right) \sqrt{4 d f -e^{2}}}+\frac{A b f \ln \left(c \,x^{2}+b x +a \right)}{2 a^{2} f^{2}-2 a b e f -4 a c d f +2 a c \,e^{2}+2 b^{2} d f -2 b c d e +2 c^{2} d^{2}}-\frac{A b f \ln \left(f \,x^{2}+e x +d \right)}{2 \left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right)}-\frac{A c e \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right)}+\frac{A c e \ln \left(f \,x^{2}+e x +d \right)}{2 a^{2} f^{2}-2 a b e f -4 a c d f +2 a c \,e^{2}+2 b^{2} d f -2 b c d e +2 c^{2} d^{2}}-\frac{B a f \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right)}+\frac{B a f \ln \left(f \,x^{2}+e x +d \right)}{2 a^{2} f^{2}-2 a b e f -4 a c d f +2 a c \,e^{2}+2 b^{2} d f -2 b c d e +2 c^{2} d^{2}}+\frac{B c d \ln \left(c \,x^{2}+b x +a \right)}{2 a^{2} f^{2}-2 a b e f -4 a c d f +2 a c \,e^{2}+2 b^{2} d f -2 b c d e +2 c^{2} d^{2}}-\frac{B c d \ln \left(f \,x^{2}+e x +d \right)}{2 \left(a^{2} f^{2}-a b e f -2 a c d f +a c \,e^{2}+b^{2} d f -b c d e +c^{2} d^{2}\right)}"," ",0,"1/2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)*ln(c*x^2+b*x+a)*A*b*f-1/2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)*c*ln(c*x^2+b*x+a)*A*e-1/2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)*ln(c*x^2+b*x+a)*B*a*f+1/2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)*c*ln(c*x^2+b*x+a)*B*d-2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*A*a*c*f+1/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*A*b^2*f-1/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*A*b*c*e+2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*A*c^2*d-1/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*B*a*b*f+2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*B*a*c*e-1/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*B*b*c*d-1/2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)*f*ln(f*x^2+e*x+d)*A*b+1/2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)*ln(f*x^2+e*x+d)*A*c*e+1/2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)*f*ln(f*x^2+e*x+d)*B*a-1/2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)*ln(f*x^2+e*x+d)*B*c*d+2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*a*f^2-1/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*b*e*f-2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*c*d*f+1/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*A*c*e^2-1/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*a*e*f+2/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*b*d*f-1/(a^2*f^2-a*b*e*f-2*a*c*d*f+a*c*e^2+b^2*d*f-b*c*d*e+c^2*d^2)/(4*d*f-e^2)^(1/2)*arctan((2*f*x+e)/(4*d*f-e^2)^(1/2))*B*c*d*e","B"
16,1,51470,1065,0.054000," ","int((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
17,1,340,134,0.006000," ","int((h*x+g)/(c*x^2+b*x+a)/(c*d*x^2+b*d*x+a*d)^2,x)","-\frac{3 b c h x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d^{2}}-\frac{6 b c h \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}} d^{2}}+\frac{6 c^{2} g x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d^{2}}+\frac{12 c^{2} g \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}} d^{2}}-\frac{3 b^{2} h}{2 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d^{2}}+\frac{3 b c g}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d^{2}}-\frac{b h x}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2} d^{2}}+\frac{c g x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2} d^{2}}-\frac{a h}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2} d^{2}}+\frac{b g}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2} d^{2}}"," ",0,"-1/2/d^2/(4*a*c-b^2)/(c*x^2+b*x+a)^2*x*b*h+1/d^2/(4*a*c-b^2)/(c*x^2+b*x+a)^2*x*c*g-1/d^2/(4*a*c-b^2)/(c*x^2+b*x+a)^2*a*h+1/2/d^2/(4*a*c-b^2)/(c*x^2+b*x+a)^2*b*g-3/d^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*c*x*b*h+6/d^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*c^2*x*g-3/2/d^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b^2*h+3/d^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b*c*g-6/d^2/(4*a*c-b^2)^(5/2)*c*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*h+12/d^2/(4*a*c-b^2)^(5/2)*c^2*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*g","B"
18,1,340,134,0.006000," ","int((h*x+g)/(c*x^2+b*x+a)^2/(c*d*x^2+b*d*x+a*d),x)","-\frac{3 b c h x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d}-\frac{6 b c h \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}} d}+\frac{6 c^{2} g x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d}+\frac{12 c^{2} g \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}} d}-\frac{3 b^{2} h}{2 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d}+\frac{3 b c g}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right) d}-\frac{b h x}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2} d}+\frac{c g x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2} d}-\frac{a h}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2} d}+\frac{b g}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2} d}"," ",0,"-1/2/d/(4*a*c-b^2)/(c*x^2+b*x+a)^2*x*b*h+1/d/(4*a*c-b^2)/(c*x^2+b*x+a)^2*x*c*g-1/d/(4*a*c-b^2)/(c*x^2+b*x+a)^2*a*h+1/2/d/(4*a*c-b^2)/(c*x^2+b*x+a)^2*b*g-3/d/(4*a*c-b^2)^2/(c*x^2+b*x+a)*c*x*b*h+6/d/(4*a*c-b^2)^2/(c*x^2+b*x+a)*c^2*x*g-3/2/d/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b^2*h+3/d/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b*c*g-6/d/(4*a*c-b^2)^(5/2)*c*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*h+12/d/(4*a*c-b^2)^(5/2)*c^2*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*g","B"
19,1,16209,558,0.051000," ","int((B*x+A)*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
20,1,59465,1027,0.032000," ","int((B*x+A)*(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
21,1,2269,370,0.044000," ","int((B*x+A)/(c*x^2+b*x+a)/(f*x^2+e*x+d)^(1/2),x)","\frac{2 A \ln \left(\frac{-\frac{\left(b f -c e +\sqrt{-4 a c +b^{2}}\, f \right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, \sqrt{4 \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b f -c e +\sqrt{-4 a c +b^{2}}\, f \right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}}{2}}{x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}}-\frac{2 A \ln \left(\frac{-\frac{\left(b f -c e -\sqrt{-4 a c +b^{2}}\, f \right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, \sqrt{4 \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b f -c e -\sqrt{-4 a c +b^{2}}\, f \right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}}{2}}{x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}}-\frac{B b \ln \left(\frac{-\frac{\left(b f -c e +\sqrt{-4 a c +b^{2}}\, f \right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, \sqrt{4 \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b f -c e +\sqrt{-4 a c +b^{2}}\, f \right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}}{2}}{x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, c}+\frac{B b \ln \left(\frac{-\frac{\left(b f -c e -\sqrt{-4 a c +b^{2}}\, f \right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, \sqrt{4 \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b f -c e -\sqrt{-4 a c +b^{2}}\, f \right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}}{2}}{x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, c}-\frac{B \ln \left(\frac{-\frac{\left(b f -c e +\sqrt{-4 a c +b^{2}}\, f \right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, \sqrt{4 \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b f -c e +\sqrt{-4 a c +b^{2}}\, f \right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}}{2}}{x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f +\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, c}-\frac{B \ln \left(\frac{-\frac{\left(b f -c e -\sqrt{-4 a c +b^{2}}\, f \right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, \sqrt{4 \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b f -c e -\sqrt{-4 a c +b^{2}}\, f \right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}{c}-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}}{2}}{x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-\frac{2 \left(2 a c f -b^{2} f +b c e -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f -\sqrt{-4 a c +b^{2}}\, c e \right)}{c^{2}}}\, c}"," ",0,"2/(-4*a*c+b^2)^(1/2)/(-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*ln((-(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2-(f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*(4*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*(f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2))/(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c))*A-1/c/(-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*ln((-(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2-(f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*(4*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*(f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2))/(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c))*B-1/(-4*a*c+b^2)^(1/2)/c/(-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*ln((-(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2-(f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*(4*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*(f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)-2*(-(-4*a*c+b^2)^(1/2)*b*f+(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2))/(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c))*b*B-2/(-4*a*c+b^2)^(1/2)/(-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*ln((-((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2-(-f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*(4*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*(-f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2))/(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))*A-1/c/(-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*ln((-((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2-(-f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*(4*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*(-f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2))/(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))*B+1/(-4*a*c+b^2)^(1/2)/c/(-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*ln((-((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2-(-f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2)*(4*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*(-f*(-4*a*c+b^2)^(1/2)+b*f-c*e)/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)-2*((-4*a*c+b^2)^(1/2)*b*f-(-4*a*c+b^2)^(1/2)*c*e+2*a*c*f-b^2*f+b*c*e-2*c^2*d)/c^2)^(1/2))/(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))*b*B","B"
22,1,784,703,0.039000," ","int((B*x+A)/(c*x^2+a)/(f*x^2+e*x+d)^(1/2),x)","-\frac{A \ln \left(\frac{-\frac{2 \left(a f -c d -\sqrt{-a c}\, e \right)}{c}+\frac{\left(c e +2 \sqrt{-a c}\, f \right) \left(x -\frac{\sqrt{-a c}}{c}\right)}{c}+2 \sqrt{-\frac{a f -c d -\sqrt{-a c}\, e}{c}}\, \sqrt{\left(x -\frac{\sqrt{-a c}}{c}\right)^{2} f +\frac{\left(c e +2 \sqrt{-a c}\, f \right) \left(x -\frac{\sqrt{-a c}}{c}\right)}{c}-\frac{a f -c d -\sqrt{-a c}\, e}{c}}}{x -\frac{\sqrt{-a c}}{c}}\right)}{2 \sqrt{-a c}\, \sqrt{-\frac{a f -c d -\sqrt{-a c}\, e}{c}}}+\frac{A \ln \left(\frac{-\frac{2 \left(a f -c d +\sqrt{-a c}\, e \right)}{c}+\frac{\left(c e -2 \sqrt{-a c}\, f \right) \left(x +\frac{\sqrt{-a c}}{c}\right)}{c}+2 \sqrt{-\frac{a f -c d +\sqrt{-a c}\, e}{c}}\, \sqrt{\left(x +\frac{\sqrt{-a c}}{c}\right)^{2} f +\frac{\left(c e -2 \sqrt{-a c}\, f \right) \left(x +\frac{\sqrt{-a c}}{c}\right)}{c}-\frac{a f -c d +\sqrt{-a c}\, e}{c}}}{x +\frac{\sqrt{-a c}}{c}}\right)}{2 \sqrt{-a c}\, \sqrt{-\frac{a f -c d +\sqrt{-a c}\, e}{c}}}-\frac{B \ln \left(\frac{-\frac{2 \left(a f -c d -\sqrt{-a c}\, e \right)}{c}+\frac{\left(c e +2 \sqrt{-a c}\, f \right) \left(x -\frac{\sqrt{-a c}}{c}\right)}{c}+2 \sqrt{-\frac{a f -c d -\sqrt{-a c}\, e}{c}}\, \sqrt{\left(x -\frac{\sqrt{-a c}}{c}\right)^{2} f +\frac{\left(c e +2 \sqrt{-a c}\, f \right) \left(x -\frac{\sqrt{-a c}}{c}\right)}{c}-\frac{a f -c d -\sqrt{-a c}\, e}{c}}}{x -\frac{\sqrt{-a c}}{c}}\right)}{2 \sqrt{-\frac{a f -c d -\sqrt{-a c}\, e}{c}}\, c}-\frac{B \ln \left(\frac{-\frac{2 \left(a f -c d +\sqrt{-a c}\, e \right)}{c}+\frac{\left(c e -2 \sqrt{-a c}\, f \right) \left(x +\frac{\sqrt{-a c}}{c}\right)}{c}+2 \sqrt{-\frac{a f -c d +\sqrt{-a c}\, e}{c}}\, \sqrt{\left(x +\frac{\sqrt{-a c}}{c}\right)^{2} f +\frac{\left(c e -2 \sqrt{-a c}\, f \right) \left(x +\frac{\sqrt{-a c}}{c}\right)}{c}-\frac{a f -c d +\sqrt{-a c}\, e}{c}}}{x +\frac{\sqrt{-a c}}{c}}\right)}{2 \sqrt{-\frac{a f -c d +\sqrt{-a c}\, e}{c}}\, c}"," ",0,"-1/2/(-a*c)^(1/2)/(-(-e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2)*ln((-2*(-e*(-a*c)^(1/2)+a*f-c*d)/c+(2*f*(-a*c)^(1/2)+c*e)/c*(x-(-a*c)^(1/2)/c)+2*(-(-e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2)*((x-(-a*c)^(1/2)/c)^2*f+(2*f*(-a*c)^(1/2)+c*e)/c*(x-(-a*c)^(1/2)/c)-(-e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2))/(x-(-a*c)^(1/2)/c))*A-1/2/c/(-(-e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2)*ln((-2*(-e*(-a*c)^(1/2)+a*f-c*d)/c+(2*f*(-a*c)^(1/2)+c*e)/c*(x-(-a*c)^(1/2)/c)+2*(-(-e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2)*((x-(-a*c)^(1/2)/c)^2*f+(2*f*(-a*c)^(1/2)+c*e)/c*(x-(-a*c)^(1/2)/c)-(-e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2))/(x-(-a*c)^(1/2)/c))*B+1/2/(-a*c)^(1/2)/(-(e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2)*ln((-2*(e*(-a*c)^(1/2)+a*f-c*d)/c+1/c*(-2*f*(-a*c)^(1/2)+c*e)*(x+(-a*c)^(1/2)/c)+2*(-(e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2)*((x+(-a*c)^(1/2)/c)^2*f+1/c*(-2*f*(-a*c)^(1/2)+c*e)*(x+(-a*c)^(1/2)/c)-(e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2))/(x+(-a*c)^(1/2)/c))*A-1/2/c/(-(e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2)*ln((-2*(e*(-a*c)^(1/2)+a*f-c*d)/c+1/c*(-2*f*(-a*c)^(1/2)+c*e)*(x+(-a*c)^(1/2)/c)+2*(-(e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2)*((x+(-a*c)^(1/2)/c)^2*f+1/c*(-2*f*(-a*c)^(1/2)+c*e)*(x+(-a*c)^(1/2)/c)-(e*(-a*c)^(1/2)+a*f-c*d)/c)^(1/2))/(x+(-a*c)^(1/2)/c))*B","A"
23,1,1771,266,0.033000," ","int((B*x+A)/(c*x^2+b*x+a)/(f*x^2+d)^(1/2),x)","\frac{2 A \ln \left(\frac{-\frac{\left(b +\sqrt{-4 a c +b^{2}}\right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, \sqrt{4 \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b +\sqrt{-4 a c +b^{2}}\right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}}{2}}{x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}}-\frac{2 A \ln \left(\frac{-\frac{\left(b -\sqrt{-4 a c +b^{2}}\right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, \sqrt{4 \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b -\sqrt{-4 a c +b^{2}}\right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}}{2}}{x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}}-\frac{B b \ln \left(\frac{-\frac{\left(b +\sqrt{-4 a c +b^{2}}\right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, \sqrt{4 \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b +\sqrt{-4 a c +b^{2}}\right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}}{2}}{x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, c}+\frac{B b \ln \left(\frac{-\frac{\left(b -\sqrt{-4 a c +b^{2}}\right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, \sqrt{4 \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b -\sqrt{-4 a c +b^{2}}\right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}}{2}}{x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, c}-\frac{B \ln \left(\frac{-\frac{\left(b +\sqrt{-4 a c +b^{2}}\right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, \sqrt{4 \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b +\sqrt{-4 a c +b^{2}}\right) \left(x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}}{2}}{x +\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d -\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, c}-\frac{B \ln \left(\frac{-\frac{\left(b -\sqrt{-4 a c +b^{2}}\right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f}{c^{2}}+\frac{\sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, \sqrt{4 \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} f -\frac{4 \left(b -\sqrt{-4 a c +b^{2}}\right) \left(x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right) f}{c}-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}}{2}}{x -\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}}\right)}{\sqrt{-\frac{2 \left(2 a c f -b^{2} f -2 c^{2} d +\sqrt{-4 a c +b^{2}}\, b f \right)}{c^{2}}}\, c}"," ",0,"2/(-4*a*c+b^2)^(1/2)/(-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*ln((-(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2-f*(b+(-4*a*c+b^2)^(1/2))/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*(4*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*f*(b+(-4*a*c+b^2)^(1/2))/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2))/(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c))*A-1/c/(-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*ln((-(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2-f*(b+(-4*a*c+b^2)^(1/2))/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*(4*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*f*(b+(-4*a*c+b^2)^(1/2))/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2))/(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c))*B-1/(-4*a*c+b^2)^(1/2)/c/(-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*ln((-(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2-f*(b+(-4*a*c+b^2)^(1/2))/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*(4*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*f*(b+(-4*a*c+b^2)^(1/2))/c*(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c)-2*(-(-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2))/(x+1/2*(b+(-4*a*c+b^2)^(1/2))/c))*b*B-2/(-4*a*c+b^2)^(1/2)/(-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*ln((-((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2-f*(b-(-4*a*c+b^2)^(1/2))/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*(4*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*f*(b-(-4*a*c+b^2)^(1/2))/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2))/(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))*A-1/c/(-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*ln((-((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2-f*(b-(-4*a*c+b^2)^(1/2))/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*(4*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*f*(b-(-4*a*c+b^2)^(1/2))/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2))/(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))*B+1/(-4*a*c+b^2)^(1/2)/c/(-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*ln((-((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2-f*(b-(-4*a*c+b^2)^(1/2))/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)+1/2*(-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2)*(4*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*f-4*f*(b-(-4*a*c+b^2)^(1/2))/c*(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)-2*((-4*a*c+b^2)^(1/2)*b*f+2*a*c*f-b^2*f-2*c^2*d)/c^2)^(1/2))/(x-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))*b*B","B"
24,1,608,81,0.021000," ","int((B*x+A)/(c*x^2+a)/(f*x^2+d)^(1/2),x)","-\frac{A \ln \left(\frac{\frac{2 \sqrt{-a c}\, \left(x -\frac{\sqrt{-a c}}{c}\right) f}{c}-\frac{2 \left(a f -c d \right)}{c}+2 \sqrt{-\frac{a f -c d}{c}}\, \sqrt{\left(x -\frac{\sqrt{-a c}}{c}\right)^{2} f +\frac{2 \sqrt{-a c}\, \left(x -\frac{\sqrt{-a c}}{c}\right) f}{c}-\frac{a f -c d}{c}}}{x -\frac{\sqrt{-a c}}{c}}\right)}{2 \sqrt{-a c}\, \sqrt{-\frac{a f -c d}{c}}}+\frac{A \ln \left(\frac{-\frac{2 \sqrt{-a c}\, \left(x +\frac{\sqrt{-a c}}{c}\right) f}{c}-\frac{2 \left(a f -c d \right)}{c}+2 \sqrt{-\frac{a f -c d}{c}}\, \sqrt{\left(x +\frac{\sqrt{-a c}}{c}\right)^{2} f -\frac{2 \sqrt{-a c}\, \left(x +\frac{\sqrt{-a c}}{c}\right) f}{c}-\frac{a f -c d}{c}}}{x +\frac{\sqrt{-a c}}{c}}\right)}{2 \sqrt{-a c}\, \sqrt{-\frac{a f -c d}{c}}}-\frac{B \ln \left(\frac{\frac{2 \sqrt{-a c}\, \left(x -\frac{\sqrt{-a c}}{c}\right) f}{c}-\frac{2 \left(a f -c d \right)}{c}+2 \sqrt{-\frac{a f -c d}{c}}\, \sqrt{\left(x -\frac{\sqrt{-a c}}{c}\right)^{2} f +\frac{2 \sqrt{-a c}\, \left(x -\frac{\sqrt{-a c}}{c}\right) f}{c}-\frac{a f -c d}{c}}}{x -\frac{\sqrt{-a c}}{c}}\right)}{2 \sqrt{-\frac{a f -c d}{c}}\, c}-\frac{B \ln \left(\frac{-\frac{2 \sqrt{-a c}\, \left(x +\frac{\sqrt{-a c}}{c}\right) f}{c}-\frac{2 \left(a f -c d \right)}{c}+2 \sqrt{-\frac{a f -c d}{c}}\, \sqrt{\left(x +\frac{\sqrt{-a c}}{c}\right)^{2} f -\frac{2 \sqrt{-a c}\, \left(x +\frac{\sqrt{-a c}}{c}\right) f}{c}-\frac{a f -c d}{c}}}{x +\frac{\sqrt{-a c}}{c}}\right)}{2 \sqrt{-\frac{a f -c d}{c}}\, c}"," ",0,"-1/2/(-a*c)^(1/2)/(-(a*f-c*d)/c)^(1/2)*ln((-2*(a*f-c*d)/c+2*f*(-a*c)^(1/2)/c*(x-(-a*c)^(1/2)/c)+2*(-(a*f-c*d)/c)^(1/2)*((x-(-a*c)^(1/2)/c)^2*f+2*f*(-a*c)^(1/2)/c*(x-(-a*c)^(1/2)/c)-(a*f-c*d)/c)^(1/2))/(x-(-a*c)^(1/2)/c))*A-1/2/c/(-(a*f-c*d)/c)^(1/2)*ln((-2*(a*f-c*d)/c+2*f*(-a*c)^(1/2)/c*(x-(-a*c)^(1/2)/c)+2*(-(a*f-c*d)/c)^(1/2)*((x-(-a*c)^(1/2)/c)^2*f+2*f*(-a*c)^(1/2)/c*(x-(-a*c)^(1/2)/c)-(a*f-c*d)/c)^(1/2))/(x-(-a*c)^(1/2)/c))*B+1/2/(-a*c)^(1/2)/(-(a*f-c*d)/c)^(1/2)*ln((-2*(a*f-c*d)/c-2*f*(-a*c)^(1/2)/c*(x+(-a*c)^(1/2)/c)+2*(-(a*f-c*d)/c)^(1/2)*((x+(-a*c)^(1/2)/c)^2*f-2*f*(-a*c)^(1/2)/c*(x+(-a*c)^(1/2)/c)-(a*f-c*d)/c)^(1/2))/(x+(-a*c)^(1/2)/c))*A-1/2/c/(-(a*f-c*d)/c)^(1/2)*ln((-2*(a*f-c*d)/c-2*f*(-a*c)^(1/2)/c*(x+(-a*c)^(1/2)/c)+2*(-(a*f-c*d)/c)^(1/2)*((x+(-a*c)^(1/2)/c)^2*f-2*f*(-a*c)^(1/2)/c*(x+(-a*c)^(1/2)/c)-(a*f-c*d)/c)^(1/2))/(x+(-a*c)^(1/2)/c))*B","B"
25,1,324,99,0.068000," ","int((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(1/2),x)","\frac{2 \sqrt{10}\, \arctanh \left(\frac{-1+\sqrt{10}+\frac{9 \left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{-1+\sqrt{10}}\, \sqrt{-18 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)-1+\sqrt{10}}}\right)}{5 \sqrt{-1+\sqrt{10}}}+\frac{\arctanh \left(\frac{-1+\sqrt{10}+\frac{9 \left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{-1+\sqrt{10}}\, \sqrt{-18 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)-1+\sqrt{10}}}\right)}{2 \sqrt{-1+\sqrt{10}}}+\frac{2 \sqrt{10}\, \arctan \left(\frac{-1-\sqrt{10}+\frac{9 \left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{1+\sqrt{10}}\, \sqrt{-18 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)-1-\sqrt{10}}}\right)}{5 \sqrt{1+\sqrt{10}}}-\frac{\arctan \left(\frac{-1-\sqrt{10}+\frac{9 \left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{1+\sqrt{10}}\, \sqrt{-18 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)-1-\sqrt{10}}}\right)}{2 \sqrt{1+\sqrt{10}}}"," ",0,"2/5*10^(1/2)/(1+10^(1/2))^(1/2)*arctan(9/2*(-2/9-2/9*10^(1/2)+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(1+10^(1/2))^(1/2)/(-18*(x-2/3+1/3*10^(1/2))^2+9*(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1-10^(1/2))^(1/2))-1/2/(1+10^(1/2))^(1/2)*arctan(9/2*(-2/9-2/9*10^(1/2)+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(1+10^(1/2))^(1/2)/(-18*(x-2/3+1/3*10^(1/2))^2+9*(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1-10^(1/2))^(1/2))+2/5*10^(1/2)/(-1+10^(1/2))^(1/2)*arctanh(9/2*(-2/9+2/9*10^(1/2)+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(-1+10^(1/2))^(1/2)/(-18*(x-2/3-1/3*10^(1/2))^2+9*(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1+10^(1/2))^(1/2))+1/2/(-1+10^(1/2))^(1/2)*arctanh(9/2*(-2/9+2/9*10^(1/2)+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(-1+10^(1/2))^(1/2)/(-18*(x-2/3-1/3*10^(1/2))^2+9*(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1+10^(1/2))^(1/2))","B"
26,1,760,118,0.027000," ","int((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(3/2),x)","\frac{32 \sqrt{10}\, x}{765 \left(-\frac{1}{9}-\frac{\sqrt{10}}{9}\right) \sqrt{-2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)-\frac{1}{9}-\frac{\sqrt{10}}{9}}}-\frac{62 x}{153 \left(-\frac{1}{9}-\frac{\sqrt{10}}{9}\right) \sqrt{-2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)-\frac{1}{9}-\frac{\sqrt{10}}{9}}}-\frac{32 \sqrt{10}\, x}{765 \left(-\frac{1}{9}+\frac{\sqrt{10}}{9}\right) \sqrt{-2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)-\frac{1}{9}+\frac{\sqrt{10}}{9}}}-\frac{62 x}{153 \left(-\frac{1}{9}+\frac{\sqrt{10}}{9}\right) \sqrt{-2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)-\frac{1}{9}+\frac{\sqrt{10}}{9}}}+\frac{2 \sqrt{10}\, \arctanh \left(\frac{-1+\sqrt{10}+\frac{9 \left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{-1+\sqrt{10}}\, \sqrt{-18 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)-1+\sqrt{10}}}\right)}{5 \left(-\frac{1}{9}+\frac{\sqrt{10}}{9}\right) \sqrt{-1+\sqrt{10}}}+\frac{\arctanh \left(\frac{-1+\sqrt{10}+\frac{9 \left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{-1+\sqrt{10}}\, \sqrt{-18 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)-1+\sqrt{10}}}\right)}{2 \left(-\frac{1}{9}+\frac{\sqrt{10}}{9}\right) \sqrt{-1+\sqrt{10}}}+\frac{2 \sqrt{10}\, \arctan \left(\frac{-1-\sqrt{10}+\frac{9 \left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{1+\sqrt{10}}\, \sqrt{-18 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)-1-\sqrt{10}}}\right)}{5 \left(-\frac{1}{9}-\frac{\sqrt{10}}{9}\right) \sqrt{1+\sqrt{10}}}-\frac{\arctan \left(\frac{-1-\sqrt{10}+\frac{9 \left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{1+\sqrt{10}}\, \sqrt{-18 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)-1-\sqrt{10}}}\right)}{2 \left(-\frac{1}{9}-\frac{\sqrt{10}}{9}\right) \sqrt{1+\sqrt{10}}}+\frac{26 \sqrt{10}}{255 \left(-\frac{1}{9}-\frac{\sqrt{10}}{9}\right) \sqrt{-2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)-\frac{1}{9}-\frac{\sqrt{10}}{9}}}+\frac{7}{51 \left(-\frac{1}{9}-\frac{\sqrt{10}}{9}\right) \sqrt{-2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{1}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)-\frac{1}{9}-\frac{\sqrt{10}}{9}}}-\frac{26 \sqrt{10}}{255 \left(-\frac{1}{9}+\frac{\sqrt{10}}{9}\right) \sqrt{-2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)-\frac{1}{9}+\frac{\sqrt{10}}{9}}}+\frac{7}{51 \left(-\frac{1}{9}+\frac{\sqrt{10}}{9}\right) \sqrt{-2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{1}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)-\frac{1}{9}+\frac{\sqrt{10}}{9}}}"," ",0,"26/255*10^(1/2)/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)+32/765/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)*10^(1/2)*x-62/153/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)*x+7/51/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)+2/5*10^(1/2)/(-1/9-1/9*10^(1/2))/(1+10^(1/2))^(1/2)*arctan(9/2*(-2/9-2/9*10^(1/2)+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(1+10^(1/2))^(1/2)/(-18*(x-2/3+1/3*10^(1/2))^2+9*(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1-10^(1/2))^(1/2))-1/2/(-1/9-1/9*10^(1/2))/(1+10^(1/2))^(1/2)*arctan(9/2*(-2/9-2/9*10^(1/2)+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(1+10^(1/2))^(1/2)/(-18*(x-2/3+1/3*10^(1/2))^2+9*(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1-10^(1/2))^(1/2))-26/255*10^(1/2)/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)-32/765/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)*10^(1/2)*x-62/153/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)*x+7/51/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)+2/5*10^(1/2)/(-1/9+1/9*10^(1/2))/(-1+10^(1/2))^(1/2)*arctanh(9/2*(-2/9+2/9*10^(1/2)+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(-1+10^(1/2))^(1/2)/(-18*(x-2/3-1/3*10^(1/2))^2+9*(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1+10^(1/2))^(1/2))+1/2/(-1/9+1/9*10^(1/2))/(-1+10^(1/2))^(1/2)*arctanh(9/2*(-2/9+2/9*10^(1/2)+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(-1+10^(1/2))^(1/2)/(-18*(x-2/3-1/3*10^(1/2))^2+9*(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1+10^(1/2))^(1/2))","B"
27,1,1560,137,0.020000," ","int((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(5/2),x)","\text{Expression too large to display}"," ",0,"248/2601/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)+248/2601/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)+7/153/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(3/2)+7/153/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(3/2)+7/51/(-1/9+1/9*10^(1/2))^2/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)+7/51/(-1/9-1/9*10^(1/2))^2/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)-32/765/(-1/9+1/9*10^(1/2))^2/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)*10^(1/2)*x-32/2295/(-1/9+1/9*10^(1/2))*10^(1/2)/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(3/2)*x+2/5*10^(1/2)/(-1/9-1/9*10^(1/2))^2/(1+10^(1/2))^(1/2)*arctan(9/2*(-2/9-2/9*10^(1/2)+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(1+10^(1/2))^(1/2)/(-18*(x-2/3+1/3*10^(1/2))^2+9*(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1-10^(1/2))^(1/2))+32/2295/(-1/9-1/9*10^(1/2))*10^(1/2)/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(3/2)*x+32/765/(-1/9-1/9*10^(1/2))^2/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)*10^(1/2)*x+2/5*10^(1/2)/(-1/9+1/9*10^(1/2))^2/(-1+10^(1/2))^(1/2)*arctanh(9/2*(-2/9+2/9*10^(1/2)+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(-1+10^(1/2))^(1/2)/(-18*(x-2/3-1/3*10^(1/2))^2+9*(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1+10^(1/2))^(1/2))+512/39015/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)*10^(1/2)*x-512/39015/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)*10^(1/2)*x-62/153/(-1/9-1/9*10^(1/2))^2/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)*x+26/255/(-1/9-1/9*10^(1/2))^2/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)*10^(1/2)-1/2/(-1/9-1/9*10^(1/2))^2/(1+10^(1/2))^(1/2)*arctan(9/2*(-2/9-2/9*10^(1/2)+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(1+10^(1/2))^(1/2)/(-18*(x-2/3+1/3*10^(1/2))^2+9*(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1-10^(1/2))^(1/2))-62/459/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(3/2)*x+26/765/(-1/9-1/9*10^(1/2))*10^(1/2)/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(3/2)-26/255/(-1/9+1/9*10^(1/2))^2/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)*10^(1/2)+1/2/(-1/9+1/9*10^(1/2))^2/(-1+10^(1/2))^(1/2)*arctanh(9/2*(-2/9+2/9*10^(1/2)+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(-1+10^(1/2))^(1/2)/(-18*(x-2/3-1/3*10^(1/2))^2+9*(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1+10^(1/2))^(1/2))-26/765/(-1/9+1/9*10^(1/2))*10^(1/2)/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(3/2)-62/153/(-1/9+1/9*10^(1/2))^2/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)*x-62/459/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(3/2)*x+128/13005*10^(1/2)/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)-992/7803/(-1/9+1/9*10^(1/2))/(-2*(x-2/3-1/3*10^(1/2))^2+(1/3-4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))-1/9+1/9*10^(1/2))^(1/2)*x-128/13005*10^(1/2)/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)-992/7803/(-1/9-1/9*10^(1/2))/(-2*(x-2/3+1/3*10^(1/2))^2+(1/3+4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))-1/9-1/9*10^(1/2))^(1/2)*x","B"
28,1,186,103,0.051000," ","int((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(1/2),x)","\frac{\left(-8+\sqrt{10}\right) \sqrt{10}\, \arctanh \left(\frac{55-17 \sqrt{10}+\frac{9 \left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{55-17 \sqrt{10}}\, \sqrt{18 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+55-17 \sqrt{10}}}\right)}{20 \sqrt{55-17 \sqrt{10}}}+\frac{\left(8+\sqrt{10}\right) \sqrt{10}\, \arctanh \left(\frac{55+17 \sqrt{10}+\frac{9 \left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{55+17 \sqrt{10}}\, \sqrt{18 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+55+17 \sqrt{10}}}\right)}{20 \sqrt{55+17 \sqrt{10}}}"," ",0,"1/20*(-8+10^(1/2))*10^(1/2)/(55-17*10^(1/2))^(1/2)*arctanh(9/2*(110/9-34/9*10^(1/2)+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(55-17*10^(1/2))^(1/2)/(18*(x-2/3+1/3*10^(1/2))^2+9*(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55-17*10^(1/2))^(1/2))+1/20*(8+10^(1/2))*10^(1/2)/(55+17*10^(1/2))^(1/2)*arctanh(9/2*(110/9+34/9*10^(1/2)+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(55+17*10^(1/2))^(1/2)/(18*(x-2/3-1/3*10^(1/2))^2+9*(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55+17*10^(1/2))^(1/2))","A"
29,1,466,122,0.019000," ","int((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(3/2),x)","-\frac{\left(-8+\sqrt{10}\right) \sqrt{10}\, \left(-\frac{\arctanh \left(\frac{55-17 \sqrt{10}+\frac{9 \left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{55-17 \sqrt{10}}\, \sqrt{18 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+55-17 \sqrt{10}}}\right)}{\left(\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right) \sqrt{55-17 \sqrt{10}}}+\frac{1}{3 \left(\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right) \sqrt{2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+\frac{55}{9}-\frac{17 \sqrt{10}}{9}}}-\frac{\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(4 x +3\right)}{3 \left(\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right) \left(\frac{440}{9}-\frac{136 \sqrt{10}}{9}-\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right)^{2}\right) \sqrt{2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+\frac{55}{9}-\frac{17 \sqrt{10}}{9}}}\right)}{20}-\frac{\left(8+\sqrt{10}\right) \sqrt{10}\, \left(-\frac{\arctanh \left(\frac{55+17 \sqrt{10}+\frac{9 \left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{55+17 \sqrt{10}}\, \sqrt{18 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+55+17 \sqrt{10}}}\right)}{\left(\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right) \sqrt{55+17 \sqrt{10}}}+\frac{1}{3 \left(\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right) \sqrt{2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+\frac{55}{9}+\frac{17 \sqrt{10}}{9}}}-\frac{\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(4 x +3\right)}{3 \left(\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right) \left(\frac{440}{9}+\frac{136 \sqrt{10}}{9}-\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right)^{2}\right) \sqrt{2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+\frac{55}{9}+\frac{17 \sqrt{10}}{9}}}\right)}{20}"," ",0,"-1/20*(-8+10^(1/2))*10^(1/2)*(1/3/(55/9-17/9*10^(1/2))/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(1/2)-1/3*(17/3-4/3*10^(1/2))/(55/9-17/9*10^(1/2))*(3+4*x)/(440/9-136/9*10^(1/2)-(17/3-4/3*10^(1/2))^2)/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(1/2)-1/(55/9-17/9*10^(1/2))/(55-17*10^(1/2))^(1/2)*arctanh(9/2*(110/9-34/9*10^(1/2)+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(55-17*10^(1/2))^(1/2)/(18*(x-2/3+1/3*10^(1/2))^2+9*(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55-17*10^(1/2))^(1/2)))-1/20*(8+10^(1/2))*10^(1/2)*(1/3/(55/9+17/9*10^(1/2))/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(1/2)-1/3*(17/3+4/3*10^(1/2))/(55/9+17/9*10^(1/2))*(3+4*x)/(440/9+136/9*10^(1/2)-(17/3+4/3*10^(1/2))^2)/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(1/2)-1/(55/9+17/9*10^(1/2))/(55+17*10^(1/2))^(1/2)*arctanh(9/2*(110/9+34/9*10^(1/2)+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(55+17*10^(1/2))^(1/2)/(18*(x-2/3-1/3*10^(1/2))^2+9*(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55+17*10^(1/2))^(1/2)))","B"
30,1,878,141,0.017000," ","int((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(5/2),x)","-\frac{\left(-8+\sqrt{10}\right) \sqrt{10}\, \left(\frac{1}{9 \left(\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right) \left(2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right)^{\frac{3}{2}}}-\frac{\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(\frac{\frac{8 x}{3}+2}{\left(\frac{440}{9}-\frac{136 \sqrt{10}}{9}-\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right)^{2}\right) \left(2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right)^{\frac{3}{2}}}+\frac{\frac{128 x}{3}+32}{\left(\frac{440}{9}-\frac{136 \sqrt{10}}{9}-\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right)^{2}\right)^{2} \sqrt{2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+\frac{55}{9}-\frac{17 \sqrt{10}}{9}}}\right)}{6 \left(\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right)}+\frac{-\frac{3 \arctanh \left(\frac{55-17 \sqrt{10}+\frac{9 \left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{55-17 \sqrt{10}}\, \sqrt{18 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+55-17 \sqrt{10}}}\right)}{\left(\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right) \sqrt{55-17 \sqrt{10}}}+\frac{1}{\left(\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right) \sqrt{2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+\frac{55}{9}-\frac{17 \sqrt{10}}{9}}}-\frac{\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(4 x +3\right)}{\left(\frac{55}{9}-\frac{17 \sqrt{10}}{9}\right) \left(\frac{440}{9}-\frac{136 \sqrt{10}}{9}-\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right)^{2}\right) \sqrt{2 \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}-\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}+\frac{\sqrt{10}}{3}\right)+\frac{55}{9}-\frac{17 \sqrt{10}}{9}}}}{\frac{55}{3}-\frac{17 \sqrt{10}}{3}}\right)}{20}-\frac{\left(8+\sqrt{10}\right) \sqrt{10}\, \left(\frac{1}{9 \left(\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right) \left(2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right)^{\frac{3}{2}}}-\frac{\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(\frac{\frac{8 x}{3}+2}{\left(\frac{440}{9}+\frac{136 \sqrt{10}}{9}-\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right)^{2}\right) \left(2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right)^{\frac{3}{2}}}+\frac{\frac{128 x}{3}+32}{\left(\frac{440}{9}+\frac{136 \sqrt{10}}{9}-\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right)^{2}\right)^{2} \sqrt{2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+\frac{55}{9}+\frac{17 \sqrt{10}}{9}}}\right)}{6 \left(\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right)}+\frac{-\frac{3 \arctanh \left(\frac{55+17 \sqrt{10}+\frac{9 \left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)}{2}}{\sqrt{55+17 \sqrt{10}}\, \sqrt{18 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+9 \left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+55+17 \sqrt{10}}}\right)}{\left(\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right) \sqrt{55+17 \sqrt{10}}}+\frac{1}{\left(\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right) \sqrt{2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+\frac{55}{9}+\frac{17 \sqrt{10}}{9}}}-\frac{\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(4 x +3\right)}{\left(\frac{55}{9}+\frac{17 \sqrt{10}}{9}\right) \left(\frac{440}{9}+\frac{136 \sqrt{10}}{9}-\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right)^{2}\right) \sqrt{2 \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)^{2}+\left(\frac{17}{3}+\frac{4 \sqrt{10}}{3}\right) \left(x -\frac{2}{3}-\frac{\sqrt{10}}{3}\right)+\frac{55}{9}+\frac{17 \sqrt{10}}{9}}}}{\frac{55}{3}+\frac{17 \sqrt{10}}{3}}\right)}{20}"," ",0,"-1/20*(-8+10^(1/2))*10^(1/2)*(1/9/(55/9-17/9*10^(1/2))/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(3/2)-1/6*(17/3-4/3*10^(1/2))/(55/9-17/9*10^(1/2))*(2/3*(4*x+3)/(440/9-136/9*10^(1/2)-(17/3-4/3*10^(1/2))^2)/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(3/2)+32/3/(440/9-136/9*10^(1/2)-(17/3-4/3*10^(1/2))^2)^2*(4*x+3)/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(1/2))+1/3/(55/9-17/9*10^(1/2))*(1/(55/9-17/9*10^(1/2))/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(1/2)-(17/3-4/3*10^(1/2))/(55/9-17/9*10^(1/2))*(4*x+3)/(440/9-136/9*10^(1/2)-(17/3-4/3*10^(1/2))^2)/(2*(x-2/3+1/3*10^(1/2))^2+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55/9-17/9*10^(1/2))^(1/2)-3/(55/9-17/9*10^(1/2))/(55-17*10^(1/2))^(1/2)*arctanh(9/2*(110/9-34/9*10^(1/2)+(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2)))/(55-17*10^(1/2))^(1/2)/(18*(x-2/3+1/3*10^(1/2))^2+9*(17/3-4/3*10^(1/2))*(x-2/3+1/3*10^(1/2))+55-17*10^(1/2))^(1/2))))-1/20*(8+10^(1/2))*10^(1/2)*(1/9/(55/9+17/9*10^(1/2))/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(3/2)-1/6*(17/3+4/3*10^(1/2))/(55/9+17/9*10^(1/2))*(2/3*(4*x+3)/(440/9+136/9*10^(1/2)-(17/3+4/3*10^(1/2))^2)/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(3/2)+32/3/(440/9+136/9*10^(1/2)-(17/3+4/3*10^(1/2))^2)^2*(4*x+3)/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(1/2))+1/3/(55/9+17/9*10^(1/2))*(1/(55/9+17/9*10^(1/2))/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(1/2)-(17/3+4/3*10^(1/2))/(55/9+17/9*10^(1/2))*(4*x+3)/(440/9+136/9*10^(1/2)-(17/3+4/3*10^(1/2))^2)/(2*(x-2/3-1/3*10^(1/2))^2+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55/9+17/9*10^(1/2))^(1/2)-3/(55/9+17/9*10^(1/2))/(55+17*10^(1/2))^(1/2)*arctanh(9/2*(110/9+34/9*10^(1/2)+(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2)))/(55+17*10^(1/2))^(1/2)/(18*(x-2/3-1/3*10^(1/2))^2+9*(17/3+4/3*10^(1/2))*(x-2/3-1/3*10^(1/2))+55+17*10^(1/2))^(1/2))))","B"
31,1,14,13,0.020000," ","int((x+1)/(x^2+2*x+4)/(x^2+2*x+5)^(1/2),x)","-\arctanh \left(\sqrt{x^{2}+2 x +5}\right)"," ",0,"-arctanh((x^2+2*x+5)^(1/2))","A"
32,1,40,37,0.012000," ","int((4+x)/(x^2+2*x+4)/(x^2+2*x+5)^(1/2),x)","-\arctanh \left(\sqrt{x^{2}+2 x +5}\right)+\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(2 x +2\right)}{6 \sqrt{x^{2}+2 x +5}}\right)"," ",0,"-arctanh((x^2+2*x+5)^(1/2))+3^(1/2)*arctan(1/6*3^(1/2)/(x^2+2*x+5)^(1/2)*(2*x+2))","A"
33,1,20,19,0.018000," ","int((1+2*x)/(x^2+x+3)/(x^2+x+5)^(1/2),x)","-\sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{2}+x +5}\, \sqrt{2}}{2}\right)"," ",0,"-arctanh(1/2*(x^2+x+5)^(1/2)*2^(1/2))*2^(1/2)","A"
34,1,45,44,0.012000," ","int(x/(x^2+x+3)/(x^2+x+5)^(1/2),x)","-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{x^{2}+x +5}\, \sqrt{2}}{2}\right)}{2}-\frac{\sqrt{22}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{22}}{11 \sqrt{x^{2}+x +5}}\right)}{22}"," ",0,"-1/2*arctanh(1/2*(x^2+x+5)^(1/2)*2^(1/2))*2^(1/2)-1/22*arctan(1/11*(1+2*x)*22^(1/2)/(x^2+x+5)^(1/2))*22^(1/2)","A"
35,1,3606,219,0.053000," ","int((B*x+A)/(b*f*x^2+b*e*x+a*e)^2/(f*x^2+e*x+d)^(1/2),x)","\text{output too large to display}"," ",0,"-1/e/(4*a*f-b*e)/(a*e-b*d)/(x+1/2/f*e-1/2/b/f*(-b*e*(4*a*f-b*e))^(1/2))*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2)*A+1/2/f/(4*a*f-b*e)/(a*e-b*d)/(x+1/2/f*e-1/2/b/f*(-b*e*(4*a*f-b*e))^(1/2))*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2)*B-1/2/f/e/(4*a*f-b*e)/b/(a*e-b*d)/(x+1/2/f*e-1/2/b/f*(-b*e*(4*a*f-b*e))^(1/2))*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2)*B*(-b*e*(4*a*f-b*e))^(1/2)+1/2/e/(4*a*f-b*e)/b*(-b*e*(4*a*f-b*e))^(1/2)/(a*e-b*d)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*A-1/4/f/(4*a*f-b*e)/b*(-b*e*(4*a*f-b*e))^(1/2)/(a*e-b*d)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*B-1/4/f/b/(a*e-b*d)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*B-2/e/(4*a*f-b*e)/(-b*e*(4*a*f-b*e))^(1/2)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*A*f+1/(4*a*f-b*e)/(-b*e*(4*a*f-b*e))^(1/2)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*B+2/e/(4*a*f-b*e)/(-b*e*(4*a*f-b*e))^(1/2)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*A*f-1/(4*a*f-b*e)/(-b*e*(4*a*f-b*e))^(1/2)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*B-1/e/(4*a*f-b*e)/(a*e-b*d)/(x+1/2/f*e+1/2/b/f*(-b*e*(4*a*f-b*e))^(1/2))*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2)*A+1/2/f/(4*a*f-b*e)/(a*e-b*d)/(x+1/2/f*e+1/2/b/f*(-b*e*(4*a*f-b*e))^(1/2))*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2)*B+1/2/f/e/(4*a*f-b*e)/b/(a*e-b*d)/(x+1/2/f*e+1/2/b/f*(-b*e*(4*a*f-b*e))^(1/2))*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2)*B*(-b*e*(4*a*f-b*e))^(1/2)-1/2/e/(4*a*f-b*e)/b*(-b*e*(4*a*f-b*e))^(1/2)/(a*e-b*d)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*A+1/4/f/(4*a*f-b*e)/b*(-b*e*(4*a*f-b*e))^(1/2)/(a*e-b*d)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*B-1/4/f/b/(a*e-b*d)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))*B","B"
36,1,48,46,0.005000," ","int((h*x+g)*(c*x^2+b*x+a)^(1/2)/(c*d*x^2+b*d*x+a*d)^2,x)","-\frac{2 \left(b h x -2 c g x +2 a h -b g \right)}{\sqrt{c \,x^{2}+b x +a}\, \left(4 a c -b^{2}\right) d^{2}}"," ",0,"-2/(c*x^2+b*x+a)^(1/2)*(b*h*x-2*c*g*x+2*a*h-b*g)/d^2/(4*a*c-b^2)","A"
37,1,94,15,0.017000," ","int((3+2*x)/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","-\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)}{6 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"-1/6*3^(1/2)*4^(1/2)/((x^2/(-3/2-x)^2-4)/(x/(-3/2-x)+1)^2)^(1/2)/(x/(-3/2-x)+1)*(3*x^2/(-3/2-x)^2-12)^(1/2)*arctanh(3*x/(-3/2-x)/(3*x^2/(-3/2-x)^2-12)^(1/2))","B"
38,1,123,75,0.013000," ","int((4*x+3)/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(-\arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{6 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"1/6*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))-arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)","A"
39,1,121,122,0.027000," ","int((h*x+g)*(c*x^2+b*x+a)^(1/2)/(c*d*x^2+b*d*x+a*d)^(3/2),x)","\frac{\sqrt{\left(c \,x^{2}+b x +a \right) d}\, \left(-2 b h \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)+4 c g \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)+\sqrt{4 a c -b^{2}}\, h \ln \left(c \,x^{2}+b x +a \right)\right)}{2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{4 a c -b^{2}}\, c \,d^{2}}"," ",0,"1/2/(c*x^2+b*x+a)^(1/2)*(d*(c*x^2+b*x+a))^(1/2)*(h*ln(c*x^2+b*x+a)*(4*a*c-b^2)^(1/2)-2*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*h+4*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c*g)/d^2/c/(4*a*c-b^2)^(1/2)","A"
40,1,103,148,0.048000," ","int(x^2*((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x)","-\frac{\left(15 a \,c^{2} d \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+15 \sqrt{d \,x^{2}+c}\, a c \,d^{\frac{3}{2}} x -24 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b \,d^{\frac{3}{2}} x^{2}-30 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,d^{\frac{3}{2}} x +16 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b c \sqrt{d}\right) \mathrm{csgn}\left(b x +a \right)}{120 d^{\frac{5}{2}}}"," ",0,"-1/120*csgn(b*x+a)*(-24*d^(3/2)*(d*x^2+c)^(3/2)*x^2*b-30*d^(3/2)*(d*x^2+c)^(3/2)*x*a+16*d^(1/2)*(d*x^2+c)^(3/2)*b*c+15*d^(3/2)*(d*x^2+c)^(1/2)*x*a*c+15*ln(x*d^(1/2)+(d*x^2+c)^(1/2))*a*c^2*d)/d^(5/2)","C"
41,1,83,112,0.010000," ","int(x*((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x)","\frac{\left(-3 b \,c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)-3 \sqrt{d \,x^{2}+c}\, b c \sqrt{d}\, x +6 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b \sqrt{d}\, x +8 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \sqrt{d}\right) \mathrm{csgn}\left(b x +a \right)}{24 d^{\frac{3}{2}}}"," ",0,"1/24*csgn(b*x+a)*(6*d^(1/2)*(d*x^2+c)^(3/2)*x*b+8*a*(d*x^2+c)^(3/2)*d^(1/2)-3*d^(1/2)*(d*x^2+c)^(1/2)*x*b*c-3*ln(d^(1/2)*x+(d*x^2+c)^(1/2))*b*c^2)/d^(3/2)","C"
42,1,65,99,0.008000," ","int(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x)","\frac{\left(3 a c d \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+3 \sqrt{d \,x^{2}+c}\, a \,d^{\frac{3}{2}} x +2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b \sqrt{d}\right) \mathrm{csgn}\left(b x +a \right)}{6 d^{\frac{3}{2}}}"," ",0,"1/6*csgn(b*x+a)*(2*b*(d*x^2+c)^(3/2)*d^(1/2)+3*d^(3/2)*(d*x^2+c)^(1/2)*x*a+3*ln(d^(1/2)*x+(d*x^2+c)^(1/2))*a*c*d)/d^(3/2)","C"
43,1,94,109,0.009000," ","int(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x,x)","-\frac{\left(2 a \sqrt{c}\, \sqrt{d}\, \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)-b c \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)-\sqrt{d \,x^{2}+c}\, b \sqrt{d}\, x -2 \sqrt{d \,x^{2}+c}\, a \sqrt{d}\right) \mathrm{csgn}\left(b x +a \right)}{2 \sqrt{d}}"," ",0,"-1/2*csgn(b*x+a)*(2*c^(1/2)*d^(1/2)*ln(2*(c^(1/2)*(d*x^2+c)^(1/2)+c)/x)*a-d^(1/2)*(d*x^2+c)^(1/2)*x*b-2*d^(1/2)*(d*x^2+c)^(1/2)*a-ln(d^(1/2)*x+(d*x^2+c)^(1/2))*b*c)/d^(1/2)","C"
44,1,118,109,0.013000," ","int(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x^2,x)","\frac{\left(a c d x \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)-b \,c^{\frac{3}{2}} \sqrt{d}\, x \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+\sqrt{d \,x^{2}+c}\, a \,d^{\frac{3}{2}} x^{2}+\sqrt{d \,x^{2}+c}\, b c \sqrt{d}\, x -\left(d \,x^{2}+c \right)^{\frac{3}{2}} a \sqrt{d}\right) \mathrm{csgn}\left(b x +a \right)}{c \sqrt{d}\, x}"," ",0,"csgn(b*x+a)*(d^(3/2)*(d*x^2+c)^(1/2)*x^2*a-d^(1/2)*c^(3/2)*ln(2*(c+(d*x^2+c)^(1/2)*c^(1/2))/x)*x*b-(d*x^2+c)^(3/2)*a*d^(1/2)+(d*x^2+c)^(1/2)*b*c*d^(1/2)*x+ln(d^(1/2)*x+(d*x^2+c)^(1/2))*x*a*c*d)/c/x/d^(1/2)","C"
45,1,141,110,0.015000," ","int(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x^3,x)","-\frac{\left(a \sqrt{c}\, d^{\frac{3}{2}} x^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)-2 b c d \,x^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)-2 \sqrt{d \,x^{2}+c}\, b \,d^{\frac{3}{2}} x^{3}-\sqrt{d \,x^{2}+c}\, a \,d^{\frac{3}{2}} x^{2}+2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b \sqrt{d}\, x +\left(d \,x^{2}+c \right)^{\frac{3}{2}} a \sqrt{d}\right) \mathrm{csgn}\left(b x +a \right)}{2 c \sqrt{d}\, x^{2}}"," ",0,"-1/2*csgn(b*x+a)*(c^(1/2)*ln(2*(c+(d*x^2+c)^(1/2)*c^(1/2))/x)*d^(3/2)*x^2*a-2*d^(3/2)*(d*x^2+c)^(1/2)*x^3*b+2*(d*x^2+c)^(3/2)*b*d^(1/2)*x-(d*x^2+c)^(1/2)*a*d^(3/2)*x^2-2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))*x^2*b*c*d+(d*x^2+c)^(3/2)*a*d^(1/2))/x^2/c/d^(1/2)","C"
46,1,530,251,0.018000," ","int(x^2*((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x)","\frac{\left(-480 a \,c^{2} d^{4} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+720 a c \,d^{3} e^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-150 a \,d^{2} e^{4} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+720 b \,c^{2} d^{3} e \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-600 b c \,d^{2} e^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+105 b d \,e^{5} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-480 \sqrt{d \,x^{2}+e x +c}\, a c \,d^{\frac{9}{2}} x +600 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{7}{2}} e^{2} x +720 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{7}{2}} e x +768 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{9}{2}} x^{2}-420 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{5}{2}} e^{3} x -240 \sqrt{d \,x^{2}+e x +c}\, a c \,d^{\frac{7}{2}} e +960 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{9}{2}} x +300 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}} e^{3}+360 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{5}{2}} e^{2}-672 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{7}{2}} e x -210 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{3}{2}} e^{4}-800 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{7}{2}} e -512 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b c \,d^{\frac{7}{2}}+560 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{5}{2}} e^{2}\right) \mathrm{csgn}\left(b x +a \right)}{3840 d^{\frac{11}{2}}}"," ",0,"1/3840*csgn(b*x+a)*(768*(d*x^2+e*x+c)^(3/2)*d^(9/2)*x^2*b+960*(d*x^2+e*x+c)^(3/2)*d^(9/2)*x*a-672*(d*x^2+e*x+c)^(3/2)*d^(7/2)*x*b*e-800*(d*x^2+e*x+c)^(3/2)*d^(7/2)*a*e-512*(d*x^2+e*x+c)^(3/2)*d^(7/2)*b*c+560*(d*x^2+e*x+c)^(3/2)*d^(5/2)*b*e^2-480*(d*x^2+e*x+c)^(1/2)*d^(9/2)*x*a*c+600*(d*x^2+e*x+c)^(1/2)*d^(7/2)*x*a*e^2+720*(d*x^2+e*x+c)^(1/2)*d^(7/2)*x*b*c*e-420*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x*b*e^3-240*(d*x^2+e*x+c)^(1/2)*d^(7/2)*a*c*e+300*(d*x^2+e*x+c)^(1/2)*d^(5/2)*a*e^3+360*(d*x^2+e*x+c)^(1/2)*d^(5/2)*b*c*e^2-210*(d*x^2+e*x+c)^(1/2)*d^(3/2)*b*e^4-480*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*a*c^2*d^4+720*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*a*c*d^3*e^2-150*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*a*d^2*e^4+720*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*b*c^2*d^3*e-600*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*b*c*d^2*e^3+105*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*b*d*e^5)/d^(11/2)","C"
47,1,381,176,0.013000," ","int(x*((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x)","\frac{\left(-96 a c \,d^{3} e \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+24 a \,d^{2} e^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-48 b \,c^{2} d^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+72 b c \,d^{2} e^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-15 b d \,e^{4} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-96 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{7}{2}} e x -48 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{7}{2}} x +60 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{5}{2}} e^{2} x -48 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}} e^{2}-24 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{5}{2}} e +96 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{7}{2}} x +30 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{3}{2}} e^{3}+128 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{7}{2}}-80 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{5}{2}} e \right) \mathrm{csgn}\left(b x +a \right)}{384 d^{\frac{9}{2}}}"," ",0,"1/384*csgn(b*x+a)*(96*d^(7/2)*(d*x^2+e*x+c)^(3/2)*x*b+128*d^(7/2)*(d*x^2+e*x+c)^(3/2)*a-80*d^(5/2)*(d*x^2+e*x+c)^(3/2)*b*e-96*d^(7/2)*(d*x^2+e*x+c)^(1/2)*x*a*e-48*d^(7/2)*(d*x^2+e*x+c)^(1/2)*x*b*c+60*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x*b*e^2-48*d^(5/2)*(d*x^2+e*x+c)^(1/2)*a*e^2-24*d^(5/2)*(d*x^2+e*x+c)^(1/2)*b*c*e+30*d^(3/2)*(d*x^2+e*x+c)^(1/2)*b*e^3-96*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*a*c*d^3*e+24*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*a*d^2*e^3-48*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*c^2*d^3+72*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*c*d^2*e^2-15*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*d*e^4)/d^(9/2)","C"
48,1,257,147,0.011000," ","int(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x)","\frac{\left(24 a c \,d^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-6 a \,d^{2} e^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-12 b c \,d^{2} e \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+3 b d \,e^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+24 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{7}{2}} x -12 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{5}{2}} e x +12 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}} e -6 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{3}{2}} e^{2}+16 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{5}{2}}\right) \mathrm{csgn}\left(b x +a \right)}{48 d^{\frac{7}{2}}}"," ",0,"1/48*csgn(b*x+a)*(16*d^(5/2)*(d*x^2+e*x+c)^(3/2)*b+24*d^(7/2)*(d*x^2+e*x+c)^(1/2)*x*a-12*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x*b*e+12*d^(5/2)*(d*x^2+e*x+c)^(1/2)*a*e-6*d^(3/2)*(d*x^2+e*x+c)^(1/2)*b*e^2+24*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*a*c*d^3-6*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*a*d^2*e^2-12*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*c*d^2*e+3*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*d*e^3)/d^(7/2)","C"
49,1,214,156,0.011000," ","int(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x,x)","-\frac{\left(8 a \sqrt{c}\, d^{\frac{5}{2}} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)-4 a \,d^{2} e \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-4 b c \,d^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+b d \,e^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-4 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{5}{2}} x -8 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}}-2 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{3}{2}} e \right) \mathrm{csgn}\left(b x +a \right)}{8 d^{\frac{5}{2}}}"," ",0,"-1/8*csgn(b*x+a)*(8*c^(1/2)*d^(5/2)*ln((2*c+e*x+2*c^(1/2)*(d*x^2+e*x+c)^(1/2))/x)*a-4*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x*b-8*d^(5/2)*(d*x^2+e*x+c)^(1/2)*a-2*d^(3/2)*(d*x^2+e*x+c)^(1/2)*b*e-4*d^2*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*a*e-4*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*c*d^2+ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*d*e^2)/d^(5/2)","C"
50,1,249,147,0.013000," ","int(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x^2,x)","\frac{\left(2 a c \,d^{2} x \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-a \sqrt{c}\, d^{\frac{3}{2}} e x \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)-2 b \,c^{\frac{3}{2}} d^{\frac{3}{2}} x \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)+b c d e x \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+2 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}} x^{2}+2 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{3}{2}} e x +2 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{3}{2}} x -2 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{3}{2}}\right) \mathrm{csgn}\left(b x +a \right)}{2 c \,d^{\frac{3}{2}} x}"," ",0,"1/2*csgn(b*x+a)*(2*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x^2*a-2*d^(3/2)*c^(3/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x*b-d^(3/2)*c^(1/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x*a*e-2*d^(3/2)*(d*x^2+e*x+c)^(3/2)*a+2*d^(3/2)*(d*x^2+e*x+c)^(1/2)*x*a*e+2*d^(3/2)*(d*x^2+e*x+c)^(1/2)*x*b*c+2*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*x*a*c*d^2+ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*d*x*b*c*e)/c/x/d^(3/2)","C"
51,1,358,160,0.016000," ","int(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x^3,x)","\frac{\left(-4 a \,c^{\frac{3}{2}} d^{\frac{5}{2}} x^{2} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)+a \sqrt{c}\, d^{\frac{3}{2}} e^{2} x^{2} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)+8 b \,c^{2} d^{2} x^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-4 b \,c^{\frac{3}{2}} d^{\frac{3}{2}} e \,x^{2} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)-2 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}} e \,x^{3}+8 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{5}{2}} x^{3}+4 \sqrt{d \,x^{2}+e x +c}\, a c \,d^{\frac{5}{2}} x^{2}-2 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{3}{2}} e^{2} x^{2}+8 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{3}{2}} e \,x^{2}+2 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{3}{2}} e x -8 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b c \,d^{\frac{3}{2}} x -4 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a c \,d^{\frac{3}{2}}\right) \mathrm{csgn}\left(b x +a \right)}{8 c^{2} d^{\frac{3}{2}} x^{2}}"," ",0,"1/8*csgn(b*x+a)*(-4*d^(5/2)*c^(3/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^2*a-2*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x^3*a*e+8*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x^3*b*c-4*d^(3/2)*c^(3/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^2*b*e+4*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x^2*a*c+d^(3/2)*c^(1/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^2*a*e^2+2*d^(3/2)*(d*x^2+e*x+c)^(3/2)*x*a*e-8*d^(3/2)*(d*x^2+e*x+c)^(3/2)*x*b*c-2*d^(3/2)*(d*x^2+e*x+c)^(1/2)*x^2*a*e^2+8*d^(3/2)*(d*x^2+e*x+c)^(1/2)*x^2*b*c*e+8*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*x^2*b*c^2*d^2-4*d^(3/2)*(d*x^2+e*x+c)^(3/2)*a*c)/x^2/c^2/d^(3/2)","C"
52,1,7739,403,0.039000," ","int(x^2*(c*x^2+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
53,1,5581,350,0.015000," ","int(x*(c*x^2+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
54,1,3249,259,0.013000," ","int((c*x^2+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"-1/2/(-4*d*f+e^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)+1/2/(-4*d*f+e^2)^(1/2)*c^(1/2)/f*ln((-1/2*c*(e+(-4*d*f+e^2)^(1/2))/f+c*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))*e+1/2*c^(1/2)/f*ln((-1/2*c*(e+(-4*d*f+e^2)^(1/2))/f+c*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))+1/2/f^2*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e+1/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*a-1/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*d+1/2/(-4*d*f+e^2)^(1/2)/f^2*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e^2+1/2/(-4*d*f+e^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)+1/2*c^(1/2)/f*ln((-1/2*c*(e-(-4*d*f+e^2)^(1/2))/f+c*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))-1/2/(-4*d*f+e^2)^(1/2)*c^(1/2)/f*ln((-1/2*c*(e-(-4*d*f+e^2)^(1/2))/f+c*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))*e+1/2/f^2*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e-1/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*a+1/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*d-1/2/(-4*d*f+e^2)^(1/2)/f^2*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e^2","B"
55,1,3544,315,0.019000," ","int((c*x^2+a)^(1/2)/x/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"f/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)-1/(e+(-4*d*f+e^2)^(1/2))*c^(1/2)*ln((-1/2*c*(e+(-4*d*f+e^2)^(1/2))/f+c*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))-1/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*c^(1/2)*ln((-1/2*c*(e+(-4*d*f+e^2)^(1/2))/f+c*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))*e-1/f/(e+(-4*d*f+e^2)^(1/2))*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e-2*f/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*a+2/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*d-1/f/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e^2+f/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)+1/(-e+(-4*d*f+e^2)^(1/2))*c^(1/2)*ln((-1/2*c*(e-(-4*d*f+e^2)^(1/2))/f+c*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))-1/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*c^(1/2)*ln((-1/2*c*(e-(-4*d*f+e^2)^(1/2))/f+c*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))*e+1/f/(-e+(-4*d*f+e^2)^(1/2))*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e-2*f/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*a+2/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*d-1/f/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e^2+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*a^(1/2)*ln((2*a+2*a^(1/2)*(c*x^2+a)^(1/2))/x)-4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*(c*x^2+a)^(1/2)","B"
56,1,3703,337,0.025000," ","int((c*x^2+a)^(1/2)/x^2/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"-2*f^2/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)+2*f/(e+(-4*d*f+e^2)^(1/2))^2*c^(1/2)*ln((-1/2*c*(e+(-4*d*f+e^2)^(1/2))/f+c*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))+2*f/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*c^(1/2)*ln((-1/2*c*(e+(-4*d*f+e^2)^(1/2))/f+c*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))*e+2/(e+(-4*d*f+e^2)^(1/2))^2*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e+4*f^2/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*a-4*f/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*d+2/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e^2+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/x*(c*x^2+a)^(3/2)-4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*c/a*x*(c*x^2+a)^(1/2)-4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+2*f^2/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)+2*f/(-e+(-4*d*f+e^2)^(1/2))^2*c^(1/2)*ln((-1/2*c*(e-(-4*d*f+e^2)^(1/2))/f+c*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))-2*f/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*c^(1/2)*ln((-1/2*c*(e-(-4*d*f+e^2)^(1/2))/f+c*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))*e+2/(-e+(-4*d*f+e^2)^(1/2))^2*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e-4*f^2/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*a+4*f/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*d-2/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e^2+16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2*a^(1/2)*ln((2*a+2*a^(1/2)*(c*x^2+a)^(1/2))/x)-16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2*(c*x^2+a)^(1/2)","B"
57,1,3993,442,0.019000," ","int((c*x^2+a)^(1/2)/x^3/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"4*f^3/(e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)-4*f^2/(e+(-4*d*f+e^2)^(1/2))^3*c^(1/2)*ln((-1/2*c*(e+(-4*d*f+e^2)^(1/2))/f+c*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))-4*f^2/(e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*c^(1/2)*ln((-1/2*c*(e+(-4*d*f+e^2)^(1/2))/f+c*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))*e-4*f/(e+(-4*d*f+e^2)^(1/2))^3*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e-8*f^3/(e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*a+8*f^2/(e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*d-4*f/(e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e^2+16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2/a/x*(c*x^2+a)^(3/2)-16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2*c/a*x*(c*x^2+a)^(1/2)-16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2*c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/x^2*(c*x^2+a)^(3/2)+2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*c/a^(1/2)*ln((2*a+2*a^(1/2)*(c*x^2+a)^(1/2))/x)-2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*c/a*(c*x^2+a)^(1/2)+4*f^3/(-e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)+4*f^2/(-e+(-4*d*f+e^2)^(1/2))^3*c^(1/2)*ln((-1/2*c*(e-(-4*d*f+e^2)^(1/2))/f+c*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))-4*f^2/(-e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*c^(1/2)*ln((-1/2*c*(e-(-4*d*f+e^2)^(1/2))/f+c*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))/c^(1/2)+((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))*e+4*f/(-e+(-4*d*f+e^2)^(1/2))^3*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e-8*f^3/(-e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*a+8*f^2/(-e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*d-4*f/(-e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e^2-64*f^4/(-e+(-4*d*f+e^2)^(1/2))^3/(e+(-4*d*f+e^2)^(1/2))^3*a^(1/2)*ln((2*a+2*a^(1/2)*(c*x^2+a)^(1/2))/x)*d+64*f^3/(-e+(-4*d*f+e^2)^(1/2))^3/(e+(-4*d*f+e^2)^(1/2))^3*a^(1/2)*ln((2*a+2*a^(1/2)*(c*x^2+a)^(1/2))/x)*e^2+64*f^4/(-e+(-4*d*f+e^2)^(1/2))^3/(e+(-4*d*f+e^2)^(1/2))^3*(c*x^2+a)^(1/2)*d-64*f^3/(-e+(-4*d*f+e^2)^(1/2))^3/(e+(-4*d*f+e^2)^(1/2))^3*(c*x^2+a)^(1/2)*e^2","B"
58,1,19148,722,0.030000," ","int(x^2*(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
59,1,14709,499,0.015000," ","int(x*(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
60,1,8954,435,0.014000," ","int((c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
61,1,9728,443,0.018000," ","int((c*x^2+a)^(3/2)/x/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
62,1,9912,529,0.020000," ","int((c*x^2+a)^(3/2)/x^2/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
63,1,10298,584,0.019000," ","int((c*x^2+a)^(3/2)/x^3/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
64,1,2397,335,0.029000," ","int(x^3/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x)","-\frac{3 \sqrt{2}\, d e \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{3 \sqrt{2}\, d e \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\sqrt{2}\, e^{3} \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{3}}-\frac{\sqrt{2}\, e^{3} \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{3}}+\frac{\sqrt{2}\, d \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\sqrt{2}\, d \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}-\frac{\sqrt{2}\, e^{2} \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{3}}-\frac{\sqrt{2}\, e^{2} \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{3}}-\frac{e \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, f^{2}}+\frac{\sqrt{c \,x^{2}+a}}{c f}"," ",0,"(c*x^2+a)^(1/2)/c/f-1/f^2*e*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)+1/2/f^2*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*d-1/2/f^3*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e^2+3/2/f^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*d*e-1/2/f^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e+(-4*d*f+e^2)^(1/2))/f*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e^3+1/2/f^2*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*d-1/2/f^3*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e^2-3/2/f^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*d*e+1/2/f^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2-c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*c*(e-(-4*d*f+e^2)^(1/2))/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e^3","B"
65,1,1796,300,0.015000," ","int(x^2/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, d \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}-\frac{\sqrt{2}\, d \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}-\frac{\sqrt{2}\, e^{2} \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\sqrt{2}\, e^{2} \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\sqrt{2}\, e \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\sqrt{2}\, e \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, f}"," ",0,"1/f*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)+1/2/f^2*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e-1/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*d+1/2/(-4*d*f+e^2)^(1/2)/f^2*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e^2+1/2/f^2*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e+1/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*d-1/2/(-4*d*f+e^2)^(1/2)/f^2*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e^2","B"
66,1,1172,257,0.013000," ","int(x/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, e \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}-\frac{\sqrt{2}\, e \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}-\frac{\sqrt{2}\, \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}-\frac{\sqrt{2}\, \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}"," ",0,"-1/2/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e-1/2/f*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))-1/2/f*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))+1/2/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e","B"
67,1,589,232,0.013000," ","int(1/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}+\frac{\sqrt{2}\, \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}"," ",0,"1/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))-1/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))","B"
68,1,681,287,0.017000," ","int(1/x/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x)","-\frac{2 \sqrt{2}\, f \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{2 \sqrt{2}\, f \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}+\frac{4 f \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{a}}"," ",0,"-2*f/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))-2*f/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a^(1/2)*ln((2*a+2*a^(1/2)*(c*x^2+a)^(1/2))/x)","B"
69,1,736,322,0.018000," ","int(1/x^2/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x)","\frac{16 e \,f^{2} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{a}}-\frac{4 \sqrt{2}\, f^{2} \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}+\frac{4 \sqrt{2}\, f^{2} \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}+\frac{4 \sqrt{c \,x^{2}+a}\, f}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a x}"," ",0,"4*f^2/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/x*(c*x^2+a)^(1/2)-4*f^2/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))+16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)","B"
70,1,911,400,0.018000," ","int(1/x^3/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x)","-\frac{64 d \,f^{4} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{3} \left(e +\sqrt{-4 d f +e^{2}}\right)^{3} \sqrt{a}}+\frac{64 e^{2} f^{3} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{3} \left(e +\sqrt{-4 d f +e^{2}}\right)^{3} \sqrt{a}}-\frac{8 \sqrt{2}\, f^{3} \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{3} \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{8 \sqrt{2}\, f^{3} \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(e +\sqrt{-4 d f +e^{2}}\right)^{3} \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{2 c f \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a^{\frac{3}{2}}}+\frac{16 \sqrt{c \,x^{2}+a}\, e \,f^{2}}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(e +\sqrt{-4 d f +e^{2}}\right)^{2} a x}+\frac{2 \sqrt{c \,x^{2}+a}\, f}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a \,x^{2}}"," ",0,"-8*f^3/(e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2/a/x*(c*x^2+a)^(1/2)+2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/x^2*(c*x^2+a)^(1/2)-2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*c/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-8*f^3/(-e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))-64*f^4/(-e+(-4*d*f+e^2)^(1/2))^3/(e+(-4*d*f+e^2)^(1/2))^3/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)*d+64*f^3/(-e+(-4*d*f+e^2)^(1/2))^3/(e+(-4*d*f+e^2)^(1/2))^3/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)*e^2","B"
71,1,6124,456,0.032000," ","int(x^3/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
72,1,4752,372,0.019000," ","int(x^2/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"1/f*x/a/(c*x^2+a)^(1/2)-1/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e+2/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*d-1/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e^2-2*(-4*d*f+e^2)^(1/2)/f*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*e+4*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*d-4/f*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*e^2+4/(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x*d-2/(-4*d*f+e^2)^(1/2)/f*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e^3*x+1/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e-2/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*d+1/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e^2-1/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e-2/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*d+1/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e^2+2*(-4*d*f+e^2)^(1/2)/f*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*e+4*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*d-4/f*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*e^2-4/(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x*d+2/(-4*d*f+e^2)^(1/2)/f*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e^3*x+1/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e+2/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*d-1/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e^2","B"
73,1,3000,370,0.015000," ","int(x/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"1/(-4*d*f+e^2)^(1/2)*f*e/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)+4*e*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x+2/(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e^2*x-1/(-4*d*f+e^2)^(1/2)*f*e/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+f/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)+2*(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x-f/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+f/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-2*(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x+4*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x-f/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))-1/(-4*d*f+e^2)^(1/2)*f*e/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-2/(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e^2*x+1/(-4*d*f+e^2)^(1/2)*f*e/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))","B"
74,1,1713,377,0.015000," ","int(1/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","-\frac{4 c^{2} e f x}{\sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{4 c^{2} e f x}{\sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}-\frac{4 c^{2} f x}{\left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}-\frac{4 c^{2} f x}{\left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}-\frac{2 \sqrt{2}\, f^{2} \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}+\frac{2 \sqrt{2}\, f^{2} \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{2 f^{2}}{\sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{2 f^{2}}{\sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}"," ",0,"-2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*f^2/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-4*c^2*f/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x-4/(-4*d*f+e^2)^(1/2)*c^2*f/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x+2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*f^2*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*f^2/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-4*c^2*f/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x+4/(-4*d*f+e^2)^(1/2)*c^2*f/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-c^2/f^2*(-4*d*f+e^2))/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x-2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*f^2*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))","B"
75,1,1945,480,0.017000," ","int(1/x/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","\frac{8 c^{2} e \,f^{2} x}{\left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{8 c^{2} e \,f^{2} x}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{8 c^{2} f^{2} x}{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}-\frac{8 c^{2} f^{2} x}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}-\frac{4 \sqrt{2}\, f^{3} \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{4 \sqrt{2}\, f^{3} \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}+\frac{4 f^{3}}{\left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{4 f^{3}}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{4 f \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a^{\frac{3}{2}}}-\frac{4 f}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{c \,x^{2}+a}\, a}"," ",0,"4*f^3/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)+8*f^2/(e+(-4*d*f+e^2)^(1/2))*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x+8*f^2/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x-4*f^3/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+4*f^3/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-8*f^2/(-e+(-4*d*f+e^2)^(1/2))*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x+8*f^2/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x-4*f^3/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))-4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/(c*x^2+a)^(1/2)+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)","B"
76,1,2046,565,0.019000," ","int(1/x^2/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x)","-\frac{16 c^{2} e \,f^{3} x}{\left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{16 c^{2} e \,f^{3} x}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}-\frac{16 c^{2} f^{3} x}{\left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}-\frac{16 c^{2} f^{3} x}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \left(4 a c -\frac{4 c^{2} d}{f}+\frac{c^{2} e^{2}}{f^{2}}-\frac{\left(-4 d f +e^{2}\right) c^{2}}{f^{2}}\right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}-\frac{8 \sqrt{2}\, f^{4} \ln \left(\frac{-\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}+\frac{8 \sqrt{2}\, f^{4} \ln \left(\frac{-\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{4 \left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{4 a \,f^{2}-4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{8 f^{4}}{\left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e +\sqrt{-4 d f +e^{2}}\right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{8 f^{4}}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \left(2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e \right) \sqrt{\left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c -\frac{\left(e -\sqrt{-4 d f +e^{2}}\right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right) c}{f}+\frac{2 a \,f^{2}-2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, c e}{2 f^{2}}}}+\frac{16 e \,f^{2} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(e +\sqrt{-4 d f +e^{2}}\right)^{2} a^{\frac{3}{2}}}-\frac{16 e \,f^{2}}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{c \,x^{2}+a}\, a}+\frac{8 c f x}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{c \,x^{2}+a}\, a^{2}}+\frac{4 f}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{c \,x^{2}+a}\, a x}"," ",0,"-8*f^4/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-16*f^3/(e+(-4*d*f+e^2)^(1/2))^2*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x-16*f^3/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x+8*f^4/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e+(-4*d*f+e^2)^(1/2))*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/x/(c*x^2+a)^(1/2)+8*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*c/a^2*x/(c*x^2+a)^(1/2)+8*f^4/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-16*f^3/(-e+(-4*d*f+e^2)^(1/2))^2*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x+16*f^3/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*c^2/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+1/2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*e*x-8*f^4/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln((-(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c-4*(e-(-4*d*f+e^2)^(1/2))*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)*c/f+2*(2*a*f^2-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))-16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2/a/(c*x^2+a)^(1/2)+16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)","B"
77,1,1817,306,0.018000," ","int(x^3*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","\frac{a d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{a d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{c \,d^{2} \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{3}}+\frac{c \,d^{2} \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{3}}+\frac{a b \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{3}{2}} f}-\frac{b^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}} f}-\frac{b d \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{c}\, f^{2}}-\frac{b d \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{c}\, f^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, b x}{4 c f}-\frac{\sqrt{d f}\, b d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{3}}+\frac{\sqrt{d f}\, b d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{3}}+\frac{\sqrt{d f}\, \sqrt{c}\, d \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{2 f^{3}}-\frac{\sqrt{d f}\, \sqrt{c}\, d \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{2 f^{3}}+\frac{\sqrt{c \,x^{2}+b x +a}\, b^{2}}{8 c^{2} f}-\frac{\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}{2 f^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}{2 f^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}{3 c f}"," ",0,"-1/3*(c*x^2+b*x+a)^(3/2)/c/f+1/4/f*b/c*x*(c*x^2+b*x+a)^(1/2)+1/8/f*b^2/c^2*(c*x^2+b*x+a)^(1/2)+1/4/f*b/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/16/f*b^3/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/2/f^2*d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)+1/2/f^3*d*ln((1/2/f*(b*f-2*(d*f)^(1/2)*c)+c*(x+(d*f)^(1/2)/f))/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)-1/4/f^2*d*ln((1/2/f*(b*f-2*(d*f)^(1/2)*c)+c*(x+(d*f)^(1/2)/f))/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b-1/2/f^3*d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*(d*f)^(1/2)*b+1/2/f^2*d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a+1/2/f^3*d^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c-1/2/f^2*d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)-1/2/f^3*d*ln((1/2*(b*f+2*(d*f)^(1/2)*c)/f+c*(x-(d*f)^(1/2)/f))/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)-1/4/f^2*d*ln((1/2*(b*f+2*(d*f)^(1/2)*c)/f+c*(x-(d*f)^(1/2)/f))/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2/f^3*d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*(d*f)^(1/2)*b+1/2/f^2*d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a+1/2/f^3*d^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c","B"
78,1,1810,246,0.017000," ","int(x^2*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","-\frac{a d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{a d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{c \,d^{2} \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{c \,d^{2} \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{b d \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{d f}\, \sqrt{c}\, f}-\frac{b d \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{d f}\, \sqrt{c}\, f}+\frac{b d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{b d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}-\frac{a \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}\, f}+\frac{b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}} f}-\frac{\sqrt{c}\, d \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{2 f^{2}}-\frac{\sqrt{c}\, d \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{2 f^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}{2 \sqrt{d f}\, f}-\frac{\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}{2 \sqrt{d f}\, f}-\frac{\sqrt{c \,x^{2}+b x +a}\, x}{2 f}-\frac{\sqrt{c \,x^{2}+b x +a}\, b}{4 c f}"," ",0,"-1/2/f*x*(c*x^2+b*x+a)^(1/2)-1/4/f/c*(c*x^2+b*x+a)^(1/2)*b-1/2/f/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/8/f/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2+1/2*d/(d*f)^(1/2)/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)-1/2*d/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)+1/4*d/(d*f)^(1/2)/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2*d/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b-1/2*d/(d*f)^(1/2)/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a-1/2*d^2/(d*f)^(1/2)/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c-1/2*d/(d*f)^(1/2)/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)-1/2*d/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)-1/4*d/(d*f)^(1/2)/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2*d/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b+1/2*d/(d*f)^(1/2)/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a+1/2*d^2/(d*f)^(1/2)/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c","B"
79,1,1667,214,0.014000," ","int(x*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","\frac{a \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{a \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{c d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{c d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}-\frac{b \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{c}\, f}-\frac{b \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{c}\, f}-\frac{\sqrt{d f}\, b \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{\sqrt{d f}\, b \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{\sqrt{d f}\, \sqrt{c}\, \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{2 f^{2}}-\frac{\sqrt{d f}\, \sqrt{c}\, \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{2 f^{2}}-\frac{\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{2 f}-\frac{\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{2 f}"," ",0,"-1/2/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)+1/2/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)-1/4/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b-1/2/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*(d*f)^(1/2)*b+1/2/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a+1/2/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c*d-1/2/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)-1/2/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)-1/4/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*(d*f)^(1/2)*b+1/2/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a+1/2/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c*d","B"
80,1,1669,202,0.014000," ","int((c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","-\frac{a \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{a \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{c d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{c d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{b \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{d f}\, \sqrt{c}}-\frac{b \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{d f}\, \sqrt{c}}+\frac{b \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{b \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{\sqrt{c}\, \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{2 f}-\frac{\sqrt{c}\, \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{2 f}+\frac{\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{2 \sqrt{d f}}-\frac{\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{2 \sqrt{d f}}"," ",0,"1/2/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)-1/2/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)+1/4/(d*f)^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b-1/2/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a-1/2/(d*f)^(1/2)/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c*d-1/2/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)-1/2/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)-1/4/(d*f)^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b+1/2/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a+1/2/(d*f)^(1/2)/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c*d","B"
81,1,1764,203,0.018000," ","int((c*x^2+b*x+a)^(1/2)/x/(-f*x^2+d),x)","\frac{a \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{a \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}+\frac{c \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{c \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{\sqrt{a}\, \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{d}+\frac{b \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}\, d}-\frac{b \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{c}\, d}-\frac{b \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{c}\, d}-\frac{\sqrt{d f}\, b \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d f}+\frac{\sqrt{d f}\, b \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d f}+\frac{\sqrt{d f}\, \sqrt{c}\, \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{2 d f}-\frac{\sqrt{d f}\, \sqrt{c}\, \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{2 d f}-\frac{\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{2 d}-\frac{\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{2 d}+\frac{\sqrt{c \,x^{2}+b x +a}}{d}"," ",0,"-1/2/d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)+1/2/d/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)-1/4/d*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b-1/2/d/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*(d*f)^(1/2)*b+1/2/d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a+1/2/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c-1/2/d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)-1/2/d/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)-1/4/d*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2/d/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*(d*f)^(1/2)*b+1/2/d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a+1/2/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c+1/d*(c*x^2+b*x+a)^(1/2)+1/2/d*b*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-1/d*a^(1/2)*ln((2*a+b*x+2*a^(1/2)*(c*x^2+b*x+a)^(1/2))/x)","B"
82,1,1819,218,0.020000," ","int((c*x^2+b*x+a)^(1/2)/x^2/(-f*x^2+d),x)","-\frac{a f \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{a f \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{c \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{c \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{b f \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{d f}\, \sqrt{c}\, d}-\frac{b f \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{d f}\, \sqrt{c}\, d}+\frac{b \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{b \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{b \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{2 \sqrt{a}\, d}+\frac{\sqrt{c}\, \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{d}-\frac{\sqrt{c}\, \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{2 d}-\frac{\sqrt{c}\, \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{2 d}+\frac{\sqrt{c \,x^{2}+b x +a}\, c x}{a d}+\frac{\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}{2 \sqrt{d f}\, d}-\frac{\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}{2 \sqrt{d f}\, d}+\frac{\sqrt{c \,x^{2}+b x +a}\, b}{a d}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}{a d x}"," ",0,"1/2*f/d/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)-1/2/d*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)+1/4*f/d/(d*f)^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2/d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b-1/2*f/d/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a-1/2/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c-1/d/a/x*(c*x^2+b*x+a)^(3/2)+1/d*b/a*(c*x^2+b*x+a)^(1/2)-1/2/d*b/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)+1/d*c/a*(c*x^2+b*x+a)^(1/2)*x+1/d*c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/2*f/d/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)-1/2/d*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)-1/4*f/d/(d*f)^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2/d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b+1/2*f/d/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a+1/2/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c","B"
83,1,1953,275,0.017000," ","int((c*x^2+b*x+a)^(1/2)/x^3/(-f*x^2+d),x)","\frac{a f \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d^{2}}+\frac{a f \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d^{2}}+\frac{c \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{c \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{\sqrt{a}\, f \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{d^{2}}-\frac{c \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{2 \sqrt{a}\, d}+\frac{b^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{3}{2}} d}+\frac{b f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}\, d^{2}}-\frac{b f \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{c}\, d^{2}}-\frac{b f \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{4 \sqrt{c}\, d^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b c x}{4 a^{2} d}-\frac{\sqrt{d f}\, b \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d^{2}}+\frac{\sqrt{d f}\, b \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d^{2}}+\frac{\sqrt{d f}\, \sqrt{c}\, \ln \left(\frac{\left(x +\frac{\sqrt{d f}}{f}\right) c +\frac{b f -2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\right)}{2 d^{2}}-\frac{\sqrt{d f}\, \sqrt{c}\, \ln \left(\frac{\left(x -\frac{\sqrt{d f}}{f}\right) c +\frac{b f +2 \sqrt{d f}\, c}{2 f}}{\sqrt{c}}+\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\right)}{2 d^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, c}{2 a d}-\frac{\sqrt{c \,x^{2}+b x +a}\, b^{2}}{4 a^{2} d}-\frac{\sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}{2 d^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}{2 d^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, f}{d^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b}{4 a^{2} d x}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}{2 a d \,x^{2}}"," ",0,"-1/2*f/d^2*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)+1/2/d^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)-1/4*f/d^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b-1/2/d^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*(d*f)^(1/2)*b+1/2*f/d^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a+1/2/d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c-1/2*f/d^2*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)-1/2/d^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)-1/4*f/d^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b+1/2/d^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*(d*f)^(1/2)*b+1/2*f/d^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a+1/2/d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c-1/2/d/a/x^2*(c*x^2+b*x+a)^(3/2)+1/4/d*b/a^2/x*(c*x^2+b*x+a)^(3/2)-1/4/d*b^2/a^2*(c*x^2+b*x+a)^(1/2)+1/8/d*b^2/a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)-1/4/d*b/a^2*c*(c*x^2+b*x+a)^(1/2)*x+1/2/d*c/a*(c*x^2+b*x+a)^(1/2)-1/2/d*c/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)+f/d^2*(c*x^2+b*x+a)^(1/2)+1/2*f/d^2*b*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-f/d^2*a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","B"
84,1,4884,405,0.032000," ","int(x^3*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"-1/5*(c*x^2+b*x+a)^(5/2)/c/f+1/16/f*b^2/c^2*(c*x^2+b*x+a)^(3/2)-3/128/f*b^4/c^3*(c*x^2+b*x+a)^(1/2)+3/256/f*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/2/f^2*d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*a-1/2/f^3*d^2*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*c-1/2/f^2*d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*a-1/2/f^3*d^2*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*c+1/2/f^4*d^3/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c^2-1/8/f^2*d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b+5/8/f^3*d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*(d*f)^(1/2)-1/16/f^2*d/c*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/32/f^2*d/c^(3/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*b^3-3/4/f^3*d^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*b+1/2/f^4*d^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)*(d*f)^(1/2)+1/2/f^3*d^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b^2+1/2/f^2*d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a^2+1/2/f^4*d^3/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c^2+1/8/f*b/c*x*(c*x^2+b*x+a)^(3/2)-3/64/f*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x+3/32/f*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a+3/16/f*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-3/32/f*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/4/f^3*d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c*(d*f)^(1/2)-3/4/f^3*d*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)*a-3/8/f^2*d/c^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*a*b-3/16/f^3*d*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2*(d*f)^(1/2)+1/f^3*d^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a*c+3/16/f^3*d*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2*(d*f)^(1/2)+1/f^3*d^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a*c+3/16/f*b/c*(c*x^2+b*x+a)^(1/2)*x*a+1/4/f^3*d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c*(d*f)^(1/2)+3/4/f^3*d*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)*a-3/8/f^2*d/c^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*a*b+1/2/f^3*d^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b^2+1/2/f^2*d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a^2+1/32/f^2*d/c^(3/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*b^3-3/4/f^3*d^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*b-1/2/f^4*d^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)*(d*f)^(1/2)-1/16/f^2*d/c*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2-1/6/f^2*d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(3/2)-1/6/f^2*d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(3/2)+1/f^3*d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*(d*f)^(1/2)*a+1/f^4*d^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*(d*f)^(1/2)*c-1/f^3*d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b*(d*f)^(1/2)*a-1/f^4*d^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b*(d*f)^(1/2)*c-1/8/f^2*d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b-5/8/f^3*d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*(d*f)^(1/2)","B"
85,1,4900,343,0.018000," ","int(x^2*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"-3/8/f/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-3/128/f/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4-1/6*d/(d*f)^(1/2)/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(3/2)-5/8*d/f^2*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b-1/2*d^2/f^3*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)+1/6*d/(d*f)^(1/2)/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(3/2)-5/8*d/f^2*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b-1/2*d^2/f^3*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)-1/8/f/c*(c*x^2+b*x+a)^(3/2)*b-3/8/f*(c*x^2+b*x+a)^(1/2)*x*a+3/64/f/c^2*(c*x^2+b*x+a)^(1/2)*b^3-d^2/(d*f)^(1/2)/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a*c+3/8*d/(d*f)^(1/2)/f/c^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*a*b-3/8*d/(d*f)^(1/2)/f/c^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*a*b+1/2*d/(d*f)^(1/2)/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a^2+1/2*d^3/(d*f)^(1/2)/f^3/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c^2-1/8*d/(d*f)^(1/2)/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b-1/16*d/(d*f)^(1/2)/f/c*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/32*d/(d*f)^(1/2)/f/c^(3/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*b^3-3/4*d^2/(d*f)^(1/2)/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*b+1/2*d^2/(d*f)^(1/2)/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b^2+d/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*a+d^2/f^3/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*c+d^2/f^3/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b*c-1/2*d/(d*f)^(1/2)/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a^2-1/2*d^3/(d*f)^(1/2)/f^3/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c^2+1/8*d/(d*f)^(1/2)/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b+1/16*d/(d*f)^(1/2)/f/c*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2-1/32*d/(d*f)^(1/2)/f/c^(3/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*b^3+3/4*d^2/(d*f)^(1/2)/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*b-1/2*d^2/(d*f)^(1/2)/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b^2+d/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b*a+d^2/(d*f)^(1/2)/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a*c-1/4/f*x*(c*x^2+b*x+a)^(3/2)-3/16*d/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2+1/2*d/(d*f)^(1/2)/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*a+1/2*d^2/(d*f)^(1/2)/f^2*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*c-1/4*d/f^2*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c-3/4*d/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*a-3/16*d/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2-1/2*d/(d*f)^(1/2)/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*a-1/2*d^2/(d*f)^(1/2)/f^2*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*c+3/32/f/c*(c*x^2+b*x+a)^(1/2)*x*b^2-3/16/f/c*(c*x^2+b*x+a)^(1/2)*b*a+3/16/f/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a-1/4*d/f^2*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c-3/4*d/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*a","B"
86,1,4567,275,0.015000," ","int(x*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"-1/6/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(3/2)-1/6/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(3/2)-1/2/f^2*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*c*d+1/2/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a^2-1/8/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b-5/8/f^2*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*(d*f)^(1/2)-1/16/f/c*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/32/f/c^(3/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*b^3-1/8/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b+5/8/f^2*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*(d*f)^(1/2)-1/16/f/c*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/32/f/c^(3/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*b^3-1/2/f^2*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*c*d+1/2/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a^2+1/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*(d*f)^(1/2)*b*a+1/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a*c*d-1/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*(d*f)^(1/2)*b*a+1/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a*c*d-1/2/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*a-1/2/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*a-3/8/f/c^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*a*b-3/4/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)*a-3/16/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2*(d*f)^(1/2)-3/4/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*d*b-1/2/f^3*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)*(d*f)^(1/2)*d+1/2/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*d*b^2+1/2/f^3/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c^2*d^2+1/4/f^2*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*(d*f)^(1/2)*c+3/4/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)*a-3/8/f/c^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*a*b+3/16/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2*(d*f)^(1/2)-3/4/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*d*b+1/2/f^3*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)*(d*f)^(1/2)*d+1/2/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*d*b^2+1/2/f^3/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c^2*d^2-1/4/f^2*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*(d*f)^(1/2)*c+1/f^3/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*(d*f)^(1/2)*b*c*d-1/f^3/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*(d*f)^(1/2)*b*c*d","B"
87,1,4574,245,0.015000," ","int((c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"-1/6/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(3/2)+1/6/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(3/2)-1/2/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)*d-1/2/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a^2+1/32/(d*f)^(1/2)/c^(3/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*b^3-1/2/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)*d+1/2/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a^2-1/4/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c+1/8/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b+1/16/(d*f)^(1/2)/c*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2-3/4/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*a-3/16/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2-1/32/(d*f)^(1/2)/c^(3/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*b^3-1/4/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c-1/8/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b-1/16/(d*f)^(1/2)/c*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2-3/4/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*a-3/16/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2+1/(d*f)^(1/2)/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a*c*d+1/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*c*d+1/2/(d*f)^(1/2)/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c^2*d^2-3/4/(d*f)^(1/2)/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*d*b+1/2/(d*f)^(1/2)/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*d*b^2+3/4/(d*f)^(1/2)/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*d*b-1/2/(d*f)^(1/2)/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*d*b^2+1/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b*c*d-1/2/(d*f)^(1/2)/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c^2*d^2-5/8/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b-1/2/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*a-5/8/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b+1/2/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*a+3/8/(d*f)^(1/2)/c^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*a*b+1/2/(d*f)^(1/2)/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*c*d+1/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b*a-3/8/(d*f)^(1/2)/c^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*a*b-1/2/(d*f)^(1/2)/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*c*d+1/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*a-1/(d*f)^(1/2)/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a*c*d","B"
88,1,4765,377,0.018000," ","int((c*x^2+b*x+a)^(3/2)/x/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"1/3/d*(c*x^2+b*x+a)^(3/2)-1/6/d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(3/2)-1/6/d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(3/2)+1/4/d*b*(c*x^2+b*x+a)^(1/2)*x+1/8/d/c*(c*x^2+b*x+a)^(1/2)*b^2-1/16/d/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^3-1/8/d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b-1/16/d/c*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2-3/4/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*b-1/2/f^2*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)*(d*f)^(1/2)+1/2/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b^2+1/2/d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a^2+1/2/d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a^2-1/8/d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b-1/16/d/c*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/32/d/c^(3/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*b^3-3/4/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*b+1/2/f^2*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)*(d*f)^(1/2)+1/2/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b^2+1/32/d/c^(3/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*b^3-1/4/d/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*(d*f)^(1/2)*c-3/4/d/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)*a-3/16/d/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2*(d*f)^(1/2)+1/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*(d*f)^(1/2)*b*c+3/16/d/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2*(d*f)^(1/2)-1/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*(d*f)^(1/2)*b*c+1/4/d/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*(d*f)^(1/2)*c+3/4/d/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*(d*f)^(1/2)*a+1/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a*c+1/2*d/f^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c^2+3/4/d*b/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a*c+1/2*d/f^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c^2+5/8/d/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*(d*f)^(1/2)-3/8/d/c^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*a*b+1/d/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*(d*f)^(1/2)*b*a-1/d/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*(d*f)^(1/2)*b*a-1/2/d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*a-1/2/f*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*c+1/d*a*(c*x^2+b*x+a)^(1/2)-1/d*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)-1/2/d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*a-1/2/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*c-5/8/d/f*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*(d*f)^(1/2)-3/8/d/c^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*a*b","B"
89,1,4799,367,0.018000," ","int((c*x^2+b*x+a)^(3/2)/x^2/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"-1/6*f/d/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(3/2)-1/4/d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c-3/4/d*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*a-3/16/d*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2-3/4/(d*f)^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*b+1/2/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b^2+3/8/d*b^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/d*b/a*(c*x^2+b*x+a)^(3/2)+1/6*f/d/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(3/2)-1/4/d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c-3/4/d*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*a-3/16/d*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/c^(1/2)*b^2+3/4/(d*f)^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(1/2)*b-1/2/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b^2-1/8*f/d/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b-1/16*f/d/(d*f)^(1/2)/c*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/32*f/d/(d*f)^(1/2)/c^(3/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*b^3+1/2*f/d/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a^2+1/2/f*d/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*c^2+1/8*f/d/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b+1/16*f/d/(d*f)^(1/2)/c*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2-1/32*f/d/(d*f)^(1/2)/c^(3/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*b^3-1/2*f/d/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a^2-1/2/f*d/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*c^2+1/d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*a+1/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*b*c+1/2*f/d/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*a+1/d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b*a+1/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*b*c-1/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))*a*c+1/d*c/a*(c*x^2+b*x+a)^(3/2)*x-5/8/d*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b-1/2/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*c-1/2/f*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)+9/4/d*b*(c*x^2+b*x+a)^(1/2)-5/8/d*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b+1/2/(d*f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*c-1/2/f*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*c^(3/2)+3/2/d*c*(c*x^2+b*x+a)^(1/2)*x+3/2/d*c^(1/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/d/a/x*(c*x^2+b*x+a)^(5/2)+3/8*f/d/(d*f)^(1/2)/c^(1/2)*ln(((x+(d*f)^(1/2)/f)*c+1/2*(b*f-2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))*a*b-3/8*f/d/(d*f)^(1/2)/c^(1/2)*ln(((x-(d*f)^(1/2)/f)*c+1/2*(b*f+2*(d*f)^(1/2)*c)/f)/c^(1/2)+((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))*a*b+1/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))*a*c-1/2*f/d/(d*f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*a-3/2/d*b*a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","B"
90,1,5056,494,0.020000," ","int((c*x^2+b*x+a)^(3/2)/x^3/(-f*x^2+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
91,1,1346,155,0.018000," ","int((c*x^2+b*x+a)^(3/2)/(-x^2+1),x)","\frac{3 a b \ln \left(\frac{\frac{b}{2}-c +\left(x +1\right) c}{\sqrt{c}}+\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\right)}{8 \sqrt{c}}-\frac{3 a b \ln \left(\frac{\frac{b}{2}+c +\left(x -1\right) c}{\sqrt{c}}+\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\right)}{8 \sqrt{c}}-\frac{3 a \sqrt{c}\, \ln \left(\frac{\frac{b}{2}-c +\left(x +1\right) c}{\sqrt{c}}+\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\right)}{4}-\frac{3 a \sqrt{c}\, \ln \left(\frac{\frac{b}{2}+c +\left(x -1\right) c}{\sqrt{c}}+\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\right)}{4}-\frac{b^{3} \ln \left(\frac{\frac{b}{2}-c +\left(x +1\right) c}{\sqrt{c}}+\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\right)}{32 c^{\frac{3}{2}}}+\frac{b^{3} \ln \left(\frac{\frac{b}{2}+c +\left(x -1\right) c}{\sqrt{c}}+\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\right)}{32 c^{\frac{3}{2}}}-\frac{3 b^{2} \ln \left(\frac{\frac{b}{2}-c +\left(x +1\right) c}{\sqrt{c}}+\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\right)}{16 \sqrt{c}}-\frac{3 b^{2} \ln \left(\frac{\frac{b}{2}+c +\left(x -1\right) c}{\sqrt{c}}+\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\right)}{16 \sqrt{c}}+\frac{3 b \sqrt{c}\, \ln \left(\frac{\frac{b}{2}-c +\left(x +1\right) c}{\sqrt{c}}+\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\right)}{4}-\frac{3 b \sqrt{c}\, \ln \left(\frac{\frac{b}{2}+c +\left(x -1\right) c}{\sqrt{c}}+\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\right)}{4}-\frac{c^{\frac{3}{2}} \ln \left(\frac{\frac{b}{2}-c +\left(x +1\right) c}{\sqrt{c}}+\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\right)}{2}-\frac{c^{\frac{3}{2}} \ln \left(\frac{\frac{b}{2}+c +\left(x -1\right) c}{\sqrt{c}}+\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\right)}{2}-\frac{\sqrt{a -b +c}\, a \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(x +1\right)+2 \sqrt{a -b +c}\, \sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}}{x +1}\right)}{2}+\frac{\sqrt{a +b +c}\, a \ln \left(\frac{2 a +2 b +2 c +\left(b +2 c \right) \left(x -1\right)+2 \sqrt{a +b +c}\, \sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}}{x -1}\right)}{2}+\frac{\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\, b x}{8}-\frac{\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\, b x}{8}+\frac{\sqrt{a -b +c}\, b \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(x +1\right)+2 \sqrt{a -b +c}\, \sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}}{x +1}\right)}{2}+\frac{\sqrt{a +b +c}\, b \ln \left(\frac{2 a +2 b +2 c +\left(b +2 c \right) \left(x -1\right)+2 \sqrt{a +b +c}\, \sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}}{x -1}\right)}{2}-\frac{\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\, c x}{4}-\frac{\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\, c x}{4}-\frac{\sqrt{a -b +c}\, c \ln \left(\frac{2 a -2 b +2 c +\left(b -2 c \right) \left(x +1\right)+2 \sqrt{a -b +c}\, \sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}}{x +1}\right)}{2}+\frac{\sqrt{a +b +c}\, c \ln \left(\frac{2 a +2 b +2 c +\left(b +2 c \right) \left(x -1\right)+2 \sqrt{a +b +c}\, \sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}}{x -1}\right)}{2}+\frac{\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\, a}{2}-\frac{\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\, a}{2}+\frac{\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\, b^{2}}{16 c}-\frac{\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\, b^{2}}{16 c}-\frac{5 \sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\, b}{8}-\frac{5 \sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\, b}{8}+\frac{\sqrt{a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)}\, c}{2}-\frac{\sqrt{a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)}\, c}{2}+\frac{\left(a -b +\left(x +1\right)^{2} c +c +\left(b -2 c \right) \left(x +1\right)\right)^{\frac{3}{2}}}{6}-\frac{\left(a +b +\left(x -1\right)^{2} c +c +\left(b +2 c \right) \left(x -1\right)\right)^{\frac{3}{2}}}{6}"," ",0,"-1/2*c^(3/2)*ln((1/2*b-c+c*(x+1))/c^(1/2)+((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))-1/2*c^(3/2)*ln((1/2*b+c+c*(x-1))/c^(1/2)+((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))+1/2*a*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2)+1/2*c*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2)-5/8*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2)*b-1/2*a*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2)-1/2*c*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2)-5/8*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2)*b+3/8*b/c^(1/2)*ln((1/2*b-c+c*(x+1))/c^(1/2)+((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))*a-3/8*b/c^(1/2)*ln((1/2*b+c+c*(x-1))/c^(1/2)+((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))*a-1/2*a*(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(x+1)+2*(a-b+c)^(1/2)*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))/(x+1))+3/4*b*ln((1/2*b-c+c*(x+1))/c^(1/2)+((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))*c^(1/2)+1/2*b*(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(x+1)+2*(a-b+c)^(1/2)*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))/(x+1))-1/2*c*(a-b+c)^(1/2)*ln((2*a-2*b+2*c+(b-2*c)*(x+1)+2*(a-b+c)^(1/2)*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))/(x+1))+1/8*b*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2)*x+1/16/c*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2)*b^2-1/32/c^(3/2)*ln((1/2*b-c+c*(x+1))/c^(1/2)+((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))*b^3-1/4*c*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2)*x+1/2*a*(a+b+c)^(1/2)*ln((2*a+2*b+2*c+(b+2*c)*(x-1)+2*(a+b+c)^(1/2)*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))/(x-1))-3/4*b*ln((1/2*b+c+c*(x-1))/c^(1/2)+((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))*c^(1/2)+1/2*b*(a+b+c)^(1/2)*ln((2*a+2*b+2*c+(b+2*c)*(x-1)+2*(a+b+c)^(1/2)*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))/(x-1))+1/2*c*(a+b+c)^(1/2)*ln((2*a+2*b+2*c+(b+2*c)*(x-1)+2*(a+b+c)^(1/2)*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))/(x-1))-1/8*b*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2)*x-1/16/c*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2)*b^2+1/32/c^(3/2)*ln((1/2*b+c+c*(x-1))/c^(1/2)+((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))*b^3-1/4*c*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2)*x-3/16/c^(1/2)*ln((1/2*b-c+c*(x+1))/c^(1/2)+((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))*b^2-3/4*c^(1/2)*ln((1/2*b-c+c*(x+1))/c^(1/2)+((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(1/2))*a-3/4*c^(1/2)*ln((1/2*b+c+c*(x-1))/c^(1/2)+((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))*a-3/16/c^(1/2)*ln((1/2*b+c+c*(x-1))/c^(1/2)+((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(1/2))*b^2+1/6*((x+1)^2*c+(b-2*c)*(x+1)+a-b+c)^(3/2)-1/6*((x-1)^2*c+(b+2*c)*(x-1)+a+b+c)^(3/2)","B"
92,1,102,59,0.015000," ","int((x^2-x-1)^(1/2)/(-x^2+1),x)","-\frac{\arctanh \left(\frac{-3 x -1}{2 \sqrt{-3 x +\left(x +1\right)^{2}-2}}\right)}{2}+\frac{\arctan \left(\frac{x -3}{2 \sqrt{x +\left(x -1\right)^{2}-2}}\right)}{2}-\frac{3 \ln \left(x -\frac{1}{2}+\sqrt{-3 x +\left(x +1\right)^{2}-2}\right)}{4}-\frac{\ln \left(x -\frac{1}{2}+\sqrt{x +\left(x -1\right)^{2}-2}\right)}{4}-\frac{\sqrt{x +\left(x -1\right)^{2}-2}}{2}+\frac{\sqrt{-3 x +\left(x +1\right)^{2}-2}}{2}"," ",0,"-1/2*((x-1)^2+x-2)^(1/2)-1/4*ln(-1/2+x+((x-1)^2+x-2)^(1/2))+1/2*arctan(1/2*(-3+x)/((x-1)^2+x-2)^(1/2))+1/2*((x+1)^2-3*x-2)^(1/2)-3/4*ln(-1/2+x+((x+1)^2-3*x-2)^(1/2))-1/2*arctanh(1/2*(-1-3*x)/((x+1)^2-3*x-2)^(1/2))","A"
93,1,789,98,0.137000," ","int((x^2+x)^(3/2)/(x^2+1),x)","\frac{\sqrt{x^{2}+x}\, x}{2}-\frac{5 \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{8}+\frac{5 \sqrt{x^{2}+x}}{4}+\frac{\sqrt{\frac{4 \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}-\frac{3 \sqrt{2}\, \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+4+3 \sqrt{2}}\, \sqrt{2}\, \left(-4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{\frac{4 \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}-\frac{3 \sqrt{2}\, \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+4+3 \sqrt{2}}}{2 \sqrt{1+\sqrt{2}}}\right)+6 \arctanh \left(\frac{\sqrt{\frac{4 \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}-\frac{3 \sqrt{2}\, \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+4+3 \sqrt{2}}}{2 \sqrt{1+\sqrt{2}}}\right)+\sqrt{-2+2 \sqrt{2}}\, \sqrt{1+\sqrt{2}}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-2+2 \sqrt{2}}\, \sqrt{\left(3 \sqrt{2}-4\right) \left(-\frac{\left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+12 \sqrt{2}+17\right)}\, \left(\frac{24 \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+\frac{17 \sqrt{2}\, \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}-\sqrt{2}\right) \left(x -\sqrt{2}-1\right) \left(3 \sqrt{2}-4\right)}{2 \left(-x +1-\sqrt{2}\right) \left(\frac{\left(x -\sqrt{2}-1\right)^{4}}{\left(-x +1-\sqrt{2}\right)^{4}}-\frac{34 \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+1\right)}\right)-2 \sqrt{-2+2 \sqrt{2}}\, \sqrt{1+\sqrt{2}}\, \arctan \left(\frac{\sqrt{-2+2 \sqrt{2}}\, \sqrt{\left(3 \sqrt{2}-4\right) \left(-\frac{\left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+12 \sqrt{2}+17\right)}\, \left(\frac{24 \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+\frac{17 \sqrt{2}\, \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}-\sqrt{2}\right) \left(x -\sqrt{2}-1\right) \left(3 \sqrt{2}-4\right)}{2 \left(-x +1-\sqrt{2}\right) \left(\frac{\left(x -\sqrt{2}-1\right)^{4}}{\left(-x +1-\sqrt{2}\right)^{4}}-\frac{34 \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}+1\right)}\right)\right)}{2 \sqrt{-\frac{\frac{3 \sqrt{2}\, \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}-\frac{4 \left(x -\sqrt{2}-1\right)^{2}}{\left(-x +1-\sqrt{2}\right)^{2}}-3 \sqrt{2}-4}{\left(\frac{x -\sqrt{2}-1}{-x +1-\sqrt{2}}+1\right)^{2}}}\, \left(\frac{x -\sqrt{2}-1}{-x +1-\sqrt{2}}+1\right) \left(3 \sqrt{2}-4\right) \sqrt{1+\sqrt{2}}}"," ",0,"1/2*x*(x^2+x)^(1/2)+5/4*(x^2+x)^(1/2)-5/8*ln(1/2+x+(x^2+x)^(1/2))+1/2*(4*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2-3*2^(1/2)*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+4+3*2^(1/2))^(1/2)*2^(1/2)*((-2+2*2^(1/2))^(1/2)*arctan(1/2*(-2+2*2^(1/2))^(1/2)*((3*2^(1/2)-4)*(-(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+12*2^(1/2)+17))^(1/2)*(24*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+17*2^(1/2)*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2-2^(1/2))*(-2^(1/2)-1+x)/(1-x-2^(1/2))*(3*2^(1/2)-4)/((-2^(1/2)-1+x)^4/(1-x-2^(1/2))^4-34*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+1))*(1+2^(1/2))^(1/2)*2^(1/2)-2*(-2+2*2^(1/2))^(1/2)*arctan(1/2*(-2+2*2^(1/2))^(1/2)*((3*2^(1/2)-4)*(-(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+12*2^(1/2)+17))^(1/2)*(24*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+17*2^(1/2)*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2-2^(1/2))*(-2^(1/2)-1+x)/(1-x-2^(1/2))*(3*2^(1/2)-4)/((-2^(1/2)-1+x)^4/(1-x-2^(1/2))^4-34*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+1))*(1+2^(1/2))^(1/2)-4*arctanh(1/2*(4*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2-3*2^(1/2)*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+4+3*2^(1/2))^(1/2)/(1+2^(1/2))^(1/2))*2^(1/2)+6*arctanh(1/2*(4*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2-3*2^(1/2)*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2+4+3*2^(1/2))^(1/2)/(1+2^(1/2))^(1/2)))/(-(3*2^(1/2)*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2-4*(-2^(1/2)-1+x)^2/(1-x-2^(1/2))^2-3*2^(1/2)-4)/((-2^(1/2)-1+x)/(1-x-2^(1/2))+1)^2)^(1/2)/((-2^(1/2)-1+x)/(1-x-2^(1/2))+1)/(3*2^(1/2)-4)/(1+2^(1/2))^(1/2)","B"
94,1,516,287,0.027000," ","int(x^4/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","-\frac{d^{2} \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{d^{2} \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{a \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}} f}-\frac{3 b^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}} f}-\frac{d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, f^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, x}{2 c f}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b}{4 c^{2} f}"," ",0,"-1/2*x*(c*x^2+b*x+a)^(1/2)/c/f+3/4*b*(c*x^2+b*x+a)^(1/2)/c^2/f-3/8/f*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2/f*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/f^2*d*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-1/2/f^2*d^2/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))+1/2/f^2*d^2/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","A"
95,1,410,219,0.018000," ","int(x^3/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","\frac{d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{b \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}} f}-\frac{\sqrt{c \,x^{2}+b x +a}}{c f}"," ",0,"-(c*x^2+b*x+a)^(1/2)/c/f+1/2/f*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2/f^2*d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))+1/2/f^2*d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","A"
96,1,399,202,0.015000," ","int(x^2/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","-\frac{d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{\ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, f}"," ",0,"-1/f*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-1/2*d/(d*f)^(1/2)/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))+1/2*d/(d*f)^(1/2)/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","A"
97,1,354,164,0.015000," ","int(x/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","\frac{\ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{\ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}"," ",0,"1/2/f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))+1/2/f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","B"
98,1,358,164,0.015000," ","int(1/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","-\frac{\ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{\ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}"," ",0,"-1/2/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))+1/2/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","B"
99,1,391,203,0.016000," ","int(1/x/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","\frac{\ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{\ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{\ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\sqrt{a}\, d}"," ",0,"1/2/d/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))+1/2/d/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))-1/d/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","A"
100,1,427,223,0.017000," ","int(1/x^2/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","-\frac{f \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{f \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}+\frac{b \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{3}{2}} d}-\frac{\sqrt{c \,x^{2}+b x +a}}{a d x}"," ",0,"-1/2*f/d/(d*f)^(1/2)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))-(c*x^2+b*x+a)^(1/2)/a/d/x+1/2/d*b/a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)+1/2*f/d/(d*f)^(1/2)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","A"
101,1,519,294,0.022000," ","int(1/x^3/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x)","\frac{f \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d^{2}}+\frac{f \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d^{2}}-\frac{f \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\sqrt{a}\, d^{2}}+\frac{c \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{3}{2}} d}-\frac{3 b^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{5}{2}} d}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b}{4 a^{2} d x}-\frac{\sqrt{c \,x^{2}+b x +a}}{2 a d \,x^{2}}"," ",0,"1/2*f/d^2/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))+1/2*f/d^2/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))-1/2*(c*x^2+b*x+a)^(1/2)/a/d/x^2+3/4*b*(c*x^2+b*x+a)^(1/2)/a^2/d/x-3/8/d*b^2/a^(5/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)+1/2/d*c/a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)-f/d^2/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","A"
102,1,1648,394,0.022000," ","int(x^4/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","-\frac{b c \,d^{2} x}{\sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{b c \,d^{2} x}{\sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{b^{2} d^{2}}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{b^{2} d^{2}}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{2 c^{2} d^{2} x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{2 c^{2} d^{2} x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{b c \,d^{2}}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{b c \,d^{2}}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}-\frac{d^{2} \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{d^{2} \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{b^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c f}-\frac{4 c d x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, f^{2}}+\frac{d^{2}}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}-\frac{d^{2}}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{b^{3}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2} f}-\frac{2 b d}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, f^{2}}+\frac{x}{\sqrt{c \,x^{2}+b x +a}\, c f}-\frac{\ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}} f}-\frac{b}{2 \sqrt{c \,x^{2}+b x +a}\, c^{2} f}"," ",0,"1/f*x/c/(c*x^2+b*x+a)^(1/2)-1/2/f*b/c^2/(c*x^2+b*x+a)^(1/2)-1/f*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-1/2/f*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-1/f/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-4/f^2*d/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x-2/f^2*d/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b+1/2/f*d^2/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)+2/f^2*d^2/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c^2-1/f*d^2/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c+1/f^2*d^2/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*c-1/2/f*d^2/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2-1/2/f*d^2/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))-1/2/f*d^2/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)+2/f^2*d^2/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c^2+1/f*d^2/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c+1/f^2*d^2/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*c+1/2/f*d^2/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/2/f*d^2/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","B"
103,1,1480,281,0.019000," ","int(x^3/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","\frac{b c d x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{b c d x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{b^{2} d}{2 \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{b^{2} d}{2 \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{2 \sqrt{d f}\, c^{2} d x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{2 \sqrt{d f}\, c^{2} d x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}-\frac{\sqrt{d f}\, b c d}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{\sqrt{d f}\, b c d}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f^{2}}+\frac{2 b x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, f}+\frac{d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{b^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c f}-\frac{d}{2 \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}-\frac{d}{2 \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{1}{\sqrt{c \,x^{2}+b x +a}\, c f}"," ",0,"1/f/c/(c*x^2+b*x+a)^(1/2)+2/f*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+1/f*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-1/2/f*d/(a*f+c*d-(d*f)^(1/2)*b)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)-2/f^2*d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*x*c^2+1/f*d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c-1/f^2*d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*b*c+1/2/f*d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/2/f*d/(a*f+c*d-(d*f)^(1/2)*b)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))-1/2/f*d/(a*f+c*d+(d*f)^(1/2)*b)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)+2/f^2*d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*x*c^2+1/f*d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c+1/f^2*d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*b*c+1/2/f*d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/2/f*d/(a*f+c*d+(d*f)^(1/2)*b)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","B"
104,1,1427,239,0.019000," ","int(x^2/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","-\frac{b c d x}{\sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{b c d x}{\sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{b^{2} d}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{b^{2} d}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{2 c^{2} d x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{2 c^{2} d x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{b c d}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{b c d}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{d \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{d \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{d}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}-\frac{d}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{2 \left(2 c x +b \right)}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, f}"," ",0,"-2/f*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+1/2*d/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)+2*d/f/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c^2-d/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c+d/f/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*c-1/2*d/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2-1/2*d/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))-1/2*d/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)+2*d/f/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c^2+d/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c+d/f/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*c+1/2*d/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/2*d/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","B"
105,1,1360,241,0.016000," ","int(x/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","\frac{b c x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{b c x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{b^{2}}{2 \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{b^{2}}{2 \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{2 \sqrt{d f}\, c^{2} x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{2 \sqrt{d f}\, c^{2} x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}-\frac{\sqrt{d f}\, b c}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, f}+\frac{\sqrt{d f}\, b c}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, f}+\frac{\ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{\ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{1}{2 \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}-\frac{1}{2 \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}"," ",0,"-1/2/(a*f+c*d-(d*f)^(1/2)*b)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)-2/f/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*x*c^2+1/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c-1/f/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*b*c+1/2/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/2/(a*f+c*d-(d*f)^(1/2)*b)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))-1/2/(a*f+c*d+(d*f)^(1/2)*b)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)+2/f/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*x*c^2+1/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c+1/f/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*b*c+1/2/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/2/(a*f+c*d+(d*f)^(1/2)*b)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","B"
106,1,1376,252,0.016000," ","int(1/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","-\frac{b c f x}{\sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{b c f x}{\sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{b^{2} f}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{b^{2} f}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{2 c^{2} x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{2 c^{2} x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{b c}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{b c}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}-\frac{f \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}}+\frac{f \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}}+\frac{f}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}-\frac{f}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}"," ",0,"1/2/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)*f/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)+2/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c^2-1/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c*f+1/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*c-1/2/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2*f-1/2/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)*f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))-1/2/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)*f/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)+2/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c^2+1/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c*f+1/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*c+1/2/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2*f+1/2/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)*f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","B"
107,1,1518,326,0.019000," ","int(1/x/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","\frac{b c f x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{b c f x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}+\frac{b^{2} f}{2 \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{b^{2} f}{2 \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{2 \sqrt{d f}\, c^{2} x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{2 \sqrt{d f}\, c^{2} x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{2 b c x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, a d}-\frac{\sqrt{d f}\, b c}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{\sqrt{d f}\, b c}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}+\frac{f \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{f \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{b^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, a d}-\frac{f}{2 \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}-\frac{f}{2 \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{\ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{a^{\frac{3}{2}} d}+\frac{1}{\sqrt{c \,x^{2}+b x +a}\, a d}"," ",0,"-1/2/d/(a*f+c*d-(d*f)^(1/2)*b)*f/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)-2/d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*x*c^2+1/d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c*f-1/d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*b*c+1/2/d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2*f+1/2/d/(a*f+c*d-(d*f)^(1/2)*b)*f/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))-1/2/d/(a*f+c*d+(d*f)^(1/2)*b)*f/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)+2/d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*x*c^2+1/d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c*f+1/d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*(d*f)^(1/2)*b*c+1/2/d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2*f+1/2/d/(a*f+c*d+(d*f)^(1/2)*b)*f/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))+1/d/a/(c*x^2+b*x+a)^(1/2)-2/d*b/a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x-1/d*b^2/a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-1/d/a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","B"
108,1,1656,382,0.019000," ","int(1/x^2/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x)","-\frac{b c \,f^{2} x}{\sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{b c \,f^{2} x}{\sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{b^{2} f^{2}}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{b^{2} f^{2}}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}+\frac{2 c^{2} f x}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{2 c^{2} f x}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}+\frac{b c f}{\left(a f +c d -\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{b c f}{\left(a f +c d +\sqrt{d f}\, b \right) \left(4 a c -b^{2}\right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{f^{2} \ln \left(\frac{\frac{2 a f +2 c d -2 \sqrt{d f}\, b}{f}+\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}}{x +\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}+\frac{f^{2} \ln \left(\frac{\frac{2 a f +2 c d +2 \sqrt{d f}\, b}{f}+\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+2 \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}}{x -\frac{\sqrt{d f}}{f}}\right)}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{8 c^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, a d}+\frac{3 b^{2} c x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, a^{2} d}+\frac{f^{2}}{2 \sqrt{d f}\, \left(a f +c d -\sqrt{d f}\, b \right) \sqrt{\left(x +\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f -2 \sqrt{d f}\, c \right) \left(x +\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d -\sqrt{d f}\, b}{f}}\, d}-\frac{f^{2}}{2 \sqrt{d f}\, \left(a f +c d +\sqrt{d f}\, b \right) \sqrt{\left(x -\frac{\sqrt{d f}}{f}\right)^{2} c +\frac{\left(b f +2 \sqrt{d f}\, c \right) \left(x -\frac{\sqrt{d f}}{f}\right)}{f}+\frac{a f +c d +\sqrt{d f}\, b}{f}}\, d}-\frac{4 b c}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, a d}+\frac{3 b^{3}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, a^{2} d}+\frac{3 b \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{5}{2}} d}-\frac{3 b}{2 \sqrt{c \,x^{2}+b x +a}\, a^{2} d}-\frac{1}{\sqrt{c \,x^{2}+b x +a}\, a d x}"," ",0,"1/2*f^2/d/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)+2*f/d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*c^2-f^2/d/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*x*b*c+f/d/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b*c-1/2*f^2/d/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/(4*a*c-b^2)/((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*b^2-1/2*f^2/d/(d*f)^(1/2)/(a*f+c*d-(d*f)^(1/2)*b)/((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d-(d*f)^(1/2)*b)/f+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+2*((a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2)*((x+(d*f)^(1/2)/f)^2*c+(b*f-2*(d*f)^(1/2)*c)*(x+(d*f)^(1/2)/f)/f+(a*f+c*d-(d*f)^(1/2)*b)/f)^(1/2))/(x+(d*f)^(1/2)/f))-1/d/a/x/(c*x^2+b*x+a)^(1/2)-3/2/d*b/a^2/(c*x^2+b*x+a)^(1/2)+3/d*b^2/a^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x+3/2/d*b^3/a^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+3/2/d*b/a^(5/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)-8/d*c^2/a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-4/d*c/a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b-1/2*f^2/d/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)+2*f/d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*c^2+f^2/d/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*x*b*c+f/d/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b*c+1/2*f^2/d/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/(4*a*c-b^2)/((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*b^2+1/2*f^2/d/(d*f)^(1/2)/(a*f+c*d+(d*f)^(1/2)*b)/((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*ln((2*(a*f+c*d+(d*f)^(1/2)*b)/f+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+2*((a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2)*((x-(d*f)^(1/2)/f)^2*c+(b*f+2*(d*f)^(1/2)*c)*(x-(d*f)^(1/2)/f)/f+(a*f+c*d+(d*f)^(1/2)*b)/f)^(1/2))/(x-(d*f)^(1/2)/f))","B"
109,1,14815,680,0.019000," ","int(x^2*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
110,1,10138,490,0.015000," ","int(x*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
111,1,6019,376,0.015000," ","int((c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
112,1,6460,460,0.019000," ","int((c*x^2+b*x+a)^(1/2)/x/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
113,1,6765,633,0.019000," ","int((c*x^2+b*x+a)^(1/2)/x^2/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
114,1,3131,478,0.032000," ","int(x^3/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"(c*x^2+b*x+a)^(1/2)/c/f-1/2*b/c^(3/2)/f*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/f^2*e*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)+1/2/f^2*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+1/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*d-1/2/f^3*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+1/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e^2+3/2/f^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+1/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*d*e-1/2/f^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+1/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e^3+1/2/f^2*2^(1/2)/(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*d-1/2/f^3*2^(1/2)/(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e^2-3/2/f^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*d*e+1/2/f^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e^3","B"
115,1,2321,407,0.017000," ","int(x^2/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","-\frac{\sqrt{2}\, d \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}+\frac{\sqrt{2}\, d \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}+\frac{\sqrt{2}\, e^{2} \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}-\frac{\sqrt{2}\, e^{2} \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\sqrt{2}\, e \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\sqrt{2}\, e \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f^{2}}+\frac{\ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, f}"," ",0,"1/c^(1/2)/f*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2/f^2*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+1/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e-1/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+1/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*d+1/2/(-4*d*f+e^2)^(1/2)/f^2*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+1/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e^2+1/2/f^2*2^(1/2)/(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e+1/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*d-1/2/(-4*d*f+e^2)^(1/2)/f^2*2^(1/2)/(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e^2","B"
116,1,1516,355,0.014000," ","int(x/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","-\frac{\sqrt{2}\, e \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}+\frac{\sqrt{2}\, e \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{2 \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, f}"," ",0,"-1/2/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*e-1/2/f*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))-1/2/f*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))+1/2/(-4*d*f+e^2)^(1/2)/f*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*e","B"
117,1,761,330,0.014000," ","int(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\frac{\sqrt{2}\, \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}"," ",0,"1/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))-1/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))","B"
118,1,859,396,0.019000," ","int(1/x/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","-\frac{2 \sqrt{2}\, f \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{2 \sqrt{2}\, f \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}+\frac{4 f \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) \sqrt{a}}"," ",0,"-2*f/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))-2*f/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","B"
119,1,983,474,0.017000," ","int(1/x^2/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\frac{16 e \,f^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{a}}+\frac{4 \sqrt{2}\, f^{2} \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{4 \sqrt{2}\, f^{2} \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{2 b f \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a^{\frac{3}{2}}}+\frac{4 \sqrt{c \,x^{2}+b x +a}\, f}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a x}"," ",0,"4*f^2/(e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/x*(c*x^2+b*x+a)^(1/2)-2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*b/a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)-4*f^2/(-e+(-4*d*f+e^2)^(1/2))^2/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))+16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","B"
120,1,1296,594,0.020000," ","int(1/x^3/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","-\frac{64 d \,f^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{3} \left(e +\sqrt{-4 d f +e^{2}}\right)^{3} \sqrt{a}}+\frac{64 e^{2} f^{3} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{3} \left(e +\sqrt{-4 d f +e^{2}}\right)^{3} \sqrt{a}}-\frac{8 \sqrt{2}\, f^{3} \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(e +\sqrt{-4 d f +e^{2}}\right)^{3} \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{8 \sqrt{2}\, f^{3} \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{3} \sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{8 b e \,f^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(e +\sqrt{-4 d f +e^{2}}\right)^{2} a^{\frac{3}{2}}}-\frac{2 c f \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a^{\frac{3}{2}}}+\frac{3 b^{2} f \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{2 \left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a^{\frac{5}{2}}}+\frac{16 \sqrt{c \,x^{2}+b x +a}\, e \,f^{2}}{\left(-e +\sqrt{-4 d f +e^{2}}\right)^{2} \left(e +\sqrt{-4 d f +e^{2}}\right)^{2} a x}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b f}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a^{2} x}+\frac{2 \sqrt{c \,x^{2}+b x +a}\, f}{\left(-e +\sqrt{-4 d f +e^{2}}\right) \left(e +\sqrt{-4 d f +e^{2}}\right) a \,x^{2}}"," ",0,"-8*f^3/(e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+16*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2/a/x*(c*x^2+b*x+a)^(1/2)-8*f^2*e/(-e+(-4*d*f+e^2)^(1/2))^2/(e+(-4*d*f+e^2)^(1/2))^2*b/a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)+2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/x^2*(c*x^2+b*x+a)^(1/2)-3*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*b/a^2/x*(c*x^2+b*x+a)^(1/2)+3/2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*b^2/a^(5/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)-2*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*c/a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)-8*f^3/(-e+(-4*d*f+e^2)^(1/2))^3/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))-64*f^4/(-e+(-4*d*f+e^2)^(1/2))^3/(e+(-4*d*f+e^2)^(1/2))^3/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*d+64*f^3/(-e+(-4*d*f+e^2)^(1/2))^3/(e+(-4*d*f+e^2)^(1/2))^3/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*e^2","B"
121,1,14651,726,0.035000," ","int(x^3/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
122,1,11341,560,0.021000," ","int(x^2/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
123,1,7163,560,0.017000," ","int(x/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
124,1,4099,609,0.018000," ","int(1/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"-2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*f^2/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-4*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2+4/(-4*d*f+e^2)^(1/2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*b*c-4/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2*e-2*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c+2/(-4*d*f+e^2)^(1/2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b^2-2/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c*e+2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*f^2*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*f^2/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-4*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2-4/(-4*d*f+e^2)^(1/2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*b*c+4/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2*e-2*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c-2/(-4*d*f+e^2)^(1/2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b^2+2/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c*e-2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*f^2*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))","B"
125,1,4594,753,0.036000," ","int(1/x/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"4*f^3/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)+8*f^2/(e+(-4*d*f+e^2)^(1/2))/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2-8*f^3/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*b*c+8*f^2/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2*e+4*f^2/(e+(-4*d*f+e^2)^(1/2))/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c-4*f^3/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b^2+4*f^2/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c*e-4*f^3/(e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+4*f^3/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-8*f^2/(-e+(-4*d*f+e^2)^(1/2))/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2-8*f^3/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*b*c+8*f^2/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2*e-4*f^2/(-e+(-4*d*f+e^2)^(1/2))/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c-4*f^3/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b^2+4*f^2/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2*d/f+c^2*e^2/f^2-(-4*d*f+e^2)*c^2/f^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c*e-4*f^3/(-e+(-4*d*f+e^2)^(1/2))/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))-4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a/(c*x^2+b*x+a)^(1/2)+8*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*b/a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))*b^2/a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+4*f/(-e+(-4*d*f+e^2)^(1/2))/(e+(-4*d*f+e^2)^(1/2))/a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","B"
126,1,159,113,0.019000," ","int(x^4/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","-\frac{\sqrt{-x^{2}-4 x -3}\, x}{4}+\frac{11 \arcsin \left(x +2\right)}{2}+\frac{5 \sqrt{-x^{2}-4 x -3}}{2}+\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(5 \arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{24 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"-1/4*x*(-x^2-4*x-3)^(1/2)+5/2*(-x^2-4*x-3)^(1/2)+11/2*arcsin(2+x)+1/24*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))+5*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)","A"
127,1,144,96,0.015000," ","int(x^3/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","-2 \arcsin \left(x +2\right)-\frac{\sqrt{-x^{2}-4 x -3}}{2}+\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(-4 \arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{24 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"-1/2*(-x^2-4*x-3)^(1/2)-2*arcsin(x+2)+1/24*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))-4*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)","A"
128,1,130,84,0.009000," ","int(x^2/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","\frac{\arcsin \left(x +2\right)}{2}-\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(-\arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{12 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"1/2*arcsin(x+2)-1/12*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))-arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)","A"
129,1,92,55,0.011000," ","int(x/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)}{12 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"1/12*3^(1/2)*4^(1/2)/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))","A"
130,1,121,78,0.011000," ","int(1/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","-\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(\arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{18 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"-1/18*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))+arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)","A"
131,1,152,106,0.019000," ","int(1/x/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(-4 x -6\right) \sqrt{3}}{6 \sqrt{-x^{2}-4 x -3}}\right)}{9}+\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(4 \arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{54 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"1/54*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))+4*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)+1/9*3^(1/2)*arctan(1/6*(-6-4*x)*3^(1/2)/(-x^2-4*x-3)^(1/2))","A"
132,1,169,123,0.020000," ","int(1/x^2/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x)","-\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(-4 x -6\right) \sqrt{3}}{6 \sqrt{-x^{2}-4 x -3}}\right)}{9}+\frac{\sqrt{-x^{2}-4 x -3}}{9 x}+\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(-5 \arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{81 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"1/81*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))-5*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)+1/9*(-x^2-4*x-3)^(1/2)/x-2/9*3^(1/2)*arctan(1/6*(-4*x-6)*3^(1/2)/(-x^2-4*x-3)^(1/2))","A"
133,1,147,119,0.019000," ","int((2+3*x)^2*(-12*x^2+31*x+30)^2*(12*x^2+17*x+6)^(1/2),x)","\frac{27 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}} x^{5}}{2}-\frac{8613 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}} x^{4}}{112}+\frac{14991 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}} x^{3}}{1792}+\frac{4267751 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}} x^{2}}{14336}+\frac{129220757 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}} x}{458752}-\frac{125455 \sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{12 x^{2}+17 x +6}\right)}{3623878656}+\frac{2473875847 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}}}{33030144}+\frac{125455 \left(24 x +17\right) \sqrt{12 x^{2}+17 x +6}}{150994944}"," ",0,"27/2*x^5*(12*x^2+17*x+6)^(3/2)-8613/112*x^4*(12*x^2+17*x+6)^(3/2)+14991/1792*x^3*(12*x^2+17*x+6)^(3/2)+4267751/14336*x^2*(12*x^2+17*x+6)^(3/2)+129220757/458752*x*(12*x^2+17*x+6)^(3/2)+2473875847/33030144*(12*x^2+17*x+6)^(3/2)-125455/3623878656*ln(1/12*(17/2+12*x)*12^(1/2)+(12*x^2+17*x+6)^(1/2))*12^(1/2)+125455/150994944*(17+24*x)*(12*x^2+17*x+6)^(1/2)","A"
134,1,96,81,0.006000," ","int((2+3*x)*(-12*x^2+31*x+30)*(12*x^2+17*x+6)^(1/2),x)","-\frac{3 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}} x^{2}}{5}+\frac{349 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}} x}{160}+\frac{97 \sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{12 x^{2}+17 x +6}\right)}{589824}+\frac{7093 \left(12 x^{2}+17 x +6\right)^{\frac{3}{2}}}{3840}-\frac{97 \left(24 x +17\right) \sqrt{12 x^{2}+17 x +6}}{24576}"," ",0,"-3/5*(12*x^2+17*x+6)^(3/2)*x^2+349/160*(12*x^2+17*x+6)^(3/2)*x+7093/3840*(12*x^2+17*x+6)^(3/2)-97/24576*(24*x+17)*(12*x^2+17*x+6)^(1/2)+97/589824*12^(1/2)*ln(1/12*(12*x+17/2)*12^(1/2)+(12*x^2+17*x+6)^(1/2))","A"
135,1,163,22,0.016000," ","int((12*x^2+17*x+6)^(1/2)/(2+3*x)/(-12*x^2+31*x+30),x)","\frac{\arctanh \left(\frac{97 x +\frac{206}{3}}{28 \sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}}\right)}{42}-\frac{97 \sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}\right)}{14112}+\frac{\sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}}\right)}{288}+\frac{\sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}}\right)}{294}-\frac{4 \sqrt{-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}}}{49}+\frac{\sqrt{x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}}}{12}-\frac{\sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}}{588}"," ",0,"-4/49*(12*(x+3/4)^2-x-3/4)^(1/2)+1/294*ln(1/12*(12*x+17/2)*12^(1/2)+(12*(x+3/4)^2-x-3/4)^(1/2))*12^(1/2)+1/12*(12*(x+2/3)^2+x+2/3)^(1/2)+1/288*ln(1/12*(12*x+17/2)*12^(1/2)+(12*(x+2/3)^2+x+2/3)^(1/2))*12^(1/2)-1/588*(12*(x-10/3)^2+97*x-382/3)^(1/2)-97/14112*ln(1/12*(12*x+17/2)*12^(1/2)+(12*(x-10/3)^2+97*x-382/3)^(1/2))*12^(1/2)+1/42*arctanh(1/28*(206/3+97*x)/(12*(x-10/3)^2+97*x-382/3)^(1/2))","B"
136,1,245,70,0.023000," ","int((12*x^2+17*x+6)^(1/2)/(2+3*x)^2/(-12*x^2+31*x+30)^2,x)","\frac{97 \arctanh \left(\frac{97 x +\frac{206}{3}}{28 \sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}}\right)}{3226944}-\frac{7057 \sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}\right)}{813189888}+\frac{\sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}}\right)}{6912}-\frac{16 \sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}}\right)}{117649}+\frac{384 \sqrt{-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}}}{117649}+\frac{\sqrt{x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}}}{288}-\frac{97 \sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}}{45177216}-\frac{\left(x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}\right)^{\frac{3}{2}}}{72 \left(x +\frac{2}{3}\right)^{2}}+\frac{32 \left(-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}\right)^{\frac{3}{2}}}{2401 \left(x +\frac{3}{4}\right)^{2}}-\frac{\left(97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}\right)^{\frac{3}{2}}}{67765824 \left(x -\frac{10}{3}\right)}+\frac{\left(24 x +17\right) \sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}}{135531648}"," ",0,"384/117649*(-x+12*(x+3/4)^2-3/4)^(1/2)-16/117649*12^(1/2)*ln(1/12*(12*x+17/2)*12^(1/2)+(-x+12*(x+3/4)^2-3/4)^(1/2))+1/288*(x+12*(x+2/3)^2+2/3)^(1/2)+1/6912*12^(1/2)*ln(1/12*(12*x+17/2)*12^(1/2)+(x+12*(x+2/3)^2+2/3)^(1/2))-97/45177216*(97*x+12*(x-10/3)^2-382/3)^(1/2)-7057/813189888*12^(1/2)*ln(1/12*(12*x+17/2)*12^(1/2)+(97*x+12*(x-10/3)^2-382/3)^(1/2))+97/3226944*arctanh(1/28*(97*x+206/3)/(97*x+12*(x-10/3)^2-382/3)^(1/2))-1/72/(x+2/3)^2*(x+12*(x+2/3)^2+2/3)^(3/2)+32/2401/(x+3/4)^2*(-x+12*(x+3/4)^2-3/4)^(3/2)-1/67765824/(x-10/3)*(97*x+12*(x-10/3)^2-382/3)^(3/2)+1/135531648*(24*x+17)*(97*x+12*(x-10/3)^2-382/3)^(1/2)","B"
137,1,306,117,0.021000," ","int((12*x^2+17*x+6)^(1/2)/(2+3*x)^3/(-12*x^2+31*x+30)^3,x)","\frac{40325 \arctanh \left(\frac{97 x +\frac{206}{3}}{28 \sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}}\right)}{637540872192}-\frac{570457 \sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}\right)}{31239502737408}-\frac{23 \sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}}\right)}{110592}+\frac{58752 \sqrt{12}\, \ln \left(\frac{\left(12 x +\frac{17}{2}\right) \sqrt{12}}{12}+\sqrt{-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}}\right)}{282475249}-\frac{\left(x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}\right)^{\frac{3}{2}}}{2592 \left(x +\frac{2}{3}\right)^{3}}-\frac{1261 \left(97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}\right)^{\frac{3}{2}}}{31239502737408 \left(x -\frac{10}{3}\right)}+\frac{1261 \left(24 x +17\right) \sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}}{62479005474816}+\frac{\left(97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}\right)^{\frac{3}{2}}}{79692609024 \left(x -\frac{10}{3}\right)^{2}}-\frac{230400 \left(-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}\right)^{\frac{3}{2}}}{5764801 \left(x +\frac{3}{4}\right)^{2}}-\frac{128 \left(-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}\right)^{\frac{3}{2}}}{352947 \left(x +\frac{3}{4}\right)^{3}}+\frac{47 \left(x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}\right)^{\frac{3}{2}}}{1152 \left(x +\frac{2}{3}\right)^{2}}-\frac{40325 \sqrt{97 x +12 \left(x -\frac{10}{3}\right)^{2}-\frac{382}{3}}}{8925572210688}-\frac{23 \sqrt{x +12 \left(x +\frac{2}{3}\right)^{2}+\frac{2}{3}}}{4608}-\frac{1410048 \sqrt{-x +12 \left(x +\frac{3}{4}\right)^{2}-\frac{3}{4}}}{282475249}"," ",0,"-1/2592/(x+2/3)^3*(x+12*(x+2/3)^2+2/3)^(3/2)-1261/31239502737408/(x-10/3)*(97*x+12*(x-10/3)^2-382/3)^(3/2)+1261/62479005474816*(24*x+17)*(97*x+12*(x-10/3)^2-382/3)^(1/2)+1/79692609024/(x-10/3)^2*(97*x+12*(x-10/3)^2-382/3)^(3/2)-230400/5764801/(x+3/4)^2*(-x+12*(x+3/4)^2-3/4)^(3/2)-128/352947/(x+3/4)^3*(-x+12*(x+3/4)^2-3/4)^(3/2)-570457/31239502737408*12^(1/2)*ln(1/12*(12*x+17/2)*12^(1/2)+(97*x+12*(x-10/3)^2-382/3)^(1/2))+47/1152/(x+2/3)^2*(x+12*(x+2/3)^2+2/3)^(3/2)-23/110592*12^(1/2)*ln(1/12*(12*x+17/2)*12^(1/2)+(x+12*(x+2/3)^2+2/3)^(1/2))+58752/282475249*12^(1/2)*ln(1/12*(12*x+17/2)*12^(1/2)+(-x+12*(x+3/4)^2-3/4)^(1/2))-40325/8925572210688*(97*x+12*(x-10/3)^2-382/3)^(1/2)+40325/637540872192*arctanh(1/28*(97*x+206/3)/(97*x+12*(x-10/3)^2-382/3)^(1/2))-23/4608*(x+12*(x+2/3)^2+2/3)^(1/2)-1410048/282475249*(-x+12*(x+3/4)^2-3/4)^(1/2)","B"
138,1,16,11,0.004000," ","int((-3+2*x)*(x^2-3*x)^(2/3),x)","\frac{3 \left(x -3\right) \left(x^{2}-3 x \right)^{\frac{2}{3}} x}{5}"," ",0,"3/5*(x-3)*x*(x^2-3*x)^(2/3)","A"
139,1,14,12,0.003000," ","int(((x-3)*x)^(2/3)*(-3+2*x),x)","\frac{3 \left(x -3\right) \left(\left(x -3\right) x \right)^{\frac{2}{3}} x}{5}"," ",0,"3/5*(x-3)*x*((x-3)*x)^(2/3)","A"
140,1,20,11,0.004000," ","int(x*(2*x^2-9*x+9)/(x^2-3*x)^(1/3),x)","\frac{3 \left(x -3\right)^{2} x^{2}}{5 \left(x^{2}-3 x \right)^{\frac{1}{3}}}"," ",0,"3/5*(x-3)^2*x^2/(x^2-3*x)^(1/3)","A"
141,1,18,11,0.004000," ","int(x*(2*x^2-9*x+9)/((x-3)*x)^(1/3),x)","\frac{3 \left(x -3\right)^{2} x^{2}}{5 \left(\left(x -3\right) x \right)^{\frac{1}{3}}}"," ",0,"3/5*(x-3)^2*x^2/((x-3)*x)^(1/3)","A"
142,0,0,205,0.135000," ","int((h*x+g)/(-c*g^2/h^2+9*c*x^2)^(1/3)/(3*h^2*x^2+g^2),x)","\int \frac{h x +g}{\left(9 c \,x^{2}-\frac{c \,g^{2}}{h^{2}}\right)^{\frac{1}{3}} \left(3 h^{2} x^{2}+g^{2}\right)}\, dx"," ",0,"int((h*x+g)/(-c*g^2/h^2+9*c*x^2)^(1/3)/(3*h^2*x^2+g^2),x)","F"
143,0,0,450,0.449000," ","int((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)","\int \frac{h x +g}{\left(c \,x^{2}+b x +\frac{2 b^{2} h^{2}+b c g h -c^{2} g^{2}}{9 c \,h^{2}}\right)^{\frac{1}{3}} \left(f \,x^{2}+\frac{b f x}{c}+\frac{\left(b^{2}+\frac{-2 b^{2} h^{2}-b c g h +c^{2} g^{2}}{3 h^{2}}\right) f}{c^{2}}\right)}\, dx"," ",0,"int((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)","F"