1,1,265,163,0.008000," ","int((e*x+d)^3*(a+b*arcsin(c*x)),x)","\frac{\frac{\left(c e x +d c \right)^{4} a}{4 c^{3} e}+\frac{b \left(\frac{e^{3} \arcsin \left(c x \right) c^{4} x^{4}}{4}+e^{2} \arcsin \left(c x \right) c^{4} x^{3} d +\frac{3 e \arcsin \left(c x \right) c^{4} x^{2} d^{2}}{2}+\arcsin \left(c x \right) c^{4} x \,d^{3}+\frac{\arcsin \left(c x \right) c^{4} d^{4}}{4 e}-\frac{e^{4} \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)+4 d c \,e^{3} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)+6 c^{2} d^{2} e^{2} \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)-4 c^{3} d^{3} e \sqrt{-c^{2} x^{2}+1}+c^{4} d^{4} \arcsin \left(c x \right)}{4 e}\right)}{c^{3}}}{c}"," ",0,"1/c*(1/4*(c*e*x+c*d)^4*a/c^3/e+b/c^3*(1/4*e^3*arcsin(c*x)*c^4*x^4+e^2*arcsin(c*x)*c^4*x^3*d+3/2*e*arcsin(c*x)*c^4*x^2*d^2+arcsin(c*x)*c^4*x*d^3+1/4/e*arcsin(c*x)*c^4*d^4-1/4/e*(e^4*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))+4*d*c*e^3*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+6*c^2*d^2*e^2*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))-4*c^3*d^3*e*(-c^2*x^2+1)^(1/2)+c^4*d^4*arcsin(c*x))))","A"
2,1,193,111,0.013000," ","int((e*x+d)^2*(a+b*arcsin(c*x)),x)","\frac{\frac{\left(c e x +d c \right)^{3} a}{3 c^{2} e}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} c^{3} x^{3}}{3}+e \arcsin \left(c x \right) c^{3} x^{2} d +\arcsin \left(c x \right) c^{3} x \,d^{2}+\frac{\arcsin \left(c x \right) c^{3} d^{3}}{3 e}-\frac{e^{3} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)+3 d c \,e^{2} \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)-3 d^{2} c^{2} e \sqrt{-c^{2} x^{2}+1}+c^{3} d^{3} \arcsin \left(c x \right)}{3 e}\right)}{c^{2}}}{c}"," ",0,"1/c*(1/3*(c*e*x+c*d)^3*a/c^2/e+b/c^2*(1/3*arcsin(c*x)*e^2*c^3*x^3+e*arcsin(c*x)*c^3*x^2*d+arcsin(c*x)*c^3*x*d^2+1/3/e*arcsin(c*x)*c^3*d^3-1/3/e*(e^3*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+3*d*c*e^2*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))-3*d^2*c^2*e*(-c^2*x^2+1)^(1/2)+c^3*d^3*arcsin(c*x))))","A"
3,1,97,86,0.006000," ","int((e*x+d)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{1}{2} x^{2} c^{2} e +c^{2} d x \right)}{c}+\frac{b \left(\frac{\arcsin \left(c x \right) c^{2} x^{2} e}{2}+\arcsin \left(c x \right) d \,c^{2} x -\frac{e \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{2}+d c \sqrt{-c^{2} x^{2}+1}\right)}{c}}{c}"," ",0,"1/c*(a/c*(1/2*x^2*c^2*e+c^2*d*x)+b/c*(1/2*arcsin(c*x)*c^2*x^2*e+arcsin(c*x)*d*c^2*x-1/2*e*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+d*c*(-c^2*x^2+1)^(1/2)))","A"
4,1,30,28,0.005000," ","int(a+b*arcsin(c*x),x)","a x +\frac{b \left(c x \arcsin \left(c x \right)+\sqrt{-c^{2} x^{2}+1}\right)}{c}"," ",0,"a*x+b/c*(c*x*arcsin(c*x)+(-c^2*x^2+1)^(1/2))","A"
5,1,759,244,0.285000," ","int((a+b*arcsin(c*x))/(e*x+d),x)","\frac{a \ln \left(c e x +d c \right)}{e}-\frac{i b \arcsin \left(c x \right)^{2}}{2 e}+\frac{i b e \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b e \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{b e \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{b e \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{c^{2} b \,d^{2} \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b \,d^{2} \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}"," ",0,"a*ln(c*e*x+c*d)/e-1/2*I*b/e*arcsin(c*x)^2+I*b*e/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+I*b*e/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-b*e*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-b*e*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+c^2*b/e*d^2*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+c^2*b/e*d^2*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^2*b/e/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2","B"
6,1,191,81,0.035000," ","int((a+b*arcsin(c*x))/(e*x+d)^2,x)","-\frac{c a}{\left(c e x +d c \right) e}-\frac{c b \arcsin \left(c x \right)}{\left(c e x +d c \right) e}-\frac{c b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{e^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-c*a/(c*e*x+c*d)/e-c*b/(c*e*x+c*d)/e*arcsin(c*x)-c*b/e^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))","B"
7,1,301,124,0.067000," ","int((a+b*arcsin(c*x))/(e*x+d)^3,x)","-\frac{c^{2} a}{2 \left(c e x +d c \right)^{2} e}-\frac{c^{2} b \arcsin \left(c x \right)}{2 \left(c e x +d c \right)^{2} e}+\frac{c^{2} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{2 e \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)}-\frac{c^{3} b d \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-1/2*c^2*a/(c*e*x+c*d)^2/e-1/2*c^2*b/(c*e*x+c*d)^2/e*arcsin(c*x)+1/2*c^2*b/e/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-1/2*c^3*b/e^2*d/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))","B"
8,1,560,176,0.010000," ","int((a+b*arcsin(c*x))/(e*x+d)^4,x)","-\frac{c^{3} a}{3 \left(c e x +d c \right)^{3} e}-\frac{c^{3} b \arcsin \left(c x \right)}{3 \left(c e x +d c \right)^{3} e}+\frac{c^{3} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{6 e^{2} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{2}}+\frac{c^{4} b d \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{2 e \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}-\frac{c^{5} b \,d^{2} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{c^{3} b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{6 e^{2} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-1/3*c^3*a/(c*e*x+c*d)^3/e-1/3*c^3*b/(c*e*x+c*d)^3/e*arcsin(c*x)+1/6*c^3*b/e^2/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)+1/2*c^4*b/e*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-1/2*c^5*b/e^2*d^2/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))+1/6*c^3*b/e^2/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))","B"
9,1,660,334,0.148000," ","int((e*x+d)^3*(a+b*arcsin(c*x))^2,x)","\frac{\frac{\left(c e x +d c \right)^{4} a^{2}}{4 c^{3} e}+\frac{b^{2} \left(\frac{e^{3} \left(8 \arcsin \left(c x \right)^{2} c^{4} x^{4}+4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}-16 \arcsin \left(c x \right)^{2} c^{2} x^{2}-c^{4} x^{4}-10 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x +5 \arcsin \left(c x \right)^{2}+5 c^{2} x^{2}-4\right)}{32}+\frac{3 d^{2} c^{2} e \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{d c \,e^{2} \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{9}+c^{3} d^{3} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+\frac{e^{3} \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+3 d c \,e^{2} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3}}+\frac{2 a b \left(\frac{e^{3} \arcsin \left(c x \right) c^{4} x^{4}}{4}+e^{2} \arcsin \left(c x \right) c^{4} x^{3} d +\frac{3 e \arcsin \left(c x \right) c^{4} x^{2} d^{2}}{2}+\arcsin \left(c x \right) c^{4} x \,d^{3}+\frac{\arcsin \left(c x \right) c^{4} d^{4}}{4 e}-\frac{e^{4} \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)+4 d c \,e^{3} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)+6 c^{2} d^{2} e^{2} \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)-4 c^{3} d^{3} e \sqrt{-c^{2} x^{2}+1}+c^{4} d^{4} \arcsin \left(c x \right)}{4 e}\right)}{c^{3}}}{c}"," ",0,"1/c*(1/4*(c*e*x+c*d)^4*a^2/c^3/e+b^2/c^3*(1/32*e^3*(8*arcsin(c*x)^2*c^4*x^4+4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3-16*arcsin(c*x)^2*c^2*x^2-c^4*x^4-10*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x+5*arcsin(c*x)^2+5*c^2*x^2-4)+3/4*d^2*c^2*e*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/9*d*c*e^2*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+c^3*d^3*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+1/4*e^3*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+3*d*c*e^2*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)))+2*a*b/c^3*(1/4*e^3*arcsin(c*x)*c^4*x^4+e^2*arcsin(c*x)*c^4*x^3*d+3/2*e*arcsin(c*x)*c^4*x^2*d^2+arcsin(c*x)*c^4*x*d^3+1/4/e*arcsin(c*x)*c^4*d^4-1/4/e*(e^4*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))+4*d*c*e^3*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+6*c^2*d^2*e^2*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))-4*c^3*d^3*e*(-c^2*x^2+1)^(1/2)+c^4*d^4*arcsin(c*x))))","A"
10,1,420,218,0.107000," ","int((e*x+d)^2*(a+b*arcsin(c*x))^2,x)","\frac{\frac{\left(c e x +d c \right)^{3} a^{2}}{3 c^{2} e}+\frac{b^{2} \left(c^{2} d^{2} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+\frac{d c e \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{2}+\frac{e^{2} \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+e^{2} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2}}+\frac{2 a b \left(\frac{\arcsin \left(c x \right) e^{2} c^{3} x^{3}}{3}+e \arcsin \left(c x \right) c^{3} x^{2} d +\arcsin \left(c x \right) c^{3} x \,d^{2}+\frac{\arcsin \left(c x \right) c^{3} d^{3}}{3 e}-\frac{e^{3} \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)+3 d c \,e^{2} \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)-3 d^{2} c^{2} e \sqrt{-c^{2} x^{2}+1}+c^{3} d^{3} \arcsin \left(c x \right)}{3 e}\right)}{c^{2}}}{c}"," ",0,"1/c*(1/3*(c*e*x+c*d)^3*a^2/c^2/e+b^2/c^2*(c^2*d^2*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+1/2*d*c*e*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/27*e^2*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+e^2*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)))+2*a*b/c^2*(1/3*arcsin(c*x)*e^2*c^3*x^3+e*arcsin(c*x)*c^3*x^2*d+arcsin(c*x)*c^3*x*d^2+1/3/e*arcsin(c*x)*c^3*d^3-1/3/e*(e^3*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))+3*d*c*e^2*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))-3*d^2*c^2*e*(-c^2*x^2+1)^(1/2)+c^3*d^3*arcsin(c*x))))","A"
11,1,198,128,0.087000," ","int((e*x+d)*(a+b*arcsin(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{1}{2} x^{2} c^{2} e +c^{2} d x \right)}{c}+\frac{b^{2} \left(\frac{e \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+d c \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)\right)}{c}+\frac{2 a b \left(\frac{\arcsin \left(c x \right) c^{2} x^{2} e}{2}+\arcsin \left(c x \right) d \,c^{2} x -\frac{e \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{2}+d c \sqrt{-c^{2} x^{2}+1}\right)}{c}}{c}"," ",0,"1/c*(a^2/c*(1/2*x^2*c^2*e+c^2*d*x)+b^2/c*(1/4*e*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+d*c*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)))+2*a*b/c*(1/2*arcsin(c*x)*c^2*x^2*e+arcsin(c*x)*d*c^2*x-1/2*e*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+d*c*(-c^2*x^2+1)^(1/2)))","A"
12,1,72,45,0.000000," ","int((a+b*arcsin(c*x))^2,x)","\frac{c x \,a^{2}+b^{2} \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+2 a b \left(c x \arcsin \left(c x \right)+\sqrt{-c^{2} x^{2}+1}\right)}{c}"," ",0,"1/c*(c*x*a^2+b^2*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+2*a*b*(c*x*arcsin(c*x)+(-c^2*x^2+1)^(1/2)))","A"
13,0,0,372,2.388000," ","int((a+b*arcsin(c*x))^2/(e*x+d),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{e x +d}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(e*x+d),x)","F"
14,1,646,319,0.697000," ","int((a+b*arcsin(c*x))^2/(e*x+d)^2,x)","-\frac{c \,a^{2}}{\left(c e x +d c \right) e}-\frac{c \,b^{2} \arcsin \left(c x \right)^{2}}{e \left(c e x +d c \right)}+\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{2 c a b \arcsin \left(c x \right)}{\left(c e x +d c \right) e}-\frac{2 c a b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{e^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-c*a^2/(c*e*x+c*d)/e-c*b^2*arcsin(c*x)^2/e/(c*e*x+c*d)+2*c*b^2*(-c^2*d^2+e^2)^(1/2)/e/(c^2*d^2-e^2)*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*c*b^2*(-c^2*d^2+e^2)^(1/2)/e/(c^2*d^2-e^2)*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/e/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/e/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*c*a*b/(c*e*x+c*d)/e*arcsin(c*x)-2*c*a*b/e^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))","B"
15,1,1173,407,1.316000," ","int((a+b*arcsin(c*x))^2/(e*x+d)^3,x)","-\frac{c^{2} a^{2}}{2 \left(c e x +d c \right)^{2} e}-\frac{i c^{3} b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, d \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)^{2}}-\frac{i c^{4} b^{2} \arcsin \left(c x \right) d^{2}}{\left(c e x +d c \right)^{2} \left(c^{2} d^{2}-e^{2}\right) e}+\frac{i c^{3} b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, d \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)^{2}}-\frac{c^{4} b^{2} \arcsin \left(c x \right)^{2} d^{2}}{2 \left(c e x +d c \right)^{2} \left(c^{2} d^{2}-e^{2}\right) e}+\frac{c^{3} b^{2} \arcsin \left(c x \right) e \sqrt{-c^{2} x^{2}+1}\, x}{\left(c e x +d c \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{3} b^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, d}{\left(c e x +d c \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b^{2} \arcsin \left(c x \right)^{2} e}{2 \left(c e x +d c \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 c^{2} b^{2} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{c^{2} b^{2} \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} e +2 i d c \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)-e \right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{c^{3} b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, d \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)^{2}}+\frac{c^{3} b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, d \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)^{2}}-\frac{2 i c^{4} b^{2} \arcsin \left(c x \right) x d}{\left(c e x +d c \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{4} b^{2} \arcsin \left(c x \right) e \,x^{2}}{\left(c e x +d c \right)^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{c^{2} a b \arcsin \left(c x \right)}{\left(c e x +d c \right)^{2} e}+\frac{c^{2} a b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{e \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)}-\frac{c^{3} a b d \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-1/2*c^2*a^2/(c*e*x+c*d)^2/e-I*c^3*b^2/e*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*d*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*c^3*b^2/e*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*d*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-I*c^4*b^2*arcsin(c*x)/(c*e*x+c*d)^2/(c^2*d^2-e^2)/e*d^2-1/2*c^4*b^2*arcsin(c*x)^2/(c*e*x+c*d)^2/(c^2*d^2-e^2)/e*d^2+c^3*b^2*arcsin(c*x)/(c*e*x+c*d)^2/(c^2*d^2-e^2)*e*(-c^2*x^2+1)^(1/2)*x+c^3*b^2*arcsin(c*x)/(c*e*x+c*d)^2/(c^2*d^2-e^2)*(-c^2*x^2+1)^(1/2)*d+1/2*c^2*b^2*arcsin(c*x)^2/(c*e*x+c*d)^2/(c^2*d^2-e^2)*e+2*c^2*b^2/e/(c^2*d^2-e^2)*ln(I*c*x+(-c^2*x^2+1)^(1/2))-c^2*b^2/e/(c^2*d^2-e^2)*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2*e+2*I*d*c*(I*c*x+(-c^2*x^2+1)^(1/2))-e)-c^3*b^2/e*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*d*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+c^3*b^2/e*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*d*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*I*c^4*b^2*arcsin(c*x)/(c*e*x+c*d)^2/(c^2*d^2-e^2)*x*d-I*c^4*b^2*arcsin(c*x)/(c*e*x+c*d)^2/(c^2*d^2-e^2)*e*x^2-c^2*a*b/(c*e*x+c*d)^2/e*arcsin(c*x)+c^2*a*b/e/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-c^3*a*b/e^2*d/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))","B"
16,1,327,373,0.101000," ","int((e*x+d)^3/(a+b*arcsin(c*x)),x)","\frac{8 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) c^{3} d^{3}+8 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) c^{3} d^{3}+12 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) c^{2} d^{2} e -12 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) c^{2} d^{2} e -6 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) c d \,e^{2}-6 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) c d \,e^{2}+6 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) c d \,e^{2}+6 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) c d \,e^{2}+2 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) e^{3}-2 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) e^{3}-\cos \left(\frac{4 a}{b}\right) \Si \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) e^{3}+\sin \left(\frac{4 a}{b}\right) \Ci \left(4 \arcsin \left(c x \right)+\frac{4 a}{b}\right) e^{3}}{8 c^{4} b}"," ",0,"1/8/c^4*(8*Si(arcsin(c*x)+a/b)*sin(a/b)*c^3*d^3+8*Ci(arcsin(c*x)+a/b)*cos(a/b)*c^3*d^3+12*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*c^2*d^2*e-12*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*c^2*d^2*e-6*Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*c*d*e^2-6*Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*c*d*e^2+6*Si(arcsin(c*x)+a/b)*sin(a/b)*c*d*e^2+6*Ci(arcsin(c*x)+a/b)*cos(a/b)*c*d*e^2+2*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*e^3-2*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*e^3-cos(4*a/b)*Si(4*arcsin(c*x)+4*a/b)*e^3+sin(4*a/b)*Ci(4*arcsin(c*x)+4*a/b)*e^3)/b","A"
17,1,206,236,0.084000," ","int((e*x+d)^2/(a+b*arcsin(c*x)),x)","\frac{4 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) c^{2} d^{2}+4 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) c^{2} d^{2}+4 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) c d e -4 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) c d e +\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) e^{2}+\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) e^{2}-\Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) e^{2}-\Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) e^{2}}{4 c^{3} b}"," ",0,"1/4/c^3*(4*Si(arcsin(c*x)+a/b)*sin(a/b)*c^2*d^2+4*Ci(arcsin(c*x)+a/b)*cos(a/b)*c^2*d^2+4*Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*c*d*e-4*Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*c*d*e+Si(arcsin(c*x)+a/b)*sin(a/b)*e^2+Ci(arcsin(c*x)+a/b)*cos(a/b)*e^2-Si(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*e^2-Ci(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*e^2)/b","A"
18,1,103,111,0.073000," ","int((e*x+d)/(a+b*arcsin(c*x)),x)","\frac{\frac{e \left(\Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)-\Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)\right)}{2 c b}+\frac{d \left(\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)+\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)\right)}{b}}{c}"," ",0,"1/c*(1/2/c*e*(Si(2*arcsin(c*x)+2*a/b)*cos(2*a/b)-Ci(2*arcsin(c*x)+2*a/b)*sin(2*a/b))/b+d*(Si(arcsin(c*x)+a/b)*sin(a/b)+Ci(arcsin(c*x)+a/b)*cos(a/b))/b)","A"
19,1,48,53,0.000000," ","int(1/(a+b*arcsin(c*x)),x)","\frac{\frac{\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{b}+\frac{\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)}{b}}{c}"," ",0,"1/c*(Si(arcsin(c*x)+a/b)*sin(a/b)/b+Ci(arcsin(c*x)+a/b)*cos(a/b)/b)","A"
20,0,0,20,3.151000," ","int(1/(e*x+d)/(a+b*arcsin(c*x)),x)","\int \frac{1}{\left(e x +d \right) \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x+d)/(a+b*arcsin(c*x)),x)","F"
21,0,0,20,1.406000," ","int(1/(e*x+d)^2/(a+b*arcsin(c*x)),x)","\int \frac{1}{\left(e x +d \right)^{2} \left(a +b \arcsin \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x+d)^2/(a+b*arcsin(c*x)),x)","F"
22,1,526,348,0.235000," ","int((e*x+d)^2/(a+b*arcsin(c*x))^2,x)","\frac{-4 \arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b \,c^{2} d^{2}+4 \arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b \,c^{2} d^{2}+8 \arcsin \left(c x \right) \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) b c d e +8 \arcsin \left(c x \right) \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) b c d e -4 \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,c^{2} d^{2}+4 \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,c^{2} d^{2}+3 \arcsin \left(c x \right) \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b \,e^{2}-3 \arcsin \left(c x \right) \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b \,e^{2}-\arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b \,e^{2}+\arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b \,e^{2}+8 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a c d e +8 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a c d e -4 \sqrt{-c^{2} x^{2}+1}\, b \,c^{2} d^{2}+3 \Si \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a \,e^{2}-3 \Ci \left(3 \arcsin \left(c x \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a \,e^{2}-\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,e^{2}+\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,e^{2}-4 \sin \left(2 \arcsin \left(c x \right)\right) b c d e +\cos \left(3 \arcsin \left(c x \right)\right) b \,e^{2}-\sqrt{-c^{2} x^{2}+1}\, b \,e^{2}}{4 c^{3} \left(a +b \arcsin \left(c x \right)\right) b^{2}}"," ",0,"1/4/c^3*(-4*arcsin(c*x)*Si(arcsin(c*x)+a/b)*cos(a/b)*b*c^2*d^2+4*arcsin(c*x)*Ci(arcsin(c*x)+a/b)*sin(a/b)*b*c^2*d^2+8*arcsin(c*x)*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*b*c*d*e+8*arcsin(c*x)*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*b*c*d*e-4*Si(arcsin(c*x)+a/b)*cos(a/b)*a*c^2*d^2+4*Ci(arcsin(c*x)+a/b)*sin(a/b)*a*c^2*d^2+3*arcsin(c*x)*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*b*e^2-3*arcsin(c*x)*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*b*e^2-arcsin(c*x)*Si(arcsin(c*x)+a/b)*cos(a/b)*b*e^2+arcsin(c*x)*Ci(arcsin(c*x)+a/b)*sin(a/b)*b*e^2+8*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a*c*d*e+8*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a*c*d*e-4*(-c^2*x^2+1)^(1/2)*b*c^2*d^2+3*Si(3*arcsin(c*x)+3*a/b)*cos(3*a/b)*a*e^2-3*Ci(3*arcsin(c*x)+3*a/b)*sin(3*a/b)*a*e^2-Si(arcsin(c*x)+a/b)*cos(a/b)*a*e^2+Ci(arcsin(c*x)+a/b)*sin(a/b)*a*e^2-4*sin(2*arcsin(c*x))*b*c*d*e+cos(3*arcsin(c*x))*b*e^2-(-c^2*x^2+1)^(1/2)*b*e^2)/(a+b*arcsin(c*x))/b^2","A"
23,1,257,177,0.125000," ","int((e*x+d)/(a+b*arcsin(c*x))^2,x)","\frac{\frac{e \left(2 \arcsin \left(c x \right) \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) b +2 \arcsin \left(c x \right) \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) b +2 \Si \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +2 \Ci \left(2 \arcsin \left(c x \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a -\sin \left(2 \arcsin \left(c x \right)\right) b \right)}{2 c \left(a +b \arcsin \left(c x \right)\right) b^{2}}-\frac{d \left(\arcsin \left(c x \right) \Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b -\arcsin \left(c x \right) \Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a -\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +\sqrt{-c^{2} x^{2}+1}\, b \right)}{\left(a +b \arcsin \left(c x \right)\right) b^{2}}}{c}"," ",0,"1/c*(1/2/c*e*(2*arcsin(c*x)*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*b+2*arcsin(c*x)*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*b+2*Si(2*arcsin(c*x)+2*a/b)*sin(2*a/b)*a+2*Ci(2*arcsin(c*x)+2*a/b)*cos(2*a/b)*a-sin(2*arcsin(c*x))*b)/(a+b*arcsin(c*x))/b^2-d*(arcsin(c*x)*Si(arcsin(c*x)+a/b)*cos(a/b)*b-arcsin(c*x)*Ci(arcsin(c*x)+a/b)*sin(a/b)*b+Si(arcsin(c*x)+a/b)*cos(a/b)*a-Ci(arcsin(c*x)+a/b)*sin(a/b)*a+(-c^2*x^2+1)^(1/2)*b)/(a+b*arcsin(c*x))/b^2)","A"
24,1,76,84,0.000000," ","int(1/(a+b*arcsin(c*x))^2,x)","\frac{-\frac{\sqrt{-c^{2} x^{2}+1}}{\left(a +b \arcsin \left(c x \right)\right) b}-\frac{\Si \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-\Ci \left(\arcsin \left(c x \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{b^{2}}}{c}"," ",0,"1/c*(-(-c^2*x^2+1)^(1/2)/(a+b*arcsin(c*x))/b-(Si(arcsin(c*x)+a/b)*cos(a/b)-Ci(arcsin(c*x)+a/b)*sin(a/b))/b^2)","A"
25,0,0,20,5.952000," ","int(1/(e*x+d)/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\left(e x +d \right) \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x+d)/(a+b*arcsin(c*x))^2,x)","F"
26,0,0,20,2.063000," ","int(1/(e*x+d)^2/(a+b*arcsin(c*x))^2,x)","\int \frac{1}{\left(e x +d \right)^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int(1/(e*x+d)^2/(a+b*arcsin(c*x))^2,x)","F"
27,0,0,73,0.447000," ","int((e*x+d)^m*(a+b*arcsin(c*x))^2,x)","\int \left(e x +d \right)^{m} \left(a +b \arcsin \left(c x \right)\right)^{2}\, dx"," ",0,"int((e*x+d)^m*(a+b*arcsin(c*x))^2,x)","F"
28,0,0,144,0.542000," ","int((e*x+d)^m*(a+b*arcsin(c*x)),x)","\int \left(e x +d \right)^{m} \left(a +b \arcsin \left(c x \right)\right)\, dx"," ",0,"int((e*x+d)^m*(a+b*arcsin(c*x)),x)","F"
29,0,0,20,2.311000," ","int((e*x+d)^m/(a+b*arcsin(c*x)),x)","\int \frac{\left(e x +d \right)^{m}}{a +b \arcsin \left(c x \right)}\, dx"," ",0,"int((e*x+d)^m/(a+b*arcsin(c*x)),x)","F"
30,0,0,20,1.323000," ","int((e*x+d)^m/(a+b*arcsin(c*x))^2,x)","\int \frac{\left(e x +d \right)^{m}}{\left(a +b \arcsin \left(c x \right)\right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(a+b*arcsin(c*x))^2,x)","F"
31,1,1286,589,1.558000," ","int((g*x+f)^3*(a+b*arcsin(c*x))*(-c^2*d*x^2+d)^(1/2),x)","\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g c \sqrt{-c^{2} x^{2}+1}\, x^{3} f^{2}}{3 c^{2} x^{2}-3}+\frac{a \,f^{3} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \sqrt{-c^{2} x^{2}+1}}{8 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \arcsin \left(c x \right) x}{2 \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)}{15 c^{4} \left(c^{2} x^{2}-1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right) x^{4}}{15 \left(c^{2} x^{2}-1\right)}-\frac{a \,g^{3} x^{2} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{5 c^{2} d}+\frac{3 a f \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}-\frac{a \,f^{2} g \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{c^{2} d}+\frac{a \,f^{3} x \sqrt{-c^{2} d \,x^{2}+d}}{2}-\frac{3 a f \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}+\frac{3 a f \,g^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{2} \sqrt{c^{2} d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) f^{2}}{c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f^{3}}{4 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right) x^{2}}{15 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{-c^{2} x^{2}+1}\, x^{3}}{45 c \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{-c^{2} x^{2}+1}\, x}{15 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \arcsin \left(c x \right) x^{3}}{8 \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \sqrt{-c^{2} x^{2}+1}}{128 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) x^{2} f^{2}}{c^{2} x^{2}-1}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} c^{2} \arcsin \left(c x \right) x^{3}}{2 c^{2} x^{2}-2}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} c^{2} \arcsin \left(c x \right) x^{6}}{5 c^{2} x^{2}-5}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} c \sqrt{-c^{2} x^{2}+1}\, x^{5}}{25 c^{2} x^{2}-25}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, x \,f^{2}}{c \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} c \sqrt{-c^{2} x^{2}+1}\, x^{4}}{16 \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{16 c \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} c^{2} \arcsin \left(c x \right) x^{5}}{4 \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \arcsin \left(c x \right) x}{8 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,c^{2} \arcsin \left(c x \right) x^{4} f^{2}}{c^{2} x^{2}-1}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f \,g^{2}}{16 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{4 c^{2} x^{2}-4}-\frac{2 a \,g^{3} \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{15 d \,c^{4}}"," ",0,"1/2*a*f^3*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/8*b*(-d*(c^2*x^2-1))^(1/2)*f^3/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^3/(c^2*x^2-1)*arcsin(c*x)*x+2/15*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/(c^2*x^2-1)*arcsin(c*x)-4/15*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c^2*x^2-1)*arcsin(c*x)*x^4-1/5*a*g^3*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d+3/8*a*f*g^2/c^2*x*(-c^2*d*x^2+d)^(1/2)-a*f^2*g/c^2/d*(-c^2*d*x^2+d)^(3/2)+1/2*a*f^3*x*(-c^2*d*x^2+d)^(1/2)-3/4*a*f*g^2*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+3/8*a*f*g^2/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/4*b*(-d*(c^2*x^2-1))^(1/2)*f^3*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/(c^2*x^2-1)*arcsin(c*x)*f^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^3*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3-1/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*f^3+1/5*b*(-d*(c^2*x^2-1))^(1/2)*g^3*c^2/(c^2*x^2-1)*arcsin(c*x)*x^6-1/15*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/(c^2*x^2-1)*arcsin(c*x)*x^2+1/25*b*(-d*(c^2*x^2-1))^(1/2)*g^3*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^5-1/45*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-2/15*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-9/8*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/(c^2*x^2-1)*arcsin(c*x)*x^3+3/128*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-2*b*(-d*(c^2*x^2-1))^(1/2)*g/(c^2*x^2-1)*arcsin(c*x)*x^2*f^2-b*(-d*(c^2*x^2-1))^(1/2)*g/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*f^2+3/16*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-3/16*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+1/3*b*(-d*(c^2*x^2-1))^(1/2)*g*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3*f^2+3/4*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5+3/8*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c^2/(c^2*x^2-1)*arcsin(c*x)*x+b*(-d*(c^2*x^2-1))^(1/2)*g*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4*f^2-3/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2*f*g^2-2/15*a*g^3/d/c^4*(-c^2*d*x^2+d)^(3/2)","B"
32,1,912,392,0.847000," ","int((g*x+f)^2*(a+b*arcsin(c*x))*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}+\frac{a \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}+\frac{a \,g^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{2} \sqrt{c^{2} d}}-\frac{2 a f g \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+\frac{a \,f^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{a \,f^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f^{2}}{4 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} g^{2}}{16 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} c^{2} \arcsin \left(c x \right) x^{5}}{4 c^{2} x^{2}-4}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) x^{3}}{8 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \sqrt{-c^{2} x^{2}+1}}{128 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) x}{8 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right)}{3 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} c^{2} \arcsin \left(c x \right) x^{3}}{2 c^{2} x^{2}-2}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} \sqrt{-c^{2} x^{2}+1}}{8 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} \arcsin \left(c x \right) x}{2 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} c \sqrt{-c^{2} x^{2}+1}\, x^{4}}{16 c^{2} x^{2}-16}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{16 c \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,c^{2} \arcsin \left(c x \right) x^{4}}{3 \left(c^{2} x^{2}-1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{4 c^{2} x^{2}-4}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g c \sqrt{-c^{2} x^{2}+1}\, x^{3}}{9 \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \sqrt{-c^{2} x^{2}+1}\, x}{3 c \left(c^{2} x^{2}-1\right)}"," ",0,"-1/4*a*g^2*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+1/8*a*g^2/c^2*x*(-c^2*d*x^2+d)^(1/2)+1/8*a*g^2/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-2/3*a*f*g/c^2/d*(-c^2*d*x^2+d)^(3/2)+1/2*a*f^2*x*(-c^2*d*x^2+d)^(1/2)+1/2*a*f^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*f^2-1/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2*g^2+1/4*b*(-d*(c^2*x^2-1))^(1/2)*g^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5-3/8*b*(-d*(c^2*x^2-1))^(1/2)*g^2/(c^2*x^2-1)*arcsin(c*x)*x^3+1/128*b*(-d*(c^2*x^2-1))^(1/2)*g^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+1/8*b*(-d*(c^2*x^2-1))^(1/2)*g^2/c^2/(c^2*x^2-1)*arcsin(c*x)*x+2/3*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/(c^2*x^2-1)*arcsin(c*x)+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3-1/8*b*(-d*(c^2*x^2-1))^(1/2)*f^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^2/(c^2*x^2-1)*arcsin(c*x)*x+1/16*b*(-d*(c^2*x^2-1))^(1/2)*g^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-1/16*b*(-d*(c^2*x^2-1))^(1/2)*g^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+2/3*b*(-d*(c^2*x^2-1))^(1/2)*f*g*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4-4/3*b*(-d*(c^2*x^2-1))^(1/2)*f*g/(c^2*x^2-1)*arcsin(c*x)*x^2+1/4*b*(-d*(c^2*x^2-1))^(1/2)*f^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+2/9*b*(-d*(c^2*x^2-1))^(1/2)*f*g*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-2/3*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x","B"
33,1,491,206,0.651000," ","int((g*x+f)*(a+b*arcsin(c*x))*(-c^2*d*x^2+d)^(1/2),x)","-\frac{a g \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}+\frac{a f x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{a f d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,c^{2} \arcsin \left(c x \right) x^{4}}{3 c^{2} x^{2}-3}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,c^{2} \arcsin \left(c x \right) x^{3}}{2 c^{2} x^{2}-2}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sqrt{-c^{2} x^{2}+1}}{8 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right) x}{2 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f}{4 c \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g c \sqrt{-c^{2} x^{2}+1}\, x^{3}}{9 c^{2} x^{2}-9}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, x}{3 c \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{4 c^{2} x^{2}-4}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)}{3 c^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a*g/c^2/d*(-c^2*d*x^2+d)^(3/2)+1/2*a*f*x*(-c^2*d*x^2+d)^(1/2)+1/2*a*f*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+1/3*b*(-d*(c^2*x^2-1))^(1/2)*g*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4-2/3*b*(-d*(c^2*x^2-1))^(1/2)*g/(c^2*x^2-1)*arcsin(c*x)*x^2+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3-1/8*b*(-d*(c^2*x^2-1))^(1/2)*f/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f/(c^2*x^2-1)*arcsin(c*x)*x-1/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*f+1/9*b*(-d*(c^2*x^2-1))^(1/2)*g*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-1/3*b*(-d*(c^2*x^2-1))^(1/2)*g/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/4*b*(-d*(c^2*x^2-1))^(1/2)*f*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+1/3*b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/(c^2*x^2-1)*arcsin(c*x)","B"
34,1,1206,694,0.606000," ","int((a+b*arcsin(c*x))*(-c^2*d*x^2+d)^(1/2)/(g*x+f),x)","\frac{a \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{g}+\frac{a \,c^{2} d f \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{g^{2} \sqrt{c^{2} d}}+\frac{a d \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right) c^{2} f^{2}}{g^{3} \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\frac{a d \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f c}{2 \left(c^{2} x^{2}-1\right) g^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} c^{2}}{\left(c^{2} x^{2}-1\right) g}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x c}{\left(c^{2} x^{2}-1\right) g}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) g}-\frac{b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) g^{2}}+\frac{b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) g^{2}}+\frac{i b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \dilog \left(-\frac{i c f}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}-\frac{\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right)}{\left(c^{2} x^{2}-1\right) g^{2}}-\frac{i b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \dilog \left(\frac{i c f}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right)}{\left(c^{2} x^{2}-1\right) g^{2}}"," ",0,"a/g*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)+a/g^2*c^2*d*f/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+a/g^3*d/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^2*f^2-a/g*d/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*f*c/g^2+b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/g*arcsin(c*x)*x^2*c^2+b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/g*(-c^2*x^2+1)^(1/2)*x*c-b*(-d*(c^2*x^2-1))^(1/2)/(c^2*x^2-1)/g*arcsin(c*x)-b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^2*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)+b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^2*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)+I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^2*dilog(-I/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f-1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))-I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^2*dilog(I/(I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))","A"
35,1,1572,814,1.050000," ","int((a+b*arcsin(c*x))*(-c^2*d*x^2+d)^(1/2)/(g*x+f)^2,x)","\frac{a \left(-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}\right)^{\frac{3}{2}}}{d \left(c^{2} f^{2}-g^{2}\right) \left(x +\frac{f}{g}\right)}-\frac{a \,c^{2} f \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{g \left(c^{2} f^{2}-g^{2}\right)}-\frac{a \,c^{4} f^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{g^{2} \left(c^{2} f^{2}-g^{2}\right) \sqrt{c^{2} d}}-\frac{a \,c^{4} f^{3} d \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g^{3} \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a \,c^{2} f d \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a \,c^{2} \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, x}{c^{2} f^{2}-g^{2}}+\frac{a \,c^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{\left(c^{2} f^{2}-g^{2}\right) \sqrt{c^{2} d}}+b \left(\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} c}{2 \left(c^{2} x^{2}-1\right) g^{2}}-\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(i \sqrt{-c^{2} x^{2}+1}\, x c +c^{2} x^{2}-1\right) \arcsin \left(c x \right) \left(c^{2} f x +g -i \sqrt{-c^{2} x^{2}+1}\, c f \right)}{\left(c^{2} x^{2}-1\right) g^{2} \left(g x +f \right)}+\frac{\sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \left(\ln \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right) \sqrt{-c^{2} f^{2}+g^{2}}\, c f -\ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} g +2 i c f \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)-g \right) c^{2} f^{2}-2 \Im \left(\arcsin \left(c x \right)\right) c^{2} f^{2}-\ln \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right) \sqrt{-c^{2} f^{2}+g^{2}}\, c f +2 \ln \left({\mathrm e}^{i \Re \left(\arcsin \left(c x \right)\right)}\right) c^{2} f^{2}-i \dilog \left(-\frac{i c f}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}-\frac{\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \sqrt{-c^{2} f^{2}+g^{2}}\, c f +i \dilog \left(\frac{i c f}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \sqrt{-c^{2} f^{2}+g^{2}}\, c f +\ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} g +2 i c f \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)-g \right) g^{2}+2 \Im \left(\arcsin \left(c x \right)\right) g^{2}-2 \ln \left({\mathrm e}^{i \Re \left(\arcsin \left(c x \right)\right)}\right) g^{2}\right) c}{\left(c^{2} x^{2}-1\right) g^{2} \left(c^{2} f^{2}-g^{2}\right)}\right)"," ",0,"a/d/(c^2*f^2-g^2)/(x+f/g)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)-a/g*c^2*f/(c^2*f^2-g^2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-a/g^2*c^4*f^2/(c^2*f^2-g^2)*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))-a/g^3*c^4*f^3/(c^2*f^2-g^2)*d/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))+a/g*c^2*f/(c^2*f^2-g^2)*d/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))+a*c^2/(c^2*f^2-g^2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*x+a*c^2/(c^2*f^2-g^2)*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+b*(1/2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*c/g^2-(-d*(c^2*x^2-1))^(1/2)*(I*(-c^2*x^2+1)^(1/2)*x*c+c^2*x^2-1)*arcsin(c*x)*(c^2*f*x+g-I*(-c^2*x^2+1)^(1/2)*c*f)/(c^2*x^2-1)/g^2/(g*x+f)+(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*(ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)*(-c^2*f^2+g^2)^(1/2)*c*f-ln((I*c*x+(-c^2*x^2+1)^(1/2))^2*g+2*I*c*f*(I*c*x+(-c^2*x^2+1)^(1/2))-g)*c^2*f^2-2*Im(arcsin(c*x))*c^2*f^2-ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)*(-c^2*f^2+g^2)^(1/2)*c*f+2*ln(exp(I*Re(arcsin(c*x))))*c^2*f^2-I*dilog(-I/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f-1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2)*c*f+I*dilog(I/(I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2)*c*f+ln((I*c*x+(-c^2*x^2+1)^(1/2))^2*g+2*I*c*f*(I*c*x+(-c^2*x^2+1)^(1/2))-g)*g^2+2*Im(arcsin(c*x))*g^2-2*ln(exp(I*Re(arcsin(c*x))))*g^2)*c/(c^2*x^2-1)/g^2/(c^2*f^2-g^2))","C"
36,1,5085,843,1.368000," ","int((g*x+f)^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
37,1,3643,596,0.941000," ","int((g*x+f)^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","\text{output too large to display}"," ",0,"5/32*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2*f^2-9/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*f^2-3/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*d*f^2-1/32*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2*d*g^2-1/6*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^7+19/48*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5+3/64*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/c^2/(c^2*x^2-1)*arcsin(c*x)*x+13/40*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/c^2/(c^2*x^2-1)*arcsin(c*x)-1/8*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^5*f^2+7/16*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3*f^2-5/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^2/(c^2*x^2-1)*x^3*f^2+43/600*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c^2*x^2-1)*x^2-15/256*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*f^2+7/300*b*(-d*(c^2*x^2-1))^(1/2)*f*g*sin(4*arcsin(c*x))*d/(c^2*x^2-1)*x^2-7/300*b*(-d*(c^2*x^2-1))^(1/2)*f*g*sin(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)+17/256*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2*f^2+1/512*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2*g^2-1/36*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6+11/192*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-3/128*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/32*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4*f^2-29/40*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/(c^2*x^2-1)*arcsin(c*x)*x^2-15/256*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*f^2-3/512*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)*g^2+1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d*c^2/(c^2*x^2-1)*x^5+1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/c^2/(c^2*x^2-1)*x-11/600*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/c^2/(c^2*x^2-1)-1/32*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^4/(c^2*x^2-1)*x^5*f^2-1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*x^2*g^2+1/512*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*g^2+1/64*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x*g^2+7/300*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*sin(4*arcsin(c*x))*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/20*b*(-d*(c^2*x^2-1))^(1/2)*f*g*sin(4*arcsin(c*x))*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+1/5*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^5-1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+5/64*I*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4*f^2+11/600*b*(-d*(c^2*x^2-1))^(1/2)*f*g*cos(4*arcsin(c*x))*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/20*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*sin(4*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*x^2+9/64*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x*f^2+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2*f^2+1/20*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*sin(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)*arcsin(c*x)-7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2*f^2-53/192*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/(c^2*x^2-1)*arcsin(c*x)*x^3-5/16*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*arcsin(c*x)*x*f^2-17/256*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*f^2-1/512*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)*g^2-5/4608*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-17/256*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*f^2-1/32*I*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/(c^2*x^2-1)*x^3+7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)*x*f^2+1/24*a*g^2/c^2*x*(-c^2*d*x^2+d)^(3/2)+1/4*a*f^2*x*(-c^2*d*x^2+d)^(3/2)-1/5*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^6+3/5*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4-1/25*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^5+2/15*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-13/40*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-11/600*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*cos(4*arcsin(c*x))*d/(c^2*x^2-1)*x^2+17/256*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*f^2+1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c^3/(c^2*x^2-1)*arcsin(c*x)*g^2+15/256*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2*f^2+3/512*I*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*x^2*g^2+11/600*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*cos(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)+7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)*f^2-1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/25*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d*c^4/(c^2*x^2-1)*x^6-1/75*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*d*c^2/(c^2*x^2-1)*x^4-1/16*I*b*(-d*(c^2*x^2-1))^(1/2)*g^2*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4+3/8*a*f^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3/40*I*b*(-d*(c^2*x^2-1))^(1/2)*f*g*cos(4*arcsin(c*x))*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-2/5*a*f*g/c^2/d*(-c^2*d*x^2+d)^(5/2)-1/6*a*g^2*x*(-c^2*d*x^2+d)^(5/2)/c^2/d+1/16*a*g^2/c^2*d*x*(-c^2*d*x^2+d)^(1/2)+1/16*a*g^2/c^2*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3/512*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d/c^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*g^2-3/40*b*(-d*(c^2*x^2-1))^(1/2)*f*g*cos(4*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*x^2+7/64*b*(-d*(c^2*x^2-1))^(1/2)*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x*f^2+9/64*b*(-d*(c^2*x^2-1))^(1/2)*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2*f^2+3/40*b*(-d*(c^2*x^2-1))^(1/2)*f*g*cos(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)*arcsin(c*x)-7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*f^2+3/8*a*f^2*d*x*(-c^2*d*x^2+d)^(1/2)","C"
38,1,2320,322,0.732000," ","int((g*x+f)*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x)),x)","\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{5}}{10 c^{2} x^{2}-10}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{4}}{8 c^{2} x^{2}-8}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{8 c^{2} x^{2}-8}-\frac{3 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \cos \left(4 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{80 c \left(c^{2} x^{2}-1\right)}+\frac{17 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \cos \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{256 \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sin \left(4 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right) x^{2}}{40 \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sin \left(4 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{40 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \cos \left(3 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{64 c \left(c^{2} x^{2}-1\right)}+\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sin \left(3 \arcsin \left(c x \right)\right) d c \,x^{2}}{256 \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{64 c \left(c^{2} x^{2}-1\right)}+\frac{a f x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4}+\frac{9 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sin \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{64 \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{16 c \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sin \left(4 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{40 c \left(c^{2} x^{2}-1\right)}+\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sin \left(4 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{600 c \left(c^{2} x^{2}-1\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \cos \left(3 \arcsin \left(c x \right)\right) d c \arcsin \left(c x \right) x^{2}}{64 \left(c^{2} x^{2}-1\right)}-\frac{a g \left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}}}{5 c^{2} d}-\frac{29 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \arcsin \left(c x \right) x^{2}}{80 \left(c^{2} x^{2}-1\right)}-\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \arcsin \left(c x \right) x}{16 \left(c^{2} x^{2}-1\right)}+\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \arcsin \left(c x \right)}{80 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sin \left(4 \arcsin \left(c x \right)\right) d \,x^{2}}{600 \left(c^{2} x^{2}-1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \sqrt{-c^{2} x^{2}+1}}{256 c \left(c^{2} x^{2}-1\right)}-\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sin \left(4 \arcsin \left(c x \right)\right) d}{600 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \cos \left(3 \arcsin \left(c x \right)\right) d}{256 c \left(c^{2} x^{2}-1\right)}+\frac{43 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,x^{2}}{1200 \left(c^{2} x^{2}-1\right)}+\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d x}{64 \left(c^{2} x^{2}-1\right)}-\frac{11 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d}{1200 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \cos \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{64 \left(c^{2} x^{2}-1\right)}+\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sin \left(3 \arcsin \left(c x \right)\right) d c \arcsin \left(c x \right) x^{2}}{64 \left(c^{2} x^{2}-1\right)}+\frac{11 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \cos \left(4 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{1200 c \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d c \sqrt{-c^{2} x^{2}+1}\, x^{3}}{15 c^{2} x^{2}-15}-\frac{15 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sin \left(3 \arcsin \left(c x \right)\right) d}{256 c \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{2} x^{4}}{150 \left(c^{2} x^{2}-1\right)}-\frac{11 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \cos \left(4 \arcsin \left(c x \right)\right) d \,x^{2}}{1200 \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{4} x^{5}}{32 \left(c^{2} x^{2}-1\right)}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{2} x^{3}}{64 \left(c^{2} x^{2}-1\right)}+\frac{11 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \cos \left(4 \arcsin \left(c x \right)\right) d}{1200 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{4} x^{6}}{50 \left(c^{2} x^{2}-1\right)}+\frac{7 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{2} \arcsin \left(c x \right) x^{3}}{16 \left(c^{2} x^{2}-1\right)}-\frac{15 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sin \left(3 \arcsin \left(c x \right)\right) d \sqrt{-c^{2} x^{2}+1}\, x}{256 \left(c^{2} x^{2}-1\right)}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \cos \left(3 \arcsin \left(c x \right)\right) d c \,x^{2}}{256 \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{5}}{50 \left(c^{2} x^{2}-1\right)}-\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \sqrt{-c^{2} x^{2}+1}\, x}{80 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{4}}{32 \left(c^{2} x^{2}-1\right)}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{32 \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{2} \arcsin \left(c x \right) x^{4}}{10 \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \cos \left(4 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right) x^{2}}{80 \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f d}{16 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{4} \arcsin \left(c x \right) x^{5}}{8 \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \cos \left(4 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{80 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{9 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sin \left(3 \arcsin \left(c x \right)\right) d \arcsin \left(c x \right)}{64 c \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g d \,c^{4} \arcsin \left(c x \right) x^{6}}{10 \left(c^{2} x^{2}-1\right)}+\frac{3 a f d x \sqrt{-c^{2} d \,x^{2}+d}}{8}+\frac{3 a f \,d^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 \sqrt{c^{2} d}}"," ",0,"-3/80*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+17/256*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/40*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*x^2+1/40*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)*arcsin(c*x)+7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)+15/256*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2-7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+1/4*a*f*x*(-c^2*d*x^2+d)^(3/2)+9/64*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/16*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+1/40*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+7/600*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2+1/10*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^5-1/5*a*g/c^2/d*(-c^2*d*x^2+d)^(5/2)-29/80*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c^2*x^2-1)*arcsin(c*x)*x^2-5/16*b*(-d*(c^2*x^2-1))^(1/2)*f*d/(c^2*x^2-1)*arcsin(c*x)*x+13/80*b*(-d*(c^2*x^2-1))^(1/2)*g*d/c^2/(c^2*x^2-1)*arcsin(c*x)+7/600*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d/(c^2*x^2-1)*x^2-17/256*b*(-d*(c^2*x^2-1))^(1/2)*f*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-7/600*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)-17/256*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d/c/(c^2*x^2-1)+43/1200*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d/(c^2*x^2-1)*x^2+7/64*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d/(c^2*x^2-1)*x-11/1200*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d/c^2/(c^2*x^2-1)+7/64*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+9/64*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d*c/(c^2*x^2-1)*arcsin(c*x)*x^2+11/1200*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+7/16*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3-15/256*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+17/256*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d*c/(c^2*x^2-1)*x^2-1/50*b*(-d*(c^2*x^2-1))^(1/2)*g*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^5+1/15*b*(-d*(c^2*x^2-1))^(1/2)*g*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-13/80*b*(-d*(c^2*x^2-1))^(1/2)*g*d/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/32*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+5/32*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+3/10*b*(-d*(c^2*x^2-1))^(1/2)*g*d*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4-3/80*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d/(c^2*x^2-1)*arcsin(c*x)*x^2-3/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*f*d-1/8*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^5-1/50*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d*c^4/(c^2*x^2-1)*x^6-11/1200*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d/(c^2*x^2-1)*x^2-1/32*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^4/(c^2*x^2-1)*x^5-5/64*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^2/(c^2*x^2-1)*x^3+11/1200*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)-15/256*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)-1/150*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d*c^2/(c^2*x^2-1)*x^4+3/80*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d/c^2/(c^2*x^2-1)*arcsin(c*x)-9/64*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d/c/(c^2*x^2-1)*arcsin(c*x)-1/10*b*(-d*(c^2*x^2-1))^(1/2)*g*d*c^4/(c^2*x^2-1)*arcsin(c*x)*x^6+3/8*a*f*d*x*(-c^2*d*x^2+d)^(1/2)+3/8*a*f*d^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))","C"
39,1,2742,999,0.550000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))/(g*x+f),x)","\frac{a \left(-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}\right)^{\frac{3}{2}}}{3 g}+\frac{a d \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{g}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right)}{3 \left(c^{2} x^{2}-1\right) g}-\frac{a d \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, c^{2} f^{2}}{g^{3}}-\frac{a \,d^{2} \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\frac{a \,d^{2} c^{4} f^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{g^{4} \sqrt{c^{2} d}}-\frac{a \,d^{2} \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right) c^{4} f^{4}}{g^{5} \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{2 a \,d^{2} \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right) c^{2} f^{2}}{g^{3} \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{3 a \,c^{2} d^{2} f \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}\right)}{2 g^{2} \sqrt{c^{2} d}}+\frac{a \,c^{2} d f \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, x}{2 g^{2}}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f d c}{4 \left(c^{2} x^{2}-1\right) g^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{3} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{4 \left(c^{2} x^{2}-1\right) g^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x \,c^{3} f^{2}}{\left(c^{2} x^{2}-1\right) g^{3}}+\frac{b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \ln \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right) c^{2} f^{2}}{\left(c^{2} x^{2}-1\right) g^{4}}-\frac{b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \ln \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right) c^{2} f^{2}}{\left(c^{2} x^{2}-1\right) g^{4}}+\frac{i b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \dilog \left(\frac{i c f}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) c^{2} f^{2}}{\left(c^{2} x^{2}-1\right) g^{4}}-\frac{i b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \dilog \left(-\frac{i c f}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}-\frac{\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) c^{2} f^{2}}{\left(c^{2} x^{2}-1\right) g^{4}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{4} \arcsin \left(c x \right) x^{3}}{2 \left(c^{2} x^{2}-1\right) g^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f^{3} d \,c^{3}}{2 \left(c^{2} x^{2}-1\right) g^{4}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d \,c^{2} \arcsin \left(c x \right) x}{2 \left(c^{2} x^{2}-1\right) g^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{2} c^{4} f^{2}}{\left(c^{2} x^{2}-1\right) g^{3}}+\frac{b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \ln \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) g^{2}}-\frac{b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \ln \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right)}{\left(c^{2} x^{2}-1\right) g^{2}}+\frac{i b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \dilog \left(-\frac{i c f}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}-\frac{\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right)}{\left(c^{2} x^{2}-1\right) g^{2}}-\frac{i b \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, d \dilog \left(\frac{i c f}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}+\frac{\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right)}{\left(c^{2} x^{2}-1\right) g^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x^{3} c^{3}}{9 \left(c^{2} x^{2}-1\right) g}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \sqrt{-c^{2} x^{2}+1}\, x c}{3 \left(c^{2} x^{2}-1\right) g}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{4} c^{4}}{3 \left(c^{2} x^{2}-1\right) g}+\frac{5 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) x^{2} c^{2}}{3 \left(c^{2} x^{2}-1\right) g}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, d \arcsin \left(c x \right) c^{2} f^{2}}{\left(c^{2} x^{2}-1\right) g^{3}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f d c \sqrt{-c^{2} x^{2}+1}}{8 \left(c^{2} x^{2}-1\right) g^{2}}"," ",0,"1/3*a/g*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)+a/g*d*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-4/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)/g*arcsin(c*x)-a/g^3*d*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*c^2*f^2+I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^4*d*dilog(I/(I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))*c^2*f^2+b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^4*d*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)*c^2*f^2-b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^4*d*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)*c^2*f^2-I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^4*d*dilog(-I/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f-1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))*c^2*f^2-a/g*d^2/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-a/g^4*d^2*c^4*f^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))-a/g^5*d^2/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^4*f^4+2*a/g^3*d^2/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^2*f^2+3/2*a/g^2*c^2*d^2*f/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+1/2*a/g^2*c^2*d*f*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*x-3/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*f*d*c/g^2+b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^2*d*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)+1/4*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^3/(c^2*x^2-1)/g^2*(-c^2*x^2+1)^(1/2)*x^2-b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)/g^3*(-c^2*x^2+1)^(1/2)*x*c^3*f^2-b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^2*d*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)+I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^2*d*dilog(-I/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f-1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^4/(c^2*x^2-1)/g^2*arcsin(c*x)*x^3+1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*f^3*d*c^3/g^4-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c^2/(c^2*x^2-1)/g^2*arcsin(c*x)*x-b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)/g^3*arcsin(c*x)*x^2*c^4*f^2-I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)/g^2*d*dilog(I/(I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))-1/9*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)/g*(-c^2*x^2+1)^(1/2)*x^3*c^3+4/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)/g*(-c^2*x^2+1)^(1/2)*x*c-1/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)/g*arcsin(c*x)*x^4*c^4+5/3*b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)/g*arcsin(c*x)*x^2*c^2+b*(-d*(c^2*x^2-1))^(1/2)*d/(c^2*x^2-1)/g^3*arcsin(c*x)*c^2*f^2-1/8*b*(-d*(c^2*x^2-1))^(1/2)*f*d*c/(c^2*x^2-1)/g^2*(-c^2*x^2+1)^(1/2)","B"
40,1,5480,1133,1.472000," ","int((g*x+f)^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
41,1,6455,830,1.018000," ","int((g*x+f)^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
42,1,4030,453,0.794000," ","int((g*x+f)*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x)),x)","\text{output too large to display}"," ",0,"5/16*a*f*d^2*x*(-c^2*d*x^2+d)^(1/2)-1/36*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^4/(c^2*x^2-1)*x^5-29/288*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^2/(c^2*x^2-1)*x^3-1/160*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d^2/(c^2*x^2-1)*x^2-11/7840*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(6*arcsin(c*x))*d^2/(c^2*x^2-1)*x^2+11/7840*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(6*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-25/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)+1/3*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3-1/32*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d^2/(c^2*x^2-1)*arcsin(c*x)*x^2-1/112*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(6*arcsin(c*x))*d^2/(c^2*x^2-1)*arcsin(c*x)*x^2+1/112*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(6*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*arcsin(c*x)-5/192*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)+1/160*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-27/512*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)+1/98*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^6/(c^2*x^2-1)*x^8-9/392*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^4/(c^2*x^2-1)*x^6-23/1568*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^2/(c^2*x^2-1)*x^4+1/72*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^6/(c^2*x^2-1)*x^7-27/512*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+33/512*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*x^2+1/98*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^7-1/56*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^5+9/224*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-23/224*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/72*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^6-1/48*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4+1/8*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+1/32*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*arcsin(c*x)-9/64*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)-5/32*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*f*d^2+1/14*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^8-9/56*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^6+47/224*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4+1/12*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^6/(c^2*x^2-1)*arcsin(c*x)*x^7-1/6*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^4/(c^2*x^2-1)*arcsin(c*x)*x^5+29/4608*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(5*arcsin(c*x))*d^2*c/(c^2*x^2-1)*x^2-25/4608*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(5*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/32*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+3/16*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+27/15680*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(6*arcsin(c*x))*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-3/32*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)*x^2-1/14*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^7+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^5+1/32*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^3+5/192*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(5*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+9/64*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/16*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/12*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^5/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^6+1/8*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4+1/64*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+3/448*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(6*arcsin(c*x))*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-1/48*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(5*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)*x^2+3/320*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/6*a*f*x*(-c^2*d*x^2+d)^(5/2)+1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*arcsin(c*x)+3/32*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)+27/512*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*x^2+5/16*a*f*d^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/112*I*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(6*arcsin(c*x))*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+23/224*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/c^2/(c^2*x^2-1)*arcsin(c*x)-25/112*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c^2*x^2-1)*arcsin(c*x)*x^2-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2/(c^2*x^2-1)*arcsin(c*x)*x-3/320*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-33/512*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d^2/c/(c^2*x^2-1)-17/288*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+3/320*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d^2/(c^2*x^2-1)*x^2+27/15680*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(6*arcsin(c*x))*d^2/(c^2*x^2-1)*x^2-27/15680*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(6*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)-29/4608*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)-3/392*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/c^2/(c^2*x^2-1)+55/1568*I*b*(-d*(c^2*x^2-1))^(1/2)*g*d^2/(c^2*x^2-1)*x^2+11/96*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2/(c^2*x^2-1)*x+5/24*a*f*d*x*(-c^2*d*x^2+d)^(3/2)-1/7*a*g/c^2/d*(-c^2*d*x^2+d)^(7/2)-11/96*I*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)+3/448*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(6*arcsin(c*x))*d^2/c^2/(c^2*x^2-1)*arcsin(c*x)+1/48*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(5*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+3/32*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+5/192*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(5*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)*x^2+9/64*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(3*arcsin(c*x))*d^2*c/(c^2*x^2-1)*arcsin(c*x)*x^2+11/7840*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(6*arcsin(c*x))*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/160*b*(-d*(c^2*x^2-1))^(1/2)*g*cos(4*arcsin(c*x))*d^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/48*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(5*arcsin(c*x))*d^2/c/(c^2*x^2-1)*arcsin(c*x)-3/448*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(6*arcsin(c*x))*d^2/(c^2*x^2-1)*arcsin(c*x)*x^2+29/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(5*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-1/64*I*b*(-d*(c^2*x^2-1))^(1/2)*g*sin(4*arcsin(c*x))*d^2/(c^2*x^2-1)*arcsin(c*x)*x^2+33/512*I*b*(-d*(c^2*x^2-1))^(1/2)*f*cos(3*arcsin(c*x))*d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+25/4608*I*b*(-d*(c^2*x^2-1))^(1/2)*f*sin(5*arcsin(c*x))*d^2*c/(c^2*x^2-1)*x^2","C"
43,1,4685,1522,0.699000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))/(g*x+f),x)","\text{output too large to display}"," ",0,"-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2*c^5/(c^2*x^2-1)/g^4*(-c^2*x^2+1)^(1/2)*x^2-I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^2*dilog(I/(I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))-1/3*a/g^3*d*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)*c^2*f^2+a/g^5*d^2*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*c^4*f^4-2*a/g^3*d^2*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*c^2*f^2-23/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g*arcsin(c*x)+3*a/g^3*d^3/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^2*f^2+1/4*a/g^2*c^2*d*f*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)*x+7/8*a/g^2*c^2*d^2*f*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*x+15/8*a/g^2*c^2*d^3*f/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))-1/2*a/g^4*d^2*c^4*f^3*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*x+1/5*a/g*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(5/2)+I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^2*dilog(-I/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f-1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))+1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2*c^4/(c^2*x^2-1)/g^4*arcsin(c*x)*x+b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g^5*arcsin(c*x)*x^2*c^6*f^4-8/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g^3*arcsin(c*x)*x^2*c^4*f^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2*c^6/(c^2*x^2-1)/g^4*arcsin(c*x)*x^3-1/4*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^6/(c^2*x^2-1)/g^2*arcsin(c*x)*x^5+11/8*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^4/(c^2*x^2-1)/g^2*arcsin(c*x)*x^3-9/8*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^2/(c^2*x^2-1)/g^2*arcsin(c*x)*x+1/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g^3*arcsin(c*x)*x^4*c^6*f^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*f^5*d^2*c^5/g^6+5/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*f^3*d^2*c^3/g^4-15/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/(c^2*x^2-1)*arcsin(c*x)^2*f*d^2*c/g^2-b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^2*arcsin(c*x)*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))+b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^2*arcsin(c*x)*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))+b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g^5*(-c^2*x^2+1)^(1/2)*x*c^5*f^4-1/16*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^5/(c^2*x^2-1)/g^2*(-c^2*x^2+1)^(1/2)*x^4+9/16*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c^3/(c^2*x^2-1)/g^2*(-c^2*x^2+1)^(1/2)*x^2+1/9*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g^3*(-c^2*x^2+1)^(1/2)*x^3*c^5*f^2-7/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g^3*(-c^2*x^2+1)^(1/2)*x*c^3*f^2+1/3*a/g*d*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(3/2)+a/g*d^2*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-5/2*a/g^4*d^3*c^4*f^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+a/g^6*d^3*c^6*f^5/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))+a/g^7*d^3/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^6*f^6-3*a/g^5*d^3/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))*c^4*f^4-a/g*d^3/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))+7/3*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g^3*arcsin(c*x)*c^2*f^2-11/45*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g*(-c^2*x^2+1)^(1/2)*x^3*c^3+23/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g*(-c^2*x^2+1)^(1/2)*x*c+1/8*b*(-d*(c^2*x^2-1))^(1/2)*f^3*d^2*c^3/(c^2*x^2-1)/g^4*(-c^2*x^2+1)^(1/2)-33/128*b*(-d*(c^2*x^2-1))^(1/2)*f*d^2*c/(c^2*x^2-1)/g^2*(-c^2*x^2+1)^(1/2)+1/25*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g*(-c^2*x^2+1)^(1/2)*x^5*c^5-b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g^5*arcsin(c*x)*c^4*f^4+1/5*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g*arcsin(c*x)*x^6*c^6-14/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g*arcsin(c*x)*x^4*c^4+34/15*b*(-d*(c^2*x^2-1))^(1/2)*d^2/(c^2*x^2-1)/g*arcsin(c*x)*x^2*c^2+I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^6*dilog(-I/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f-1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))*c^4*f^4-b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^6*arcsin(c*x)*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*c^4*f^4+b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^6*arcsin(c*x)*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*c^4*f^4+2*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^4*arcsin(c*x)*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*c^2*f^2-2*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^4*arcsin(c*x)*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*c^2*f^2-I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^6*dilog(I/(I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))*c^4*f^4-2*I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^4*dilog(-I/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f-1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(-I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))*c^2*f^2+2*I*b*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*d^2/(c^2*x^2-1)/g^4*dilog(I/(I*c*f+(-c^2*f^2+g^2)^(1/2))*c*f+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(I*c*x+(-c^2*x^2+1)^(1/2))*g+1/(I*c*f+(-c^2*f^2+g^2)^(1/2))*(-c^2*f^2+g^2)^(1/2))*c^2*f^2","B"
44,1,843,402,1.243000," ","int((g*x+f)^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,g^{3} x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 c^{2} d}-\frac{2 a \,g^{3} \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,c^{4}}-\frac{3 a f \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{3 a f \,g^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{2} \sqrt{c^{2} d}}-\frac{3 a \,f^{2} g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+\frac{a \,f^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) f^{2}}{c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f \,g^{2}}{16 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g^{3} \cos \left(4 \arcsin \left(c x \right)\right)}{24 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)}{24 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sin \left(4 \arcsin \left(c x \right)\right)}{72 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f^{3}}{2 c d \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right) x^{2}}{3 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \cos \left(3 \arcsin \left(c x \right)\right)}{16 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f \,g^{2}}{4 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{13 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{-c^{2} x^{2}+1}\, x}{18 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) x^{2} f^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \arcsin \left(c x \right) x}{8 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, x \,f^{2}}{c d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/3*a*g^3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)-2/3*a*g^3/d/c^4*(-c^2*d*x^2+d)^(1/2)-3/2*a*f*g^2*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+3/2*a*f*g^2/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3*a*f^2*g/c^2/d*(-c^2*d*x^2+d)^(1/2)+a*f^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3*b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)*f^2+3/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*f*g^2-1/24*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*arcsin(c*x)*g^3*cos(4*arcsin(c*x))+17/24*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d/(c^2*x^2-1)*arcsin(c*x)+1/72*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*g^3*sin(4*arcsin(c*x))-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^2*f^3-2/3*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d/(c^2*x^2-1)*arcsin(c*x)*x^2+3/16*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*f*g^2*cos(3*arcsin(c*x))-3/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^2*f*g^2-13/18*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-3*b*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*arcsin(c*x)*x^2*f^2+3/8*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*f*g^2*arcsin(c*x)*sin(3*arcsin(c*x))+3/8*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*f*g^2*arcsin(c*x)*x-3*b*(-d*(c^2*x^2-1))^(1/2)*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*f^2","B"
45,1,548,242,0.871000," ","int((g*x+f)^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{a \,g^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{2} \sqrt{c^{2} d}}-\frac{2 a f g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+\frac{a \,f^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f^{2}}{2 c d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} g^{2}}{4 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \sqrt{-c^{2} x^{2}+1}\, x}{c d \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right) x^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right)}{c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2}}{16 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) x}{8 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \cos \left(3 \arcsin \left(c x \right)\right)}{16 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*a*g^2*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+1/2*a*g^2/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-2*a*f*g/c^2/d*(-c^2*d*x^2+d)^(1/2)+a*f^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^2*f^2-1/4*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^2*g^2-2*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-2*b*(-d*(c^2*x^2-1))^(1/2)*f*g/d/(c^2*x^2-1)*arcsin(c*x)*x^2+2*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)+1/16*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*g^2+1/8*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*g^2*arcsin(c*x)*x+1/16*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*cos(3*arcsin(c*x))+1/8*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*arcsin(c*x)*sin(3*arcsin(c*x))","B"
46,1,236,114,0.638000," ","int((g*x+f)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+\frac{a f \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f}{2 c d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, x}{c d \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) x^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)}{c^{2} d \left(c^{2} x^{2}-1\right)}"," ",0,"-a*g/c^2/d*(-c^2*d*x^2+d)^(1/2)+a*f/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^2*f-b*(-d*(c^2*x^2-1))^(1/2)*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-b*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*arcsin(c*x)*x^2+b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)","B"
47,1,502,374,0.390000," ","int((a+b*arcsin(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-c^{2} x^{2}+1}\, \left(i \ln \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right)-i \ln \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right)+\dilog \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right)-\dilog \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right)\right)}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)}"," ",0,"-a/g/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-I*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*f^2+g^2)^(1/2)*(-c^2*x^2+1)^(1/2)*(I*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)-I*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)+dilog((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))-dilog((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2))))/d/(c^2*x^2-1)/(c^2*f^2-g^2)","A"
48,1,1678,495,0.954000," ","int((a+b*arcsin(c*x))/(g*x+f)^2/(-c^2*d*x^2+d)^(1/2),x)","\frac{a \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{d \left(c^{2} f^{2}-g^{2}\right) \left(x +\frac{f}{g}\right)}-\frac{a \,c^{2} f \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{g \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \left(-c^{2} x^{2}+1\right) x \,c^{2} f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{3} c^{4} f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}+\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \sqrt{-c^{2} f^{2}+g^{2}}\, \dilog \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} c^{2} g}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}-\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \sqrt{-c^{2} f^{2}+g^{2}}\, \dilog \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,c^{2} f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \sqrt{-c^{2} f^{2}+g^{2}}\, f \arcsin \left(c x \right) \ln \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right)}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \sqrt{-c^{2} f^{2}+g^{2}}\, f \arcsin \left(c x \right) \ln \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right)}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c f}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x c g}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right) \left(g x +f \right)}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} g +2 i c f \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)-g \right) f^{2}}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}-\frac{2 b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) f^{2}}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \ln \left(\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2} g +2 i c f \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)-g \right) g^{2}}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}+\frac{2 b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g^{2}}{d \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}"," ",0,"a/d/(c^2*f^2-g^2)/(x+f/g)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)-a/g*c^2*f/(c^2*f^2-g^2)/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))+b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*(-c^2*x^2+1)*x*c^2*f+b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*x^3*c^4*f+I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/(c^2*f^2-g^2)^2*c^2*(-c^2*f^2+g^2)^(1/2)*dilog((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*f+b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*x^2*c^2*g+I*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*(-c^2*x^2+1)^(1/2)*c*f-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*x*c^2*f-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*g+b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/(c^2*f^2-g^2)^2*c^2*(-c^2*f^2+g^2)^(1/2)*f*arcsin(c*x)*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))-b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/(c^2*f^2-g^2)^2*c^2*(-c^2*f^2+g^2)^(1/2)*f*arcsin(c*x)*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))+I*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d/(c^2*x^2-1)/(c^2*f^2-g^2)/(g*x+f)*(-c^2*x^2+1)^(1/2)*x*c*g-I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/(c^2*f^2-g^2)^2*c^2*(-c^2*f^2+g^2)^(1/2)*dilog((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*f+b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/(c^2*f^2-g^2)^2*c^3*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2*g+2*I*c*f*(I*c*x+(-c^2*x^2+1)^(1/2))-g)*f^2-2*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/(c^2*f^2-g^2)^2*c^3*ln(I*c*x+(-c^2*x^2+1)^(1/2))*f^2-b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/(c^2*f^2-g^2)^2*c*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2*g+2*I*c*f*(I*c*x+(-c^2*x^2+1)^(1/2))-g)*g^2+2*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d/(c^2*x^2-1)/(c^2*f^2-g^2)^2*c*ln(I*c*x+(-c^2*x^2+1)^(1/2))*g^2","B"
49,1,1158,289,1.201000," ","int((g*x+f)^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a \,g^{3} x^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 a \,g^{3}}{d \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{3 a f \,g^{2} x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a f \,g^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{3 a \,f^{2} g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a \,f^{3} x}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,f^{3}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) f^{2} g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f^{3}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) g^{3}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f^{3}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) g^{3}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f^{2} g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f \,g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f^{2} g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f \,g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{-c^{2} x^{2}+1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \arcsin \left(c x \right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x f \,g^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f \,g^{2}}{2 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right) g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"-a*g^3*x^2/c^2/d/(-c^2*d*x^2+d)^(1/2)+2*a*g^3/d/c^4/(-c^2*d*x^2+d)^(1/2)+3*a*f*g^2*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-3*a*f*g^2/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3*a*f^2*g/c^2/d/(-c^2*d*x^2+d)^(1/2)+a*f^3/d*x/(-c^2*d*x^2+d)^(1/2)-b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*x*f^3-3*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*f^2*g-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c/d^2/(c^2*x^2-1)*f^3+b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^4/d^2/(c^2*x^2-1)*g^3-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f^3-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*g^3-2*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)+3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^2/d^2/(c^2*x^2-1)*f^2*g-3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^3/d^2/(c^2*x^2-1)*f*g^2-3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f^2*g-3*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f*g^2+b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*f^3*arcsin(c*x)-3*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*x*f*g^2+b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*x^2+3/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*arcsin(c*x)^2*f*g^2+3*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*f*arcsin(c*x)*g^2","C"
50,1,867,193,0.849000," ","int((g*x+f)^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a \,g^{2} x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a \,g^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{2 a f g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a \,f^{2} x}{d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2} \arcsin \left(c x \right)^{2}}{2 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) f^{2}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \left(-c^{2} x^{2}+1\right) f g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} f g}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,f^{2}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,g^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f^{2}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f^{2}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a*g^2*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-a*g^2/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+2*a*f*g/c^2/d/(-c^2*d*x^2+d)^(1/2)+a*f^2/d*x/(-c^2*d*x^2+d)^(1/2)+1/2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*g^2*arcsin(c*x)^2+I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*arcsin(c*x)*g^2+I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*arcsin(c*x)*f^2-2*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/c^2/d^2/(c^2*x^2-1)*(-c^2*x^2+1)*f*g-2*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)*x^2*f*g-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)*x*f^2-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/c^2/d^2/(c^2*x^2-1)*x*g^2-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f^2-2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f*g-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*g^2-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)*f^2+2*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)*f*g-b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)*g^2","C"
51,1,443,130,0.652000," ","int((g*x+f)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(3/2),x)","\frac{a g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a f x}{d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x f}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a*g/c^2/d/(-c^2*d*x^2+d)^(1/2)+a*f/d*x/(-c^2*d*x^2+d)^(1/2)+I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*f*arcsin(c*x)-b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*x*f-b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*g-b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c/d^2/(c^2*x^2-1)*f+b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^2/d^2/(c^2*x^2-1)*g-b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f-b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*g","C"
52,1,1519,612,0.816000," ","int((a+b*arcsin(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x)","-\frac{a g}{d \left(c^{2} f^{2}-g^{2}\right) \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a f \,c^{2} x}{\left(c^{2} f^{2}-g^{2}\right) d \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}+\frac{a g \ln \left(\frac{-\frac{2 d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}+2 \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}\, \sqrt{-c^{2} d \left(x +\frac{f}{g}\right)^{2}+\frac{2 c^{2} d f \left(x +\frac{f}{g}\right)}{g}-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}{x +\frac{f}{g}}\right)}{d \left(c^{2} f^{2}-g^{2}\right) \sqrt{-\frac{d \left(c^{2} f^{2}-g^{2}\right)}{g^{2}}}}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c f}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,c^{2} f}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)}+\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \left(-c^{2} f^{2}+g^{2}\right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) c f}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \left(-c^{2} f^{2}+g^{2}\right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) c f}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}-\frac{2 b \sqrt{-c^{2} x^{2}+1}\, \left(-c^{2} f^{2}+g^{2}\right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) c f}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}-\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) g^{2}}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}+\frac{i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \dilog \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) g^{2}}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(\frac{-i c f -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{-i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right) g^{2}}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-c^{2} f^{2}+g^{2}}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(\frac{i c f +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) g +\sqrt{-c^{2} f^{2}+g^{2}}}{i c f +\sqrt{-c^{2} f^{2}+g^{2}}}\right) \arcsin \left(c x \right) g^{2}}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \left(-c^{2} f^{2}+g^{2}\right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) g}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \left(-c^{2} f^{2}+g^{2}\right) \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) g}{d^{2} \left(c^{2} x^{2}-1\right) \left(c^{2} f^{2}-g^{2}\right)^{2}}"," ",0,"-a*g/d/(c^2*f^2-g^2)/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)+a*f/(c^2*f^2-g^2)/d/(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2)*c^2*x+a*g/d/(c^2*f^2-g^2)/(-d*(c^2*f^2-g^2)/g^2)^(1/2)*ln((-2*d*(c^2*f^2-g^2)/g^2+2*c^2*d*f/g*(x+f/g)+2*(-d*(c^2*f^2-g^2)/g^2)^(1/2)*(-c^2*d*(x+f/g)^2+2*c^2*d*f/g*(x+f/g)-d*(c^2*f^2-g^2)/g^2)^(1/2))/(x+f/g))-I*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)*(-c^2*x^2+1)^(1/2)*c*f-b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)*x*c^2*f+b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)*g+b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*c*f+b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)*c*f-2*b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*ln(I*c*x+(-c^2*x^2+1)^(1/2))*c*f-I*b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*dilog((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*g^2+I*b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*dilog((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*g^2-b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*ln((-I*c*f-(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(-I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)*g^2+b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*ln((I*c*f+(I*c*x+(-c^2*x^2+1)^(1/2))*g+(-c^2*f^2+g^2)^(1/2))/(I*c*f+(-c^2*f^2+g^2)^(1/2)))*arcsin(c*x)*g^2-b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*g+b*(-c^2*x^2+1)^(1/2)*(-c^2*f^2+g^2)*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)/(c^2*f^2-g^2)^2*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)*g","B"
53,1,6743,482,2.691000," ","int((g*x+f)^4*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
54,1,5098,372,1.179000," ","int((g*x+f)^3*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
55,1,3765,245,0.962000," ","int((g*x+f)^2*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)*x^2*g^2+4*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*arcsin(c*x)*x^3*g^2+I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*x*f^2-6*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)*x^2*f*g+7*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*x^5*g^2+17/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*x^3*f^2-2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*x^7*g^2-2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*x^5*f^2-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*x^2*f^2+1/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)/c^3/d^3/(c^2*x^2-1)*g^2-2/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c/d^3/(c^2*x^2-1)*f^2+1/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^3/d^3/(c^2*x^2-1)*g^2+1/3*a*g^2/c^2*x/d/(-c^2*d*x^2+d)^(3/2)-1/3*a*g^2/c^2/d^2*x/(-c^2*d*x^2+d)^(1/2)+2/3*a*f*g/c^2/d/(-c^2*d*x^2+d)^(3/2)-2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c^2*(-c^2*x^2+1)*arcsin(c*x)*x*g^2-8/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c^2*(-c^2*x^2+1)*arcsin(c*x)*f*g+4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)*x*f*g+2*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*x^2*f*g+16/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*arcsin(c*x)*x^2*f*g+1/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^2/d^3/(c^2*x^2-1)*f*g-14/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*x^6*f*g+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*x^5*g^2-5/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*x^3*f^2+16/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*x^4*f*g-8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*f^2+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*g^2+4/3*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/c/d^3/(c^2*x^2-1)*f^2-2/3*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/c^3/d^3/(c^2*x^2-1)*g^2+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6*x^8*f*g+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*(-c^2*x^2+1)*x^5*f^2+8*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*x^4*f*g-b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*x^3*f*g+I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c^2*(-c^2*x^2+1)*x*g^2-1/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)/c^2/d^3/(c^2*x^2-1)*f*g-8/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*x^6*f*g-2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*arcsin(c*x)*x^5*g^2-4*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)*x*f^2-22/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)*x^3*g^2+2/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)*f^2+2/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c^3*(-c^2*x^2+1)^(1/2)*g^2-I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*x*f^2+8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*x^3*g^2+2/3*a*f^2/d^2*x/(-c^2*d*x^2+d)^(1/2)-7/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2*g^2+4/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*(-c^2*x^2+1)*x^6*f*g-8/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*arcsin(c*x)*x^4*f*g+I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4*g^2-2*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4*f^2-10/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*x^4*f*g+14/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2*f^2-2*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*x^2*f*g-I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c^2*x*g^2+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6*x^7*f^2+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*x^7*g^2+2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c^2*arcsin(c*x)*x*g^2-2/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)/c/d^3/(c^2*x^2-1)*f^2-7/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*x^5*f^2-7/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*x^5*g^2+8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*x^3*f^2-5/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*x^3*g^2+1/3*a*f^2*x/d/(-c^2*d*x^2+d)^(3/2)","C"
56,1,2236,202,0.759000," ","int((g*x+f)*(a+b*arcsin(c*x))/(-c^2*d*x^2+d)^(5/2),x)","-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, x^{2} g}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f x}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{3} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{4} f}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{14 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2} f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{4 i b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right)}{3 c \,d^{3} \left(c^{2} x^{2}-1\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f x \arcsin \left(c x \right)}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) c}-\frac{3 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} g}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{a f x}{3 d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}+\frac{2 a f x}{3 d^{2} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a g}{3 c^{2} d \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \left(-c^{2} x^{2}+1\right) \arcsin \left(c x \right) x^{4} g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) c}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \left(-c^{2} x^{2}+1\right) x^{3} f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \left(-c^{2} x^{2}+1\right) x^{5} f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{5 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \left(-c^{2} x^{2}+1\right) x^{4} g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \left(-c^{2} x^{2}+1\right) x^{6} g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{4} g}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{17 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} \arcsin \left(c x \right) x^{3} f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \arcsin \left(c x \right) x^{6} g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} \arcsin \left(c x \right) x^{5} f}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{8 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) \arcsin \left(c x \right) x^{2} g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{4 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) \arcsin \left(c x \right) g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) c^{2}}+\frac{2 b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, x g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right) c}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{3} g}{2 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c \sqrt{-c^{2} x^{2}+1}\, x^{2} f}{2 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) g}{6 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}-\frac{2 b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f}{3 c \,d^{3} \left(c^{2} x^{2}-1\right)}+\frac{b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) g}{6 c^{2} d^{3} \left(c^{2} x^{2}-1\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{6} x^{7} f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} x^{6} g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{7 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{4} x^{5} f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{2 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{6} x^{8} g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{4} g}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{8 i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, c^{2} x^{3} f}{3 d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}-\frac{2 b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f}{3 c \,d^{3} \left(c^{2} x^{2}-1\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) x f}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}+\frac{i b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \left(-c^{2} x^{2}+1\right) x^{2} g}{d^{3} \left(3 c^{6} x^{6}-10 c^{4} x^{4}+11 c^{2} x^{2}-4\right)}"," ",0,"-4*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*f*x*arcsin(c*x)+2/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)*f-I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*x^2*g-I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*f*x-3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*arcsin(c*x)*x^2*g+1/3*a*f*x/d/(-c^2*d*x^2+d)^(3/2)+2/3*a*f/d^2*x/(-c^2*d*x^2+d)^(1/2)+1/3*a*g/c^2/d/(-c^2*d*x^2+d)^(3/2)+4/3*I*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^3/(c^2*x^2-1)*f*arcsin(c*x)-8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*f-5/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*x^3*f+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*(-c^2*x^2+1)*x^5*f-4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*arcsin(c*x)*x^4*g-5/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*(-c^2*x^2+1)*x^4*g+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*(-c^2*x^2+1)*x^6*g-1/6*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*g-2/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c/d^3/(c^2*x^2-1)*f+1/6*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^2/d^3/(c^2*x^2-1)*g+4*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*x^4*g+17/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*arcsin(c*x)*x^3*f+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6*x^7*f-7/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*x^6*g-7/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*x^5*f+2/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^6*x^8*g+8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*x^4*g+8/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^2*x^3*f-4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*x^6*g-2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^4*arcsin(c*x)*x^5*f-2/3*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^3/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f+I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*x*f+8/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*arcsin(c*x)*x^2*g-4/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c^2*(-c^2*x^2+1)*arcsin(c*x)*g+2/3*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)/c*(-c^2*x^2+1)^(1/2)*x*g-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*x^3*g-1/2*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*x^2*f+I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*(-c^2*x^2+1)*x^2*g-2*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c^3*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4*f+14/3*I*b*(-d*(c^2*x^2-1))^(1/2)/d^3/(3*c^6*x^6-10*c^4*x^4+11*c^2*x^2-4)*c*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2*f","C"
57,1,8289,1102,0.806000," ","int((a+b*arcsin(c*x))/(g*x+f)/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
58,1,2947,1020,1.698000," ","int((g*x+f)^3*(a+b*arcsin(c*x))^2*(-c^2*d*x^2+d)^(1/2),x)","\text{output too large to display}"," ",0,"3/8*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c^2/(c^2*x^2-1)*arcsin(c*x)^2*x+b^2*(-d*(c^2*x^2-1))^(1/2)*g*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^4*f^2+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f^3*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+2/25*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^5-2/45*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^3-4/15*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+3/64*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^3*f*g^2+3/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^5+2*a*b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/(c^2*x^2-1)*arcsin(c*x)*f^2+a*b*(-d*(c^2*x^2-1))^(1/2)*f^3*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+2/25*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^5-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*f^3+2/5*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3*c^2/(c^2*x^2-1)*arcsin(c*x)*x^6-2/15*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/(c^2*x^2-1)*arcsin(c*x)*x^2-2/45*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-4/15*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-9/4*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/(c^2*x^2-1)*arcsin(c*x)*x^3+3/64*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-4*a*b*(-d*(c^2*x^2-1))^(1/2)*g/(c^2*x^2-1)*arcsin(c*x)*x^2*f^2+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*f^3*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+3/2*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5+3/4*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c^2/(c^2*x^2-1)*arcsin(c*x)*x+2*a*b*(-d*(c^2*x^2-1))^(1/2)*g*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4*f^2-3/8*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*g*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^3*f^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x*f^2+3/8*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^4+3/8*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-3/8*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*g*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3*f^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)*g/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*f^2-3/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2*f*g^2-4/15*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/(c^2*x^2-1)*arcsin(c*x)^2*x^4+9/64*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2/(c^2*x^2-1)*x^3+16/9*b^2*(-d*(c^2*x^2-1))^(1/2)*g/(c^2*x^2-1)*x^2*f^2-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f^3/(c^2*x^2-1)*arcsin(c*x)^2*x-2/125*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3*c^2/(c^2*x^2-1)*x^6+878/3375*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/(c^2*x^2-1)*x^2+2/15*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/(c^2*x^2-1)*arcsin(c*x)^2-14/9*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c^2/(c^2*x^2-1)*f^2-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f^3*c^2/(c^2*x^2-1)*x^3-1/5*a^2*g^3*x^2*(-c^2*d*x^2+d)^(3/2)/c^2/d+3/8*a^2*f*g^2/c^2*x*(-c^2*d*x^2+d)^(1/2)-a^2*f^2*g/c^2/d*(-c^2*d*x^2+d)^(3/2)+32/3375*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/(c^2*x^2-1)*x^4+1/2*a^2*f^3*x*(-c^2*d*x^2+d)^(1/2)-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f^3/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^3*f^3+1/5*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^6-1/15*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^2-3/32*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2*c^2/(c^2*x^2-1)*x^5-3/64*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2/c^2/(c^2*x^2-1)*x-2/9*b^2*(-d*(c^2*x^2-1))^(1/2)*g*c^2/(c^2*x^2-1)*x^4*f^2+b^2*(-d*(c^2*x^2-1))^(1/2)*g/c^2/(c^2*x^2-1)*arcsin(c*x)^2*f^2+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f^3*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^3-9/8*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g^2/(c^2*x^2-1)*arcsin(c*x)^2*x^3-2*b^2*(-d*(c^2*x^2-1))^(1/2)*g/(c^2*x^2-1)*arcsin(c*x)^2*x^2*f^2-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*f^3/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-a*b*(-d*(c^2*x^2-1))^(1/2)*f^3/(c^2*x^2-1)*arcsin(c*x)*x+4/15*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/(c^2*x^2-1)*arcsin(c*x)-8/15*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/(c^2*x^2-1)*arcsin(c*x)*x^4+3/8*a^2*f*g^2/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3/4*a^2*f*g^2*x*(-c^2*d*x^2+d)^(3/2)/c^2/d+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f^3/(c^2*x^2-1)*x-2/15*a^2*g^3/d/c^4*(-c^2*d*x^2+d)^(3/2)+1/2*a^2*f^3*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-856/3375*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/(c^2*x^2-1)","B"
59,1,2051,647,1.019000," ","int((g*x+f)^2*(a+b*arcsin(c*x))^2*(-c^2*d*x^2+d)^(1/2),x)","\frac{a^{2} f^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} c \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 c^{2} x^{2}-2}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g c \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{3}}{9 \left(c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x}{3 c \left(c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,c^{2} \arcsin \left(c x \right) x^{4}}{3 \left(c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g c \sqrt{-c^{2} x^{2}+1}\, x^{3}}{9 \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \sqrt{-c^{2} x^{2}+1}\, x}{3 c \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} x}{4 c^{2} x^{2}-4}+\frac{a^{2} g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{8 c^{2}}+\frac{a^{2} f^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} c \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{4}}{8 c^{2} x^{2}-8}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} x^{3}}{64 \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} c \sqrt{-c^{2} x^{2}+1}\, x^{4}}{8 c^{2} x^{2}-8}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} c^{2} \arcsin \left(c x \right)^{2} x^{3}}{2 c^{2} x^{2}-2}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} c^{2} \arcsin \left(c x \right)^{2} x^{5}}{4 c^{2} x^{2}-4}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) x}{4 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f^{2}}{2 c \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} g^{2}}{8 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, x^{2}}{8 c \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,c^{2} \arcsin \left(c x \right)^{2} x^{4}}{3 \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} f^{2}}{6 c \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} g^{2}}{24 c^{3} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right)^{2} x}{8 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,c^{2} x^{4}}{27 \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right)^{2}}{3 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right)^{2} x^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{64 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{4 c \left(c^{2} x^{2}-1\right)}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) x^{3}}{4 \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \sqrt{-c^{2} x^{2}+1}}{64 c^{3} \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} \arcsin \left(c x \right) x}{c^{2} x^{2}-1}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} \sqrt{-c^{2} x^{2}+1}}{4 c \left(c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right)}{3 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} c^{2} \arcsin \left(c x \right) x^{3}}{c^{2} x^{2}-1}-\frac{8 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \sqrt{-c^{2} x^{2}+1}\, x^{2}}{8 c \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} c^{2} \arcsin \left(c x \right) x^{5}}{2 c^{2} x^{2}-2}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 c^{2} x^{2}-2}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} \arcsin \left(c x \right)^{2} x}{2 \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} c^{2} x^{5}}{32 \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} x}{64 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{2} c^{2} x^{3}}{4 \left(c^{2} x^{2}-1\right)}-\frac{28 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g}{27 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right)^{2} x^{3}}{8 \left(c^{2} x^{2}-1\right)}+\frac{32 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,x^{2}}{27 \left(c^{2} x^{2}-1\right)}+\frac{a^{2} g^{2} d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{8 c^{2} \sqrt{c^{2} d}}-\frac{2 a^{2} f g \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}-\frac{a^{2} g^{2} x \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{4 c^{2} d}"," ",0,"1/2*a^2*f^2*x*(-c^2*d*x^2+d)^(1/2)+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f^2/(c^2*x^2-1)*x+4/9*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^3-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4+4/9*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/8*a^2*g^2/c^2*x*(-c^2*d*x^2+d)^(1/2)+1/2*a^2*f^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3/64*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2/(c^2*x^2-1)*x^3+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*g^2/c^2/(c^2*x^2-1)*arcsin(c*x)*x+1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*g^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^4-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*f^2-1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^2*g^2+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^4-1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2/c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f^2*c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*x^2+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^4-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^3*f^2-1/24*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/(c^2*x^2-1)*arcsin(c*x)^3*g^2+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^5+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2/c^2/(c^2*x^2-1)*arcsin(c*x)^2*x-4/27*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g*c^2/(c^2*x^2-1)*x^4+2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/(c^2*x^2-1)*arcsin(c*x)^2+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f^2*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^3-4/3*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/(c^2*x^2-1)*arcsin(c*x)^2*x^2+1/64*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2/c^3/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f^2/c/(c^2*x^2-1)*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-3/4*a*b*(-d*(c^2*x^2-1))^(1/2)*g^2/(c^2*x^2-1)*arcsin(c*x)*x^3+1/64*a*b*(-d*(c^2*x^2-1))^(1/2)*g^2/c^3/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-a*b*(-d*(c^2*x^2-1))^(1/2)*f^2/(c^2*x^2-1)*arcsin(c*x)*x-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*f^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)+4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/(c^2*x^2-1)*arcsin(c*x)+a*b*(-d*(c^2*x^2-1))^(1/2)*f^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*g^2*c^2/(c^2*x^2-1)*arcsin(c*x)*x^5+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*f^2*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-8/3*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g/(c^2*x^2-1)*arcsin(c*x)*x^2-1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*g^2/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f^2/(c^2*x^2-1)*arcsin(c*x)^2*x-1/32*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2*c^2/(c^2*x^2-1)*x^5-1/64*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2/c^2/(c^2*x^2-1)*x-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f^2*c^2/(c^2*x^2-1)*x^3-28/27*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/(c^2*x^2-1)-3/8*b^2*(-d*(c^2*x^2-1))^(1/2)*g^2/(c^2*x^2-1)*arcsin(c*x)^2*x^3+32/27*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/(c^2*x^2-1)*x^2+1/8*a^2*g^2/c^2*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-2/3*a^2*f*g/c^2/d*(-c^2*d*x^2+d)^(3/2)-1/4*a^2*g^2*x*(-c^2*d*x^2+d)^(3/2)/c^2/d","B"
60,1,1139,346,0.789000," ","int((g*x+f)*(a+b*arcsin(c*x))^2*(-c^2*d*x^2+d)^(1/2),x)","-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) x^{2}}{3 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,c^{2} \arcsin \left(c x \right)^{2} x^{4}}{3 c^{2} x^{2}-3}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,c^{2} \arcsin \left(c x \right)^{2} x^{3}}{2 c^{2} x^{2}-2}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,c^{2} \arcsin \left(c x \right) x^{3}}{c^{2} x^{2}-1}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g c \sqrt{-c^{2} x^{2}+1}\, x^{3}}{9 \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, x}{3 c \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f}{2 c \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,c^{2} \arcsin \left(c x \right) x^{4}}{3 \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{3}}{9 \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{3 c \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f c \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x^{2}}{2 c^{2} x^{2}-2}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f c \sqrt{-c^{2} x^{2}+1}\, x^{2}}{2 c^{2} x^{2}-2}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,c^{2} x^{4}}{27 \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)^{2}}{3 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,c^{2} x^{3}}{4 \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)^{2} x^{2}}{3 \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right)^{2} x}{2 \left(c^{2} x^{2}-1\right)}+\frac{a^{2} f d \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 \sqrt{c^{2} d}}-\frac{a^{2} g \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}{3 c^{2} d}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sqrt{-c^{2} x^{2}+1}}{4 c \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right) x}{c^{2} x^{2}-1}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)}{3 c^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)}{4 c \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} f}{6 c \left(c^{2} x^{2}-1\right)}-\frac{14 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g}{27 c^{2} \left(c^{2} x^{2}-1\right)}+\frac{16 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,x^{2}}{27 \left(c^{2} x^{2}-1\right)}+\frac{a^{2} f x \sqrt{-c^{2} d \,x^{2}+d}}{2}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f x}{4 c^{2} x^{2}-4}"," ",0,"-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*g/(c^2*x^2-1)*arcsin(c*x)*x^2+a*b*(-d*(c^2*x^2-1))^(1/2)*f*c^2/(c^2*x^2-1)*arcsin(c*x)*x^3+2/9*a*b*(-d*(c^2*x^2-1))^(1/2)*g*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^3-2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*g/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*f*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x^2-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^2*f+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*g*c^2/(c^2*x^2-1)*arcsin(c*x)*x^4+2/9*b^2*(-d*(c^2*x^2-1))^(1/2)*g*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^3-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f*c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x^2-2/27*b^2*(-d*(c^2*x^2-1))^(1/2)*g*c^2/(c^2*x^2-1)*x^4+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c^2/(c^2*x^2-1)*arcsin(c*x)^2-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f*c^2/(c^2*x^2-1)*x^3-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*g/(c^2*x^2-1)*arcsin(c*x)^2*x^2-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f/(c^2*x^2-1)*arcsin(c*x)^2*x+1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f/(c^2*x^2-1)*x+1/2*a^2*f*d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/3*a^2*g/c^2/d*(-c^2*d*x^2+d)^(3/2)-1/4*a*b*(-d*(c^2*x^2-1))^(1/2)*f/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)-a*b*(-d*(c^2*x^2-1))^(1/2)*f/(c^2*x^2-1)*arcsin(c*x)*x+2/3*a*b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/(c^2*x^2-1)*arcsin(c*x)-1/4*b^2*(-d*(c^2*x^2-1))^(1/2)*f/c/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/(c^2*x^2-1)*arcsin(c*x)^3*f+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*g*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^4+1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*f*c^2/(c^2*x^2-1)*arcsin(c*x)^2*x^3-14/27*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c^2/(c^2*x^2-1)+16/27*b^2*(-d*(c^2*x^2-1))^(1/2)*g/(c^2*x^2-1)*x^2+1/2*a^2*f*x*(-c^2*d*x^2+d)^(1/2)","B"
61,0,0,1382,0.802000," ","int((a+b*arcsin(c*x))^2*(-c^2*d*x^2+d)^(1/2)/(g*x+f),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2} \sqrt{-c^{2} d \,x^{2}+d}}{g x +f}\, dx"," ",0,"int((a+b*arcsin(c*x))^2*(-c^2*d*x^2+d)^(1/2)/(g*x+f),x)","F"
62,1,12962,1495,1.692000," ","int((g*x+f)^3*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
63,1,9278,980,1.213000," ","int((g*x+f)^2*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
64,1,5957,547,0.937000," ","int((g*x+f)*(-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
65,0,0,1882,0.661000," ","int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/(g*x+f),x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{g x +f}\, dx"," ",0,"int((-c^2*d*x^2+d)^(3/2)*(a+b*arcsin(c*x))^2/(g*x+f),x)","F"
66,1,11465,2048,1.966000," ","int((g*x+f)^3*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
67,1,16441,1367,1.073000," ","int((g*x+f)^2*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
68,1,10373,780,1.093000," ","int((g*x+f)*(-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
69,0,0,2791,0.811000," ","int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/(g*x+f),x)","\int \frac{\left(-c^{2} d \,x^{2}+d \right)^{\frac{5}{2}} \left(a +b \arcsin \left(c x \right)\right)^{2}}{g x +f}\, dx"," ",0,"int((-c^2*d*x^2+d)^(5/2)*(a+b*arcsin(c*x))^2/(g*x+f),x)","F"
70,1,1886,624,1.428000," ","int((g*x+f)^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} f \,g^{2}}{2 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{13 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{-c^{2} x^{2}+1}\, x}{9 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) x^{2} f^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \cos \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g^{3} \cos \left(4 \arcsin \left(c x \right)\right)}{12 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f^{3}}{c d \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right) x^{2}}{3 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{4 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{2 a^{2} g^{3} \sqrt{-c^{2} d \,x^{2}+d}}{3 d \,c^{4}}-\frac{161 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3}}{108 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{a^{2} g^{3} x^{2} \sqrt{-c^{2} d \,x^{2}+d}}{3 c^{2} d}+\frac{3 a^{2} f \,g^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{2} \sqrt{c^{2} d}}-\frac{3 a^{2} f^{2} g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f \,g^{2}}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) f^{2}}{c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} f x \arcsin \left(c x \right)^{2}}{8 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} f \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{8 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{13 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{9 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2} f \arcsin \left(c x \right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} f \arcsin \left(c x \right) \cos \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{6 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,x^{2} f^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \cos \left(4 \arcsin \left(c x \right)\right)}{108 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{40 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} x^{2}}{27 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{17 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)^{2}}{24 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{6 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,f^{2}}{c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{3 a^{2} f \,g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}+\frac{a^{2} f^{3} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{6 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x \,f^{2}}{c d \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \,g^{2} \arcsin \left(c x \right) x}{4 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f \,g^{2}}{2 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, x \,f^{2}}{c d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g^{3} \sin \left(4 \arcsin \left(c x \right)\right)}{36 c^{4} d \left(c^{2} x^{2}-1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)^{2} x^{2} f^{2}}{d \left(c^{2} x^{2}-1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} f x}{16 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} f \sin \left(3 \arcsin \left(c x \right)\right)}{16 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} f^{3}}{3 c d \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)^{2} x^{2}}{3 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)^{2} f^{2}}{c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \cos \left(4 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{24 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{17 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)}{12 c^{4} d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sin \left(4 \arcsin \left(c x \right)\right)}{36 c^{4} d \left(c^{2} x^{2}-1\right)}"," ",0,"-1/2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^3*f*g^2-13/9*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-6*a*b*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*arcsin(c*x)*x^2*f^2+3/8*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*f*g^2*cos(3*arcsin(c*x))-1/12*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*arcsin(c*x)*g^3*cos(4*arcsin(c*x))-a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^2*f^3-4/3*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d/(c^2*x^2-1)*arcsin(c*x)*x^2+3/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*f*g^2*arcsin(c*x)*sin(3*arcsin(c*x))-2/3*a^2*g^3/d/c^4*(-c^2*d*x^2+d)^(1/2)-161/108*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d/(c^2*x^2-1)-1/3*a^2*g^3*x^2/c^2/d*(-c^2*d*x^2+d)^(1/2)+3/2*a^2*f*g^2/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-3*a^2*f^2*g/c^2/d*(-c^2*d*x^2+d)^(1/2)+3/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*f*g^2+6*a*b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)*f^2+3/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*g^2*f*x*arcsin(c*x)^2+3/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*f*sin(3*arcsin(c*x))*arcsin(c*x)^2-13/9*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+3/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*g^2*f*arcsin(c*x)+3/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*f*arcsin(c*x)*cos(3*arcsin(c*x))+6*b^2*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*x^2*f^2+1/108*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*g^3*cos(4*arcsin(c*x))+40/27*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d/(c^2*x^2-1)*x^2+17/24*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d/(c^2*x^2-1)*arcsin(c*x)^2-6*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)*f^2-3/2*a^2*f*g^2*x/c^2/d*(-c^2*d*x^2+d)^(1/2)+a^2*f^3/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-6*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x*f^2+3/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*f*g^2*arcsin(c*x)*x-3/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^2*f*g^2-6*a*b*(-d*(c^2*x^2-1))^(1/2)*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x*f^2+1/36*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*arcsin(c*x)*g^3*sin(4*arcsin(c*x))-3*b^2*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*arcsin(c*x)^2*x^2*f^2-3/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*g^2*f*x-3/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*f*sin(3*arcsin(c*x))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^3*f^3-2/3*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d/(c^2*x^2-1)*arcsin(c*x)^2*x^2+3*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)^2*f^2-1/24*b^2*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*g^3*cos(4*arcsin(c*x))*arcsin(c*x)^2+17/12*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d/(c^2*x^2-1)*arcsin(c*x)+1/36*a*b*(-d*(c^2*x^2-1))^(1/2)/c^4/d/(c^2*x^2-1)*g^3*sin(4*arcsin(c*x))","B"
71,1,1187,370,1.000000," ","int((g*x+f)^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) \sin \left(3 \arcsin \left(c x \right)\right)}{4 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f^{2}}{c d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} f^{2}}{3 c d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} g^{2}}{6 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right)^{2}}{c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2}}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \cos \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right)^{2} x^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2}}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2} \arcsin \left(c x \right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} x \arcsin \left(c x \right)^{2}}{8 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) \cos \left(3 \arcsin \left(c x \right)\right)}{8 c^{3} d \left(c^{2} x^{2}-1\right)}+\frac{a^{2} g^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{2 c^{2} \sqrt{c^{2} d}}-\frac{2 a^{2} f g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}-\frac{a^{2} g^{2} x \sqrt{-c^{2} d \,x^{2}+d}}{2 c^{2} d}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} g^{2}}{2 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right) x^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \arcsin \left(c x \right)}{c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \arcsin \left(c x \right) x}{4 c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} \sin \left(3 \arcsin \left(c x \right)\right)}{16 c^{3} d \left(c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g}{c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \,x^{2}}{d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{2} x}{16 c^{2} d \left(c^{2} x^{2}-1\right)}+\frac{a^{2} f^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{c d \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f g \sqrt{-c^{2} x^{2}+1}\, x}{c d \left(c^{2} x^{2}-1\right)}"," ",0,"1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*arcsin(c*x)*sin(3*arcsin(c*x))-a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^2*f^2-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^3*f^2-1/6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^3*g^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)^2+1/8*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*g^2+1/8*a*b*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*cos(3*arcsin(c*x))-2*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/d/(c^2*x^2-1)*arcsin(c*x)^2*x^2+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*sin(3*arcsin(c*x))*arcsin(c*x)^2+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*g^2*arcsin(c*x)+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*g^2*x*arcsin(c*x)^2+1/8*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*arcsin(c*x)*cos(3*arcsin(c*x))+1/2*a^2*g^2/c^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-2*a^2*f*g/c^2/d*(-c^2*d*x^2+d)^(1/2)-1/2*a^2*g^2*x/c^2/d*(-c^2*d*x^2+d)^(1/2)-1/2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d/(c^2*x^2-1)*arcsin(c*x)^2*g^2-4*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g/d/(c^2*x^2-1)*arcsin(c*x)*x^2+4*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)+1/4*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*g^2*arcsin(c*x)*x-1/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d/(c^2*x^2-1)*g^2*sin(3*arcsin(c*x))-4*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/c^2/d/(c^2*x^2-1)+4*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/d/(c^2*x^2-1)*x^2-1/16*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d/(c^2*x^2-1)*g^2*x+a^2*f^2/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-4*b^2*(-d*(c^2*x^2-1))^(1/2)*f*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-4*a*b*(-d*(c^2*x^2-1))^(1/2)*f*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x","B"
72,1,513,157,0.669000," ","int((g*x+f)*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(1/2),x)","-\frac{a^{2} g \sqrt{-c^{2} d \,x^{2}+d}}{c^{2} d}+\frac{a^{2} f \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{\sqrt{c^{2} d}}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} f}{3 c d \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{c d \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)^{2} x^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \,x^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)^{2}}{c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g}{c^{2} d \left(c^{2} x^{2}-1\right)}-\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f}{c d \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \sqrt{-c^{2} x^{2}+1}\, x}{c d \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) x^{2}}{d \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right)}{c^{2} d \left(c^{2} x^{2}-1\right)}"," ",0,"-a^2*g/c^2/d*(-c^2*d*x^2+d)^(1/2)+a^2*f/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))-1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^3*f-2*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x-b^2*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*arcsin(c*x)^2*x^2+2*b^2*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*x^2+b^2*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)-a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d/(c^2*x^2-1)*arcsin(c*x)^2*f-2*a*b*(-d*(c^2*x^2-1))^(1/2)*g/c/d/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x-2*a*b*(-d*(c^2*x^2-1))^(1/2)*g/d/(c^2*x^2-1)*arcsin(c*x)*x^2+2*a*b*(-d*(c^2*x^2-1))^(1/2)*g/c^2/d/(c^2*x^2-1)*arcsin(c*x)","B"
73,0,0,579,1.092000," ","int((a+b*arcsin(c*x))^2/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(g x +f \right) \sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(g*x+f)/(-c^2*d*x^2+d)^(1/2),x)","F"
74,0,0,1098,3.349000," ","int((a+b*arcsin(c*x))^2/(g*x+f)^2/(-c^2*d*x^2+d)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(g x +f \right)^{2} \sqrt{-c^{2} d \,x^{2}+d}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(g*x+f)^2/(-c^2*d*x^2+d)^(1/2),x)","F"
75,1,2663,731,1.391000," ","int((g*x+f)^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{-c^{2} x^{2}+1}\, x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right) x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) f^{2} g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{3} f \,g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x f \,g^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) x}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a^{2} f^{3} x}{d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{6 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right) g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) g^{3}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f^{3}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) g^{3}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, f^{3}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f^{3} \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{3} \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{3} \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f^{3} \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{3} \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{3} \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f \,g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f^{2} g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f \,g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f^{3} \arcsin \left(c x \right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{6 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f \,g^{2} \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f^{2} g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{6 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f^{2} g \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{6 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f^{2} g \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, f \,g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f^{3}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x \,f^{3}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)^{2}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 a^{2} f \,g^{2} x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{3 a^{2} f \,g^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{3 a^{2} f^{2} g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a^{2} g^{3} x^{2}}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3}}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right)^{2} f \,g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{6 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x f \,g^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{6 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f^{2} g \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{6 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f^{2} g \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{3 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f \,g^{2} \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a^{2} g^{3}}{d \,c^{4} \sqrt{-c^{2} d \,x^{2}+d}}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)^{2} x^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{3 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} f^{2} g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,f^{3}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g^{3} \arcsin \left(c x \right)}{c^{4} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"6*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*f^2*g*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*x+2*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*x^2-6*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*f^2*g-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c/d^2/(c^2*x^2-1)*f^3+2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^4/d^2/(c^2*x^2-1)*g^3-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f^3-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*g^3+b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*arcsin(c*x)^3*f*g^2+I*b^2*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*f^3-3*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x*f*g^2+I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*f^3*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*f^3*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*g^3*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*g^3*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^3/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*x+2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*g^3*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^4/d^2/(c^2*x^2-1)*g^3*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+a^2*f^3/d*x/(-c^2*d*x^2+d)^(1/2)+6*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*f*arcsin(c*x)*g^2-6*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^3/d^2/(c^2*x^2-1)*f*g^2-6*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f^2*g-6*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f*g^2+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*f^3*arcsin(c*x)-6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*f*g^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)-b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x*f^3-2*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d^2/(c^2*x^2-1)*x^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)^2+3*a^2*f*g^2*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-3*a^2*f*g^2/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+3*a^2*f^2*g/c^2/d/(-c^2*d*x^2+d)^(1/2)-a^2*g^3*x^2/c^2/d/(-c^2*d*x^2+d)^(1/2)+2*b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d^2/(c^2*x^2-1)+3*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*arcsin(c*x)^2*f*g^2-6*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*x*f*g^2+6*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^2/d^2/(c^2*x^2-1)*f^2*g+2*a^2*g^3/d/c^4/(-c^2*d*x^2+d)^(1/2)+6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*f^2*g*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-6*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*f^2*g*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3*I*b^2*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*f*g^2-6*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*f^2*g*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+3*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*f*g^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)+b^2*(-d*(c^2*x^2-1))^(1/2)*g^3/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x^2-3*b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*f^2*g-2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*x*f^3-4*a*b*(-d*(c^2*x^2-1))^(1/2)*g^3/c^4/d^2/(c^2*x^2-1)*arcsin(c*x)","B"
76,1,1861,516,0.913000," ","int((g*x+f)^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x^{2} f g}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,g^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{4 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f g \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) \left(-c^{2} x^{2}+1\right) f g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2} \arcsin \left(c x \right)^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x \,f^{2}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f^{2}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f^{2}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f^{2} \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2} \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, f^{2}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f^{2} \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2} \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a^{2} g^{2} x}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{a^{2} g^{2} \arctan \left(\frac{\sqrt{c^{2} d}\, x}{\sqrt{-c^{2} d \,x^{2}+d}}\right)}{c^{2} d \sqrt{c^{2} d}}+\frac{2 a^{2} f g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{4 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) f^{2}}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g^{2}}{c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f g \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{4 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f g \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{4 i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, f g \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x \,f^{2}}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x^{2} f g}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x \,g^{2}}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \sqrt{-c^{2} x^{2}+1}\, g^{2} \arcsin \left(c x \right)^{3}}{3 c^{3} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \left(-c^{2} x^{2}+1\right) f g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{a^{2} f^{2} x}{d \sqrt{-c^{2} d \,x^{2}+d}}"," ",0,"-4*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)*x^2*f*g-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/c^2/d^2/(c^2*x^2-1)*x*g^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*g^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)*f^2-2*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)*g^2-4*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/c^2/d^2/(c^2*x^2-1)*(-c^2*x^2+1)*f*g-4*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f*g+4*a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)*f*g+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*arcsin(c*x)*f^2+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^3/d^2/(c^2*x^2-1)*arcsin(c*x)*g^2-4*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*f*g*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-4*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*f*g*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+4*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*f*g*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))+4*I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^2/d^2/(c^2*x^2-1)*f*g*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+a*b*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*g^2*arcsin(c*x)^2-b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/d^2/(c^2*x^2-1)*x*f^2+a^2*g^2*x/c^2/d/(-c^2*d*x^2+d)^(1/2)-a^2*g^2/c^2/d/(c^2*d)^(1/2)*arctan((c^2*d)^(1/2)*x/(-c^2*d*x^2+d)^(1/2))+2*a^2*f*g/c^2/d/(-c^2*d*x^2+d)^(1/2)-2*a*b*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)/d^2/(c^2*x^2-1)*x*f^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/d^2/(c^2*x^2-1)*x^2*f*g-b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/c^2/d^2/(c^2*x^2-1)*x*g^2+1/3*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*g^2*arcsin(c*x)^3+I*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/c/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*f^2+I*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/c^3/d^2/(c^2*x^2-1)*(-c^2*x^2+1)^(1/2)*g^2-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*f^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c/d^2/(c^2*x^2-1)*f^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*g^2*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+I*b^2*(-d*(c^2*x^2-1))^(1/2)*(-c^2*x^2+1)^(1/2)/c^3/d^2/(c^2*x^2-1)*g^2*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-2*b^2*(-d*(c^2*x^2-1))^(1/2)*arcsin(c*x)^2/c^2/d^2/(c^2*x^2-1)*(-c^2*x^2+1)*f*g+a^2*f^2/d*x/(-c^2*d*x^2+d)^(1/2)","B"
77,1,1047,419,0.775000," ","int((g*x+f)*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(3/2),x)","\frac{a^{2} g}{c^{2} d \sqrt{-c^{2} d \,x^{2}+d}}+\frac{a^{2} f x}{d \sqrt{-c^{2} d \,x^{2}+d}}-\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \dilog \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} x f}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right) \ln \left(1+\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \dilog \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 i a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \arcsin \left(c x \right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, f \polylog \left(2, -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right)^{2}\right)}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) \ln \left(1+i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 b^{2} \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, g \arcsin \left(c x \right) \ln \left(1-i \left(i c x +\sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}+\frac{i b^{2} \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right)^{2} \sqrt{-c^{2} x^{2}+1}\, f}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) x f}{d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \arcsin \left(c x \right) g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) f}{c \,d^{2} \left(c^{2} x^{2}-1\right)}+\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}+i\right) g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) f}{c \,d^{2} \left(c^{2} x^{2}-1\right)}-\frac{2 a b \sqrt{-c^{2} x^{2}+1}\, \sqrt{-d \left(c^{2} x^{2}-1\right)}\, \ln \left(i c x +\sqrt{-c^{2} x^{2}+1}-i\right) g}{c^{2} d^{2} \left(c^{2} x^{2}-1\right)}"," ",0,"a^2*g/c^2/d/(-c^2*d*x^2+d)^(1/2)+a^2*f/d*x/(-c^2*d*x^2+d)^(1/2)+I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*f*polylog(2,-(I*c*x+(-c^2*x^2+1)^(1/2))^2)-b^2*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)^2*x*f-b^2*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)^2*g-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*f*arcsin(c*x)*ln(1+(I*c*x+(-c^2*x^2+1)^(1/2))^2)+2*I*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*f*arcsin(c*x)+I*b^2*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*arcsin(c*x)^2*(-c^2*x^2+1)^(1/2)*f+2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*g*dilog(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*g*arcsin(c*x)*ln(1+I*(I*c*x+(-c^2*x^2+1)^(1/2)))+2*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*g*arcsin(c*x)*ln(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*I*b^2*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*g*dilog(1-I*(I*c*x+(-c^2*x^2+1)^(1/2)))-2*a*b*(-d*(c^2*x^2-1))^(1/2)/d^2/(c^2*x^2-1)*arcsin(c*x)*x*f-2*a*b*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*arcsin(c*x)*g-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c/d^2/(c^2*x^2-1)*f+2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)*ln(I*c*x+(-c^2*x^2+1)^(1/2)+I)/c^2/d^2/(c^2*x^2-1)*g-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*f-2*a*b*(-c^2*x^2+1)^(1/2)*(-d*(c^2*x^2-1))^(1/2)/c^2/d^2/(c^2*x^2-1)*ln(I*c*x+(-c^2*x^2+1)^(1/2)-I)*g","B"
78,0,0,1107,5.681000," ","int((a+b*arcsin(c*x))^2/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(g x +f \right) \left(-c^{2} d \,x^{2}+d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2/(g*x+f)/(-c^2*d*x^2+d)^(3/2),x)","F"
79,1,13136,1473,1.596000," ","int((g*x+f)^3*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
80,1,9710,974,1.213000," ","int((g*x+f)^2*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
81,1,5897,610,0.889000," ","int((g*x+f)*(a+b*arcsin(c*x))^2/(-c^2*d*x^2+d)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
82,0,0,35,9.680000," ","int((a+b*arcsin(c*x))^n*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{n} \ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arcsin(c*x))^n*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
83,0,0,671,13.881000," ","int((a+b*arcsin(c*x))^3*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{3} \ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arcsin(c*x))^3*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
84,0,0,541,11.741000," ","int((a+b*arcsin(c*x))^2*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right)^{2} \ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arcsin(c*x))^2*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
85,0,0,409,9.223000," ","int((a+b*arcsin(c*x))*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(c x \right)\right) \ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int((a+b*arcsin(c*x))*ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
86,0,0,252,0.233000," ","int(ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","\int \frac{\ln \left(h \left(g x +f \right)^{m}\right)}{\sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(ln(h*(g*x+f)^m)/(-c^2*x^2+1)^(1/2),x)","F"
87,0,0,35,5.047000," ","int(ln(h*(g*x+f)^m)/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","\int \frac{\ln \left(h \left(g x +f \right)^{m}\right)}{\left(a +b \arcsin \left(c x \right)\right) \sqrt{-c^{2} x^{2}+1}}\, dx"," ",0,"int(ln(h*(g*x+f)^m)/(a+b*arcsin(c*x))/(-c^2*x^2+1)^(1/2),x)","F"
88,1,490,324,0.022000," ","int((e*x+d)^3*(g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e^{3} g \,c^{5} x^{5}}{5}+\frac{\left(3 d c \,e^{2} g +e^{3} c f \right) c^{4} x^{4}}{4}+\frac{\left(3 c^{2} d^{2} e g +3 d \,c^{2} e^{2} f \right) c^{3} x^{3}}{3}+\frac{\left(c^{3} d^{3} g +3 c^{3} d^{2} e f \right) c^{2} x^{2}}{2}+c^{5} d^{3} f x \right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} g \,c^{5} x^{5}}{5}+\frac{3 \arcsin \left(c x \right) c^{5} x^{4} d \,e^{2} g}{4}+\frac{\arcsin \left(c x \right) c^{5} x^{4} e^{3} f}{4}+\arcsin \left(c x \right) c^{5} x^{3} d^{2} e g +\arcsin \left(c x \right) c^{5} x^{3} d \,e^{2} f +\frac{\arcsin \left(c x \right) c^{5} x^{2} d^{3} g}{2}+\frac{3 \arcsin \left(c x \right) c^{5} x^{2} d^{2} e f}{2}+\arcsin \left(c x \right) c^{5} d^{3} f x -\frac{e^{3} g \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{\left(15 d c \,e^{2} g +5 e^{3} c f \right) \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{20}-\frac{\left(20 c^{2} d^{2} e g +20 d \,c^{2} e^{2} f \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{20}-\frac{\left(10 c^{3} d^{3} g +30 c^{3} d^{2} e f \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{20}+c^{4} d^{3} f \sqrt{-c^{2} x^{2}+1}\right)}{c^{4}}}{c}"," ",0,"1/c*(a/c^4*(1/5*e^3*g*c^5*x^5+1/4*(3*c*d*e^2*g+c*e^3*f)*c^4*x^4+1/3*(3*c^2*d^2*e*g+3*c^2*d*e^2*f)*c^3*x^3+1/2*(c^3*d^3*g+3*c^3*d^2*e*f)*c^2*x^2+c^5*d^3*f*x)+b/c^4*(1/5*arcsin(c*x)*e^3*g*c^5*x^5+3/4*arcsin(c*x)*c^5*x^4*d*e^2*g+1/4*arcsin(c*x)*c^5*x^4*e^3*f+arcsin(c*x)*c^5*x^3*d^2*e*g+arcsin(c*x)*c^5*x^3*d*e^2*f+1/2*arcsin(c*x)*c^5*x^2*d^3*g+3/2*arcsin(c*x)*c^5*x^2*d^2*e*f+arcsin(c*x)*c^5*d^3*f*x-1/5*e^3*g*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/20*(15*c*d*e^2*g+5*c*e^3*f)*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/20*(20*c^2*d^2*e*g+20*c^2*d*e^2*f)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/20*(10*c^3*d^3*g+30*c^3*d^2*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^4*d^3*f*(-c^2*x^2+1)^(1/2)))","A"
89,1,338,225,0.006000," ","int((e*x+d)^2*(g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e^{2} g \,c^{4} x^{4}}{4}+\frac{\left(2 d c e g +e^{2} c f \right) c^{3} x^{3}}{3}+\frac{\left(c^{2} d^{2} g +2 d \,c^{2} e f \right) c^{2} x^{2}}{2}+c^{4} d^{2} f x \right)}{c^{3}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} g \,c^{4} x^{4}}{4}+\frac{2 \arcsin \left(c x \right) c^{4} x^{3} d e g}{3}+\frac{\arcsin \left(c x \right) c^{4} x^{3} e^{2} f}{3}+\frac{\arcsin \left(c x \right) c^{4} x^{2} d^{2} g}{2}+\arcsin \left(c x \right) c^{4} x^{2} d e f +\arcsin \left(c x \right) c^{4} d^{2} f x -\frac{e^{2} g \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}-\frac{\left(8 d c e g +4 e^{2} c f \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{12}-\frac{\left(6 c^{2} d^{2} g +12 d \,c^{2} e f \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{12}+c^{3} d^{2} f \sqrt{-c^{2} x^{2}+1}\right)}{c^{3}}}{c}"," ",0,"1/c*(a/c^3*(1/4*e^2*g*c^4*x^4+1/3*(2*c*d*e*g+c*e^2*f)*c^3*x^3+1/2*(c^2*d^2*g+2*c^2*d*e*f)*c^2*x^2+c^4*d^2*f*x)+b/c^3*(1/4*arcsin(c*x)*e^2*g*c^4*x^4+2/3*arcsin(c*x)*c^4*x^3*d*e*g+1/3*arcsin(c*x)*c^4*x^3*e^2*f+1/2*arcsin(c*x)*c^4*x^2*d^2*g+arcsin(c*x)*c^4*x^2*d*e*f+arcsin(c*x)*c^4*d^2*f*x-1/4*e^2*g*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/12*(8*c*d*e*g+4*c*e^2*f)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/12*(6*c^2*d^2*g+12*c^2*d*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^3*d^2*f*(-c^2*x^2+1)^(1/2)))","A"
90,1,198,131,0.008000," ","int((e*x+d)*(g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e g \,c^{3} x^{3}}{3}+\frac{\left(d c g +e c f \right) c^{2} x^{2}}{2}+c^{3} f d x \right)}{c^{2}}+\frac{b \left(\frac{\arcsin \left(c x \right) e g \,c^{3} x^{3}}{3}+\frac{\arcsin \left(c x \right) c^{3} x^{2} d g}{2}+\frac{\arcsin \left(c x \right) c^{3} x^{2} e f}{2}+\arcsin \left(c x \right) c^{3} f d x -\frac{e g \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{3}-\frac{\left(3 d c g +3 e c f \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{6}+c^{2} f d \sqrt{-c^{2} x^{2}+1}\right)}{c^{2}}}{c}"," ",0,"1/c*(a/c^2*(1/3*e*g*c^3*x^3+1/2*(c*d*g+c*e*f)*c^2*x^2+c^3*f*d*x)+b/c^2*(1/3*arcsin(c*x)*e*g*c^3*x^3+1/2*arcsin(c*x)*c^3*x^2*d*g+1/2*arcsin(c*x)*c^3*x^2*e*f+arcsin(c*x)*c^3*f*d*x-1/3*e*g*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/6*(3*c*d*g+3*c*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^2*f*d*(-c^2*x^2+1)^(1/2)))","A"
91,1,1566,357,0.707000," ","int((g*x+f)*(a+b*arcsin(c*x))/(e*x+d),x)","\frac{a g x}{e}-\frac{a \ln \left(c e x +d c \right) d g}{e^{2}}+\frac{a \ln \left(c e x +d c \right) f}{e}-\frac{c^{2} b \,d^{3} g \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b f \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{b d g \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{b d g \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{b e f \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{i c^{2} b f \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i b d g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b \arcsin \left(c x \right)^{2} d g}{2 e^{2}}-\frac{i b d g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{c^{2} b f \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{c^{2} b \,d^{3} g \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b f \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{i b e f \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b e f \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i c^{2} b \,d^{3} g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{b e f \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i c^{2} b \,d^{3} g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{b \arcsin \left(c x \right) g x}{e}-\frac{i b \arcsin \left(c x \right)^{2} f}{2 e}+\frac{b g \sqrt{-c^{2} x^{2}+1}}{c e}"," ",0,"a*g/e*x-a/e^2*ln(c*e*x+c*d)*d*g+a/e*ln(c*e*x+c*d)*f-c^2*b/e^2*d^3*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+c^2*b/e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2+b*d*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+b*d*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-b*e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*b*e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+1/2*I*b*arcsin(c*x)^2/e^2*d*g+I*c^2*b/e^2*d^3*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*b*d*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+c^2*b/e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-c^2*b/e^2*d^3*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2+I*b*e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2+I*c^2*b/e^2*d^3*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-b*e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*b*d*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+b*arcsin(c*x)*g/e*x-1/2*I*b*arcsin(c*x)^2/e*f+b*g*(-c^2*x^2+1)^(1/2)/c/e","B"
92,1,976,367,1.415000," ","int((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^2,x)","\frac{c a d g}{e^{2} \left(c e x +d c \right)}-\frac{c a f}{e \left(c e x +d c \right)}+\frac{a g \ln \left(c e x +d c \right)}{e^{2}}+\frac{i b g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{c b \arcsin \left(c x \right) d g}{e^{2} \left(c e x +d c \right)}-\frac{c b \arcsin \left(c x \right) f}{e \left(c e x +d c \right)}-\frac{2 c b d g \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e^{2} \sqrt{c^{2} d^{2}-e^{2}}}+\frac{i b g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{c^{2} b g \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{i b g \arcsin \left(c x \right)^{2}}{2 e^{2}}-\frac{i c^{2} b g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b g \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 c b f \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}-\frac{b \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) \arcsin \left(c x \right) g}{c^{2} d^{2}-e^{2}}-\frac{b \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) \arcsin \left(c x \right) g}{c^{2} d^{2}-e^{2}}"," ",0,"c*a/e^2/(c*e*x+c*d)*d*g-c*a/e/(c*e*x+c*d)*f+a*g/e^2*ln(c*e*x+c*d)-I*c^2*b/e^2*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2+c*b*arcsin(c*x)/e^2/(c*e*x+c*d)*d*g-c*b*arcsin(c*x)/e/(c*e*x+c*d)*f-2*c*b/e^2*d*g/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))-I*c^2*b/e^2*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2+c^2*b/e^2*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-1/2*I*b*g*arcsin(c*x)^2/e^2+I*b*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+c^2*b/e^2*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2+I*b*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+2*c*b/e*f/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))-b*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))/(c^2*d^2-e^2)*arcsin(c*x)*g-b*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))/(c^2*d^2-e^2)*arcsin(c*x)*g","B"
93,1,805,186,0.016000," ","int((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^3,x)","-\frac{c a g}{e^{2} \left(c e x +d c \right)}+\frac{c^{2} a d g}{2 e^{2} \left(c e x +d c \right)^{2}}-\frac{c^{2} a f}{2 e \left(c e x +d c \right)^{2}}-\frac{c b \arcsin \left(c x \right) g}{e^{2} \left(c e x +d c \right)}+\frac{c^{2} b \arcsin \left(c x \right) d g}{2 e^{2} \left(c e x +d c \right)^{2}}-\frac{c^{2} b \arcsin \left(c x \right) f}{2 e \left(c e x +d c \right)^{2}}-\frac{c^{2} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d g}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)}+\frac{c^{2} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{2 e \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)}+\frac{c^{3} b \,d^{2} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) g}{2 e^{3} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{3} b d \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c b g \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{e^{3} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-c*a*g/e^2/(c*e*x+c*d)+1/2*c^2*a/e^2/(c*e*x+c*d)^2*d*g-1/2*c^2*a/e/(c*e*x+c*d)^2*f-c*b*arcsin(c*x)*g/e^2/(c*e*x+c*d)+1/2*c^2*b*arcsin(c*x)/e^2/(c*e*x+c*d)^2*d*g-1/2*c^2*b*arcsin(c*x)/e/(c*e*x+c*d)^2*f-1/2*c^2*b/e^2/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g+1/2*c^2*b/e/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+1/2*c^3*b/e^3*d^2/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g-1/2*c^3*b/e^2*d/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-c*b/e^3*g/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))","B"
94,1,1269,237,0.017000," ","int((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^4,x)","-\frac{c^{2} a g}{2 e^{2} \left(c e x +d c \right)^{2}}+\frac{c^{3} a d g}{3 e^{2} \left(c e x +d c \right)^{3}}-\frac{c^{3} a f}{3 e \left(c e x +d c \right)^{3}}-\frac{c^{2} b \arcsin \left(c x \right) g}{2 e^{2} \left(c e x +d c \right)^{2}}+\frac{c^{3} b \arcsin \left(c x \right) d g}{3 e^{2} \left(c e x +d c \right)^{3}}-\frac{c^{3} b \arcsin \left(c x \right) f}{3 e \left(c e x +d c \right)^{3}}+\frac{c^{2} b g \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)}-\frac{2 c^{3} b g d \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{3 e^{3} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{3} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d g}{6 e^{3} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{2}}+\frac{c^{3} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{6 e^{2} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{2}}-\frac{c^{4} b \,d^{2} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, g}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}+\frac{c^{4} b d \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{2 e \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}+\frac{c^{5} b \,d^{3} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) g}{2 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{5} b \,d^{2} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{c^{3} b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{6 e^{2} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-1/2*c^2*a*g/e^2/(c*e*x+c*d)^2+1/3*c^3*a/e^2/(c*e*x+c*d)^3*d*g-1/3*c^3*a/e/(c*e*x+c*d)^3*f-1/2*c^2*b*arcsin(c*x)*g/e^2/(c*e*x+c*d)^2+1/3*c^3*b*arcsin(c*x)/e^2/(c*e*x+c*d)^3*d*g-1/3*c^3*b*arcsin(c*x)/e/(c*e*x+c*d)^3*f+1/2*c^2*b/e^2*g/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-2/3*c^3*b/e^3*g*d/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))-1/6*c^3*b/e^3/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g+1/6*c^3*b/e^2/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-1/2*c^4*b/e^2*d^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g+1/2*c^4*b/e*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+1/2*c^5*b/e^3*d^3/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g-1/2*c^5*b/e^2*d^2/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f+1/6*c^3*b/e^2/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f","B"
95,1,1804,336,0.022000," ","int((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^5,x)","\frac{c^{4} a d g}{4 e^{2} \left(c e x +d c \right)^{4}}-\frac{c^{4} a f}{4 e \left(c e x +d c \right)^{4}}-\frac{c^{3} a g}{3 e^{2} \left(c e x +d c \right)^{3}}+\frac{c^{4} b \arcsin \left(c x \right) d g}{4 e^{2} \left(c e x +d c \right)^{4}}-\frac{c^{4} b \arcsin \left(c x \right) f}{4 e \left(c e x +d c \right)^{4}}-\frac{c^{3} b \arcsin \left(c x \right) g}{3 e^{2} \left(c e x +d c \right)^{3}}+\frac{c^{3} b g \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{6 e^{3} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{2}}+\frac{2 c^{4} b g d \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{3 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}-\frac{7 c^{5} b g \,d^{2} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{8 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{c^{3} b g \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{6 e^{3} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{4} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d g}{12 e^{4} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{3}}+\frac{c^{4} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{12 e^{3} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{3}}-\frac{5 c^{5} b \,d^{2} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, g}{24 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)^{2}}+\frac{5 c^{5} b d \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{24 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)^{2}}-\frac{5 c^{6} b \,d^{3} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, g}{8 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{3} \left(c x +\frac{d c}{e}\right)}+\frac{5 c^{6} b \,d^{2} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{8 e \left(c^{2} d^{2}-e^{2}\right)^{3} \left(c x +\frac{d c}{e}\right)}+\frac{5 c^{7} b \,d^{4} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) g}{8 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{3} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{5 c^{7} b \,d^{3} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{8 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{3} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{3 c^{5} b d \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{8 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{4} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{6 e \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}"," ",0,"1/4*c^4*a/e^2/(c*e*x+c*d)^4*d*g-1/4*c^4*a/e/(c*e*x+c*d)^4*f-1/3*c^3*a*g/e^2/(c*e*x+c*d)^3+1/4*c^4*b*arcsin(c*x)/e^2/(c*e*x+c*d)^4*d*g-1/4*c^4*b*arcsin(c*x)/e/(c*e*x+c*d)^4*f-1/3*c^3*b*arcsin(c*x)*g/e^2/(c*e*x+c*d)^3+1/6*c^3*b/e^3*g/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)+2/3*c^4*b/e^2*g*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-7/8*c^5*b/e^3*g*d^2/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))+1/6*c^3*b/e^3*g/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))-1/12*c^4*b/e^4/(c^2*d^2-e^2)/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g+1/12*c^4*b/e^3/(c^2*d^2-e^2)/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-5/24*c^5*b/e^3*d^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g+5/24*c^5*b/e^2*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-5/8*c^6*b/e^2*d^3/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g+5/8*c^6*b/e*d^2/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+5/8*c^7*b/e^3*d^4/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g-5/8*c^7*b/e^2*d^3/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f+3/8*c^5*b/e^2*d/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-1/6*c^4*b/e/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f","B"
96,1,2431,429,0.031000," ","int((g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^6,x)","-\frac{c^{4} a g}{4 e^{2} \left(c e x +d c \right)^{4}}-\frac{c^{5} a f}{5 e \left(c e x +d c \right)^{5}}+\frac{17 c^{5} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d g}{60 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)^{2}}-\frac{11 c^{6} b d \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{24 e \left(c^{2} d^{2}-e^{2}\right)^{3} \left(c x +\frac{d c}{e}\right)}+\frac{7 c^{6} b d \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{60 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)^{3}}+\frac{9 c^{5} b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) d g}{20 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{7 c^{7} b \,d^{2} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{24 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{3} \left(c x +\frac{d c}{e}\right)^{2}}-\frac{7 c^{8} b \,d^{4} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, g}{8 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{4} \left(c x +\frac{d c}{e}\right)}+\frac{7 c^{8} b \,d^{3} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{8 e \left(c^{2} d^{2}-e^{2}\right)^{4} \left(c x +\frac{d c}{e}\right)}-\frac{c^{5} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d g}{20 e^{5} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{4}}-\frac{7 c^{7} b \,d^{3} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, g}{24 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{3} \left(c x +\frac{d c}{e}\right)^{2}}-\frac{7 c^{6} b \,d^{2} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, g}{60 e^{4} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)^{3}}+\frac{7 c^{9} b \,d^{5} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) g}{8 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{4} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{3 c^{5} b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{40 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{c^{5} b \arcsin \left(c x \right) d g}{5 e^{2} \left(c e x +d c \right)^{5}}+\frac{c^{5} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{20 e^{4} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{4}}-\frac{3 c^{5} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{40 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)^{2}}+\frac{c^{4} b g \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{12 e^{4} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{3}}-\frac{c^{4} b g \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{6 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}+\frac{c^{5} a d g}{5 e^{2} \left(c e x +d c \right)^{5}}-\frac{c^{5} b \arcsin \left(c x \right) f}{5 e \left(c e x +d c \right)^{5}}-\frac{c^{4} b \arcsin \left(c x \right) g}{4 e^{2} \left(c e x +d c \right)^{4}}+\frac{13 c^{6} b \,d^{2} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, g}{12 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{3} \left(c x +\frac{d c}{e}\right)}-\frac{7 c^{9} b \,d^{4} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{8 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{4} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{11 c^{7} b \,d^{3} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) g}{8 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{3} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{3 c^{7} b \,d^{2} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{4 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{3} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"-1/4*c^4*a*g/e^2/(c*e*x+c*d)^4-1/5*c^5*a/e/(c*e*x+c*d)^5*f+17/60*c^5*b/e^3/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g-11/24*c^6*b/e*d/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+7/60*c^6*b/e^3*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+9/20*c^5*b/e^3/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*d*g+7/24*c^7*b/e^2*d^2/(c^2*d^2-e^2)^3/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-7/8*c^8*b/e^2*d^4/(c^2*d^2-e^2)^4/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g+7/8*c^8*b/e*d^3/(c^2*d^2-e^2)^4/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-1/20*c^5*b/e^5/(c^2*d^2-e^2)/(c*x+d*c/e)^4*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g-7/24*c^7*b/e^3*d^3/(c^2*d^2-e^2)^3/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g-7/60*c^6*b/e^4*d^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g+7/8*c^9*b/e^3*d^5/(c^2*d^2-e^2)^4/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g-3/40*c^5*b/e^2/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f+1/5*c^5*b*arcsin(c*x)/e^2/(c*e*x+c*d)^5*d*g+1/20*c^5*b/e^4/(c^2*d^2-e^2)/(c*x+d*c/e)^4*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-3/40*c^5*b/e^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+1/12*c^4*b/e^4*g/(c^2*d^2-e^2)/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-1/6*c^4*b/e^2*g/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)+1/5*c^5*a/e^2/(c*e*x+c*d)^5*d*g-1/5*c^5*b*arcsin(c*x)/e/(c*e*x+c*d)^5*f-1/4*c^4*b*arcsin(c*x)*g/e^2/(c*e*x+c*d)^4+13/12*c^6*b/e^2*d^2/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g-7/8*c^9*b/e^2*d^4/(c^2*d^2-e^2)^4/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-11/8*c^7*b/e^3*d^3/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g+3/4*c^7*b/e^2*d^2/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f","B"
97,1,705,477,0.018000," ","int((e*x+d)^3*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e^{3} h \,c^{6} x^{6}}{6}+\frac{\left(3 d c \,e^{2} h +e^{3} c g \right) c^{5} x^{5}}{5}+\frac{\left(3 c^{2} d^{2} e h +3 d \,c^{2} e^{2} g +e^{3} f \,c^{2}\right) c^{4} x^{4}}{4}+\frac{\left(c^{3} d^{3} h +3 c^{3} d^{2} e g +3 d \,c^{3} e^{2} f \right) c^{3} x^{3}}{3}+\frac{\left(c^{4} d^{3} g +3 c^{4} d^{2} e f \right) c^{2} x^{2}}{2}+c^{6} d^{3} f x \right)}{c^{5}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} h \,c^{6} x^{6}}{6}+\frac{3 \arcsin \left(c x \right) c^{6} x^{5} d \,e^{2} h}{5}+\frac{\arcsin \left(c x \right) c^{6} x^{5} e^{3} g}{5}+\frac{3 \arcsin \left(c x \right) c^{6} x^{4} d^{2} e h}{4}+\frac{3 \arcsin \left(c x \right) c^{6} x^{4} d \,e^{2} g}{4}+\frac{\arcsin \left(c x \right) c^{6} x^{4} e^{3} f}{4}+\frac{\arcsin \left(c x \right) c^{6} x^{3} d^{3} h}{3}+\arcsin \left(c x \right) c^{6} x^{3} d^{2} e g +\arcsin \left(c x \right) c^{6} x^{3} d \,e^{2} f +\frac{\arcsin \left(c x \right) c^{6} x^{2} d^{3} g}{2}+\frac{3 \arcsin \left(c x \right) c^{6} x^{2} d^{2} e f}{2}+\arcsin \left(c x \right) c^{6} d^{3} f x -\frac{e^{3} h \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{6}-\frac{\left(36 d c \,e^{2} h +12 e^{3} c g \right) \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{60}-\frac{\left(45 c^{2} d^{2} e h +45 d \,c^{2} e^{2} g +15 e^{3} f \,c^{2}\right) \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{60}-\frac{\left(20 c^{3} d^{3} h +60 c^{3} d^{2} e g +60 d \,c^{3} e^{2} f \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{60}-\frac{\left(30 c^{4} d^{3} g +90 c^{4} d^{2} e f \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{60}+c^{5} d^{3} f \sqrt{-c^{2} x^{2}+1}\right)}{c^{5}}}{c}"," ",0,"1/c*(a/c^5*(1/6*e^3*h*c^6*x^6+1/5*(3*c*d*e^2*h+c*e^3*g)*c^5*x^5+1/4*(3*c^2*d^2*e*h+3*c^2*d*e^2*g+c^2*e^3*f)*c^4*x^4+1/3*(c^3*d^3*h+3*c^3*d^2*e*g+3*c^3*d*e^2*f)*c^3*x^3+1/2*(c^4*d^3*g+3*c^4*d^2*e*f)*c^2*x^2+c^6*d^3*f*x)+b/c^5*(1/6*arcsin(c*x)*e^3*h*c^6*x^6+3/5*arcsin(c*x)*c^6*x^5*d*e^2*h+1/5*arcsin(c*x)*c^6*x^5*e^3*g+3/4*arcsin(c*x)*c^6*x^4*d^2*e*h+3/4*arcsin(c*x)*c^6*x^4*d*e^2*g+1/4*arcsin(c*x)*c^6*x^4*e^3*f+1/3*arcsin(c*x)*c^6*x^3*d^3*h+arcsin(c*x)*c^6*x^3*d^2*e*g+arcsin(c*x)*c^6*x^3*d*e^2*f+1/2*arcsin(c*x)*c^6*x^2*d^3*g+3/2*arcsin(c*x)*c^6*x^2*d^2*e*f+arcsin(c*x)*c^6*d^3*f*x-1/6*e^3*h*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-1/60*(36*c*d*e^2*h+12*c*e^3*g)*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/60*(45*c^2*d^2*e*h+45*c^2*d*e^2*g+15*c^2*e^3*f)*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/60*(20*c^3*d^3*h+60*c^3*d^2*e*g+60*c^3*d*e^2*f)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/60*(30*c^4*d^3*g+90*c^4*d^2*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^5*d^3*f*(-c^2*x^2+1)^(1/2)))","A"
98,1,502,332,0.006000," ","int((e*x+d)^2*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e^{2} h \,c^{5} x^{5}}{5}+\frac{\left(2 d c e h +e^{2} c g \right) c^{4} x^{4}}{4}+\frac{\left(c^{2} d^{2} h +2 d \,c^{2} e g +e^{2} f \,c^{2}\right) c^{3} x^{3}}{3}+\frac{\left(c^{3} d^{2} g +2 d \,c^{3} e f \right) c^{2} x^{2}}{2}+c^{5} d^{2} f x \right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} h \,c^{5} x^{5}}{5}+\frac{\arcsin \left(c x \right) c^{5} x^{4} d e h}{2}+\frac{\arcsin \left(c x \right) c^{5} x^{4} e^{2} g}{4}+\frac{\arcsin \left(c x \right) c^{5} x^{3} d^{2} h}{3}+\frac{2 \arcsin \left(c x \right) c^{5} x^{3} d e g}{3}+\frac{\arcsin \left(c x \right) c^{5} x^{3} e^{2} f}{3}+\frac{\arcsin \left(c x \right) c^{5} x^{2} d^{2} g}{2}+\arcsin \left(c x \right) c^{5} x^{2} d e f +\arcsin \left(c x \right) c^{5} d^{2} f x -\frac{e^{2} h \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{\left(30 d c e h +15 e^{2} c g \right) \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{60}-\frac{\left(20 c^{2} d^{2} h +40 d \,c^{2} e g +20 e^{2} f \,c^{2}\right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{60}-\frac{\left(30 c^{3} d^{2} g +60 d \,c^{3} e f \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{60}+c^{4} d^{2} f \sqrt{-c^{2} x^{2}+1}\right)}{c^{4}}}{c}"," ",0,"1/c*(a/c^4*(1/5*e^2*h*c^5*x^5+1/4*(2*c*d*e*h+c*e^2*g)*c^4*x^4+1/3*(c^2*d^2*h+2*c^2*d*e*g+c^2*e^2*f)*c^3*x^3+1/2*(c^3*d^2*g+2*c^3*d*e*f)*c^2*x^2+c^5*d^2*f*x)+b/c^4*(1/5*arcsin(c*x)*e^2*h*c^5*x^5+1/2*arcsin(c*x)*c^5*x^4*d*e*h+1/4*arcsin(c*x)*c^5*x^4*e^2*g+1/3*arcsin(c*x)*c^5*x^3*d^2*h+2/3*arcsin(c*x)*c^5*x^3*d*e*g+1/3*arcsin(c*x)*c^5*x^3*e^2*f+1/2*arcsin(c*x)*c^5*x^2*d^2*g+arcsin(c*x)*c^5*x^2*d*e*f+arcsin(c*x)*c^5*d^2*f*x-1/5*e^2*h*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/60*(30*c*d*e*h+15*c*e^2*g)*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/60*(20*c^2*d^2*h+40*c^2*d*e*g+20*c^2*e^2*f)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/60*(30*c^3*d^2*g+60*c^3*d*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^4*d^2*f*(-c^2*x^2+1)^(1/2)))","A"
99,1,307,200,0.008000," ","int((e*x+d)*(h*x^2+g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e h \,c^{4} x^{4}}{4}+\frac{\left(d c h +e c g \right) c^{3} x^{3}}{3}+\frac{\left(d \,c^{2} g +e f \,c^{2}\right) c^{2} x^{2}}{2}+c^{4} f d x \right)}{c^{3}}+\frac{b \left(\frac{\arcsin \left(c x \right) e h \,c^{4} x^{4}}{4}+\frac{\arcsin \left(c x \right) c^{4} x^{3} d h}{3}+\frac{\arcsin \left(c x \right) c^{4} x^{3} e g}{3}+\frac{\arcsin \left(c x \right) c^{4} x^{2} d g}{2}+\frac{\arcsin \left(c x \right) c^{4} x^{2} e f}{2}+\arcsin \left(c x \right) c^{4} f d x -\frac{e h \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}-\frac{\left(4 d c h +4 e c g \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{12}-\frac{\left(6 d \,c^{2} g +6 e f \,c^{2}\right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{12}+d \,c^{3} f \sqrt{-c^{2} x^{2}+1}\right)}{c^{3}}}{c}"," ",0,"1/c*(a/c^3*(1/4*e*h*c^4*x^4+1/3*(c*d*h+c*e*g)*c^3*x^3+1/2*(c^2*d*g+c^2*e*f)*c^2*x^2+c^4*f*d*x)+b/c^3*(1/4*arcsin(c*x)*e*h*c^4*x^4+1/3*arcsin(c*x)*c^4*x^3*d*h+1/3*arcsin(c*x)*c^4*x^3*e*g+1/2*arcsin(c*x)*c^4*x^2*d*g+1/2*arcsin(c*x)*c^4*x^2*e*f+arcsin(c*x)*c^4*f*d*x-1/4*e*h*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/12*(4*c*d*h+4*c*e*g)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/12*(6*c^2*d*g+6*c^2*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+d*c^3*f*(-c^2*x^2+1)^(1/2)))","A"
100,1,2446,464,0.742000," ","int((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d),x)","-\frac{i c^{2} b \,d^{4} h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}+\frac{a g x}{e}+\frac{a \ln \left(c e x +d c \right) f}{e}+\frac{b g \sqrt{-c^{2} x^{2}+1}}{c e}+\frac{b \arcsin \left(c x \right) g x}{e}-\frac{c^{2} b \,d^{3} g \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b f \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b f \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b f \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{c^{2} b \,d^{3} g \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b f \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i b \arcsin \left(c x \right)^{2} d^{2} h}{2 e^{3}}-\frac{i b \arcsin \left(c x \right)^{2} f}{2 e}-\frac{i c^{2} b \,d^{4} h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}-\frac{b \,d^{2} h \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{b \,d^{2} h \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{i b \,d^{2} h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{i b \,d^{2} h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{a \ln \left(c e x +d c \right) d^{2} h}{e^{3}}+\frac{b h \sin \left(2 \arcsin \left(c x \right)\right)}{8 c^{2} e}-\frac{a x d h}{e^{2}}-\frac{i b d g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b e f \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b e f \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{b e f \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{b d g \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{b d g \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{b e f \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{i b d g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b \arcsin \left(c x \right)^{2} d g}{2 e^{2}}-\frac{b h \arcsin \left(c x \right) \cos \left(2 \arcsin \left(c x \right)\right)}{4 c^{2} e}-\frac{b \sqrt{-c^{2} x^{2}+1}\, d h}{c \,e^{2}}-\frac{b \arcsin \left(c x \right) x d h}{e^{2}}+\frac{a h \,x^{2}}{2 e}+\frac{c^{2} b \,d^{4} h \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b \,d^{4} h \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}+\frac{i c^{2} b \,d^{3} g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{i c^{2} b \,d^{3} g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{a \ln \left(c e x +d c \right) d g}{e^{2}}"," ",0,"a*g/e*x+a/e*ln(c*e*x+c*d)*f+b*g*(-c^2*x^2+1)^(1/2)/c/e+b*arcsin(c*x)*g/e*x-1/2*I*b*arcsin(c*x)^2/e*f-c^2*b/e^2*d^3*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+c^2*b/e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^2*b/e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2+I*c^2*b/e^2*d^3*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2+c^2*b/e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-c^2*b/e^2*d^3*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*c^2*b/e^2*d^3*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*b/e*d^2*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+I*b/e*d^2*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-b/e*d^2*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-b/e*d^2*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+a/e^3*ln(c*e*x+c*d)*d^2*h+1/8/c^2*b/e*h*sin(2*arcsin(c*x))-a/e^2*x*d*h+b*d*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+b*d*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-b*e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+1/2*I*b*arcsin(c*x)^2/e^2*d*g+I*b*e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+I*b*e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*b*d*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-b*e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*b*d*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-1/4/c^2*b/e*h*arcsin(c*x)*cos(2*arcsin(c*x))-1/c*b/e^2*(-c^2*x^2+1)^(1/2)*d*h-b*arcsin(c*x)/e^2*x*d*h-1/2*I*b*arcsin(c*x)^2/e^3*d^2*h+1/2*a/e*h*x^2+c^2*b/e^3*d^4*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+c^2*b/e^3*d^4*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e^3*d^4*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e^3*d^4*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-a/e^2*ln(c*e*x+c*d)*d*g","B"
101,1,1910,467,1.487000," ","int((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^2,x)","\frac{c a d g}{e^{2} \left(c e x +d c \right)}-\frac{c b \arcsin \left(c x \right) f}{e \left(c e x +d c \right)}+\frac{c b \arcsin \left(c x \right) d g}{e^{2} \left(c e x +d c \right)}+\frac{b h \sqrt{-c^{2} x^{2}+1}}{c \,e^{2}}+\frac{2 c b \,d^{2} h \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e^{3} \sqrt{c^{2} d^{2}-e^{2}}}+\frac{2 b d h \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 b d h \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{2 i b d h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{2 i b d h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{c b \arcsin \left(c x \right) d^{2} h}{e^{3} \left(c e x +d c \right)}+\frac{2 c b f \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \sqrt{c^{2} d^{2}-e^{2}}}+\frac{a h x}{e^{2}}-\frac{2 c b d g \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e^{2} \sqrt{c^{2} d^{2}-e^{2}}}-\frac{2 c^{2} b \,d^{3} h \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}-\frac{2 c^{2} b \,d^{3} h \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 i c^{2} b \,d^{3} h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 i c^{2} b \,d^{3} h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}-\frac{c a \,d^{2} h}{e^{3} \left(c e x +d c \right)}+\frac{i b \arcsin \left(c x \right)^{2} d h}{e^{3}}+\frac{a g \ln \left(c e x +d c \right)}{e^{2}}+\frac{c^{2} b g \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{c^{2} b g \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{2} b g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{i b g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}+\frac{i b g \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{c^{2} d^{2}-e^{2}}-\frac{i b g \arcsin \left(c x \right)^{2}}{2 e^{2}}-\frac{b \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) \arcsin \left(c x \right) g}{c^{2} d^{2}-e^{2}}-\frac{b \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) \arcsin \left(c x \right) g}{c^{2} d^{2}-e^{2}}-\frac{c a f}{e \left(c e x +d c \right)}-\frac{2 a \ln \left(c e x +d c \right) d h}{e^{3}}+\frac{b \arcsin \left(c x \right) h x}{e^{2}}"," ",0,"c*a/e^2/(c*e*x+c*d)*d*g-c*b*arcsin(c*x)/e/(c*e*x+c*d)*f+c*b*arcsin(c*x)/e^2/(c*e*x+c*d)*d*g+b*h*(-c^2*x^2+1)^(1/2)/c/e^2-1/2*I*b*g*arcsin(c*x)^2/e^2-c*b*arcsin(c*x)/e^3/(c*e*x+c*d)*d^2*h+2*c*b/e^3*d^2*h/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+2*b/e*d*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+2*b/e*d*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*I*b/e*d*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*I*b/e*d*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+2*c*b/e*f/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+a*h/e^2*x-2*c*b/e^2*d*g/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))-2*c^2*b/e^3*d^3*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*c^2*b/e^3*d^3*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+2*I*c^2*b/e^3*d^3*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+2*I*c^2*b/e^3*d^3*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-c*a/e^3/(c*e*x+c*d)*d^2*h+I*b*arcsin(c*x)^2/e^3*d*h+a*g/e^2*ln(c*e*x+c*d)+I*b*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-b*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))/(c^2*d^2-e^2)*arcsin(c*x)*g-b*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))/(c^2*d^2-e^2)*arcsin(c*x)*g-c*a/e/(c*e*x+c*d)*f+I*b*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*a/e^3*ln(c*e*x+c*d)*d*h+b*arcsin(c*x)*h/e^2*x-I*c^2*b/e^2*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2+c^2*b/e^2*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2+c^2*b/e^2*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^2*b/e^2*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2","B"
102,1,2697,489,2.551000," ","int((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^3,x)","-\frac{2 c^{2} b \arcsin \left(c x \right) x d h}{\left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}+\frac{c^{3} b e \sqrt{-c^{2} x^{2}+1}\, x f}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}+\frac{c^{2} b e \arcsin \left(c x \right) x g}{\left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}+\frac{3 c^{4} b \arcsin \left(c x \right) d^{4} h}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e^{3}}-\frac{c^{4} b \arcsin \left(c x \right) d^{3} g}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e^{2}}-\frac{c^{4} b \arcsin \left(c x \right) d^{2} f}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e}+\frac{c^{3} b \sqrt{-c^{2} x^{2}+1}\, d^{3} h}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e^{2}}-\frac{c^{3} b \sqrt{-c^{2} x^{2}+1}\, d^{2} g}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e}-\frac{3 c^{2} b \arcsin \left(c x \right) d^{2} h}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e}-\frac{c^{3} b \sqrt{-c^{2} x^{2}+1}\, x d g}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}-\frac{i c^{4} b \,x^{2} d^{2} h}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e}-\frac{i c^{4} b x \,d^{3} h}{\left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e^{2}}+\frac{a h \ln \left(c e x +d c \right)}{e^{3}}-\frac{3 c^{3} b \,d^{3} h \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}}}+\frac{4 c b d h \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}}}+\frac{c^{3} b d f \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}}}+\frac{c^{3} b \,d^{2} g \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{e^{2} \left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}}}+\frac{c^{2} b \arcsin \left(c x \right) g d}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}-\frac{i c^{4} b \,d^{4} h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2}}+\frac{2 i c^{2} b h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)^{2}}+\frac{2 i c^{2} b h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)^{2}}-\frac{i c^{4} b \,d^{4} h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2}}-\frac{c^{2} a \,d^{2} h}{2 e^{3} \left(c e x +d c \right)^{2}}+\frac{2 c a d h}{e^{3} \left(c e x +d c \right)}+\frac{b e h \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{\left(c^{2} d^{2}-e^{2}\right)^{2}}+\frac{b e h \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{\left(c^{2} d^{2}-e^{2}\right)^{2}}+\frac{i b h \arcsin \left(c x \right)^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{i b e h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{\left(c^{2} d^{2}-e^{2}\right)^{2}}-\frac{i b e h \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{\left(c^{2} d^{2}-e^{2}\right)^{2}}+\frac{c^{2} a d g}{2 e^{2} \left(c e x +d c \right)^{2}}-\frac{2 c b g \arctan \left(\frac{2 \left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +2 i d c}{2 \sqrt{c^{2} d^{2}-e^{2}}}\right)}{\left(c^{2} d^{2}-e^{2}\right)^{\frac{3}{2}}}+\frac{i b \arcsin \left(c x \right)^{2} h}{2 e^{3}}+\frac{c^{3} b \sqrt{-c^{2} x^{2}+1}\, x \,d^{2} h}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e}-\frac{c^{4} b \arcsin \left(c x \right) x \,d^{2} g}{\left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e}+\frac{2 c^{4} b \arcsin \left(c x \right) x \,d^{3} h}{\left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e^{2}}+\frac{i c^{4} b g \,d^{2} x}{\left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e}+\frac{c^{2} b e \arcsin \left(c x \right) f}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}+\frac{c^{3} b \sqrt{-c^{2} x^{2}+1}\, d f}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}-\frac{c^{2} a f}{2 e \left(c e x +d c \right)^{2}}-\frac{c a g}{e^{2} \left(c e x +d c \right)}-\frac{2 c^{2} b h \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)^{2}}-\frac{2 c^{2} b \,d^{2} h \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e \left(c^{2} d^{2}-e^{2}\right)^{2}}-\frac{i c^{4} b e \,x^{2} f}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}-\frac{i c^{2} b \,d^{2} h \arcsin \left(c x \right)^{2}}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}-\frac{i c^{4} b \,d^{4} h}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e^{3}}+\frac{i c^{4} b \,d^{3} g}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e^{2}}-\frac{i c^{4} b \,d^{2} f}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2} e}+\frac{i c^{4} b \,x^{2} d g}{2 \left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}-\frac{i c^{4} b x d f}{\left(c^{2} d^{2}-e^{2}\right) \left(c e x +d c \right)^{2}}+\frac{c^{4} b \,d^{4} h \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2}}+\frac{c^{4} b \,d^{4} h \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right)}{e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2}}"," ",0,"-2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*arcsin(c*x)*x*d*h+1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*(-c^2*x^2+1)^(1/2)*x*f+c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*arcsin(c*x)*x*g-2*c^2*b/e/(c^2*d^2-e^2)^2*h*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-2*c^2*b/e/(c^2*d^2-e^2)^2*d^2*h*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*x^2*f-I*c^4*b/e^3/(c^2*d^2-e^2)^2*d^4*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+2*I*c^2*b/e/(c^2*d^2-e^2)^2*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^2*b/e^3/(c^2*d^2-e^2)*d^2*h*arcsin(c*x)^2-1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^3*d^4*h+1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*d^3*g-1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*d^2*f+2*I*c^2*b/e/(c^2*d^2-e^2)^2*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^4*b/e^3/(c^2*d^2-e^2)^2*d^4*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x^2*d*g-I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x*d*f+3/2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^3*arcsin(c*x)*d^4*h-1/2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*arcsin(c*x)*d^3*g-1/2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*arcsin(c*x)*d^2*f+1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*(-c^2*x^2+1)^(1/2)*d^3*h-1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*(-c^2*x^2+1)^(1/2)*d^2*g-3/2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*arcsin(c*x)*d^2*h+c^4*b/e^3/(c^2*d^2-e^2)^2*d^4*h*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+c^4*b/e^3/(c^2*d^2-e^2)^2*d^4*h*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*(-c^2*x^2+1)^(1/2)*x*d*g+a*h/e^3*ln(c*e*x+c*d)+1/2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*arcsin(c*x)*g*d-3*c^3*b/e^3/(c^2*d^2-e^2)^(3/2)*d^3*h*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))-1/2*c^2*a/e^3/(c*e*x+c*d)^2*d^2*h+2*c*a/e^3/(c*e*x+c*d)*d*h+b*e/(c^2*d^2-e^2)^2*h*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+b*e/(c^2*d^2-e^2)^2*h*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*b/e/(c^2*d^2-e^2)*h*arcsin(c*x)^2-I*b*e/(c^2*d^2-e^2)^2*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-I*b*e/(c^2*d^2-e^2)^2*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*c*b/(c^2*d^2-e^2)^(3/2)*g*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+1/2*c^2*a/e^2/(c*e*x+c*d)^2*d*g+1/2*I*b*arcsin(c*x)^2*h/e^3+1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*(-c^2*x^2+1)^(1/2)*x*d^2*h-c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*arcsin(c*x)*x*d^2*g+2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*arcsin(c*x)*x*d^3*h+I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*g*d^2*x-1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*x^2*d^2*h-I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*x*d^3*h+4*c*b/e/(c^2*d^2-e^2)^(3/2)*d*h*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+c^3*b/e/(c^2*d^2-e^2)^(3/2)*d*f*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+c^3*b/e^2/(c^2*d^2-e^2)^(3/2)*d^2*g*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+1/2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*arcsin(c*x)*f+1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*(-c^2*x^2+1)^(1/2)*d*f-1/2*c^2*a/e/(c*e*x+c*d)^2*f-c*a*g/e^2/(c*e*x+c*d)","B"
103,1,2173,329,0.017000," ","int((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^4,x)","\frac{7 c^{3} b \,d^{2} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) h}{6 e^{4} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c a h}{e^{3} \left(c e x +d c \right)}+\frac{c^{3} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d^{2} h}{6 e^{4} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{2}}-\frac{c^{5} b \,d^{4} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) h}{2 e^{4} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{3} a f}{3 e \left(c e x +d c \right)^{3}}+\frac{c^{3} b \arcsin \left(c x \right) d g}{3 e^{2} \left(c e x +d c \right)^{3}}+\frac{c^{2} b g \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)}+\frac{c^{3} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{6 e^{2} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{2}}+\frac{c^{3} b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{6 e^{2} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{2} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d h}{e^{3} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)}+\frac{c^{4} b \,d^{3} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, h}{2 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}+\frac{c^{2} b \arcsin \left(c x \right) d h}{e^{3} \left(c e x +d c \right)^{2}}-\frac{c^{3} b \arcsin \left(c x \right) d^{2} h}{3 e^{3} \left(c e x +d c \right)^{3}}+\frac{c^{3} a d g}{3 e^{2} \left(c e x +d c \right)^{3}}-\frac{c^{2} b \arcsin \left(c x \right) g}{2 e^{2} \left(c e x +d c \right)^{2}}-\frac{c^{3} b \arcsin \left(c x \right) f}{3 e \left(c e x +d c \right)^{3}}+\frac{c^{4} b d \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, f}{2 e \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}+\frac{c^{5} b \,d^{3} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) g}{2 e^{3} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{5} b \,d^{2} \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c^{4} b \,d^{2} \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, g}{2 e^{2} \left(c^{2} d^{2}-e^{2}\right)^{2} \left(c x +\frac{d c}{e}\right)}-\frac{c^{3} b \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, d g}{6 e^{3} \left(c^{2} d^{2}-e^{2}\right) \left(c x +\frac{d c}{e}\right)^{2}}-\frac{2 c^{3} b g d \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{3 e^{3} \left(c^{2} d^{2}-e^{2}\right) \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c b h \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right)}{e^{4} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c b \arcsin \left(c x \right) h}{e^{3} \left(c e x +d c \right)}+\frac{c^{2} a d h}{e^{3} \left(c e x +d c \right)^{2}}-\frac{c^{3} a \,d^{2} h}{3 e^{3} \left(c e x +d c \right)^{3}}-\frac{c^{2} a g}{2 e^{2} \left(c e x +d c \right)^{2}}"," ",0,"7/6*c^3*b/e^4*d^2/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*h-c*a*h/e^3/(c*e*x+c*d)+1/6*c^3*b/e^4/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d^2*h-1/2*c^5*b/e^4*d^4/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*h-1/3*c^3*a/e/(c*e*x+c*d)^3*f+1/3*c^3*b*arcsin(c*x)/e^2/(c*e*x+c*d)^3*d*g+1/2*c^2*b/e^2*g/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)+1/6*c^3*b/e^2/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+1/6*c^3*b/e^2/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-c^2*b/e^3/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*h+1/2*c^4*b/e^3*d^3/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*h+c^2*b*arcsin(c*x)/e^3/(c*e*x+c*d)^2*d*h-1/3*c^3*b*arcsin(c*x)/e^3/(c*e*x+c*d)^3*d^2*h+1/3*c^3*a/e^2/(c*e*x+c*d)^3*d*g-1/2*c^2*b*arcsin(c*x)*g/e^2/(c*e*x+c*d)^2-1/3*c^3*b*arcsin(c*x)/e/(c*e*x+c*d)^3*f+1/2*c^4*b/e*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+1/2*c^5*b/e^3*d^3/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g-1/2*c^5*b/e^2*d^2/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-1/2*c^4*b/e^2*d^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g-1/6*c^3*b/e^3/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g-2/3*c^3*b/e^3*g*d/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))-c*b/e^4*h/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))-c*b*arcsin(c*x)*h/e^3/(c*e*x+c*d)+c^2*a/e^3/(c*e*x+c*d)^2*d*h-1/3*c^3*a/e^3/(c*e*x+c*d)^3*d^2*h-1/2*c^2*a*g/e^2/(c*e*x+c*d)^2","B"
104,1,3005,444,0.024000," ","int((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^5,x)","\text{output too large to display}"," ",0,"-1/2*c^2*a*h/e^3/(c*e*x+c*d)^2+5/8*c^7*b/e^3*d^4/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g-5/8*c^7*b/e^2*d^3/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f+3/8*c^5*b/e^2*d/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-1/4*c^4*a/e/(c*e*x+c*d)^4*f-1/3*c^3*a*g/e^2/(c*e*x+c*d)^3+1/12*c^4*b/e^5/(c^2*d^2-e^2)/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d^2*h+11/8*c^5*b/e^4*d^3/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*h-5/6*c^3*b/e^4*h*d/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))+5/8*c^6*b/e^3*d^4/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*h+5/24*c^5*b/e^4*d^3/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*h-5/8*c^7*b/e^4*d^5/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*h+5/8*c^6*b/e*d^2/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+5/24*c^5*b/e^2*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-5/8*c^6*b/e^2*d^3/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g-5/24*c^5*b/e^3*d^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g+2/3*c^4*b/e^2*g*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-7/8*c^5*b/e^3*g*d^2/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))-1/12*c^4*b/e^4/(c^2*d^2-e^2)/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g+1/4*c^4*b*arcsin(c*x)/e^2/(c*e*x+c*d)^4*d*g+1/6*c^3*b/e^3*g/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)+1/6*c^3*b/e^3*g/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))+1/12*c^4*b/e^3/(c^2*d^2-e^2)/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-1/6*c^4*b/e/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+2/3*c^3*a/e^3/(c*e*x+c*d)^3*d*h-1/2*c^2*b*arcsin(c*x)*h/e^3/(c*e*x+c*d)^2-1/4*c^4*a/e^3/(c*e*x+c*d)^4*d^2*h+1/2*c^2*b/e^3*h/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-1/4*c^4*b*arcsin(c*x)/e^3/(c*e*x+c*d)^4*d^2*h+2/3*c^3*b*arcsin(c*x)/e^3/(c*e*x+c*d)^3*d*h-1/3*c^3*b/e^4/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*h-7/6*c^4*b/e^3*d^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*h+1/4*c^4*a/e^2/(c*e*x+c*d)^4*d*g-1/4*c^4*b*arcsin(c*x)/e/(c*e*x+c*d)^4*f-1/3*c^3*b*arcsin(c*x)*g/e^2/(c*e*x+c*d)^3","B"
105,1,4077,563,0.019000," ","int((h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^6,x)","\text{output too large to display}"," ",0,"-1/4*c^4*a*g/e^2/(c*e*x+c*d)^4+7/60*c^6*b/e^5*d^3/(c^2*d^2-e^2)^2/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*h+7/8*c^8*b/e^3*d^5/(c^2*d^2-e^2)^4/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*h-1/6*c^4*b/e^5/(c^2*d^2-e^2)/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*h-59/120*c^5*b/e^4/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d^2*h-7/8*c^9*b/e^4*d^6/(c^2*d^2-e^2)^4/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*h+2*c^7*b/e^4*d^4/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*h+5/6*c^4*b/e^3*h*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-53/40*c^5*b/e^4*h*d^2/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))+7/24*c^7*b/e^4*d^4/(c^2*d^2-e^2)^3/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*h+1/20*c^5*b/e^6/(c^2*d^2-e^2)/(c*x+d*c/e)^4*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d^2*h-41/24*c^6*b/e^3*d^3/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*h-1/5*c^5*a/e/(c*e*x+c*d)^5*f-1/5*c^5*a/e^3/(c*e*x+c*d)^5*d^2*h+1/2*c^4*a/e^3/(c*e*x+c*d)^4*d*h-1/3*c^3*b*arcsin(c*x)*h/e^3/(c*e*x+c*d)^3+17/60*c^5*b/e^3/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g-11/24*c^6*b/e*d/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+7/60*c^6*b/e^3*d/(c^2*d^2-e^2)^2/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+9/20*c^5*b/e^3/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*d*g+7/24*c^7*b/e^2*d^2/(c^2*d^2-e^2)^3/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-7/8*c^8*b/e^2*d^4/(c^2*d^2-e^2)^4/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g+7/8*c^8*b/e*d^3/(c^2*d^2-e^2)^4/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-1/20*c^5*b/e^5/(c^2*d^2-e^2)/(c*x+d*c/e)^4*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g-7/24*c^7*b/e^3*d^3/(c^2*d^2-e^2)^3/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g-7/60*c^6*b/e^4*d^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g+7/8*c^9*b/e^3*d^5/(c^2*d^2-e^2)^4/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g-3/40*c^5*b/e^2/(c^2*d^2-e^2)^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f+1/5*c^5*b*arcsin(c*x)/e^2/(c*e*x+c*d)^5*d*g+1/20*c^5*b/e^4/(c^2*d^2-e^2)/(c*x+d*c/e)^4*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-3/40*c^5*b/e^2/(c^2*d^2-e^2)^2/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f+1/12*c^4*b/e^4*g/(c^2*d^2-e^2)/(c*x+d*c/e)^3*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-1/6*c^4*b/e^2*g/(c^2*d^2-e^2)^2/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)+1/5*c^5*a/e^2/(c*e*x+c*d)^5*d*g-1/5*c^5*b*arcsin(c*x)/e/(c*e*x+c*d)^5*f-1/4*c^4*b*arcsin(c*x)*g/e^2/(c*e*x+c*d)^4+13/12*c^6*b/e^2*d^2/(c^2*d^2-e^2)^3/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*g-7/8*c^9*b/e^2*d^4/(c^2*d^2-e^2)^4/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-11/8*c^7*b/e^3*d^3/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g+3/4*c^7*b/e^2*d^2/(c^2*d^2-e^2)^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-1/3*c^3*a*h/e^3/(c*e*x+c*d)^3+1/6*c^3*b/e^4*h/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))+1/6*c^3*b/e^4*h/(c^2*d^2-e^2)/(c*x+d*c/e)^2*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)-1/5*c^5*b*arcsin(c*x)/e^3/(c*e*x+c*d)^5*d^2*h+1/2*c^4*b*arcsin(c*x)/e^3/(c*e*x+c*d)^4*d*h","B"
106,1,932,643,0.019000," ","int((e*x+d)^3*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e^{3} i \,c^{7} x^{7}}{7}+\frac{\left(3 d c \,e^{2} i +e^{3} c h \right) c^{6} x^{6}}{6}+\frac{\left(3 c^{2} d^{2} e i +3 d \,c^{2} e^{2} h +e^{3} c^{2} g \right) c^{5} x^{5}}{5}+\frac{\left(c^{3} d^{3} i +3 c^{3} d^{2} e h +3 d \,c^{3} e^{2} g +e^{3} f \,c^{3}\right) c^{4} x^{4}}{4}+\frac{\left(c^{4} d^{3} h +3 c^{4} d^{2} e g +3 d \,c^{4} e^{2} f \right) c^{3} x^{3}}{3}+\frac{\left(c^{5} d^{3} g +3 c^{5} d^{2} e f \right) c^{2} x^{2}}{2}+c^{7} d^{3} f x \right)}{c^{6}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{3} i \,c^{7} x^{7}}{7}+\frac{\arcsin \left(c x \right) c^{7} x^{6} d \,e^{2} i}{2}+\frac{\arcsin \left(c x \right) c^{7} x^{6} e^{3} h}{6}+\frac{3 \arcsin \left(c x \right) c^{7} x^{5} d^{2} e i}{5}+\frac{3 \arcsin \left(c x \right) c^{7} x^{5} d \,e^{2} h}{5}+\frac{\arcsin \left(c x \right) c^{7} x^{5} e^{3} g}{5}+\frac{\arcsin \left(c x \right) c^{7} x^{4} d^{3} i}{4}+\frac{3 \arcsin \left(c x \right) c^{7} x^{4} d^{2} e h}{4}+\frac{3 \arcsin \left(c x \right) c^{7} x^{4} d \,e^{2} g}{4}+\frac{\arcsin \left(c x \right) c^{7} x^{4} e^{3} f}{4}+\frac{\arcsin \left(c x \right) c^{7} x^{3} d^{3} h}{3}+\arcsin \left(c x \right) c^{7} x^{3} d^{2} e g +\arcsin \left(c x \right) c^{7} x^{3} d \,e^{2} f +\frac{\arcsin \left(c x \right) c^{7} x^{2} d^{3} g}{2}+\frac{3 \arcsin \left(c x \right) c^{7} x^{2} d^{2} e f}{2}+\arcsin \left(c x \right) c^{7} d^{3} f x -\frac{e^{3} i \left(-\frac{c^{6} x^{6} \sqrt{-c^{2} x^{2}+1}}{7}-\frac{6 c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{8 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{35}-\frac{16 \sqrt{-c^{2} x^{2}+1}}{35}\right)}{7}-\frac{\left(210 d c \,e^{2} i +70 e^{3} c h \right) \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{420}-\frac{\left(252 c^{2} d^{2} e i +252 d \,c^{2} e^{2} h +84 e^{3} c^{2} g \right) \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{420}-\frac{\left(105 c^{3} d^{3} i +315 c^{3} d^{2} e h +315 d \,c^{3} e^{2} g +105 e^{3} f \,c^{3}\right) \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{420}-\frac{\left(140 c^{4} d^{3} h +420 c^{4} d^{2} e g +420 d \,c^{4} e^{2} f \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{420}-\frac{\left(210 c^{5} d^{3} g +630 c^{5} d^{2} e f \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{420}+c^{6} d^{3} f \sqrt{-c^{2} x^{2}+1}\right)}{c^{6}}}{c}"," ",0,"1/c*(a/c^6*(1/7*e^3*i*c^7*x^7+1/6*(3*c*d*e^2*i+c*e^3*h)*c^6*x^6+1/5*(3*c^2*d^2*e*i+3*c^2*d*e^2*h+c^2*e^3*g)*c^5*x^5+1/4*(c^3*d^3*i+3*c^3*d^2*e*h+3*c^3*d*e^2*g+c^3*e^3*f)*c^4*x^4+1/3*(c^4*d^3*h+3*c^4*d^2*e*g+3*c^4*d*e^2*f)*c^3*x^3+1/2*(c^5*d^3*g+3*c^5*d^2*e*f)*c^2*x^2+c^7*d^3*f*x)+b/c^6*(1/7*arcsin(c*x)*e^3*i*c^7*x^7+1/2*arcsin(c*x)*c^7*x^6*d*e^2*i+1/6*arcsin(c*x)*c^7*x^6*e^3*h+3/5*arcsin(c*x)*c^7*x^5*d^2*e*i+3/5*arcsin(c*x)*c^7*x^5*d*e^2*h+1/5*arcsin(c*x)*c^7*x^5*e^3*g+1/4*arcsin(c*x)*c^7*x^4*d^3*i+3/4*arcsin(c*x)*c^7*x^4*d^2*e*h+3/4*arcsin(c*x)*c^7*x^4*d*e^2*g+1/4*arcsin(c*x)*c^7*x^4*e^3*f+1/3*arcsin(c*x)*c^7*x^3*d^3*h+arcsin(c*x)*c^7*x^3*d^2*e*g+arcsin(c*x)*c^7*x^3*d*e^2*f+1/2*arcsin(c*x)*c^7*x^2*d^3*g+3/2*arcsin(c*x)*c^7*x^2*d^2*e*f+arcsin(c*x)*c^7*d^3*f*x-1/7*e^3*i*(-1/7*c^6*x^6*(-c^2*x^2+1)^(1/2)-6/35*c^4*x^4*(-c^2*x^2+1)^(1/2)-8/35*c^2*x^2*(-c^2*x^2+1)^(1/2)-16/35*(-c^2*x^2+1)^(1/2))-1/420*(210*c*d*e^2*i+70*c*e^3*h)*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-1/420*(252*c^2*d^2*e*i+252*c^2*d*e^2*h+84*c^2*e^3*g)*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/420*(105*c^3*d^3*i+315*c^3*d^2*e*h+315*c^3*d*e^2*g+105*c^3*e^3*f)*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/420*(140*c^4*d^3*h+420*c^4*d^2*e*g+420*c^4*d*e^2*f)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/420*(210*c^5*d^3*g+630*c^5*d^2*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^6*d^3*f*(-c^2*x^2+1)^(1/2)))","A"
107,1,674,449,0.007000," ","int((e*x+d)^2*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e^{2} i \,c^{6} x^{6}}{6}+\frac{\left(2 d c e i +e^{2} c h \right) c^{5} x^{5}}{5}+\frac{\left(c^{2} d^{2} i +2 d \,c^{2} e h +e^{2} c^{2} g \right) c^{4} x^{4}}{4}+\frac{\left(c^{3} d^{2} h +2 d \,c^{3} e g +e^{2} f \,c^{3}\right) c^{3} x^{3}}{3}+\frac{\left(c^{4} d^{2} g +2 d \,c^{4} e f \right) c^{2} x^{2}}{2}+c^{6} d^{2} f x \right)}{c^{5}}+\frac{b \left(\frac{\arcsin \left(c x \right) e^{2} i \,c^{6} x^{6}}{6}+\frac{2 \arcsin \left(c x \right) c^{6} x^{5} d e i}{5}+\frac{\arcsin \left(c x \right) c^{6} x^{5} e^{2} h}{5}+\frac{\arcsin \left(c x \right) c^{6} x^{4} d^{2} i}{4}+\frac{\arcsin \left(c x \right) c^{6} x^{4} d e h}{2}+\frac{\arcsin \left(c x \right) c^{6} x^{4} e^{2} g}{4}+\frac{\arcsin \left(c x \right) c^{6} x^{3} d^{2} h}{3}+\frac{2 \arcsin \left(c x \right) c^{6} x^{3} d e g}{3}+\frac{\arcsin \left(c x \right) c^{6} x^{3} e^{2} f}{3}+\frac{\arcsin \left(c x \right) c^{6} x^{2} d^{2} g}{2}+\arcsin \left(c x \right) c^{6} x^{2} d e f +\arcsin \left(c x \right) c^{6} d^{2} f x -\frac{e^{2} i \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{6}-\frac{\left(24 d c e i +12 e^{2} c h \right) \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{60}-\frac{\left(15 c^{2} d^{2} i +30 d \,c^{2} e h +15 e^{2} c^{2} g \right) \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{60}-\frac{\left(20 c^{3} d^{2} h +40 d \,c^{3} e g +20 e^{2} f \,c^{3}\right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{60}-\frac{\left(30 c^{4} d^{2} g +60 d \,c^{4} e f \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{60}+c^{5} d^{2} f \sqrt{-c^{2} x^{2}+1}\right)}{c^{5}}}{c}"," ",0,"1/c*(a/c^5*(1/6*e^2*i*c^6*x^6+1/5*(2*c*d*e*i+c*e^2*h)*c^5*x^5+1/4*(c^2*d^2*i+2*c^2*d*e*h+c^2*e^2*g)*c^4*x^4+1/3*(c^3*d^2*h+2*c^3*d*e*g+c^3*e^2*f)*c^3*x^3+1/2*(c^4*d^2*g+2*c^4*d*e*f)*c^2*x^2+c^6*d^2*f*x)+b/c^5*(1/6*arcsin(c*x)*e^2*i*c^6*x^6+2/5*arcsin(c*x)*c^6*x^5*d*e*i+1/5*arcsin(c*x)*c^6*x^5*e^2*h+1/4*arcsin(c*x)*c^6*x^4*d^2*i+1/2*arcsin(c*x)*c^6*x^4*d*e*h+1/4*arcsin(c*x)*c^6*x^4*e^2*g+1/3*arcsin(c*x)*c^6*x^3*d^2*h+2/3*arcsin(c*x)*c^6*x^3*d*e*g+1/3*arcsin(c*x)*c^6*x^3*e^2*f+1/2*arcsin(c*x)*c^6*x^2*d^2*g+arcsin(c*x)*c^6*x^2*d*e*f+arcsin(c*x)*c^6*d^2*f*x-1/6*e^2*i*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-1/60*(24*c*d*e*i+12*c*e^2*h)*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/60*(15*c^2*d^2*i+30*c^2*d*e*h+15*c^2*e^2*g)*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/60*(20*c^3*d^2*h+40*c^3*d*e*g+20*c^3*e^2*f)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/60*(30*c^4*d^2*g+60*c^4*d*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^5*d^2*f*(-c^2*x^2+1)^(1/2)))","A"
108,1,428,277,0.007000," ","int((e*x+d)*(i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x)),x)","\frac{\frac{a \left(\frac{e i \,c^{5} x^{5}}{5}+\frac{\left(d c i +e c h \right) c^{4} x^{4}}{4}+\frac{\left(d \,c^{2} h +e \,c^{2} g \right) c^{3} x^{3}}{3}+\frac{\left(d \,c^{3} g +e f \,c^{3}\right) c^{2} x^{2}}{2}+c^{5} f d x \right)}{c^{4}}+\frac{b \left(\frac{\arcsin \left(c x \right) e i \,c^{5} x^{5}}{5}+\frac{\arcsin \left(c x \right) c^{5} x^{4} d i}{4}+\frac{\arcsin \left(c x \right) c^{5} x^{4} e h}{4}+\frac{\arcsin \left(c x \right) c^{5} x^{3} d h}{3}+\frac{\arcsin \left(c x \right) c^{5} x^{3} e g}{3}+\frac{\arcsin \left(c x \right) c^{5} x^{2} d g}{2}+\frac{\arcsin \left(c x \right) c^{5} x^{2} e f}{2}+\arcsin \left(c x \right) c^{5} f d x -\frac{e i \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{\left(15 d c i +15 e c h \right) \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{60}-\frac{\left(20 d \,c^{2} h +20 e \,c^{2} g \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{60}-\frac{\left(30 d \,c^{3} g +30 e f \,c^{3}\right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{60}+c^{4} d f \sqrt{-c^{2} x^{2}+1}\right)}{c^{4}}}{c}"," ",0,"1/c*(a/c^4*(1/5*e*i*c^5*x^5+1/4*(c*d*i+c*e*h)*c^4*x^4+1/3*(c^2*d*h+c^2*e*g)*c^3*x^3+1/2*(c^3*d*g+c^3*e*f)*c^2*x^2+c^5*f*d*x)+b/c^4*(1/5*arcsin(c*x)*e*i*c^5*x^5+1/4*arcsin(c*x)*c^5*x^4*d*i+1/4*arcsin(c*x)*c^5*x^4*e*h+1/3*arcsin(c*x)*c^5*x^3*d*h+1/3*arcsin(c*x)*c^5*x^3*e*g+1/2*arcsin(c*x)*c^5*x^2*d*g+1/2*arcsin(c*x)*c^5*x^2*e*f+arcsin(c*x)*c^5*f*d*x-1/5*e*i*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/60*(15*c*d*i+15*c*e*h)*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/60*(20*c^2*d*h+20*c^2*e*g)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/60*(30*c^3*d*g+30*c^3*e*f)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^4*d*f*(-c^2*x^2+1)^(1/2)))","A"
109,1,3418,621,0.871000," ","int((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d),x)","\text{output too large to display}"," ",0,"a*g/e*x+a/e*ln(c*e*x+c*d)*f+b*g*(-c^2*x^2+1)^(1/2)/c/e+b*arcsin(c*x)*g/e*x-1/2*I*b*arcsin(c*x)^2/e*f-c^2*b/e^2*d^3*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+c^2*b/e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^2*b/e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2+I*c^2*b/e^2*d^3*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2+c^2*b/e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-c^2*b/e^2*d^3*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*c^2*b/e^2*d^3*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*b/e*d^2*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+I*b/e*d^2*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-b/e*d^2*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-b/e*d^2*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+b*arcsin(c*x)/e^3*x*d^2*i-1/8/c^2*b/e^2*sin(2*arcsin(c*x))*d*i+1/c*b/e^3*(-c^2*x^2+1)^(1/2)*d^2*i-1/12/c^3*b*arcsin(c*x)*i/e*sin(3*arcsin(c*x))+1/4/c^2*b/e*arcsin(c*x)*x*i+1/3*a/e*i*x^3+a/e^3*x*d^2*i+a/e^3*ln(c*e*x+c*d)*d^2*h+1/8/c^2*b/e*h*sin(2*arcsin(c*x))-a/e^2*x*d*h+I*c^2*b/e^4*d^5*i/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-c^2*b/e^4*d^5*i*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-c^2*b/e^4*d^5*i*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*c^2*b/e^4*d^5*i/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+b*d*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+b*d*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-b*e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+1/2*I*b*arcsin(c*x)^2/e^2*d*g+I*b*e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+I*b*e*f/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*b*d*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-b*e*f*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*b*d*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+1/2*I*b*arcsin(c*x)^2/e^4*d^3*i-1/4/c^2*b/e*h*arcsin(c*x)*cos(2*arcsin(c*x))-1/c*b/e^2*(-c^2*x^2+1)^(1/2)*d*h-b*arcsin(c*x)/e^2*x*d*h-1/2*I*b*arcsin(c*x)^2/e^3*d^2*h-1/2*a/e^2*x^2*d*i-a/e^4*ln(c*e*x+c*d)*d^3*i-1/36/c^3*b*i/e*cos(3*arcsin(c*x))+1/4/c^3*b/e*(-c^2*x^2+1)^(1/2)*i+b/e^2*d^3*i*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+b/e^2*d^3*i*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+1/4/c^2*b/e^2*arcsin(c*x)*cos(2*arcsin(c*x))*d*i-I*b/e^2*d^3*i/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*b/e^2*d^3*i/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+1/2*a/e*h*x^2+c^2*b/e^3*d^4*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+c^2*b/e^3*d^4*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e^3*d^4*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*c^2*b/e^3*d^4*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-a/e^2*ln(c*e*x+c*d)*d*g","B"
110,1,2921,616,1.625000," ","int((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^2,x)","\text{output too large to display}"," ",0,"c*a/e^2/(c*e*x+c*d)*d*g-c*b*arcsin(c*x)/e/(c*e*x+c*d)*f+c*b*arcsin(c*x)/e^2/(c*e*x+c*d)*d*g+b*h*(-c^2*x^2+1)^(1/2)/c/e^2-1/2*I*b*g*arcsin(c*x)^2/e^2+c*a/e^4/(c*e*x+c*d)*d^3*i+1/4*b*i*x*(-c^2*x^2+1)^(1/2)/c/e^2-c*b*arcsin(c*x)/e^3/(c*e*x+c*d)*d^2*h+2*c*b/e^3*d^2*h/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+2*b/e*d*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+2*b/e*d*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*I*b/e*d*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*I*b/e*d*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+1/2*a/e^2*i*x^2+2*c*b/e*f/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+a*h/e^2*x-2*c*b/e^2*d*g/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+3*a/e^4*ln(c*e*x+c*d)*d^2*i-2*a/e^3*d*i*x-2*c*b/e^4*d^3*i/(c^2*d^2-e^2)^(1/2)*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+c*b*arcsin(c*x)/e^4/(c*e*x+c*d)*d^3*i-3*b/e^2*d^2*i*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-3*b/e^2*d^2*i*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+3*I*b/e^2*d^2*i/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+3*I*b/e^2*d^2*i/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2/c*b/e^3*(-c^2*x^2+1)^(1/2)*d*i-2*b*arcsin(c*x)/e^3*d*i*x-3/2*I*b*arcsin(c*x)^2/e^4*d^2*i-2*c^2*b/e^3*d^3*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*c^2*b/e^3*d^3*h*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+2*I*c^2*b/e^3*d^3*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+2*I*c^2*b/e^3*d^3*h/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-c*a/e^3/(c*e*x+c*d)*d^2*h+I*b*arcsin(c*x)^2/e^3*d*h+3*c^2*b/e^4*d^4*i*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+3*c^2*b/e^4*d^4*i*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-3*I*c^2*b/e^4*d^4*i/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+1/2*b*arcsin(c*x)/e^2*i*x^2-3*I*c^2*b/e^4*d^4*i/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+a*g/e^2*ln(c*e*x+c*d)+I*b*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-b*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))/(c^2*d^2-e^2)*arcsin(c*x)*g-b*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))/(c^2*d^2-e^2)*arcsin(c*x)*g-1/4*b*i*arcsin(c*x)/c^2/e^2-c*a/e/(c*e*x+c*d)*f+I*b*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*a/e^3*ln(c*e*x+c*d)*d*h+b*arcsin(c*x)*h/e^2*x-I*c^2*b/e^2*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2+c^2*b/e^2*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2+c^2*b/e^2*g*arcsin(c*x)/(c^2*d^2-e^2)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^2*b/e^2*g/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2","B"
111,1,4530,979,1.872000," ","int((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"-2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*arcsin(c*x)*x*d*h+1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*(-c^2*x^2+1)^(1/2)*x*f+c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*arcsin(c*x)*x*g-2*c^2*b/e/(c^2*d^2-e^2)^2*h*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-2*c^2*b/e/(c^2*d^2-e^2)^2*d^2*h*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*x^2*f-I*c^4*b/e^3/(c^2*d^2-e^2)^2*d^4*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+2*I*c^2*b/e/(c^2*d^2-e^2)^2*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^2*b/e^3/(c^2*d^2-e^2)*d^2*h*arcsin(c*x)^2-1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^3*d^4*h+1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*d^3*g-1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*d^2*f+2*I*c^2*b/e/(c^2*d^2-e^2)^2*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2-I*c^4*b/e^3/(c^2*d^2-e^2)^2*d^4*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x^2*d*g-I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x*d*f+3/2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^3*arcsin(c*x)*d^4*h-1/2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*arcsin(c*x)*d^3*g-1/2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*arcsin(c*x)*d^2*f+1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*(-c^2*x^2+1)^(1/2)*d^3*h-1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*(-c^2*x^2+1)^(1/2)*d^2*g-3/2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*arcsin(c*x)*d^2*h+c^4*b/e^3/(c^2*d^2-e^2)^2*d^4*h*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+c^4*b/e^3/(c^2*d^2-e^2)^2*d^4*h*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*(-c^2*x^2+1)^(1/2)*x*d*g+a*i/e^3*x+a*h/e^3*ln(c*e*x+c*d)+1/2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*arcsin(c*x)*g*d-3*c^3*b/e^3/(c^2*d^2-e^2)^(3/2)*d^3*h*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))-1/2*c^2*a/e^3/(c*e*x+c*d)^2*d^2*h+2*c*a/e^3/(c*e*x+c*d)*d*h+b*e/(c^2*d^2-e^2)^2*h*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+b*e/(c^2*d^2-e^2)^2*h*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*b/e/(c^2*d^2-e^2)*h*arcsin(c*x)^2-I*b*e/(c^2*d^2-e^2)^2*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-I*b*e/(c^2*d^2-e^2)^2*h*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+b*arcsin(c*x)*i/e^3*x-2*c*b/(c^2*d^2-e^2)^(3/2)*g*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))-6*I*c^2*b/e^2/(c^2*d^2-e^2)^2*d^3*i*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+3*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*arcsin(c*x)*x*d^2*i-1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*(-c^2*x^2+1)^(1/2)*x*d^3*i-3*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^3*arcsin(c*x)*x*d^4*i+I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^3*x*d^4*i+1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*x^2*d^3*i+1/2*c^2*a/e^4/(c*e*x+c*d)^2*d^3*i-3*c*a/e^4/(c*e*x+c*d)*d^2*i-3*b/(c^2*d^2-e^2)^2*d*i*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-3*b/(c^2*d^2-e^2)^2*d*i*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-3/2*I*b*arcsin(c*x)^2/e^4*d*i+3*I*b/(c^2*d^2-e^2)^2*d*i*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+3*I*b/(c^2*d^2-e^2)^2*d*i*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+1/2*c^2*a/e^2/(c*e*x+c*d)^2*d*g+3*I*c^4*b/e^4/(c^2*d^2-e^2)^2*d^5*i*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+3*I*c^4*b/e^4/(c^2*d^2-e^2)^2*d^5*i*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+5/2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*arcsin(c*x)*d^3*i-3*c^4*b/e^4/(c^2*d^2-e^2)^2*d^5*i*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-3*c^4*b/e^4/(c^2*d^2-e^2)^2*d^5*i*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+6*c^2*b/e^2/(c^2*d^2-e^2)^2*d^3*i*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+6*c^2*b/e^2/(c^2*d^2-e^2)^2*d^3*i*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-5/2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^4*arcsin(c*x)*d^5*i-1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^3*(-c^2*x^2+1)^(1/2)*d^4*i+3*I*c^2*b/e^4/(c^2*d^2-e^2)*d^3*i*arcsin(c*x)^2+1/2*I*b*arcsin(c*x)^2*h/e^3+1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*(-c^2*x^2+1)^(1/2)*x*d^2*h-c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*arcsin(c*x)*x*d^2*g+2*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*arcsin(c*x)*x*d^3*h+I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*g*d^2*x-1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*x^2*d^2*h-I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*x*d^3*h+b*i*(-c^2*x^2+1)^(1/2)/c/e^3-6*c*b/e^2/(c^2*d^2-e^2)^(3/2)*d^2*i*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+5*c^3*b/e^4/(c^2*d^2-e^2)^(3/2)*d^4*i*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))-3*I*b/e^2/(c^2*d^2-e^2)*d*i*arcsin(c*x)^2-3*a/e^4*ln(c*e*x+c*d)*d*i+4*c*b/e/(c^2*d^2-e^2)^(3/2)*d*h*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+c^3*b/e/(c^2*d^2-e^2)^(3/2)*d*f*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+c^3*b/e^2/(c^2*d^2-e^2)^(3/2)*d^2*g*arctan(1/2*(2*(I*c*x+(-c^2*x^2+1)^(1/2))*e+2*I*d*c)/(c^2*d^2-e^2)^(1/2))+1/2*c^2*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*arcsin(c*x)*f+1/2*c^3*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2*(-c^2*x^2+1)^(1/2)*d*f-1/2*c^2*a/e/(c*e*x+c*d)^2*f-c*a*g/e^2/(c*e*x+c*d)+1/2*I*c^4*b/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^4*d^5*i-6*I*c^2*b/e^2/(c^2*d^2-e^2)^2*d^3*i*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))","B"
112,1,5670,1225,3.735000," ","int((i*x^3+h*x^2+g*x+f)*(a+b*arcsin(c*x))/(e*x+d)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
113,1,3096,941,1.763000," ","int((g*x+f)*(a+b*arcsin(c*x))^2/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"c^3*b^2/e*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*d*f*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-c^2*a*b/e^2/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*d*g-c^3*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*(-c^2*x^2+1)^(1/2)*x*d*g-c^4*b^2*arcsin(c*x)^2/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*x*d^2*g+c^3*b^2/e^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*g*d^2*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-c^3*b^2/e*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*d*f*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-c^3*b^2/e^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*g*d^2*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))+I*c^4*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*d^3*g+c^3*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*(-c^2*x^2+1)^(1/2)*x*f+I*c^4*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x^2*d*g+I*c^3*b^2/e^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*g*d^2*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+I*c^3*b^2/e*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*d*f*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))+c^3*a*b/e^3*d^2/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*g-c^3*a*b/e^2*d/(c^2*d^2-e^2)/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f-I*c^4*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*d^2*f-2*I*c^4*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*x*d*f-I*c^4*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*x^2*f-I*c^3*b^2/e*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*d*f*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-I*c^3*b^2/e^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*g*d^2*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+1/2*c^2*b^2*arcsin(c*x)^2/(c^2*d^2-e^2)/(c*e*x+c*d)^2*d*g+2*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*g*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*g*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))+1/2*c^2*b^2*arcsin(c*x)^2/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*f+2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*g*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))-2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)^2*g*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))-2*c*a*b/e^3*g/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))-2*c^2*b^2/e^2/(c^2*d^2-e^2)*d*g*ln(I*c*x+(-c^2*x^2+1)^(1/2))+c^2*b^2/e^2/(c^2*d^2-e^2)*d*g*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2*e+2*I*d*c*(I*c*x+(-c^2*x^2+1)^(1/2))-e)-2*c*a*b*arcsin(c*x)*g/e^2/(c*e*x+c*d)-c^2*a*b*arcsin(c*x)/e/(c*e*x+c*d)^2*f+1/2*c^2*a^2/e^2/(c*e*x+c*d)^2*d*g-c^2*b^2/e/(c^2*d^2-e^2)*f*ln((I*c*x+(-c^2*x^2+1)^(1/2))^2*e+2*I*d*c*(I*c*x+(-c^2*x^2+1)^(1/2))-e)+2*c^2*b^2/e/(c^2*d^2-e^2)*f*ln(I*c*x+(-c^2*x^2+1)^(1/2))-c*a^2*g/e^2/(c*e*x+c*d)+2*I*c^4*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*g*d^2*x+c^2*b^2*arcsin(c*x)^2/(c^2*d^2-e^2)/(c*e*x+c*d)^2*e*x*g-1/2*c^4*b^2*arcsin(c*x)^2/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e^2*d^3*g-1/2*c^4*b^2*arcsin(c*x)^2/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*d^2*f+c^3*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2*(-c^2*x^2+1)^(1/2)*d*f+c^2*a*b*arcsin(c*x)/e^2/(c*e*x+c*d)^2*d*g+c^2*a*b/e/(c^2*d^2-e^2)/(c*x+d*c/e)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2)*f-1/2*c^2*a^2/e/(c*e*x+c*d)^2*f-c^3*b^2*arcsin(c*x)/(c^2*d^2-e^2)/(c*e*x+c*d)^2/e*(-c^2*x^2+1)^(1/2)*d^2*g","B"
114,0,0,1726,8.677000," ","int((g*x+f)^2*(a+b*arcsin(c*x))^2/(e*x+d)^3,x)","\int \frac{\left(g x +f \right)^{2} \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((g*x+f)^2*(a+b*arcsin(c*x))^2/(e*x+d)^3,x)","F"
115,1,2600,932,0.323000," ","int((h*x+g)^3*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{h^{3} f \,c^{6} x^{6}}{6}+\frac{\left(h^{3} c e +3 c g \,h^{2} f \right) c^{5} x^{5}}{5}+\frac{\left(h^{3} c^{2} d +3 c^{2} g \,h^{2} e +3 c^{2} g^{2} h f \right) c^{4} x^{4}}{4}+\frac{\left(3 c^{3} g \,h^{2} d +3 c^{3} g^{2} h e +c^{3} g^{3} f \right) c^{3} x^{3}}{3}+\frac{\left(3 c^{4} g^{2} h d +c^{4} g^{3} e \right) c^{2} x^{2}}{2}+c^{6} g^{3} d x \right)}{c^{5}}+\frac{b^{2} \left(c^{5} g^{3} d \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+\frac{3 c^{4} g^{2} h d \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{c^{4} g^{3} e \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{c^{3} g \,h^{2} d \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{9}+\frac{c^{3} g^{2} h e \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{9}+\frac{c^{3} g^{3} f \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+\frac{h^{3} c^{2} d \left(8 \arcsin \left(c x \right)^{2} c^{4} x^{4}+4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}-16 \arcsin \left(c x \right)^{2} c^{2} x^{2}-c^{4} x^{4}-10 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x +5 \arcsin \left(c x \right)^{2}+5 c^{2} x^{2}-4\right)}{32}+\frac{3 c^{2} g \,h^{2} e \left(8 \arcsin \left(c x \right)^{2} c^{4} x^{4}+4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}-16 \arcsin \left(c x \right)^{2} c^{2} x^{2}-c^{4} x^{4}-10 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x +5 \arcsin \left(c x \right)^{2}+5 c^{2} x^{2}-4\right)}{32}+\frac{3 c^{2} g^{2} h f \left(8 \arcsin \left(c x \right)^{2} c^{4} x^{4}+4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}-16 \arcsin \left(c x \right)^{2} c^{2} x^{2}-c^{4} x^{4}-10 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x +5 \arcsin \left(c x \right)^{2}+5 c^{2} x^{2}-4\right)}{32}+\frac{h^{3} c e \left(675 \arcsin \left(c x \right)^{2} c^{5} x^{5}+270 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{4} x^{4}-2250 \arcsin \left(c x \right)^{2} c^{3} x^{3}-54 c^{5} x^{5}-1140 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}+3375 c x \arcsin \left(c x \right)^{2}+380 c^{3} x^{3}+4470 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}-4470 c x \right)}{3375}+\frac{c g \,h^{2} f \left(675 \arcsin \left(c x \right)^{2} c^{5} x^{5}+270 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{4} x^{4}-2250 \arcsin \left(c x \right)^{2} c^{3} x^{3}-54 c^{5} x^{5}-1140 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}+3375 c x \arcsin \left(c x \right)^{2}+380 c^{3} x^{3}+4470 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}-4470 c x \right)}{1125}+\frac{h^{3} f \left(144 \arcsin \left(c x \right)^{2} c^{6} x^{6}+48 \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) c^{5} x^{5}-432 \arcsin \left(c x \right)^{2} c^{4} x^{4}-8 c^{6} x^{6}-156 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}+432 \arcsin \left(c x \right)^{2} c^{2} x^{2}+39 c^{4} x^{4}+198 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -99 \arcsin \left(c x \right)^{2}-99 c^{2} x^{2}+68\right)}{864}+3 c^{3} g \,h^{2} d \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+3 c^{3} g^{2} h e \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+c^{3} g^{3} f \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+\frac{h^{3} c^{2} d \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{3 c^{2} g \,h^{2} e \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{3 c^{2} g^{2} h f \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{2 h^{3} c e \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+\frac{2 c g \,h^{2} f \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{9}+\frac{h^{3} f \left(8 \arcsin \left(c x \right)^{2} c^{4} x^{4}+4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}-16 \arcsin \left(c x \right)^{2} c^{2} x^{2}-c^{4} x^{4}-10 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x +5 \arcsin \left(c x \right)^{2}+5 c^{2} x^{2}-4\right)}{16}+h^{3} c e \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+3 c g \,h^{2} f \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+\frac{h^{3} f \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}\right)}{c^{5}}+\frac{2 a b \left(\frac{\arcsin \left(c x \right) h^{3} f \,c^{6} x^{6}}{6}+\frac{\arcsin \left(c x \right) c^{6} x^{5} e \,h^{3}}{5}+\frac{3 \arcsin \left(c x \right) c^{6} x^{5} f g \,h^{2}}{5}+\frac{\arcsin \left(c x \right) c^{6} x^{4} d \,h^{3}}{4}+\frac{3 \arcsin \left(c x \right) c^{6} x^{4} e g \,h^{2}}{4}+\frac{3 \arcsin \left(c x \right) c^{6} x^{4} f \,g^{2} h}{4}+\arcsin \left(c x \right) c^{6} x^{3} d g \,h^{2}+\arcsin \left(c x \right) c^{6} x^{3} e \,g^{2} h +\frac{\arcsin \left(c x \right) c^{6} x^{3} f \,g^{3}}{3}+\frac{3 \arcsin \left(c x \right) c^{6} x^{2} d \,g^{2} h}{2}+\frac{\arcsin \left(c x \right) c^{6} x^{2} e \,g^{3}}{2}+\arcsin \left(c x \right) c^{6} g^{3} d x -\frac{h^{3} f \left(-\frac{c^{5} x^{5} \sqrt{-c^{2} x^{2}+1}}{6}-\frac{5 c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{24}-\frac{5 c x \sqrt{-c^{2} x^{2}+1}}{16}+\frac{5 \arcsin \left(c x \right)}{16}\right)}{6}-\frac{\left(12 h^{3} c e +36 c g \,h^{2} f \right) \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{60}-\frac{\left(15 h^{3} c^{2} d +45 c^{2} g \,h^{2} e +45 c^{2} g^{2} h f \right) \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{60}-\frac{\left(60 c^{3} g \,h^{2} d +60 c^{3} g^{2} h e +20 c^{3} g^{3} f \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{60}-\frac{\left(90 c^{4} g^{2} h d +30 c^{4} g^{3} e \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{60}+c^{5} g^{3} d \sqrt{-c^{2} x^{2}+1}\right)}{c^{5}}}{c}"," ",0,"1/c*(a^2/c^5*(1/6*h^3*f*c^6*x^6+1/5*(c*e*h^3+3*c*f*g*h^2)*c^5*x^5+1/4*(c^2*d*h^3+3*c^2*e*g*h^2+3*c^2*f*g^2*h)*c^4*x^4+1/3*(3*c^3*d*g*h^2+3*c^3*e*g^2*h+c^3*f*g^3)*c^3*x^3+1/2*(3*c^4*d*g^2*h+c^4*e*g^3)*c^2*x^2+c^6*g^3*d*x)+b^2/c^5*(c^5*g^3*d*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+3/4*c^4*g^2*h*d*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/4*c^4*g^3*e*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/9*c^3*g*h^2*d*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+1/9*c^3*g^2*h*e*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+1/27*c^3*g^3*f*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+1/32*h^3*c^2*d*(8*arcsin(c*x)^2*c^4*x^4+4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3-16*arcsin(c*x)^2*c^2*x^2-c^4*x^4-10*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x+5*arcsin(c*x)^2+5*c^2*x^2-4)+3/32*c^2*g*h^2*e*(8*arcsin(c*x)^2*c^4*x^4+4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3-16*arcsin(c*x)^2*c^2*x^2-c^4*x^4-10*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x+5*arcsin(c*x)^2+5*c^2*x^2-4)+3/32*c^2*g^2*h*f*(8*arcsin(c*x)^2*c^4*x^4+4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3-16*arcsin(c*x)^2*c^2*x^2-c^4*x^4-10*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x+5*arcsin(c*x)^2+5*c^2*x^2-4)+1/3375*h^3*c*e*(675*arcsin(c*x)^2*c^5*x^5+270*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^4*x^4-2250*arcsin(c*x)^2*c^3*x^3-54*c^5*x^5-1140*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2+3375*c*x*arcsin(c*x)^2+380*c^3*x^3+4470*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-4470*c*x)+1/1125*c*g*h^2*f*(675*arcsin(c*x)^2*c^5*x^5+270*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^4*x^4-2250*arcsin(c*x)^2*c^3*x^3-54*c^5*x^5-1140*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2+3375*c*x*arcsin(c*x)^2+380*c^3*x^3+4470*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-4470*c*x)+1/864*h^3*f*(144*arcsin(c*x)^2*c^6*x^6+48*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*c^5*x^5-432*arcsin(c*x)^2*c^4*x^4-8*c^6*x^6-156*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3+432*arcsin(c*x)^2*c^2*x^2+39*c^4*x^4+198*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-99*arcsin(c*x)^2-99*c^2*x^2+68)+3*c^3*g*h^2*d*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+3*c^3*g^2*h*e*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+c^3*g^3*f*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+1/4*h^3*c^2*d*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+3/4*c^2*g*h^2*e*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+3/4*c^2*g^2*h*f*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+2/27*h^3*c*e*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+2/9*c*g*h^2*f*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+1/16*h^3*f*(8*arcsin(c*x)^2*c^4*x^4+4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3-16*arcsin(c*x)^2*c^2*x^2-c^4*x^4-10*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x+5*arcsin(c*x)^2+5*c^2*x^2-4)+h^3*c*e*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+3*c*g*h^2*f*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+1/4*h^3*f*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2))+2*a*b/c^5*(1/6*arcsin(c*x)*h^3*f*c^6*x^6+1/5*arcsin(c*x)*c^6*x^5*e*h^3+3/5*arcsin(c*x)*c^6*x^5*f*g*h^2+1/4*arcsin(c*x)*c^6*x^4*d*h^3+3/4*arcsin(c*x)*c^6*x^4*e*g*h^2+3/4*arcsin(c*x)*c^6*x^4*f*g^2*h+arcsin(c*x)*c^6*x^3*d*g*h^2+arcsin(c*x)*c^6*x^3*e*g^2*h+1/3*arcsin(c*x)*c^6*x^3*f*g^3+3/2*arcsin(c*x)*c^6*x^2*d*g^2*h+1/2*arcsin(c*x)*c^6*x^2*e*g^3+arcsin(c*x)*c^6*g^3*d*x-1/6*h^3*f*(-1/6*c^5*x^5*(-c^2*x^2+1)^(1/2)-5/24*c^3*x^3*(-c^2*x^2+1)^(1/2)-5/16*c*x*(-c^2*x^2+1)^(1/2)+5/16*arcsin(c*x))-1/60*(12*c*e*h^3+36*c*f*g*h^2)*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/60*(15*c^2*d*h^3+45*c^2*e*g*h^2+45*c^2*f*g^2*h)*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/60*(60*c^3*d*g*h^2+60*c^3*e*g^2*h+20*c^3*f*g^3)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/60*(90*c^4*d*g^2*h+30*c^4*e*g^3)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^5*g^3*d*(-c^2*x^2+1)^(1/2)))","B"
116,1,1633,639,0.225000," ","int((h*x+g)^2*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{h^{2} f \,c^{5} x^{5}}{5}+\frac{\left(h^{2} c e +2 c g h f \right) c^{4} x^{4}}{4}+\frac{\left(h^{2} c^{2} d +2 c^{2} g h e +c^{2} g^{2} f \right) c^{3} x^{3}}{3}+\frac{\left(2 c^{3} g h d +c^{3} g^{2} e \right) c^{2} x^{2}}{2}+c^{5} g^{2} d x \right)}{c^{4}}+\frac{b^{2} \left(\frac{h^{2} c e \left(8 \arcsin \left(c x \right)^{2} c^{4} x^{4}+4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}-16 \arcsin \left(c x \right)^{2} c^{2} x^{2}-c^{4} x^{4}-10 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x +5 \arcsin \left(c x \right)^{2}+5 c^{2} x^{2}-4\right)}{32}+\frac{c g h f \left(8 \arcsin \left(c x \right)^{2} c^{4} x^{4}+4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}-16 \arcsin \left(c x \right)^{2} c^{2} x^{2}-c^{4} x^{4}-10 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x +5 \arcsin \left(c x \right)^{2}+5 c^{2} x^{2}-4\right)}{16}+\frac{c^{3} g h d \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{2}+\frac{c^{3} g^{2} e \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{h^{2} f \left(675 \arcsin \left(c x \right)^{2} c^{5} x^{5}+270 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{4} x^{4}-2250 \arcsin \left(c x \right)^{2} c^{3} x^{3}-54 c^{5} x^{5}-1140 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}+3375 c x \arcsin \left(c x \right)^{2}+380 c^{3} x^{3}+4470 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}-4470 c x \right)}{3375}+\frac{h^{2} c^{2} d \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+\frac{2 c^{2} g h e \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+\frac{c^{2} g^{2} f \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+c^{4} g^{2} d \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+\frac{h^{2} c e \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{c g h f \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{2}+\frac{2 h^{2} f \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+h^{2} c^{2} d \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+2 c^{2} g h e \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+c^{2} g^{2} f \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+h^{2} f \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{4}}+\frac{2 a b \left(\frac{\arcsin \left(c x \right) h^{2} f \,c^{5} x^{5}}{5}+\frac{\arcsin \left(c x \right) c^{5} x^{4} e \,h^{2}}{4}+\frac{\arcsin \left(c x \right) c^{5} x^{4} f g h}{2}+\frac{\arcsin \left(c x \right) c^{5} x^{3} d \,h^{2}}{3}+\frac{2 \arcsin \left(c x \right) c^{5} x^{3} e g h}{3}+\frac{\arcsin \left(c x \right) c^{5} x^{3} f \,g^{2}}{3}+\arcsin \left(c x \right) c^{5} x^{2} d g h +\frac{\arcsin \left(c x \right) c^{5} x^{2} e \,g^{2}}{2}+\arcsin \left(c x \right) c^{5} g^{2} d x -\frac{h^{2} f \left(-\frac{c^{4} x^{4} \sqrt{-c^{2} x^{2}+1}}{5}-\frac{4 c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{15}-\frac{8 \sqrt{-c^{2} x^{2}+1}}{15}\right)}{5}-\frac{\left(15 h^{2} c e +30 c g h f \right) \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{60}-\frac{\left(20 h^{2} c^{2} d +40 c^{2} g h e +20 c^{2} g^{2} f \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{60}-\frac{\left(60 c^{3} g h d +30 c^{3} g^{2} e \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{60}+c^{4} g^{2} d \sqrt{-c^{2} x^{2}+1}\right)}{c^{4}}}{c}"," ",0,"1/c*(a^2/c^4*(1/5*h^2*f*c^5*x^5+1/4*(c*e*h^2+2*c*f*g*h)*c^4*x^4+1/3*(c^2*d*h^2+2*c^2*e*g*h+c^2*f*g^2)*c^3*x^3+1/2*(2*c^3*d*g*h+c^3*e*g^2)*c^2*x^2+c^5*g^2*d*x)+b^2/c^4*(1/32*h^2*c*e*(8*arcsin(c*x)^2*c^4*x^4+4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3-16*arcsin(c*x)^2*c^2*x^2-c^4*x^4-10*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x+5*arcsin(c*x)^2+5*c^2*x^2-4)+1/16*c*g*h*f*(8*arcsin(c*x)^2*c^4*x^4+4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3-16*arcsin(c*x)^2*c^2*x^2-c^4*x^4-10*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x+5*arcsin(c*x)^2+5*c^2*x^2-4)+1/2*c^3*g*h*d*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/4*c^3*g^2*e*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/3375*h^2*f*(675*arcsin(c*x)^2*c^5*x^5+270*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^4*x^4-2250*arcsin(c*x)^2*c^3*x^3-54*c^5*x^5-1140*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2+3375*c*x*arcsin(c*x)^2+380*c^3*x^3+4470*arcsin(c*x)*(-c^2*x^2+1)^(1/2)-4470*c*x)+1/27*h^2*c^2*d*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+2/27*c^2*g*h*e*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+1/27*c^2*g^2*f*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+c^4*g^2*d*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+1/4*h^2*c*e*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/2*c*g*h*f*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+2/27*h^2*f*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+h^2*c^2*d*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+2*c^2*g*h*e*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+c^2*g^2*f*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+h^2*f*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)))+2*a*b/c^4*(1/5*arcsin(c*x)*h^2*f*c^5*x^5+1/4*arcsin(c*x)*c^5*x^4*e*h^2+1/2*arcsin(c*x)*c^5*x^4*f*g*h+1/3*arcsin(c*x)*c^5*x^3*d*h^2+2/3*arcsin(c*x)*c^5*x^3*e*g*h+1/3*arcsin(c*x)*c^5*x^3*f*g^2+arcsin(c*x)*c^5*x^2*d*g*h+1/2*arcsin(c*x)*c^5*x^2*e*g^2+arcsin(c*x)*c^5*g^2*d*x-1/5*h^2*f*(-1/5*c^4*x^4*(-c^2*x^2+1)^(1/2)-4/15*c^2*x^2*(-c^2*x^2+1)^(1/2)-8/15*(-c^2*x^2+1)^(1/2))-1/60*(15*c*e*h^2+30*c*f*g*h)*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/60*(20*c^2*d*h^2+40*c^2*e*g*h+20*c^2*f*g^2)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/60*(60*c^3*d*g*h+30*c^3*e*g^2)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+c^4*g^2*d*(-c^2*x^2+1)^(1/2)))","B"
117,1,870,383,0.158000," ","int((h*x+g)*(f*x^2+e*x+d)*(a+b*arcsin(c*x))^2,x)","\frac{\frac{a^{2} \left(\frac{h f \,c^{4} x^{4}}{4}+\frac{\left(e c h +c f g \right) c^{3} x^{3}}{3}+\frac{\left(d \,c^{2} h +e \,c^{2} g \right) c^{2} x^{2}}{2}+d \,c^{4} g x \right)}{c^{3}}+\frac{b^{2} \left(\frac{h f \left(8 \arcsin \left(c x \right)^{2} c^{4} x^{4}+4 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{3} x^{3}-16 \arcsin \left(c x \right)^{2} c^{2} x^{2}-c^{4} x^{4}-10 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x +5 \arcsin \left(c x \right)^{2}+5 c^{2} x^{2}-4\right)}{32}+\frac{d \,c^{2} h \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{e \,c^{2} g \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+\frac{e c h \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+\frac{c f g \left(9 \arcsin \left(c x \right)^{2} c^{3} x^{3}+6 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c^{2} x^{2}-27 c x \arcsin \left(c x \right)^{2}-2 c^{3} x^{3}-42 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}+42 c x \right)}{27}+d \,c^{3} g \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+\frac{h f \left(2 \arcsin \left(c x \right)^{2} c^{2} x^{2}+2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\, c x -\arcsin \left(c x \right)^{2}-c^{2} x^{2}\right)}{4}+e c h \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)+c f g \left(c x \arcsin \left(c x \right)^{2}-2 c x +2 \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}\right)\right)}{c^{3}}+\frac{2 a b \left(\frac{\arcsin \left(c x \right) h f \,c^{4} x^{4}}{4}+\frac{\arcsin \left(c x \right) c^{4} x^{3} e h}{3}+\frac{\arcsin \left(c x \right) c^{4} x^{3} f g}{3}+\frac{\arcsin \left(c x \right) c^{4} x^{2} d h}{2}+\frac{\arcsin \left(c x \right) c^{4} x^{2} e g}{2}+\arcsin \left(c x \right) d \,c^{4} g x -\frac{h f \left(-\frac{c^{3} x^{3} \sqrt{-c^{2} x^{2}+1}}{4}-\frac{3 c x \sqrt{-c^{2} x^{2}+1}}{8}+\frac{3 \arcsin \left(c x \right)}{8}\right)}{4}-\frac{\left(4 e c h +4 c f g \right) \left(-\frac{c^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{3}-\frac{2 \sqrt{-c^{2} x^{2}+1}}{3}\right)}{12}-\frac{\left(6 d \,c^{2} h +6 e \,c^{2} g \right) \left(-\frac{c x \sqrt{-c^{2} x^{2}+1}}{2}+\frac{\arcsin \left(c x \right)}{2}\right)}{12}+d \,c^{3} g \sqrt{-c^{2} x^{2}+1}\right)}{c^{3}}}{c}"," ",0,"1/c*(a^2/c^3*(1/4*h*f*c^4*x^4+1/3*(c*e*h+c*f*g)*c^3*x^3+1/2*(c^2*d*h+c^2*e*g)*c^2*x^2+d*c^4*g*x)+b^2/c^3*(1/32*h*f*(8*arcsin(c*x)^2*c^4*x^4+4*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^3*x^3-16*arcsin(c*x)^2*c^2*x^2-c^4*x^4-10*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x+5*arcsin(c*x)^2+5*c^2*x^2-4)+1/4*d*c^2*h*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/4*e*c^2*g*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+1/27*e*c*h*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+1/27*c*f*g*(9*arcsin(c*x)^2*c^3*x^3+6*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c^2*x^2-27*c*x*arcsin(c*x)^2-2*c^3*x^3-42*arcsin(c*x)*(-c^2*x^2+1)^(1/2)+42*c*x)+d*c^3*g*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+1/4*h*f*(2*arcsin(c*x)^2*c^2*x^2+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)*c*x-arcsin(c*x)^2-c^2*x^2)+e*c*h*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2))+c*f*g*(c*x*arcsin(c*x)^2-2*c*x+2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)))+2*a*b/c^3*(1/4*arcsin(c*x)*h*f*c^4*x^4+1/3*arcsin(c*x)*c^4*x^3*e*h+1/3*arcsin(c*x)*c^4*x^3*f*g+1/2*arcsin(c*x)*c^4*x^2*d*h+1/2*arcsin(c*x)*c^4*x^2*e*g+arcsin(c*x)*d*c^4*g*x-1/4*h*f*(-1/4*c^3*x^3*(-c^2*x^2+1)^(1/2)-3/8*c*x*(-c^2*x^2+1)^(1/2)+3/8*arcsin(c*x))-1/12*(4*c*e*h+4*c*f*g)*(-1/3*c^2*x^2*(-c^2*x^2+1)^(1/2)-2/3*(-c^2*x^2+1)^(1/2))-1/12*(6*c^2*d*h+6*c^2*e*g)*(-1/2*c*x*(-c^2*x^2+1)^(1/2)+1/2*arcsin(c*x))+d*c^3*g*(-c^2*x^2+1)^(1/2)))","B"
118,0,0,1087,4.554000," ","int((f*x^2+e*x+d)*(a+b*arcsin(c*x))^2/(h*x+g),x)","\int \frac{\left(f \,x^{2}+e x +d \right) \left(a +b \arcsin \left(c x \right)\right)^{2}}{h x +g}\, dx"," ",0,"int((f*x^2+e*x+d)*(a+b*arcsin(c*x))^2/(h*x+g),x)","F"
119,0,0,1365,5.756000," ","int((f*x^2+e*x+d)*(a+b*arcsin(c*x))^2/(h*x+g)^2,x)","\int \frac{\left(f \,x^{2}+e x +d \right) \left(a +b \arcsin \left(c x \right)\right)^{2}}{\left(h x +g \right)^{2}}\, dx"," ",0,"int((f*x^2+e*x+d)*(a+b*arcsin(c*x))^2/(h*x+g)^2,x)","F"
120,1,1399,520,1.147000," ","int((e*h*x^2+2*d*h*x+e*f)*(a+b*arcsin(c*x))^2/(e*x+d)^2,x)","\frac{a^{2} h x}{e}+\frac{c \,a^{2} d^{2} h}{e^{2} \left(c e x +d c \right)}-\frac{c \,a^{2} f}{c e x +d c}+\frac{2 b^{2} h \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{c e}+\frac{b^{2} h \arcsin \left(c x \right)^{2} x}{e}-\frac{2 b^{2} h x}{e}+\frac{c \,b^{2} \arcsin \left(c x \right)^{2} d^{2} h}{e^{2} \left(c e x +d c \right)}-\frac{c \,b^{2} \arcsin \left(c x \right)^{2} f}{c e x +d c}-\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2} h}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) f}{c^{2} d^{2}-e^{2}}+\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2} h}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}-\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) f}{c^{2} d^{2}-e^{2}}-\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) f}{c^{2} d^{2}-e^{2}}+\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) f}{c^{2} d^{2}-e^{2}}-\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) h \,d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) h \,d^{2}}{e^{2} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 a b \arcsin \left(c x \right) h x}{e}+\frac{2 c a b \arcsin \left(c x \right) d^{2} h}{e^{2} \left(c e x +d c \right)}-\frac{2 c a b \arcsin \left(c x \right) f}{c e x +d c}+\frac{2 a b h \sqrt{-c^{2} x^{2}+1}}{c e}+\frac{2 c a b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) d^{2} h}{e^{3} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{2 c a b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f}{e \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}"," ",0,"a^2*h/e*x+c*a^2/e^2/(c*e*x+c*d)*d^2*h-c*a^2/(c*e*x+c*d)*f+2*b^2*h*arcsin(c*x)*(-c^2*x^2+1)^(1/2)/c/e+b^2*h/e*arcsin(c*x)^2*x-2*b^2*h*x/e+c*b^2*arcsin(c*x)^2/e^2/(c*e*x+c*d)*d^2*h-c*b^2*arcsin(c*x)^2/(c*e*x+c*d)*f-2*c*b^2*(-c^2*d^2+e^2)^(1/2)/e^2/(c^2*d^2-e^2)*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2*h+2*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*f+2*c*b^2*(-c^2*d^2+e^2)^(1/2)/e^2/(c^2*d^2-e^2)*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2*h-2*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*f+2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*f-2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/e^2/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*h*d^2-2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*f+2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/e^2/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*h*d^2+2*a*b*arcsin(c*x)*h/e*x+2*c*a*b*arcsin(c*x)/e^2/(c*e*x+c*d)*d^2*h-2*c*a*b*arcsin(c*x)/(c*e*x+c*d)*f+2*a*b*h*(-c^2*x^2+1)^(1/2)/c/e+2*c*a*b/e^3/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*d^2*h-2*c*a*b/e/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f","B"
121,1,2609,886,3.700000," ","int((e*h*x^2+2*d*h*x+e*f)^2*(a+b*arcsin(c*x))^2/(e*x+d)^2,x)","-\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) h^{2} d^{4}}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) h^{2} d^{4}}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}-\frac{c \,a^{2} e \,f^{2}}{c e x +d c}+\frac{b^{2} d \,h^{2}}{4 c^{2} e}+\frac{4 a b \,h^{2} \sqrt{-c^{2} x^{2}+1}}{9 c^{3}}-\frac{b^{2} \sin \left(3 \arcsin \left(c x \right)\right) \arcsin \left(c x \right)^{2} h^{2}}{12 c^{3}}-\frac{b^{2} h^{2} \arcsin \left(c x \right) \cos \left(3 \arcsin \left(c x \right)\right)}{18 c^{3}}+\frac{b^{2} h^{2} \arcsin \left(c x \right)^{2} x}{4 c^{2}}+\frac{2 a b \arcsin \left(c x \right) h^{2} x^{3}}{3}+2 b^{2} h \arcsin \left(c x \right)^{2} x f +\frac{a^{2} h^{2} d \,x^{2}}{e}-\frac{a^{2} h^{2} d^{2} x}{e^{2}}+\frac{2 b^{2} h^{2} d^{2} x}{e^{2}}+\frac{4 c a b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) d^{2} f h}{e^{2} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{4 c a b \arcsin \left(c x \right) d^{2} f h}{e \left(c e x +d c \right)}+\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{4} h^{2}}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}-\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{4} h^{2}}{e^{3} \left(c^{2} d^{2}-e^{2}\right)}+\frac{b^{2} d \,h^{2} x \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{c e}-\frac{c \,a^{2} d^{4} h^{2}}{e^{3} \left(c e x +d c \right)}-\frac{2 c a b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) f^{2}}{\sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}-\frac{c \,b^{2} \arcsin \left(c x \right)^{2} e \,f^{2}}{c e x +d c}+4 a b \arcsin \left(c x \right) h f x -\frac{b^{2} h^{2} \arcsin \left(c x \right)^{2} x \,d^{2}}{e^{2}}+\frac{b^{2} d \,h^{2} \arcsin \left(c x \right)^{2} x^{2}}{e}+\frac{4 b^{2} h \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) f}{c}+\frac{4 a b f h \sqrt{-c^{2} x^{2}+1}}{c}+\frac{2 a b \,h^{2} x^{2} \sqrt{-c^{2} x^{2}+1}}{9 c}+2 a^{2} h f x -4 b^{2} h f x +\frac{b^{2} h^{2} \sin \left(3 \arcsin \left(c x \right)\right)}{54 c^{3}}+\frac{4 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) f h \,d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{4 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2} f h}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{4 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) d^{2} f h}{e \left(c^{2} d^{2}-e^{2}\right)}-\frac{4 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) f h \,d^{2}}{e \left(c^{2} d^{2}-e^{2}\right)}+\frac{2 c \,a^{2} d^{2} f h}{e \left(c e x +d c \right)}-\frac{a b d \,h^{2} \arcsin \left(c x \right)}{c^{2} e}-\frac{2 c a b \arcsin \left(c x \right) d^{4} h^{2}}{e^{3} \left(c e x +d c \right)}+\frac{a b d \,h^{2} \sqrt{-c^{2} x^{2}+1}\, x}{c e}+\frac{2 c \,b^{2} \arcsin \left(c x \right)^{2} d^{2} f h}{e \left(c e x +d c \right)}-\frac{2 c a b \ln \left(\frac{-\frac{2 \left(c^{2} d^{2}-e^{2}\right)}{e^{2}}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}+2 \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\left(c x +\frac{d c}{e}\right)^{2}+\frac{2 d c \left(c x +\frac{d c}{e}\right)}{e}-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}{c x +\frac{d c}{e}}\right) d^{4} h^{2}}{e^{4} \sqrt{-\frac{c^{2} d^{2}-e^{2}}{e^{2}}}}+\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, e \arcsin \left(c x \right) \ln \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) f^{2}}{c^{2} d^{2}-e^{2}}-\frac{2 c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, e \arcsin \left(c x \right) \ln \left(\frac{-i d c -\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{-i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) f^{2}}{c^{2} d^{2}-e^{2}}-\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e +\sqrt{-c^{2} d^{2}+e^{2}}}{i d c +\sqrt{-c^{2} d^{2}+e^{2}}}\right) f^{2} e}{c^{2} d^{2}-e^{2}}+\frac{2 i c \,b^{2} \sqrt{-c^{2} d^{2}+e^{2}}\, \dilog \left(\frac{i d c +\left(i c x +\sqrt{-c^{2} x^{2}+1}\right) e -\sqrt{-c^{2} d^{2}+e^{2}}}{i d c -\sqrt{-c^{2} d^{2}+e^{2}}}\right) f^{2} e}{c^{2} d^{2}-e^{2}}-\frac{b^{2} d \,h^{2} \arcsin \left(c x \right)^{2}}{2 c^{2} e}-\frac{b^{2} h^{2} x}{2 c^{2}}-\frac{2 c a b \arcsin \left(c x \right) e \,f^{2}}{c e x +d c}-\frac{c \,b^{2} \arcsin \left(c x \right)^{2} d^{4} h^{2}}{e^{3} \left(c e x +d c \right)}-\frac{2 a b \,d^{2} h^{2} \sqrt{-c^{2} x^{2}+1}}{c \,e^{2}}-\frac{2 b^{2} h^{2} \sqrt{-c^{2} x^{2}+1}\, \arcsin \left(c x \right) d^{2}}{c \,e^{2}}+\frac{2 a b \arcsin \left(c x \right) d \,h^{2} x^{2}}{e}-\frac{2 a b \arcsin \left(c x \right) h^{2} d^{2} x}{e^{2}}+\frac{b^{2} h^{2} \arcsin \left(c x \right) \sqrt{-c^{2} x^{2}+1}}{2 c^{3}}+\frac{a^{2} h^{2} x^{3}}{3}-\frac{b^{2} d \,h^{2} x^{2}}{2 e}"," ",0,"-c*a^2*e/(c*e*x+c*d)*f^2+1/4/c^2*b^2/e*d*h^2+4/9/c^3*a*b*h^2*(-c^2*x^2+1)^(1/2)-1/12/c^3*b^2*sin(3*arcsin(c*x))*arcsin(c*x)^2*h^2-1/18/c^3*b^2*h^2*arcsin(c*x)*cos(3*arcsin(c*x))+1/4/c^2*b^2*h^2*arcsin(c*x)^2*x+2/3*a*b*arcsin(c*x)*h^2*x^3+2*b^2*h*arcsin(c*x)^2*x*f+a^2*h^2/e*d*x^2-a^2*h^2/e^2*d^2*x+2*b^2*h^2/e^2*d^2*x+4*c*a*b/e^2/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*d^2*f*h+2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/e^3/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*h^2*d^4-2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/e^3/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*h^2*d^4+4*c*a*b*arcsin(c*x)/e/(c*e*x+c*d)*d^2*f*h+2*c*b^2*(-c^2*d^2+e^2)^(1/2)/e^3/(c^2*d^2-e^2)*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^4*h^2-2*c*b^2*(-c^2*d^2+e^2)^(1/2)/e^3/(c^2*d^2-e^2)*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^4*h^2+b^2*d*h^2*x*arcsin(c*x)*(-c^2*x^2+1)^(1/2)/c/e-c*a^2/e^3/(c*e*x+c*d)*d^4*h^2-2*c*a*b/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*f^2-c*b^2*arcsin(c*x)^2*e/(c*e*x+c*d)*f^2+4*a*b*arcsin(c*x)*h*f*x-b^2*h^2/e^2*arcsin(c*x)^2*x*d^2+b^2/e*d*h^2*arcsin(c*x)^2*x^2+4/c*b^2*h*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*f+4/c*a*b*f*h*(-c^2*x^2+1)^(1/2)+2/9/c*a*b*h^2*x^2*(-c^2*x^2+1)^(1/2)+2*a^2*h*f*x-4*b^2*h*f*x+1/54/c^3*b^2*h^2*sin(3*arcsin(c*x))+4*c*b^2*(-c^2*d^2+e^2)^(1/2)/e/(c^2*d^2-e^2)*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2*f*h-4*c*b^2*(-c^2*d^2+e^2)^(1/2)/e/(c^2*d^2-e^2)*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*d^2*f*h-4*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/e/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*f*h*d^2+4*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/e/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*f*h*d^2+2*c*a^2/e/(c*e*x+c*d)*d^2*f*h-1/c^2*a*b/e*d*h^2*arcsin(c*x)-2*c*a*b*arcsin(c*x)/e^3/(c*e*x+c*d)*d^4*h^2+1/c*a*b/e*d*h^2*(-c^2*x^2+1)^(1/2)*x+2*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)*e*arcsin(c*x)*ln((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*f^2+2*c*b^2*arcsin(c*x)^2/e/(c*e*x+c*d)*d^2*f*h-2*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)*e*arcsin(c*x)*ln((-I*d*c-(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(-I*d*c+(-c^2*d^2+e^2)^(1/2)))*f^2-2*c*a*b/e^4/(-(c^2*d^2-e^2)/e^2)^(1/2)*ln((-2*(c^2*d^2-e^2)/e^2+2*d*c/e*(c*x+d*c/e)+2*(-(c^2*d^2-e^2)/e^2)^(1/2)*(-(c*x+d*c/e)^2+2*d*c/e*(c*x+d*c/e)-(c^2*d^2-e^2)/e^2)^(1/2))/(c*x+d*c/e))*d^4*h^2-2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e+(-c^2*d^2+e^2)^(1/2))/(I*d*c+(-c^2*d^2+e^2)^(1/2)))*f^2*e+2*I*c*b^2*(-c^2*d^2+e^2)^(1/2)/(c^2*d^2-e^2)*dilog((I*d*c+(I*c*x+(-c^2*x^2+1)^(1/2))*e-(-c^2*d^2+e^2)^(1/2))/(I*d*c-(-c^2*d^2+e^2)^(1/2)))*f^2*e-1/2*b^2*d*h^2*arcsin(c*x)^2/c^2/e-1/2*b^2*h^2*x/c^2-2*c*a*b*arcsin(c*x)*e/(c*e*x+c*d)*f^2-c*b^2*arcsin(c*x)^2/e^3/(c*e*x+c*d)*d^4*h^2-2/c*a*b/e^2*d^2*h^2*(-c^2*x^2+1)^(1/2)-2/c*b^2*h^2/e^2*(-c^2*x^2+1)^(1/2)*arcsin(c*x)*d^2+2*a*b*arcsin(c*x)/e*d*h^2*x^2-2*a*b*arcsin(c*x)*h^2/e^2*d^2*x+1/2*b^2*h^2*arcsin(c*x)*(-c^2*x^2+1)^(1/2)/c^3+1/3*a^2*h^2*x^3-1/2*b^2*d*h^2*x^2/e","B"
122,1,213,121,0.017000," ","int(x^3*arcsin(b*x+a),x)","\frac{\frac{\arcsin \left(b x +a \right) \left(b x +a \right)^{4}}{4}-\arcsin \left(b x +a \right) \left(b x +a \right)^{3} a +\frac{3 \arcsin \left(b x +a \right) \left(b x +a \right)^{2} a^{2}}{2}-\arcsin \left(b x +a \right) \left(b x +a \right) a^{3}+\frac{\left(b x +a \right)^{3} \sqrt{1-\left(b x +a \right)^{2}}}{16}+\frac{3 \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}}{32}-\frac{3 \arcsin \left(b x +a \right)}{32}+a \left(-\frac{\left(b x +a \right)^{2} \sqrt{1-\left(b x +a \right)^{2}}}{3}-\frac{2 \sqrt{1-\left(b x +a \right)^{2}}}{3}\right)-\frac{3 a^{2} \left(-\frac{\left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}}{2}+\frac{\arcsin \left(b x +a \right)}{2}\right)}{2}-a^{3} \sqrt{1-\left(b x +a \right)^{2}}}{b^{4}}"," ",0,"1/b^4*(1/4*arcsin(b*x+a)*(b*x+a)^4-arcsin(b*x+a)*(b*x+a)^3*a+3/2*arcsin(b*x+a)*(b*x+a)^2*a^2-arcsin(b*x+a)*(b*x+a)*a^3+1/16*(b*x+a)^3*(1-(b*x+a)^2)^(1/2)+3/32*(b*x+a)*(1-(b*x+a)^2)^(1/2)-3/32*arcsin(b*x+a)+a*(-1/3*(b*x+a)^2*(1-(b*x+a)^2)^(1/2)-2/3*(1-(b*x+a)^2)^(1/2))-3/2*a^2*(-1/2*(b*x+a)*(1-(b*x+a)^2)^(1/2)+1/2*arcsin(b*x+a))-a^3*(1-(b*x+a)^2)^(1/2))","A"
123,1,137,82,0.008000," ","int(x^2*arcsin(b*x+a),x)","\frac{\frac{\arcsin \left(b x +a \right) \left(b x +a \right)^{3}}{3}-\arcsin \left(b x +a \right) \left(b x +a \right)^{2} a +\arcsin \left(b x +a \right) \left(b x +a \right) a^{2}+\frac{\left(b x +a \right)^{2} \sqrt{1-\left(b x +a \right)^{2}}}{9}+\frac{2 \sqrt{1-\left(b x +a \right)^{2}}}{9}+a \left(-\frac{\left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}}{2}+\frac{\arcsin \left(b x +a \right)}{2}\right)+a^{2} \sqrt{1-\left(b x +a \right)^{2}}}{b^{3}}"," ",0,"1/b^3*(1/3*arcsin(b*x+a)*(b*x+a)^3-arcsin(b*x+a)*(b*x+a)^2*a+arcsin(b*x+a)*(b*x+a)*a^2+1/9*(b*x+a)^2*(1-(b*x+a)^2)^(1/2)+2/9*(1-(b*x+a)^2)^(1/2)+a*(-1/2*(b*x+a)*(1-(b*x+a)^2)^(1/2)+1/2*arcsin(b*x+a))+a^2*(1-(b*x+a)^2)^(1/2))","A"
124,1,79,68,0.006000," ","int(x*arcsin(b*x+a),x)","\frac{\frac{\arcsin \left(b x +a \right) \left(b x +a \right)^{2}}{2}-\arcsin \left(b x +a \right) a \left(b x +a \right)+\frac{\left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}}{4}-\frac{\arcsin \left(b x +a \right)}{4}-a \sqrt{1-\left(b x +a \right)^{2}}}{b^{2}}"," ",0,"1/b^2*(1/2*arcsin(b*x+a)*(b*x+a)^2-arcsin(b*x+a)*a*(b*x+a)+1/4*(b*x+a)*(1-(b*x+a)^2)^(1/2)-1/4*arcsin(b*x+a)-a*(1-(b*x+a)^2)^(1/2))","A"
125,1,31,33,0.004000," ","int(arcsin(b*x+a),x)","\frac{\left(b x +a \right) \arcsin \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}}{b}"," ",0,"1/b*((b*x+a)*arcsin(b*x+a)+(1-(b*x+a)^2)^(1/2))","A"
126,1,579,204,0.260000," ","int(arcsin(b*x+a)/x,x)","-\frac{i \arcsin \left(b x +a \right)^{2}}{2}-\frac{\arcsin \left(b x +a \right) \ln \left(\frac{i a -\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a -\sqrt{-a^{2}+1}}\right)}{a^{2}-1}-\frac{\arcsin \left(b x +a \right) \ln \left(\frac{i a +\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a +\sqrt{-a^{2}+1}}\right)}{a^{2}-1}+\frac{\arcsin \left(b x +a \right) \ln \left(\frac{i a -\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a -\sqrt{-a^{2}+1}}\right) a^{2}}{a^{2}-1}+\frac{\arcsin \left(b x +a \right) \ln \left(\frac{i a +\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a +\sqrt{-a^{2}+1}}\right) a^{2}}{a^{2}-1}-\frac{i \dilog \left(\frac{i a -\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a -\sqrt{-a^{2}+1}}\right) a^{2}}{a^{2}-1}-\frac{i \dilog \left(\frac{i a +\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a +\sqrt{-a^{2}+1}}\right) a^{2}}{a^{2}-1}+\frac{i \dilog \left(\frac{i a +\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a +\sqrt{-a^{2}+1}}\right)}{a^{2}-1}+\frac{i \dilog \left(\frac{i a -\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a -\sqrt{-a^{2}+1}}\right)}{a^{2}-1}"," ",0,"-1/2*I*arcsin(b*x+a)^2-arcsin(b*x+a)/(a^2-1)*ln((I*a-(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a-(-a^2+1)^(1/2)))-arcsin(b*x+a)/(a^2-1)*ln((I*a+(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a+(-a^2+1)^(1/2)))+arcsin(b*x+a)/(a^2-1)*ln((I*a-(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a-(-a^2+1)^(1/2)))*a^2+arcsin(b*x+a)/(a^2-1)*ln((I*a+(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a+(-a^2+1)^(1/2)))*a^2-I/(a^2-1)*dilog((I*a-(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a-(-a^2+1)^(1/2)))*a^2-I/(a^2-1)*dilog((I*a+(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a+(-a^2+1)^(1/2)))*a^2+I/(a^2-1)*dilog((I*a+(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a+(-a^2+1)^(1/2)))+I/(a^2-1)*dilog((I*a-(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a-(-a^2+1)^(1/2)))","B"
127,1,78,58,0.017000," ","int(arcsin(b*x+a)/x^2,x)","-\frac{\arcsin \left(b x +a \right)}{x}-\frac{b \ln \left(\frac{-2 a^{2}+2-2 a b x +2 \sqrt{-a^{2}+1}\, \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b x}\right)}{\sqrt{-a^{2}+1}}"," ",0,"-arcsin(b*x+a)/x-b/(-a^2+1)^(1/2)*ln((-2*a^2+2-2*a*b*x+2*(-a^2+1)^(1/2)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))/b/x)","A"
128,1,118,89,0.010000," ","int(arcsin(b*x+a)/x^3,x)","-\frac{\arcsin \left(b x +a \right)}{2 x^{2}}-\frac{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(-a^{2}+1\right) x}-\frac{b^{2} a \ln \left(\frac{-2 a^{2}+2-2 a b x +2 \sqrt{-a^{2}+1}\, \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b x}\right)}{2 \left(-a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-1/2*arcsin(b*x+a)/x^2-1/2*b/(-a^2+1)/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2*b^2*a/(-a^2+1)^(3/2)*ln((-2*a^2+2-2*a*b*x+2*(-a^2+1)^(1/2)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))/b/x)","A"
129,1,227,126,0.008000," ","int(arcsin(b*x+a)/x^4,x)","-\frac{\arcsin \left(b x +a \right)}{3 x^{3}}-\frac{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{6 \left(-a^{2}+1\right) x^{2}}-\frac{b^{2} a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{2 \left(-a^{2}+1\right)^{2} x}-\frac{b^{3} a^{2} \ln \left(\frac{-2 a^{2}+2-2 a b x +2 \sqrt{-a^{2}+1}\, \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b x}\right)}{2 \left(-a^{2}+1\right)^{\frac{5}{2}}}-\frac{b^{3} \ln \left(\frac{-2 a^{2}+2-2 a b x +2 \sqrt{-a^{2}+1}\, \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b x}\right)}{6 \left(-a^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-1/3*arcsin(b*x+a)/x^3-1/6*b/(-a^2+1)/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2*b^2*a/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-1/2*b^3*a^2/(-a^2+1)^(5/2)*ln((-2*a^2+2-2*a*b*x+2*(-a^2+1)^(1/2)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))/b/x)-1/6*b^3/(-a^2+1)^(3/2)*ln((-2*a^2+2-2*a*b*x+2*(-a^2+1)^(1/2)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))/b/x)","A"
130,1,309,164,0.008000," ","int(arcsin(b*x+a)/x^5,x)","-\frac{\arcsin \left(b x +a \right)}{4 x^{4}}-\frac{b \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{12 \left(-a^{2}+1\right) x^{3}}-\frac{5 b^{2} a \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{24 \left(-a^{2}+1\right)^{2} x^{2}}-\frac{5 b^{3} a^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{8 \left(-a^{2}+1\right)^{3} x}-\frac{5 b^{4} a^{3} \ln \left(\frac{-2 a^{2}+2-2 a b x +2 \sqrt{-a^{2}+1}\, \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b x}\right)}{8 \left(-a^{2}+1\right)^{\frac{7}{2}}}-\frac{3 b^{4} a \ln \left(\frac{-2 a^{2}+2-2 a b x +2 \sqrt{-a^{2}+1}\, \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{b x}\right)}{8 \left(-a^{2}+1\right)^{\frac{5}{2}}}-\frac{b^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}}{6 \left(-a^{2}+1\right)^{2} x}"," ",0,"-1/4*arcsin(b*x+a)/x^4-1/12*b/(-a^2+1)/x^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-5/24*b^2*a/(-a^2+1)^2/x^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-5/8*b^3*a^2/(-a^2+1)^3/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)-5/8*b^4*a^3/(-a^2+1)^(7/2)*ln((-2*a^2+2-2*a*b*x+2*(-a^2+1)^(1/2)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))/b/x)-3/8*b^4*a/(-a^2+1)^(5/2)*ln((-2*a^2+2-2*a*b*x+2*(-a^2+1)^(1/2)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2))/b/x)-1/6*b^3/(-a^2+1)^2/x*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)","A"
131,1,435,303,0.130000," ","int(x^3*arcsin(b*x+a)^2,x)","\frac{\frac{\arcsin \left(b x +a \right)^{2} \left(-1+\left(b x +a \right)^{2}\right)^{2}}{4}-\frac{\arcsin \left(b x +a \right) \left(-2 \left(b x +a \right)^{3} \sqrt{1-\left(b x +a \right)^{2}}+5 \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}+3 \arcsin \left(b x +a \right)\right)}{16}-\frac{5 \arcsin \left(b x +a \right)^{2}}{32}-\frac{\left(-1+\left(b x +a \right)^{2}\right)^{2}}{32}-\frac{5 \left(b x +a \right)^{2}}{32}-\frac{3}{32}+\frac{3 a^{2} \left(2 \arcsin \left(b x +a \right)^{2} \left(b x +a \right)^{2}+2 \sqrt{1-\left(b x +a \right)^{2}}\, \arcsin \left(b x +a \right) \left(b x +a \right)-\arcsin \left(b x +a \right)^{2}-\left(b x +a \right)^{2}\right)}{4}-\frac{a \left(9 \arcsin \left(b x +a \right)^{2} \left(b x +a \right)^{3}+6 \sqrt{1-\left(b x +a \right)^{2}}\, \arcsin \left(b x +a \right) \left(b x +a \right)^{2}-27 \arcsin \left(b x +a \right)^{2} \left(b x +a \right)-2 \left(b x +a \right)^{3}-42 \arcsin \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}+42 b x +42 a \right)}{9}-a^{3} \left(\arcsin \left(b x +a \right)^{2} \left(b x +a \right)-2 b x -2 a +2 \arcsin \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}\right)+\frac{\arcsin \left(b x +a \right)^{2} \left(-1+\left(b x +a \right)^{2}\right)}{2}+\frac{\arcsin \left(b x +a \right) \left(\left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}+\arcsin \left(b x +a \right)\right)}{2}-3 a \left(\arcsin \left(b x +a \right)^{2} \left(b x +a \right)-2 b x -2 a +2 \arcsin \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}\right)}{b^{4}}"," ",0,"1/b^4*(1/4*arcsin(b*x+a)^2*(-1+(b*x+a)^2)^2-1/16*arcsin(b*x+a)*(-2*(b*x+a)^3*(1-(b*x+a)^2)^(1/2)+5*(b*x+a)*(1-(b*x+a)^2)^(1/2)+3*arcsin(b*x+a))-5/32*arcsin(b*x+a)^2-1/32*(-1+(b*x+a)^2)^2-5/32*(b*x+a)^2-3/32+3/4*a^2*(2*arcsin(b*x+a)^2*(b*x+a)^2+2*(1-(b*x+a)^2)^(1/2)*arcsin(b*x+a)*(b*x+a)-arcsin(b*x+a)^2-(b*x+a)^2)-1/9*a*(9*arcsin(b*x+a)^2*(b*x+a)^3+6*(1-(b*x+a)^2)^(1/2)*arcsin(b*x+a)*(b*x+a)^2-27*arcsin(b*x+a)^2*(b*x+a)-2*(b*x+a)^3-42*arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2)+42*b*x+42*a)-a^3*(arcsin(b*x+a)^2*(b*x+a)-2*b*x-2*a+2*arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2))+1/2*arcsin(b*x+a)^2*(-1+(b*x+a)^2)+1/2*arcsin(b*x+a)*((b*x+a)*(1-(b*x+a)^2)^(1/2)+arcsin(b*x+a))-3*a*(arcsin(b*x+a)^2*(b*x+a)-2*b*x-2*a+2*arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2)))","A"
132,1,231,196,0.119000," ","int(x^2*arcsin(b*x+a)^2,x)","\frac{-\frac{a \left(2 \arcsin \left(b x +a \right)^{2} \left(b x +a \right)^{2}+2 \sqrt{1-\left(b x +a \right)^{2}}\, \arcsin \left(b x +a \right) \left(b x +a \right)-\arcsin \left(b x +a \right)^{2}-\left(b x +a \right)^{2}\right)}{2}+\frac{\arcsin \left(b x +a \right)^{2} \left(\left(b x +a \right)^{2}-3\right) \left(b x +a \right)}{3}-\frac{2 b x}{3}-\frac{2 a}{3}+\frac{2 \arcsin \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}}{3}+\frac{2 \arcsin \left(b x +a \right) \left(-1+\left(b x +a \right)^{2}\right) \sqrt{1-\left(b x +a \right)^{2}}}{9}-\frac{2 \left(\left(b x +a \right)^{2}-3\right) \left(b x +a \right)}{27}+a^{2} \left(\arcsin \left(b x +a \right)^{2} \left(b x +a \right)-2 b x -2 a +2 \arcsin \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}\right)+\arcsin \left(b x +a \right)^{2} \left(b x +a \right)}{b^{3}}"," ",0,"1/b^3*(-1/2*a*(2*arcsin(b*x+a)^2*(b*x+a)^2+2*(1-(b*x+a)^2)^(1/2)*arcsin(b*x+a)*(b*x+a)-arcsin(b*x+a)^2-(b*x+a)^2)+1/3*arcsin(b*x+a)^2*((b*x+a)^2-3)*(b*x+a)-2/3*b*x-2/3*a+2/3*arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2)+2/9*arcsin(b*x+a)*(-1+(b*x+a)^2)*(1-(b*x+a)^2)^(1/2)-2/27*((b*x+a)^2-3)*(b*x+a)+a^2*(arcsin(b*x+a)^2*(b*x+a)-2*b*x-2*a+2*arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2))+arcsin(b*x+a)^2*(b*x+a))","A"
133,1,124,116,0.085000," ","int(x*arcsin(b*x+a)^2,x)","\frac{\frac{\arcsin \left(b x +a \right)^{2} \left(-1+\left(b x +a \right)^{2}\right)}{2}+\frac{\arcsin \left(b x +a \right) \left(\left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}+\arcsin \left(b x +a \right)\right)}{2}-\frac{\arcsin \left(b x +a \right)^{2}}{4}-\frac{\left(b x +a \right)^{2}}{4}-a \left(\arcsin \left(b x +a \right)^{2} \left(b x +a \right)-2 b x -2 a +2 \arcsin \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}\right)}{b^{2}}"," ",0,"1/b^2*(1/2*arcsin(b*x+a)^2*(-1+(b*x+a)^2)+1/2*arcsin(b*x+a)*((b*x+a)*(1-(b*x+a)^2)^(1/2)+arcsin(b*x+a))-1/4*arcsin(b*x+a)^2-1/4*(b*x+a)^2-a*(arcsin(b*x+a)^2*(b*x+a)-2*b*x-2*a+2*arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2)))","A"
134,1,48,45,0.069000," ","int(arcsin(b*x+a)^2,x)","\frac{\arcsin \left(b x +a \right)^{2} \left(b x +a \right)-2 b x -2 a +2 \arcsin \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}}{b}"," ",0,"1/b*(arcsin(b*x+a)^2*(b*x+a)-2*b*x-2*a+2*arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2))","A"
135,0,0,308,1.697000," ","int(arcsin(b*x+a)^2/x,x)","\int \frac{\arcsin \left(b x +a \right)^{2}}{x}\, dx"," ",0,"int(arcsin(b*x+a)^2/x,x)","F"
136,1,333,248,0.653000," ","int(arcsin(b*x+a)^2/x^2,x)","-\frac{\arcsin \left(b x +a \right)^{2}}{x}-\frac{2 b \sqrt{-a^{2}+1}\, \arcsin \left(b x +a \right) \ln \left(\frac{i a +\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a +\sqrt{-a^{2}+1}}\right)}{a^{2}-1}+\frac{2 b \sqrt{-a^{2}+1}\, \arcsin \left(b x +a \right) \ln \left(\frac{i a -\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a -\sqrt{-a^{2}+1}}\right)}{a^{2}-1}+\frac{2 i b \sqrt{-a^{2}+1}\, \dilog \left(\frac{i a +\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a +\sqrt{-a^{2}+1}}\right)}{a^{2}-1}-\frac{2 i b \sqrt{-a^{2}+1}\, \dilog \left(\frac{i a -\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a -\sqrt{-a^{2}+1}}\right)}{a^{2}-1}"," ",0,"-arcsin(b*x+a)^2/x-2*b*(-a^2+1)^(1/2)/(a^2-1)*arcsin(b*x+a)*ln((I*a+(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a+(-a^2+1)^(1/2)))+2*b*(-a^2+1)^(1/2)/(a^2-1)*arcsin(b*x+a)*ln((I*a-(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a-(-a^2+1)^(1/2)))+2*I*b*(-a^2+1)^(1/2)/(a^2-1)*dilog((I*a+(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a+(-a^2+1)^(1/2)))-2*I*b*(-a^2+1)^(1/2)/(a^2-1)*dilog((I*a-(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a-(-a^2+1)^(1/2)))","A"
137,1,526,286,0.979000," ","int(arcsin(b*x+a)^2/x^3,x)","-\frac{i b^{2} \arcsin \left(b x +a \right)}{a^{2}-1}+\frac{b \arcsin \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}}{\left(a^{2}-1\right) x}-\frac{\arcsin \left(b x +a \right)^{2} a^{2}}{2 \left(a^{2}-1\right) x^{2}}+\frac{\arcsin \left(b x +a \right)^{2}}{2 \left(a^{2}-1\right) x^{2}}+\frac{2 b^{2} \ln \left(i \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)}{a^{2}-1}-\frac{b^{2} \ln \left(2 i a \left(i \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)-\left(i \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)^{2}+1\right)}{a^{2}-1}+\frac{b^{2} \sqrt{-a^{2}+1}\, a \arcsin \left(b x +a \right) \ln \left(\frac{i a +\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a +\sqrt{-a^{2}+1}}\right)}{\left(a^{2}-1\right)^{2}}-\frac{b^{2} \sqrt{-a^{2}+1}\, a \arcsin \left(b x +a \right) \ln \left(\frac{i a -\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a -\sqrt{-a^{2}+1}}\right)}{\left(a^{2}-1\right)^{2}}-\frac{i b^{2} \sqrt{-a^{2}+1}\, \dilog \left(\frac{i a +\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a +\sqrt{-a^{2}+1}}\right) a}{\left(a^{2}-1\right)^{2}}+\frac{i b^{2} \sqrt{-a^{2}+1}\, \dilog \left(\frac{i a -\sqrt{-a^{2}+1}-i \left(b x +a \right)-\sqrt{1-\left(b x +a \right)^{2}}}{i a -\sqrt{-a^{2}+1}}\right) a}{\left(a^{2}-1\right)^{2}}"," ",0,"-I*b^2*arcsin(b*x+a)/(a^2-1)+b*arcsin(b*x+a)/(a^2-1)/x*(1-(b*x+a)^2)^(1/2)-1/2*arcsin(b*x+a)^2/(a^2-1)/x^2*a^2+1/2*arcsin(b*x+a)^2/(a^2-1)/x^2+2*b^2/(a^2-1)*ln(I*(b*x+a)+(1-(b*x+a)^2)^(1/2))-b^2/(a^2-1)*ln(2*I*a*(I*(b*x+a)+(1-(b*x+a)^2)^(1/2))-(I*(b*x+a)+(1-(b*x+a)^2)^(1/2))^2+1)+b^2*(-a^2+1)^(1/2)/(a^2-1)^2*a*arcsin(b*x+a)*ln((I*a+(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a+(-a^2+1)^(1/2)))-b^2*(-a^2+1)^(1/2)/(a^2-1)^2*a*arcsin(b*x+a)*ln((I*a-(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a-(-a^2+1)^(1/2)))-I*b^2*(-a^2+1)^(1/2)/(a^2-1)^2*dilog((I*a+(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a+(-a^2+1)^(1/2)))*a+I*b^2*(-a^2+1)^(1/2)/(a^2-1)^2*dilog((I*a-(-a^2+1)^(1/2)-I*(b*x+a)-(1-(b*x+a)^2)^(1/2))/(I*a-(-a^2+1)^(1/2)))*a","A"
138,1,344,329,0.116000," ","int(x^2*arcsin(b*x+a)^3,x)","\frac{-\frac{a \left(4 \arcsin \left(b x +a \right)^{3} \left(b x +a \right)^{2}+6 \arcsin \left(b x +a \right)^{2} \sqrt{1-\left(b x +a \right)^{2}}\, \left(b x +a \right)-2 \arcsin \left(b x +a \right)^{3}-6 \arcsin \left(b x +a \right) \left(b x +a \right)^{2}-3 \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}+3 \arcsin \left(b x +a \right)\right)}{4}+\frac{\arcsin \left(b x +a \right)^{3} \left(\left(b x +a \right)^{2}-3\right) \left(b x +a \right)}{3}+\arcsin \left(b x +a \right)^{2} \sqrt{1-\left(b x +a \right)^{2}}-\frac{14 \sqrt{1-\left(b x +a \right)^{2}}}{9}-2 \left(b x +a \right) \arcsin \left(b x +a \right)+\frac{\arcsin \left(b x +a \right)^{2} \left(-1+\left(b x +a \right)^{2}\right) \sqrt{1-\left(b x +a \right)^{2}}}{3}-\frac{2 \arcsin \left(b x +a \right) \left(\left(b x +a \right)^{2}-3\right) \left(b x +a \right)}{9}-\frac{2 \left(-1+\left(b x +a \right)^{2}\right) \sqrt{1-\left(b x +a \right)^{2}}}{27}+a^{2} \left(\arcsin \left(b x +a \right)^{3} \left(b x +a \right)+3 \arcsin \left(b x +a \right)^{2} \sqrt{1-\left(b x +a \right)^{2}}-6 \sqrt{1-\left(b x +a \right)^{2}}-6 \left(b x +a \right) \arcsin \left(b x +a \right)\right)+\arcsin \left(b x +a \right)^{3} \left(b x +a \right)}{b^{3}}"," ",0,"1/b^3*(-1/4*a*(4*arcsin(b*x+a)^3*(b*x+a)^2+6*arcsin(b*x+a)^2*(1-(b*x+a)^2)^(1/2)*(b*x+a)-2*arcsin(b*x+a)^3-6*arcsin(b*x+a)*(b*x+a)^2-3*(b*x+a)*(1-(b*x+a)^2)^(1/2)+3*arcsin(b*x+a))+1/3*arcsin(b*x+a)^3*((b*x+a)^2-3)*(b*x+a)+arcsin(b*x+a)^2*(1-(b*x+a)^2)^(1/2)-14/9*(1-(b*x+a)^2)^(1/2)-2*(b*x+a)*arcsin(b*x+a)+1/3*arcsin(b*x+a)^2*(-1+(b*x+a)^2)*(1-(b*x+a)^2)^(1/2)-2/9*arcsin(b*x+a)*((b*x+a)^2-3)*(b*x+a)-2/27*(-1+(b*x+a)^2)*(1-(b*x+a)^2)^(1/2)+a^2*(arcsin(b*x+a)^3*(b*x+a)+3*arcsin(b*x+a)^2*(1-(b*x+a)^2)^(1/2)-6*(1-(b*x+a)^2)^(1/2)-6*(b*x+a)*arcsin(b*x+a))+arcsin(b*x+a)^3*(b*x+a))","A"
139,1,185,189,0.090000," ","int(x*arcsin(b*x+a)^3,x)","\frac{\frac{\arcsin \left(b x +a \right)^{3} \left(-1+\left(b x +a \right)^{2}\right)}{2}+\frac{3 \arcsin \left(b x +a \right)^{2} \left(\left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}+\arcsin \left(b x +a \right)\right)}{4}-\frac{3 \arcsin \left(b x +a \right) \left(-1+\left(b x +a \right)^{2}\right)}{4}-\frac{3 \left(b x +a \right) \sqrt{1-\left(b x +a \right)^{2}}}{8}-\frac{3 \arcsin \left(b x +a \right)}{8}-\frac{\arcsin \left(b x +a \right)^{3}}{2}-a \left(\arcsin \left(b x +a \right)^{3} \left(b x +a \right)+3 \arcsin \left(b x +a \right)^{2} \sqrt{1-\left(b x +a \right)^{2}}-6 \sqrt{1-\left(b x +a \right)^{2}}-6 \left(b x +a \right) \arcsin \left(b x +a \right)\right)}{b^{2}}"," ",0,"1/b^2*(1/2*arcsin(b*x+a)^3*(-1+(b*x+a)^2)+3/4*arcsin(b*x+a)^2*((b*x+a)*(1-(b*x+a)^2)^(1/2)+arcsin(b*x+a))-3/4*arcsin(b*x+a)*(-1+(b*x+a)^2)-3/8*(b*x+a)*(1-(b*x+a)^2)^(1/2)-3/8*arcsin(b*x+a)-1/2*arcsin(b*x+a)^3-a*(arcsin(b*x+a)^3*(b*x+a)+3*arcsin(b*x+a)^2*(1-(b*x+a)^2)^(1/2)-6*(1-(b*x+a)^2)^(1/2)-6*(b*x+a)*arcsin(b*x+a)))","A"
140,1,71,78,0.075000," ","int(arcsin(b*x+a)^3,x)","\frac{\arcsin \left(b x +a \right)^{3} \left(b x +a \right)+3 \arcsin \left(b x +a \right)^{2} \sqrt{1-\left(b x +a \right)^{2}}-6 \sqrt{1-\left(b x +a \right)^{2}}-6 \left(b x +a \right) \arcsin \left(b x +a \right)}{b}"," ",0,"1/b*(arcsin(b*x+a)^3*(b*x+a)+3*arcsin(b*x+a)^2*(1-(b*x+a)^2)^(1/2)-6*(1-(b*x+a)^2)^(1/2)-6*(b*x+a)*arcsin(b*x+a))","A"
141,0,0,414,1.538000," ","int(arcsin(b*x+a)^3/x,x)","\int \frac{\arcsin \left(b x +a \right)^{3}}{x}\, dx"," ",0,"int(arcsin(b*x+a)^3/x,x)","F"
142,0,0,342,1.030000," ","int(arcsin(b*x+a)^3/x^2,x)","\int \frac{\arcsin \left(b x +a \right)^{3}}{x^{2}}\, dx"," ",0,"int(arcsin(b*x+a)^3/x^2,x)","F"
143,1,49,56,0.089000," ","int(x^2/arcsin(b*x+a),x)","\frac{-a \Si \left(2 \arcsin \left(b x +a \right)\right)+\frac{\Ci \left(\arcsin \left(b x +a \right)\right)}{4}-\frac{\Ci \left(3 \arcsin \left(b x +a \right)\right)}{4}+a^{2} \Ci \left(\arcsin \left(b x +a \right)\right)}{b^{3}}"," ",0,"1/b^3*(-a*Si(2*arcsin(b*x+a))+1/4*Ci(arcsin(b*x+a))-1/4*Ci(3*arcsin(b*x+a))+a^2*Ci(arcsin(b*x+a)))","A"
144,1,27,28,0.069000," ","int(x/arcsin(b*x+a),x)","\frac{\frac{\Si \left(2 \arcsin \left(b x +a \right)\right)}{2}-a \Ci \left(\arcsin \left(b x +a \right)\right)}{b^{2}}"," ",0,"1/b^2*(1/2*Si(2*arcsin(b*x+a))-a*Ci(arcsin(b*x+a)))","A"
145,1,12,11,0.064000," ","int(1/arcsin(b*x+a),x)","\frac{\Ci \left(\arcsin \left(b x +a \right)\right)}{b}"," ",0,"Ci(arcsin(b*x+a))/b","A"
146,0,0,14,0.654000," ","int(1/x/arcsin(b*x+a),x)","\int \frac{1}{x \arcsin \left(b x +a \right)}\, dx"," ",0,"int(1/x/arcsin(b*x+a),x)","F"
147,1,149,78,0.118000," ","int(x^2/arcsin(b*x+a)^2,x)","\frac{-\frac{a \left(2 \Ci \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)-\sin \left(2 \arcsin \left(b x +a \right)\right)\right)}{\arcsin \left(b x +a \right)}-\frac{\sqrt{1-\left(b x +a \right)^{2}}}{4 \arcsin \left(b x +a \right)}-\frac{\Si \left(\arcsin \left(b x +a \right)\right)}{4}+\frac{\cos \left(3 \arcsin \left(b x +a \right)\right)}{4 \arcsin \left(b x +a \right)}+\frac{3 \Si \left(3 \arcsin \left(b x +a \right)\right)}{4}-\frac{a^{2} \left(\Si \left(\arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)}{\arcsin \left(b x +a \right)}}{b^{3}}"," ",0,"1/b^3*(-a*(2*Ci(2*arcsin(b*x+a))*arcsin(b*x+a)-sin(2*arcsin(b*x+a)))/arcsin(b*x+a)-1/4/arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2)-1/4*Si(arcsin(b*x+a))+1/4/arcsin(b*x+a)*cos(3*arcsin(b*x+a))+3/4*Si(3*arcsin(b*x+a))-a^2*(Si(arcsin(b*x+a))*arcsin(b*x+a)+(1-(b*x+a)^2)^(1/2))/arcsin(b*x+a))","A"
148,1,72,53,0.091000," ","int(x/arcsin(b*x+a)^2,x)","\frac{-\frac{\sin \left(2 \arcsin \left(b x +a \right)\right)}{2 \arcsin \left(b x +a \right)}+\Ci \left(2 \arcsin \left(b x +a \right)\right)+\frac{a \left(\Si \left(\arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)}{\arcsin \left(b x +a \right)}}{b^{2}}"," ",0,"1/b^2*(-1/2/arcsin(b*x+a)*sin(2*arcsin(b*x+a))+Ci(2*arcsin(b*x+a))+a*(Si(arcsin(b*x+a))*arcsin(b*x+a)+(1-(b*x+a)^2)^(1/2))/arcsin(b*x+a))","A"
149,1,38,39,0.086000," ","int(1/arcsin(b*x+a)^2,x)","\frac{-\frac{\sqrt{1-\left(b x +a \right)^{2}}}{\arcsin \left(b x +a \right)}-\Si \left(\arcsin \left(b x +a \right)\right)}{b}"," ",0,"1/b*(-1/arcsin(b*x+a)*(1-(b*x+a)^2)^(1/2)-Si(arcsin(b*x+a)))","A"
150,0,0,14,1.336000," ","int(1/x/arcsin(b*x+a)^2,x)","\int \frac{1}{x \arcsin \left(b x +a \right)^{2}}\, dx"," ",0,"int(1/x/arcsin(b*x+a)^2,x)","F"
151,1,215,162,0.164000," ","int(x^2/arcsin(b*x+a)^3,x)","\frac{\frac{a \left(4 \Si \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}+2 \cos \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+\sin \left(2 \arcsin \left(b x +a \right)\right)\right)}{2 \arcsin \left(b x +a \right)^{2}}-\frac{\sqrt{1-\left(b x +a \right)^{2}}}{8 \arcsin \left(b x +a \right)^{2}}+\frac{b x +a}{8 \arcsin \left(b x +a \right)}-\frac{\Ci \left(\arcsin \left(b x +a \right)\right)}{8}+\frac{\cos \left(3 \arcsin \left(b x +a \right)\right)}{8 \arcsin \left(b x +a \right)^{2}}-\frac{3 \sin \left(3 \arcsin \left(b x +a \right)\right)}{8 \arcsin \left(b x +a \right)}+\frac{9 \Ci \left(3 \arcsin \left(b x +a \right)\right)}{8}-\frac{a^{2} \left(\Ci \left(\arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}-\left(b x +a \right) \arcsin \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)}{2 \arcsin \left(b x +a \right)^{2}}}{b^{3}}"," ",0,"1/b^3*(1/2*a*(4*Si(2*arcsin(b*x+a))*arcsin(b*x+a)^2+2*cos(2*arcsin(b*x+a))*arcsin(b*x+a)+sin(2*arcsin(b*x+a)))/arcsin(b*x+a)^2-1/8/arcsin(b*x+a)^2*(1-(b*x+a)^2)^(1/2)+1/8*(b*x+a)/arcsin(b*x+a)-1/8*Ci(arcsin(b*x+a))+1/8/arcsin(b*x+a)^2*cos(3*arcsin(b*x+a))-3/8*sin(3*arcsin(b*x+a))/arcsin(b*x+a)+9/8*Ci(3*arcsin(b*x+a))-1/2*a^2*(Ci(arcsin(b*x+a))*arcsin(b*x+a)^2-(b*x+a)*arcsin(b*x+a)+(1-(b*x+a)^2)^(1/2))/arcsin(b*x+a)^2)","A"
152,1,109,98,0.111000," ","int(x/arcsin(b*x+a)^3,x)","\frac{-\frac{\sin \left(2 \arcsin \left(b x +a \right)\right)}{4 \arcsin \left(b x +a \right)^{2}}-\frac{\cos \left(2 \arcsin \left(b x +a \right)\right)}{2 \arcsin \left(b x +a \right)}-\Si \left(2 \arcsin \left(b x +a \right)\right)+\frac{a \left(\Ci \left(\arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}-\left(b x +a \right) \arcsin \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)}{2 \arcsin \left(b x +a \right)^{2}}}{b^{2}}"," ",0,"1/b^2*(-1/4/arcsin(b*x+a)^2*sin(2*arcsin(b*x+a))-1/2/arcsin(b*x+a)*cos(2*arcsin(b*x+a))-Si(2*arcsin(b*x+a))+1/2*a*(Ci(arcsin(b*x+a))*arcsin(b*x+a)^2-(b*x+a)*arcsin(b*x+a)+(1-(b*x+a)^2)^(1/2))/arcsin(b*x+a)^2)","A"
153,1,53,57,0.030000," ","int(1/arcsin(b*x+a)^3,x)","\frac{-\frac{\sqrt{1-\left(b x +a \right)^{2}}}{2 \arcsin \left(b x +a \right)^{2}}+\frac{b x +a}{2 \arcsin \left(b x +a \right)}-\frac{\Ci \left(\arcsin \left(b x +a \right)\right)}{2}}{b}"," ",0,"1/b*(-1/2/arcsin(b*x+a)^2*(1-(b*x+a)^2)^(1/2)+1/2*(b*x+a)/arcsin(b*x+a)-1/2*Ci(arcsin(b*x+a)))","A"
154,0,0,14,1.487000," ","int(1/x/arcsin(b*x+a)^3,x)","\int \frac{1}{x \arcsin \left(b x +a \right)^{3}}\, dx"," ",0,"int(1/x/arcsin(b*x+a)^3,x)","F"
155,1,748,422,0.603000," ","int(x^2*(a+b*arcsin(d*x+c))^(1/2),x)","\frac{36 \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sin \left(\frac{a}{b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b \,c^{2}-36 \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b \,c^{2}+\sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, b -\sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, b +9 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sin \left(\frac{a}{b}\right) b -9 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b -18 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b c -18 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \cos \left(\frac{2 a}{b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b c +72 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b \,c^{2}+36 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \arcsin \left(d x +c \right) b c +72 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,c^{2}+36 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a c -6 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) \arcsin \left(d x +c \right) b +18 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b -6 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a +18 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a}{72 d^{3} \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/72/d^3*(36*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*sin(a/b)*(a+b*arcsin(d*x+c))^(1/2)*b*c^2-36*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b*c^2+(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*3^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*b-(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*3^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*b+9*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*sin(a/b)*b-9*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b-18*(1/b)^(1/2)*Pi^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b*c-18*(1/b)^(1/2)*Pi^(1/2)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*cos(2*a/b)*(a+b*arcsin(d*x+c))^(1/2)*b*c+72*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b*c^2+36*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*arcsin(d*x+c)*b*c+72*sin((a+b*arcsin(d*x+c))/b-a/b)*a*c^2+36*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*c-6*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*arcsin(d*x+c)*b+18*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b-6*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a+18*sin((a+b*arcsin(d*x+c))/b-a/b)*a)/(a+b*arcsin(d*x+c))^(1/2)","A"
156,1,369,216,0.358000," ","int(x*(a+b*arcsin(d*x+c))^(1/2),x)","-\frac{-4 \sqrt{2}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b c +4 \sqrt{2}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b c -\cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b -\sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b +8 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b c +2 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b +8 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a c +2 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a}{8 d^{2} \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/8/d^2/(a+b*arcsin(d*x+c))^(1/2)*(-4*2^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*Pi^(1/2)*b*c+4*2^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*Pi^(1/2)*b*c-cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*Pi^(1/2)*b-sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*Pi^(1/2)*b+8*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b*c+2*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b+8*sin((a+b*arcsin(d*x+c))/b-a/b)*a*c+2*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a)","A"
157,1,194,108,0.161000," ","int((a+b*arcsin(d*x+c))^(1/2),x)","\frac{-\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b +\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sin \left(\frac{a}{b}\right) b +2 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b +2 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a}{2 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/2/d/(a+b*arcsin(d*x+c))^(1/2)*(-2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b+2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*sin(a/b)*b+2*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b+2*sin((a+b*arcsin(d*x+c))/b-a/b)*a)","A"
158,1,577,275,0.404000," ","int(x*(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{-24 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2} c -24 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2} c +3 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-3 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}+32 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2} c +8 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}+64 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b c +48 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2} c +16 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b -6 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}+32 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} c +48 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b c +8 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2}-6 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b}{32 d^{2} \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/32/d^2*(-24*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2*c-24*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2*c+3*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-3*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2+32*arcsin(d*x+c)^2*sin((a+b*arcsin(d*x+c))/b-a/b)*b^2*c+8*arcsin(d*x+c)^2*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2+64*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b*c+48*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2*c+16*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b-6*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2+32*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2*c+48*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b*c+8*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2-6*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b)/(a+b*arcsin(d*x+c))^(1/2)","B"
159,1,296,139,0.187000," ","int((a+b*arcsin(d*x+c))^(3/2),x)","\frac{-3 \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-3 \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}+4 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}+8 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b +6 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}+4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2}+6 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b}{4 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/4/d/(a+b*arcsin(d*x+c))^(1/2)*(-3*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-3*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2+4*arcsin(d*x+c)^2*sin((a+b*arcsin(d*x+c))/b-a/b)*b^2+8*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b+6*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2+4*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2+6*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b)","B"
160,1,859,330,0.445000," ","int(x*(a+b*arcsin(d*x+c))^(5/2),x)","-\frac{240 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{3} c -240 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{3} c +128 \arcsin \left(d x +c \right)^{3} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3} c +15 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{3}+15 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{3}+32 \arcsin \left(d x +c \right)^{3} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}+384 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2} c +320 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3} c +96 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}-40 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}+384 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b c -480 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3} c +640 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2} c +96 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2} b -30 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}-80 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}+128 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{3} c -480 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2} c +320 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b c +32 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{3}-30 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}-40 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2} b}{128 d^{2} \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/128/d^2*(240*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^3*c-240*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^3*c+128*arcsin(d*x+c)^3*sin((a+b*arcsin(d*x+c))/b-a/b)*b^3*c+15*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^3+15*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^3+32*arcsin(d*x+c)^3*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3+384*arcsin(d*x+c)^2*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b^2*c+320*arcsin(d*x+c)^2*cos((a+b*arcsin(d*x+c))/b-a/b)*b^3*c+96*arcsin(d*x+c)^2*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2-40*arcsin(d*x+c)^2*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3+384*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2*b*c-480*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b^3*c+640*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b^2*c+96*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2*b-30*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3-80*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2+128*sin((a+b*arcsin(d*x+c))/b-a/b)*a^3*c-480*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b^2*c+320*cos((a+b*arcsin(d*x+c))/b-a/b)*a^2*b*c+32*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^3-30*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2-40*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2*b)/(a+b*arcsin(d*x+c))^(1/2)","B"
161,1,433,164,0.279000," ","int((a+b*arcsin(d*x+c))^(5/2),x)","\frac{15 \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, b^{3}-15 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, b^{3}+8 \arcsin \left(d x +c \right)^{3} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}+24 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}+20 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}+24 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b -30 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}+40 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}+8 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{3}-30 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}+20 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b}{8 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/8/d/(a+b*arcsin(d*x+c))^(1/2)*(15*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*b^3-15*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*b^3+8*arcsin(d*x+c)^3*sin((a+b*arcsin(d*x+c))/b-a/b)*b^3+24*arcsin(d*x+c)^2*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b^2+20*arcsin(d*x+c)^2*cos((a+b*arcsin(d*x+c))/b-a/b)*b^3+24*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2*b-30*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b^3+40*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b^2+8*sin((a+b*arcsin(d*x+c))/b-a/b)*a^3-30*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b^2+20*cos((a+b*arcsin(d*x+c))/b-a/b)*a^2*b)","B"
162,1,608,197,0.284000," ","int((a+b*arcsin(d*x+c))^(7/2),x)","\frac{105 \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{2}\, b^{4}+105 \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{2}\, b^{4}+16 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{4} b^{4}+64 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{3} a \,b^{3}+56 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{3} b^{4}+96 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} a^{2} b^{2}-140 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} b^{4}+168 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} a \,b^{3}+64 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a^{3} b -280 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a \,b^{3}+168 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a^{2} b^{2}-210 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b^{4}+16 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{4}-140 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b^{2}+56 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{3} b -210 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{3}}{16 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/16/d/(a+b*arcsin(d*x+c))^(1/2)*(105*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*2^(1/2)*b^4+105*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*2^(1/2)*b^4+16*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^4*b^4+64*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^3*a*b^3+56*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^3*b^4+96*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*a^2*b^2-140*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*b^4+168*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*a*b^3+64*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a^3*b-280*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a*b^3+168*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a^2*b^2-210*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b^4+16*sin((a+b*arcsin(d*x+c))/b-a/b)*a^4-140*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2*b^2+56*cos((a+b*arcsin(d*x+c))/b-a/b)*a^3*b-210*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b^3)","B"
163,1,339,344,0.495000," ","int(x^2/(a+b*arcsin(d*x+c))^(1/2),x)","-\frac{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \left(-12 \sqrt{2}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2}-12 \sqrt{2}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c^{2}+\sqrt{3}\, \sqrt{2}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{3}\, \sqrt{2}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-3 \sqrt{2}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-3 \sqrt{2}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+12 \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c -12 \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) c \right)}{12 d^{3}}"," ",0,"-1/12/d^3*Pi^(1/2)*(1/b)^(1/2)*(-12*2^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*c^2-12*2^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*c^2+3^(1/2)*2^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+3^(1/2)*2^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)-3*2^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)-3*2^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+12*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*c-12*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*c)","A"
164,1,164,167,0.299000," ","int(x/(a+b*arcsin(d*x+c))^(1/2),x)","-\frac{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \left(2 \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, c +2 \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, c -\cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right)}{2 d^{2}}"," ",0,"-1/2/d^2*Pi^(1/2)*(1/b)^(1/2)*(2*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*c+2*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*c-cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b))","A"
165,1,87,85,0.068000," ","int(1/(a+b*arcsin(d*x+c))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \left(\cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right)}{d}"," ",0,"2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b))/d","A"
166,1,300,239,0.358000," ","int(x/(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{-2 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}\, c +2 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}\, c -2 \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-2 \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-2 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) c +\sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right)}{d^{2} b \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/d^2/b*(-2*2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)*c+2*2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)*c-2*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)-2*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)-2*cos((a+b*arcsin(d*x+c))/b-a/b)*c+sin(2*(a+b*arcsin(d*x+c))/b-2*a/b))/(a+b*arcsin(d*x+c))^(1/2)","A"
167,1,161,120,0.174000," ","int(1/(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-\sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+\cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right)\right)}{d b \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-2/d/b*(2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)-2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)+cos((a+b*arcsin(d*x+c))/b-a/b))/(a+b*arcsin(d*x+c))^(1/2)","A"
168,1,681,312,0.402000," ","int(x/(a+b*arcsin(d*x+c))^(5/2),x)","-\frac{-4 \sqrt{2}\, \arcsin \left(d x +c \right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b c -4 \sqrt{2}\, \arcsin \left(d x +c \right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b c -4 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a c -4 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a c +8 \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b -8 \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b +8 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a -8 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a +4 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b c +4 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b -2 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b c +4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a c +\sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b +4 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a}{3 d^{2} b^{2} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-1/3/d^2/b^2*(-4*2^(1/2)*arcsin(d*x+c)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b*c-4*2^(1/2)*arcsin(d*x+c)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b*c-4*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*c-4*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*c+8*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b-8*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b+8*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a-8*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a+4*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b*c+4*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b-2*cos((a+b*arcsin(d*x+c))/b-a/b)*b*c+4*sin((a+b*arcsin(d*x+c))/b-a/b)*a*c+sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b+4*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a)/(a+b*arcsin(d*x+c))^(3/2)","B"
169,1,355,145,0.190000," ","int(1/(a+b*arcsin(d*x+c))^(5/2),x)","\frac{-\frac{4 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, b}{3}-\frac{4 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, b}{3}-\frac{4 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, a}{3}-\frac{4 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, a}{3}+\frac{4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b}{3}-\frac{2 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b}{3}+\frac{4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a}{3}}{d \,b^{2} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"2/3/d/b^2*(-2*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*b-2*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*b-2*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*a-2*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*a+2*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b-cos((a+b*arcsin(d*x+c))/b-a/b)*b+2*sin((a+b*arcsin(d*x+c))/b-a/b)*a)/(a+b*arcsin(d*x+c))^(3/2)","B"
170,1,1172,384,0.464000," ","int(x/(a+b*arcsin(d*x+c))^(7/2),x)","\frac{-8 \sqrt{2}\, \arcsin \left(d x +c \right)^{2} \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2} c +8 \sqrt{2}\, \arcsin \left(d x +c \right)^{2} \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2} c -16 \sqrt{2}\, \arcsin \left(d x +c \right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a b c +16 \sqrt{2}\, \arcsin \left(d x +c \right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a b c -8 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a^{2} c +8 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a^{2} c -32 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right)^{2} \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-32 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right)^{2} \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-64 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a b -64 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a b -32 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a^{2}-32 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a^{2}-8 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2} c +16 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-16 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b c -4 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2} c +32 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b -4 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-8 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} c +6 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2} c -4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b c +16 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2}-3 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-4 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b}{15 d^{2} b^{3} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/15/d^2/b^3*(-8*2^(1/2)*arcsin(d*x+c)^2*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2*c+8*2^(1/2)*arcsin(d*x+c)^2*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2*c-16*2^(1/2)*arcsin(d*x+c)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*b*c+16*2^(1/2)*arcsin(d*x+c)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*b*c-8*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a^2*c+8*2^(1/2)*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a^2*c-32*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)^2*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-32*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)^2*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-64*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*b-64*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*b-32*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a^2-32*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a^2-8*arcsin(d*x+c)^2*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2*c+16*arcsin(d*x+c)^2*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-16*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b*c-4*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b^2*c+32*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b-4*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-8*cos((a+b*arcsin(d*x+c))/b-a/b)*a^2*c+6*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2*c-4*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b*c+16*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2-3*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-4*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b)/(a+b*arcsin(d*x+c))^(5/2)","B"
171,1,600,178,0.205000," ","int(1/(a+b*arcsin(d*x+c))^(7/2),x)","\frac{\frac{8 \arcsin \left(d x +c \right)^{2} \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b^{2}}{15}-\frac{8 \arcsin \left(d x +c \right)^{2} \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b^{2}}{15}+\frac{16 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a b}{15}-\frac{16 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a b}{15}+\frac{8 \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a^{2}}{15}-\frac{8 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a^{2}}{15}+\frac{8 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}}{15}+\frac{16 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b}{15}+\frac{4 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}}{15}+\frac{8 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2}}{15}-\frac{2 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}}{5}+\frac{4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b}{15}}{d \,b^{3} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"2/15/d/b^3*(4*arcsin(d*x+c)^2*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*b^2-4*arcsin(d*x+c)^2*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*b^2+8*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a*b-8*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a*b+4*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a^2-4*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a^2+4*arcsin(d*x+c)^2*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2+8*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b+2*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b^2+4*cos((a+b*arcsin(d*x+c))/b-a/b)*a^2-3*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2+2*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b)/(a+b*arcsin(d*x+c))^(5/2)","B"
172,0,0,18,2.118000," ","int(x^m*(a+b*arcsin(d*x+c))^n,x)","\int x^{m} \left(a +b \arcsin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(x^m*(a+b*arcsin(d*x+c))^n,x)","F"
173,0,0,569,0.736000," ","int(x^2*(a+b*arcsin(d*x+c))^n,x)","\int x^{2} \left(a +b \arcsin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(x^2*(a+b*arcsin(d*x+c))^n,x)","F"
174,0,0,283,0.501000," ","int(x*(a+b*arcsin(d*x+c))^n,x)","\int x \left(a +b \arcsin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(x*(a+b*arcsin(d*x+c))^n,x)","F"
175,0,0,135,0.129000," ","int((a+b*arcsin(d*x+c))^n,x)","\int \left(a +b \arcsin \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^n,x)","F"
176,0,0,18,0.259000," ","int((a+b*arcsin(d*x+c))^n/x,x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{n}}{x}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^n/x,x)","F"
177,1,99,92,0.020000," ","int((d*e*x+c*e)^4*(a+b*arcsin(d*x+c)),x)","\frac{\frac{e^{4} \left(d x +c \right)^{5} a}{5}+e^{4} b \left(\frac{\left(d x +c \right)^{5} \arcsin \left(d x +c \right)}{5}+\frac{\left(d x +c \right)^{4} \sqrt{1-\left(d x +c \right)^{2}}}{25}+\frac{4 \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{75}+\frac{8 \sqrt{1-\left(d x +c \right)^{2}}}{75}\right)}{d}"," ",0,"1/d*(1/5*e^4*(d*x+c)^5*a+e^4*b*(1/5*(d*x+c)^5*arcsin(d*x+c)+1/25*(d*x+c)^4*(1-(d*x+c)^2)^(1/2)+4/75*(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+8/75*(1-(d*x+c)^2)^(1/2)))","A"
178,1,90,97,0.009000," ","int((d*e*x+c*e)^3*(a+b*arcsin(d*x+c)),x)","\frac{\frac{e^{3} \left(d x +c \right)^{4} a}{4}+e^{3} b \left(\frac{\left(d x +c \right)^{4} \arcsin \left(d x +c \right)}{4}+\frac{\left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}}{16}+\frac{3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{32}-\frac{3 \arcsin \left(d x +c \right)}{32}\right)}{d}"," ",0,"1/d*(1/4*e^3*(d*x+c)^4*a+e^3*b*(1/4*(d*x+c)^4*arcsin(d*x+c)+1/16*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)+3/32*(d*x+c)*(1-(d*x+c)^2)^(1/2)-3/32*arcsin(d*x+c)))","A"
179,1,77,70,0.008000," ","int((d*e*x+c*e)^2*(a+b*arcsin(d*x+c)),x)","\frac{\frac{e^{2} \left(d x +c \right)^{3} a}{3}+e^{2} b \left(\frac{\arcsin \left(d x +c \right) \left(d x +c \right)^{3}}{3}+\frac{\left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{9}+\frac{2 \sqrt{1-\left(d x +c \right)^{2}}}{9}\right)}{d}"," ",0,"1/d*(1/3*e^2*(d*x+c)^3*a+e^2*b*(1/3*arcsin(d*x+c)*(d*x+c)^3+1/9*(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+2/9*(1-(d*x+c)^2)^(1/2)))","A"
180,1,64,62,0.007000," ","int((d*e*x+c*e)*(a+b*arcsin(d*x+c)),x)","\frac{\frac{e \left(d x +c \right)^{2} a}{2}+b e \left(\frac{\arcsin \left(d x +c \right) \left(d x +c \right)^{2}}{2}+\frac{\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{4}-\frac{\arcsin \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(1/2*e*(d*x+c)^2*a+b*e*(1/2*arcsin(d*x+c)*(d*x+c)^2+1/4*(d*x+c)*(1-(d*x+c)^2)^(1/2)-1/4*arcsin(d*x+c)))","A"
181,1,36,38,0.004000," ","int(a+b*arcsin(d*x+c),x)","a x +\frac{b \left(\left(d x +c \right) \arcsin \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d}"," ",0,"a*x+b/d*((d*x+c)*arcsin(d*x+c)+(1-(d*x+c)^2)^(1/2))","A"
182,1,182,107,0.086000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e),x)","\frac{a \ln \left(d x +c \right)}{d e}-\frac{i b \arcsin \left(d x +c \right)^{2}}{2 d e}+\frac{b \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{b \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{i b \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{i b \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}"," ",0,"1/d*a/e*ln(d*x+c)-1/2*I/d*b/e*arcsin(d*x+c)^2+1/d*b/e*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+1/d*b/e*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-I/d*b/e*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-I/d*b/e*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))","A"
183,1,56,51,0.010000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^2,x)","\frac{-\frac{a}{e^{2} \left(d x +c \right)}+\frac{b \left(-\frac{\arcsin \left(d x +c \right)}{d x +c}-\arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)\right)}{e^{2}}}{d}"," ",0,"1/d*(-a/e^2/(d*x+c)+b/e^2*(-1/(d*x+c)*arcsin(d*x+c)-arctanh(1/(1-(d*x+c)^2)^(1/2))))","A"
184,1,62,58,0.007000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^3,x)","\frac{-\frac{a}{2 e^{3} \left(d x +c \right)^{2}}+\frac{b \left(-\frac{\arcsin \left(d x +c \right)}{2 \left(d x +c \right)^{2}}-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{2 \left(d x +c \right)}\right)}{e^{3}}}{d}"," ",0,"1/d*(-1/2*a/e^3/(d*x+c)^2+b/e^3*(-1/2/(d*x+c)^2*arcsin(d*x+c)-1/2/(d*x+c)*(1-(d*x+c)^2)^(1/2)))","A"
185,1,78,81,0.008000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^4,x)","\frac{-\frac{a}{3 e^{4} \left(d x +c \right)^{3}}+\frac{b \left(-\frac{\arcsin \left(d x +c \right)}{3 \left(d x +c \right)^{3}}-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{6 \left(d x +c \right)^{2}}-\frac{\arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{6}\right)}{e^{4}}}{d}"," ",0,"1/d*(-1/3*a/e^4/(d*x+c)^3+b/e^4*(-1/3/(d*x+c)^3*arcsin(d*x+c)-1/6/(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-1/6*arctanh(1/(1-(d*x+c)^2)^(1/2))))","A"
186,1,84,87,0.011000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^5,x)","\frac{-\frac{a}{4 e^{5} \left(d x +c \right)^{4}}+\frac{b \left(-\frac{\arcsin \left(d x +c \right)}{4 \left(d x +c \right)^{4}}-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{12 \left(d x +c \right)^{3}}-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{6 \left(d x +c \right)}\right)}{e^{5}}}{d}"," ",0,"1/d*(-1/4*a/e^5/(d*x+c)^4+b/e^5*(-1/4/(d*x+c)^4*arcsin(d*x+c)-1/12/(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-1/6/(d*x+c)*(1-(d*x+c)^2)^(1/2)))","A"
187,1,100,110,0.009000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^6,x)","\frac{-\frac{a}{5 e^{6} \left(d x +c \right)^{5}}+\frac{b \left(-\frac{\arcsin \left(d x +c \right)}{5 \left(d x +c \right)^{5}}-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{20 \left(d x +c \right)^{4}}-\frac{3 \sqrt{1-\left(d x +c \right)^{2}}}{40 \left(d x +c \right)^{2}}-\frac{3 \arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{40}\right)}{e^{6}}}{d}"," ",0,"1/d*(-1/5*a/e^6/(d*x+c)^5+b/e^6*(-1/5/(d*x+c)^5*arcsin(d*x+c)-1/20/(d*x+c)^4*(1-(d*x+c)^2)^(1/2)-3/40/(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-3/40*arctanh(1/(1-(d*x+c)^2)^(1/2))))","A"
188,1,194,183,0.045000," ","int((d*e*x+c*e)^4*(a+b*arcsin(d*x+c))^2,x)","\frac{\frac{e^{4} \left(d x +c \right)^{5} a^{2}}{5}+e^{4} b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{5}}{5}+\frac{2 \arcsin \left(d x +c \right) \left(3 \left(d x +c \right)^{4}+4 \left(d x +c \right)^{2}+8\right) \sqrt{1-\left(d x +c \right)^{2}}}{75}-\frac{2 \left(d x +c \right)^{5}}{125}-\frac{8 \left(d x +c \right)^{3}}{225}-\frac{16 d x}{75}-\frac{16 c}{75}\right)+2 e^{4} a b \left(\frac{\left(d x +c \right)^{5} \arcsin \left(d x +c \right)}{5}+\frac{\left(d x +c \right)^{4} \sqrt{1-\left(d x +c \right)^{2}}}{25}+\frac{4 \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{75}+\frac{8 \sqrt{1-\left(d x +c \right)^{2}}}{75}\right)}{d}"," ",0,"1/d*(1/5*e^4*(d*x+c)^5*a^2+e^4*b^2*(1/5*arcsin(d*x+c)^2*(d*x+c)^5+2/75*arcsin(d*x+c)*(3*(d*x+c)^4+4*(d*x+c)^2+8)*(1-(d*x+c)^2)^(1/2)-2/125*(d*x+c)^5-8/225*(d*x+c)^3-16/75*d*x-16/75*c)+2*e^4*a*b*(1/5*(d*x+c)^5*arcsin(d*x+c)+1/25*(d*x+c)^4*(1-(d*x+c)^2)^(1/2)+4/75*(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+8/75*(1-(d*x+c)^2)^(1/2)))","A"
189,1,206,160,0.057000," ","int((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^2,x)","\frac{\frac{e^{3} \left(d x +c \right)^{4} a^{2}}{4}+e^{3} b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{4}}{4}-\frac{\arcsin \left(d x +c \right) \left(-2 \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+3 \arcsin \left(d x +c \right)\right)}{16}+\frac{3 \arcsin \left(d x +c \right)^{2}}{32}-\frac{\left(d x +c \right)^{4}}{32}-\frac{3 \left(d x +c \right)^{2}}{32}\right)+2 e^{3} a b \left(\frac{\left(d x +c \right)^{4} \arcsin \left(d x +c \right)}{4}+\frac{\left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}}{16}+\frac{3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{32}-\frac{3 \arcsin \left(d x +c \right)}{32}\right)}{d}"," ",0,"1/d*(1/4*e^3*(d*x+c)^4*a^2+e^3*b^2*(1/4*arcsin(d*x+c)^2*(d*x+c)^4-1/16*arcsin(d*x+c)*(-2*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-3*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3*arcsin(d*x+c))+3/32*arcsin(d*x+c)^2-1/32*(d*x+c)^4-3/32*(d*x+c)^2)+2*e^3*a*b*(1/4*(d*x+c)^4*arcsin(d*x+c)+1/16*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)+3/32*(d*x+c)*(1-(d*x+c)^2)^(1/2)-3/32*arcsin(d*x+c)))","A"
190,1,152,126,0.041000," ","int((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^2,x)","\frac{\frac{e^{2} \left(d x +c \right)^{3} a^{2}}{3}+e^{2} b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{3}}{3}+\frac{2 \arcsin \left(d x +c \right) \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{9}-\frac{2 \left(d x +c \right)^{3}}{27}-\frac{4 d x}{9}-\frac{4 c}{9}\right)+2 e^{2} a b \left(\frac{\arcsin \left(d x +c \right) \left(d x +c \right)^{3}}{3}+\frac{\left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{9}+\frac{2 \sqrt{1-\left(d x +c \right)^{2}}}{9}\right)}{d}"," ",0,"1/d*(1/3*e^2*(d*x+c)^3*a^2+e^2*b^2*(1/3*arcsin(d*x+c)^2*(d*x+c)^3+2/9*arcsin(d*x+c)*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2)-2/27*(d*x+c)^3-4/9*d*x-4/9*c)+2*e^2*a*b*(1/3*arcsin(d*x+c)*(d*x+c)^3+1/9*(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+2/9*(1-(d*x+c)^2)^(1/2)))","A"
191,1,146,95,0.053000," ","int((d*e*x+c*e)*(a+b*arcsin(d*x+c))^2,x)","\frac{\frac{e \left(d x +c \right)^{2} a^{2}}{2}+e \,b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right)^{2}-1\right)}{2}+\frac{\arcsin \left(d x +c \right) \left(\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+\arcsin \left(d x +c \right)\right)}{2}-\frac{\arcsin \left(d x +c \right)^{2}}{4}-\frac{\left(d x +c \right)^{2}}{4}\right)+2 e a b \left(\frac{\arcsin \left(d x +c \right) \left(d x +c \right)^{2}}{2}+\frac{\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{4}-\frac{\arcsin \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(1/2*e*(d*x+c)^2*a^2+e*b^2*(1/2*arcsin(d*x+c)^2*((d*x+c)^2-1)+1/2*arcsin(d*x+c)*((d*x+c)*(1-(d*x+c)^2)^(1/2)+arcsin(d*x+c))-1/4*arcsin(d*x+c)^2-1/4*(d*x+c)^2)+2*e*a*b*(1/2*arcsin(d*x+c)*(d*x+c)^2+1/4*(d*x+c)*(1-(d*x+c)^2)^(1/2)-1/4*arcsin(d*x+c)))","A"
192,1,92,57,0.065000," ","int((a+b*arcsin(d*x+c))^2,x)","\frac{\left(d x +c \right) a^{2}+b^{2} \left(\arcsin \left(d x +c \right)^{2} \left(d x +c \right)-2 d x -2 c +2 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\right)+2 a b \left(\left(d x +c \right) \arcsin \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d}"," ",0,"1/d*((d*x+c)*a^2+b^2*(arcsin(d*x+c)^2*(d*x+c)-2*d*x-2*c+2*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2))+2*a*b*((d*x+c)*arcsin(d*x+c)+(1-(d*x+c)^2)^(1/2)))","A"
193,1,455,156,0.085000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e),x)","\frac{a^{2} \ln \left(d x +c \right)}{d e}-\frac{i b^{2} \arcsin \left(d x +c \right)^{3}}{3 d e}+\frac{b^{2} \arcsin \left(d x +c \right)^{2} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 i b^{2} \arcsin \left(d x +c \right) \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 b^{2} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{2} \arcsin \left(d x +c \right)^{2} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 i b^{2} \arcsin \left(d x +c \right) \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 b^{2} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{i a b \arcsin \left(d x +c \right)^{2}}{d e}+\frac{2 a b \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{2 a b \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 i a b \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 i a b \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}"," ",0,"1/d*a^2/e*ln(d*x+c)-1/3*I/d*b^2/e*arcsin(d*x+c)^3+1/d*b^2/e*arcsin(d*x+c)^2*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2*I/d*b^2/e*arcsin(d*x+c)*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+2/d*b^2/e*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+1/d*b^2/e*arcsin(d*x+c)^2*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2*I/d*b^2/e*arcsin(d*x+c)*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+2/d*b^2/e*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-I/d*a*b/e*arcsin(d*x+c)^2+2/d*a*b/e*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+2/d*a*b/e*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2*I/d*a*b/e*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2*I/d*a*b/e*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))","B"
194,1,251,144,0.092000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^2,x)","-\frac{a^{2}}{d \,e^{2} \left(d x +c \right)}-\frac{b^{2} \arcsin \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}+\frac{2 b^{2} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{2 b^{2} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{2 i b^{2} \dilog \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{2 i b^{2} \dilog \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{2 a b \arcsin \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{2 a b \arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}"," ",0,"-1/d*a^2/e^2/(d*x+c)-1/d*b^2/e^2/(d*x+c)*arcsin(d*x+c)^2+2/d*b^2/e^2*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2/d*b^2/e^2*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+2*I/d*b^2/e^2*dilog(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2*I/d*b^2/e^2*dilog(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2/d*a*b/e^2/(d*x+c)*arcsin(d*x+c)-2/d*a*b/e^2*arctanh(1/(1-(d*x+c)^2)^(1/2))","A"
195,1,152,83,0.098000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^3,x)","-\frac{a^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b^{2} \arcsin \left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{b^{2} \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}+\frac{b^{2} \ln \left(d x +c \right)}{d \,e^{3}}-\frac{a b \arcsin \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{a b \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}"," ",0,"-1/2/d*a^2/e^3/(d*x+c)^2-1/2/d*b^2/e^3/(d*x+c)^2*arcsin(d*x+c)^2-1/d*b^2/e^3*arcsin(d*x+c)/(d*x+c)*(1-(d*x+c)^2)^(1/2)+b^2*ln(d*x+c)/d/e^3-1/d*a*b/e^3/(d*x+c)^2*arcsin(d*x+c)-1/d*a*b/e^3/(d*x+c)*(1-(d*x+c)^2)^(1/2)","A"
196,1,336,201,0.429000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^4,x)","-\frac{a^{2}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{2} \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{b^{2} \arcsin \left(d x +c \right)^{2}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{2}}{3 d \,e^{4} \left(d x +c \right)}-\frac{b^{2} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}+\frac{i b^{2} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}+\frac{b^{2} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}-\frac{i b^{2} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}-\frac{2 a b \arcsin \left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{a b \sqrt{1-\left(d x +c \right)^{2}}}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{a b \arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{3 d \,e^{4}}"," ",0,"-1/3/d*a^2/e^4/(d*x+c)^3-1/3/d*b^2/e^4/(d*x+c)^2*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2)-1/3/d*b^2/e^4/(d*x+c)^3*arcsin(d*x+c)^2-1/3*b^2/d/e^4/(d*x+c)-1/3/d*b^2/e^4*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+1/3*I*b^2*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))/d/e^4+1/3/d*b^2/e^4*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-1/3*I*b^2*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))/d/e^4-2/3/d*a*b/e^4/(d*x+c)^3*arcsin(d*x+c)-1/3/d*a*b/e^4/(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-1/3/d*a*b/e^4*arctanh(1/(1-(d*x+c)^2)^(1/2))","A"
197,1,383,304,0.049000," ","int((d*e*x+c*e)^4*(a+b*arcsin(d*x+c))^3,x)","\frac{\frac{e^{4} \left(d x +c \right)^{5} a^{3}}{5}+e^{4} b^{3} \left(\frac{\left(d x +c \right)^{5} \arcsin \left(d x +c \right)^{3}}{5}+\frac{\arcsin \left(d x +c \right)^{2} \left(3 \left(d x +c \right)^{4}+4 \left(d x +c \right)^{2}+8\right) \sqrt{1-\left(d x +c \right)^{2}}}{25}-\frac{16 \sqrt{1-\left(d x +c \right)^{2}}}{25}-\frac{16 \left(d x +c \right) \arcsin \left(d x +c \right)}{25}-\frac{6 \left(d x +c \right)^{5} \arcsin \left(d x +c \right)}{125}-\frac{2 \left(3 \left(d x +c \right)^{4}+4 \left(d x +c \right)^{2}+8\right) \sqrt{1-\left(d x +c \right)^{2}}}{625}-\frac{8 \arcsin \left(d x +c \right) \left(d x +c \right)^{3}}{75}-\frac{8 \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{225}\right)+3 e^{4} a \,b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{5}}{5}+\frac{2 \arcsin \left(d x +c \right) \left(3 \left(d x +c \right)^{4}+4 \left(d x +c \right)^{2}+8\right) \sqrt{1-\left(d x +c \right)^{2}}}{75}-\frac{2 \left(d x +c \right)^{5}}{125}-\frac{8 \left(d x +c \right)^{3}}{225}-\frac{16 d x}{75}-\frac{16 c}{75}\right)+3 e^{4} a^{2} b \left(\frac{\left(d x +c \right)^{5} \arcsin \left(d x +c \right)}{5}+\frac{\left(d x +c \right)^{4} \sqrt{1-\left(d x +c \right)^{2}}}{25}+\frac{4 \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{75}+\frac{8 \sqrt{1-\left(d x +c \right)^{2}}}{75}\right)}{d}"," ",0,"1/d*(1/5*e^4*(d*x+c)^5*a^3+e^4*b^3*(1/5*(d*x+c)^5*arcsin(d*x+c)^3+1/25*arcsin(d*x+c)^2*(3*(d*x+c)^4+4*(d*x+c)^2+8)*(1-(d*x+c)^2)^(1/2)-16/25*(1-(d*x+c)^2)^(1/2)-16/25*(d*x+c)*arcsin(d*x+c)-6/125*(d*x+c)^5*arcsin(d*x+c)-2/625*(3*(d*x+c)^4+4*(d*x+c)^2+8)*(1-(d*x+c)^2)^(1/2)-8/75*arcsin(d*x+c)*(d*x+c)^3-8/225*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2))+3*e^4*a*b^2*(1/5*arcsin(d*x+c)^2*(d*x+c)^5+2/75*arcsin(d*x+c)*(3*(d*x+c)^4+4*(d*x+c)^2+8)*(1-(d*x+c)^2)^(1/2)-2/125*(d*x+c)^5-8/225*(d*x+c)^3-16/75*d*x-16/75*c)+3*e^4*a^2*b*(1/5*(d*x+c)^5*arcsin(d*x+c)+1/25*(d*x+c)^4*(1-(d*x+c)^2)^(1/2)+4/75*(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+8/75*(1-(d*x+c)^2)^(1/2)))","A"
198,1,397,261,0.070000," ","int((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^3,x)","\frac{\frac{e^{3} \left(d x +c \right)^{4} a^{3}}{4}+e^{3} b^{3} \left(\frac{\left(d x +c \right)^{4} \arcsin \left(d x +c \right)^{3}}{4}-\frac{3 \arcsin \left(d x +c \right)^{2} \left(-2 \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+3 \arcsin \left(d x +c \right)\right)}{32}-\frac{3 \left(d x +c \right)^{4} \arcsin \left(d x +c \right)}{32}-\frac{3 \left(d x +c \right) \left(2 \left(d x +c \right)^{2}+3\right) \sqrt{1-\left(d x +c \right)^{2}}}{256}-\frac{27 \arcsin \left(d x +c \right)}{256}-\frac{9 \arcsin \left(d x +c \right) \left(\left(d x +c \right)^{2}-1\right)}{32}-\frac{9 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{64}+\frac{3 \arcsin \left(d x +c \right)^{3}}{16}\right)+3 e^{3} a \,b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{4}}{4}-\frac{\arcsin \left(d x +c \right) \left(-2 \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+3 \arcsin \left(d x +c \right)\right)}{16}+\frac{3 \arcsin \left(d x +c \right)^{2}}{32}-\frac{\left(d x +c \right)^{4}}{32}-\frac{3 \left(d x +c \right)^{2}}{32}\right)+3 e^{3} a^{2} b \left(\frac{\left(d x +c \right)^{4} \arcsin \left(d x +c \right)}{4}+\frac{\left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}}{16}+\frac{3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{32}-\frac{3 \arcsin \left(d x +c \right)}{32}\right)}{d}"," ",0,"1/d*(1/4*e^3*(d*x+c)^4*a^3+e^3*b^3*(1/4*(d*x+c)^4*arcsin(d*x+c)^3-3/32*arcsin(d*x+c)^2*(-2*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-3*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3*arcsin(d*x+c))-3/32*(d*x+c)^4*arcsin(d*x+c)-3/256*(d*x+c)*(2*(d*x+c)^2+3)*(1-(d*x+c)^2)^(1/2)-27/256*arcsin(d*x+c)-9/32*arcsin(d*x+c)*((d*x+c)^2-1)-9/64*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3/16*arcsin(d*x+c)^3)+3*e^3*a*b^2*(1/4*arcsin(d*x+c)^2*(d*x+c)^4-1/16*arcsin(d*x+c)*(-2*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-3*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3*arcsin(d*x+c))+3/32*arcsin(d*x+c)^2-1/32*(d*x+c)^4-3/32*(d*x+c)^2)+3*e^3*a^2*b*(1/4*(d*x+c)^4*arcsin(d*x+c)+1/16*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)+3/32*(d*x+c)*(1-(d*x+c)^2)^(1/2)-3/32*arcsin(d*x+c)))","A"
199,1,280,211,0.040000," ","int((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^3,x)","\frac{\frac{e^{2} \left(d x +c \right)^{3} a^{3}}{3}+e^{2} b^{3} \left(\frac{\left(d x +c \right)^{3} \arcsin \left(d x +c \right)^{3}}{3}+\frac{\arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{3}-\frac{4 \sqrt{1-\left(d x +c \right)^{2}}}{3}-\frac{4 \left(d x +c \right) \arcsin \left(d x +c \right)}{3}-\frac{2 \arcsin \left(d x +c \right) \left(d x +c \right)^{3}}{9}-\frac{2 \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{27}\right)+3 e^{2} a \,b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{3}}{3}+\frac{2 \arcsin \left(d x +c \right) \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{9}-\frac{2 \left(d x +c \right)^{3}}{27}-\frac{4 d x}{9}-\frac{4 c}{9}\right)+3 e^{2} a^{2} b \left(\frac{\arcsin \left(d x +c \right) \left(d x +c \right)^{3}}{3}+\frac{\left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{9}+\frac{2 \sqrt{1-\left(d x +c \right)^{2}}}{9}\right)}{d}"," ",0,"1/d*(1/3*e^2*(d*x+c)^3*a^3+e^2*b^3*(1/3*(d*x+c)^3*arcsin(d*x+c)^3+1/3*arcsin(d*x+c)^2*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2)-4/3*(1-(d*x+c)^2)^(1/2)-4/3*(d*x+c)*arcsin(d*x+c)-2/9*arcsin(d*x+c)*(d*x+c)^3-2/27*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2))+3*e^2*a*b^2*(1/3*arcsin(d*x+c)^2*(d*x+c)^3+2/9*arcsin(d*x+c)*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2)-2/27*(d*x+c)^3-4/9*d*x-4/9*c)+3*e^2*a^2*b*(1/3*arcsin(d*x+c)*(d*x+c)^3+1/9*(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+2/9*(1-(d*x+c)^2)^(1/2)))","A"
200,1,266,149,0.056000," ","int((d*e*x+c*e)*(a+b*arcsin(d*x+c))^3,x)","\frac{\frac{e \left(d x +c \right)^{2} a^{3}}{2}+e \,b^{3} \left(\frac{\arcsin \left(d x +c \right)^{3} \left(\left(d x +c \right)^{2}-1\right)}{2}+\frac{3 \arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+\arcsin \left(d x +c \right)\right)}{4}-\frac{3 \arcsin \left(d x +c \right) \left(\left(d x +c \right)^{2}-1\right)}{4}-\frac{3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{8}-\frac{3 \arcsin \left(d x +c \right)}{8}-\frac{\arcsin \left(d x +c \right)^{3}}{2}\right)+3 e a \,b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right)^{2}-1\right)}{2}+\frac{\arcsin \left(d x +c \right) \left(\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+\arcsin \left(d x +c \right)\right)}{2}-\frac{\arcsin \left(d x +c \right)^{2}}{4}-\frac{\left(d x +c \right)^{2}}{4}\right)+3 e \,a^{2} b \left(\frac{\arcsin \left(d x +c \right) \left(d x +c \right)^{2}}{2}+\frac{\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{4}-\frac{\arcsin \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(1/2*e*(d*x+c)^2*a^3+e*b^3*(1/2*arcsin(d*x+c)^3*((d*x+c)^2-1)+3/4*arcsin(d*x+c)^2*((d*x+c)*(1-(d*x+c)^2)^(1/2)+arcsin(d*x+c))-3/4*arcsin(d*x+c)*((d*x+c)^2-1)-3/8*(d*x+c)*(1-(d*x+c)^2)^(1/2)-3/8*arcsin(d*x+c)-1/2*arcsin(d*x+c)^3)+3*e*a*b^2*(1/2*arcsin(d*x+c)^2*((d*x+c)^2-1)+1/2*arcsin(d*x+c)*((d*x+c)*(1-(d*x+c)^2)^(1/2)+arcsin(d*x+c))-1/4*arcsin(d*x+c)^2-1/4*(d*x+c)^2)+3*e*a^2*b*(1/2*arcsin(d*x+c)*(d*x+c)^2+1/4*(d*x+c)*(1-(d*x+c)^2)^(1/2)-1/4*arcsin(d*x+c)))","A"
201,1,166,100,0.044000," ","int((a+b*arcsin(d*x+c))^3,x)","\frac{\left(d x +c \right) a^{3}+b^{3} \left(\left(d x +c \right) \arcsin \left(d x +c \right)^{3}+3 \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}-6 \sqrt{1-\left(d x +c \right)^{2}}-6 \left(d x +c \right) \arcsin \left(d x +c \right)\right)+3 a \,b^{2} \left(\arcsin \left(d x +c \right)^{2} \left(d x +c \right)-2 d x -2 c +2 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\right)+3 a^{2} b \left(\left(d x +c \right) \arcsin \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d}"," ",0,"1/d*((d*x+c)*a^3+b^3*((d*x+c)*arcsin(d*x+c)^3+3*arcsin(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-6*(1-(d*x+c)^2)^(1/2)-6*(d*x+c)*arcsin(d*x+c))+3*a*b^2*(arcsin(d*x+c)^2*(d*x+c)-2*d*x-2*c+2*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2))+3*a^2*b*((d*x+c)*arcsin(d*x+c)+(1-(d*x+c)^2)^(1/2)))","A"
202,1,828,206,0.085000," ","int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e),x)","\frac{a^{3} \ln \left(d x +c \right)}{d e}-\frac{3 i b^{3} \arcsin \left(d x +c \right)^{2} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{3} \arcsin \left(d x +c \right)^{3} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{6 i a \,b^{2} \arcsin \left(d x +c \right) \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 b^{3} \arcsin \left(d x +c \right) \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{3 i a^{2} b \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{3} \arcsin \left(d x +c \right)^{3} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{i a \,b^{2} \arcsin \left(d x +c \right)^{3}}{d e}+\frac{6 b^{3} \arcsin \left(d x +c \right) \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{3 i a^{2} b \arcsin \left(d x +c \right)^{2}}{2 d e}-\frac{3 i a^{2} b \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 a \,b^{2} \arcsin \left(d x +c \right)^{2} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 i b^{3} \polylog \left(4, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 a \,b^{2} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 a \,b^{2} \arcsin \left(d x +c \right)^{2} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 i b^{3} \polylog \left(4, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 a \,b^{2} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{6 i a \,b^{2} \arcsin \left(d x +c \right) \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 a^{2} b \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{3 a^{2} b \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{i b^{3} \arcsin \left(d x +c \right)^{4}}{4 d e}-\frac{3 i b^{3} \arcsin \left(d x +c \right)^{2} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}"," ",0,"1/d*a^3/e*ln(d*x+c)-3*I/d*a^2*b/e*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+1/d*b^3/e*arcsin(d*x+c)^3*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-3*I/d*a^2*b/e*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+6/d*b^3/e*arcsin(d*x+c)*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-6*I/d*a*b^2/e*arcsin(d*x+c)*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+1/d*b^3/e*arcsin(d*x+c)^3*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-3*I/d*b^3/e*arcsin(d*x+c)^2*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+6/d*b^3/e*arcsin(d*x+c)*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-6*I/d*a*b^2/e*arcsin(d*x+c)*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-I/d*a*b^2/e*arcsin(d*x+c)^3+3/d*a*b^2/e*arcsin(d*x+c)^2*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-3/2*I/d*a^2*b/e*arcsin(d*x+c)^2+6/d*a*b^2/e*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+3/d*a*b^2/e*arcsin(d*x+c)^2*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-1/4*I/d*b^3/e*arcsin(d*x+c)^4+6/d*a*b^2/e*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+6*I/d*b^3/e*polylog(4,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+3/d*a^2*b/e*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+3/d*a^2*b/e*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+6*I/d*b^3/e*polylog(4,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-3*I/d*b^3/e*arcsin(d*x+c)^2*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))","B"
203,1,532,238,0.245000," ","int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^2,x)","-\frac{a^{3}}{d \,e^{2} \left(d x +c \right)}-\frac{b^{3} \arcsin \left(d x +c \right)^{3}}{d \,e^{2} \left(d x +c \right)}-\frac{3 b^{3} \arcsin \left(d x +c \right)^{2} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{6 i b^{3} \arcsin \left(d x +c \right) \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 b^{3} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{3 b^{3} \arcsin \left(d x +c \right)^{2} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 i b^{3} \arcsin \left(d x +c \right) \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{6 b^{3} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{3 a \,b^{2} \arcsin \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}+\frac{6 a \,b^{2} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 a \,b^{2} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{6 i a \,b^{2} \dilog \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 i a \,b^{2} \dilog \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{3 a^{2} b \arcsin \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{3 a^{2} b \arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}"," ",0,"-1/d*a^3/e^2/(d*x+c)-1/d*b^3/e^2/(d*x+c)*arcsin(d*x+c)^3-3/d*b^3/e^2*arcsin(d*x+c)^2*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+6*I/d*b^3/e^2*arcsin(d*x+c)*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-6*b^3*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))/d/e^2+3/d*b^3/e^2*arcsin(d*x+c)^2*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-6*I/d*b^3/e^2*arcsin(d*x+c)*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+6*b^3*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))/d/e^2-3/d*a*b^2/e^2/(d*x+c)*arcsin(d*x+c)^2+6/d*a*b^2/e^2*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-6/d*a*b^2/e^2*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+6*I/d*a*b^2/e^2*dilog(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-6*I/d*a*b^2/e^2*dilog(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-3/d*a^2*b/e^2/(d*x+c)*arcsin(d*x+c)-3/d*a^2*b/e^2*arctanh(1/(1-(d*x+c)^2)^(1/2))","B"
204,1,403,179,0.291000," ","int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^3,x)","-\frac{a^{3}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 i b^{3} \arcsin \left(d x +c \right)^{2}}{2 d \,e^{3}}-\frac{3 b^{3} \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{2 d \,e^{3} \left(d x +c \right)}-\frac{b^{3} \arcsin \left(d x +c \right)^{3}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{3 b^{3} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{3 b^{3} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{3 i b^{3} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{3 i b^{3} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{3 a \,b^{2} \arcsin \left(d x +c \right)^{2}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}+\frac{3 a \,b^{2} \ln \left(d x +c \right)}{d \,e^{3}}-\frac{3 a^{2} b \arcsin \left(d x +c \right)}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{3 a^{2} b \sqrt{1-\left(d x +c \right)^{2}}}{2 d \,e^{3} \left(d x +c \right)}"," ",0,"-1/2/d*a^3/e^3/(d*x+c)^2-3/2*I/d*b^3/e^3*arcsin(d*x+c)^2-3/2/d*b^3/e^3*arcsin(d*x+c)^2/(d*x+c)*(1-(d*x+c)^2)^(1/2)-1/2/d*b^3/e^3*arcsin(d*x+c)^3/(d*x+c)^2+3/d*b^3/e^3*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+3/d*b^3/e^3*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-3*I/d*b^3/e^3*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-3*I/d*b^3/e^3*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-3/2/d*a*b^2/e^3*arcsin(d*x+c)^2/(d*x+c)^2-3/d*a*b^2/e^3*arcsin(d*x+c)/(d*x+c)*(1-(d*x+c)^2)^(1/2)+3/d*a*b^2/e^3*ln(d*x+c)-3/2/d*a^2*b/e^3/(d*x+c)^2*arcsin(d*x+c)-3/2/d*a^2*b/e^3/(d*x+c)*(1-(d*x+c)^2)^(1/2)","B"
205,1,716,331,0.434000," ","int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^4,x)","-\frac{a^{3}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{3} \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{2 d \,e^{4} \left(d x +c \right)^{2}}-\frac{b^{3} \arcsin \left(d x +c \right)^{3}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{b^{3} \arcsin \left(d x +c \right)}{d \,e^{4} \left(d x +c \right)}-\frac{b^{3} \arcsin \left(d x +c \right)^{2} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{2 d \,e^{4}}-\frac{i a \,b^{2} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{b^{3} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{b^{3} \arcsin \left(d x +c \right)^{2} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{2 d \,e^{4}}+\frac{i a \,b^{2} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{b^{3} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 b^{3} \arctanh \left(i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{a \,b^{2} \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{4} \left(d x +c \right)^{2}}-\frac{a \,b^{2} \arcsin \left(d x +c \right)^{2}}{d \,e^{4} \left(d x +c \right)^{3}}-\frac{a \,b^{2}}{d \,e^{4} \left(d x +c \right)}-\frac{a \,b^{2} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{i b^{3} \arcsin \left(d x +c \right) \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{a \,b^{2} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{i b^{3} \arcsin \left(d x +c \right) \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{a^{2} b \arcsin \left(d x +c \right)}{d \,e^{4} \left(d x +c \right)^{3}}-\frac{a^{2} b \sqrt{1-\left(d x +c \right)^{2}}}{2 d \,e^{4} \left(d x +c \right)^{2}}-\frac{a^{2} b \arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{2 d \,e^{4}}"," ",0,"-1/3/d*a^3/e^4/(d*x+c)^3-1/2/d*b^3/e^4/(d*x+c)^2*arcsin(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-1/3/d*b^3/e^4/(d*x+c)^3*arcsin(d*x+c)^3-1/d*b^3/e^4/(d*x+c)*arcsin(d*x+c)-1/2/d*b^3/e^4*arcsin(d*x+c)^2*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-I/d*b^3/e^4*arcsin(d*x+c)*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-b^3*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))/d/e^4+1/2/d*b^3/e^4*arcsin(d*x+c)^2*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+I/d*b^3/e^4*arcsin(d*x+c)*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+b^3*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))/d/e^4-2/d*b^3/e^4*arctanh(I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-1/d*a*b^2/e^4/(d*x+c)^2*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2)-1/d*a*b^2/e^4/(d*x+c)^3*arcsin(d*x+c)^2-1/d*a*b^2/e^4/(d*x+c)-1/d*a*b^2/e^4*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+I/d*a*b^2/e^4*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+1/d*a*b^2/e^4*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-I/d*a*b^2/e^4*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-1/d*a^2*b/e^4/(d*x+c)^3*arcsin(d*x+c)-1/2/d*a^2*b/e^4/(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-1/2/d*a^2*b/e^4*arctanh(1/(1-(d*x+c)^2)^(1/2))","B"
206,1,654,327,0.072000," ","int((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^4,x)","\frac{\frac{e^{3} \left(d x +c \right)^{4} a^{4}}{4}+e^{3} b^{4} \left(\frac{\left(d x +c \right)^{4} \arcsin \left(d x +c \right)^{4}}{4}-\frac{\arcsin \left(d x +c \right)^{3} \left(-2 \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+3 \arcsin \left(d x +c \right)\right)}{8}-\frac{3 \arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{4}}{16}+\frac{3 \arcsin \left(d x +c \right) \left(-2 \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+3 \arcsin \left(d x +c \right)\right)}{64}+\frac{27 \arcsin \left(d x +c \right)^{2}}{128}+\frac{3 \left(d x +c \right)^{4}}{128}+\frac{45 \left(d x +c \right)^{2}}{128}-\frac{9 \arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right)^{2}-1\right)}{16}-\frac{9 \arcsin \left(d x +c \right) \left(\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+\arcsin \left(d x +c \right)\right)}{16}+\frac{9 \arcsin \left(d x +c \right)^{4}}{32}\right)+4 e^{3} a \,b^{3} \left(\frac{\left(d x +c \right)^{4} \arcsin \left(d x +c \right)^{3}}{4}-\frac{3 \arcsin \left(d x +c \right)^{2} \left(-2 \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+3 \arcsin \left(d x +c \right)\right)}{32}-\frac{3 \left(d x +c \right)^{4} \arcsin \left(d x +c \right)}{32}-\frac{3 \left(d x +c \right) \left(2 \left(d x +c \right)^{2}+3\right) \sqrt{1-\left(d x +c \right)^{2}}}{256}-\frac{27 \arcsin \left(d x +c \right)}{256}-\frac{9 \arcsin \left(d x +c \right) \left(\left(d x +c \right)^{2}-1\right)}{32}-\frac{9 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{64}+\frac{3 \arcsin \left(d x +c \right)^{3}}{16}\right)+6 e^{3} a^{2} b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{4}}{4}-\frac{\arcsin \left(d x +c \right) \left(-2 \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+3 \arcsin \left(d x +c \right)\right)}{16}+\frac{3 \arcsin \left(d x +c \right)^{2}}{32}-\frac{\left(d x +c \right)^{4}}{32}-\frac{3 \left(d x +c \right)^{2}}{32}\right)+4 e^{3} a^{3} b \left(\frac{\left(d x +c \right)^{4} \arcsin \left(d x +c \right)}{4}+\frac{\left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}}{16}+\frac{3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{32}-\frac{3 \arcsin \left(d x +c \right)}{32}\right)}{d}"," ",0,"1/d*(1/4*e^3*(d*x+c)^4*a^4+e^3*b^4*(1/4*(d*x+c)^4*arcsin(d*x+c)^4-1/8*arcsin(d*x+c)^3*(-2*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-3*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3*arcsin(d*x+c))-3/16*arcsin(d*x+c)^2*(d*x+c)^4+3/64*arcsin(d*x+c)*(-2*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-3*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3*arcsin(d*x+c))+27/128*arcsin(d*x+c)^2+3/128*(d*x+c)^4+45/128*(d*x+c)^2-9/16*arcsin(d*x+c)^2*((d*x+c)^2-1)-9/16*arcsin(d*x+c)*((d*x+c)*(1-(d*x+c)^2)^(1/2)+arcsin(d*x+c))+9/32*arcsin(d*x+c)^4)+4*e^3*a*b^3*(1/4*(d*x+c)^4*arcsin(d*x+c)^3-3/32*arcsin(d*x+c)^2*(-2*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-3*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3*arcsin(d*x+c))-3/32*(d*x+c)^4*arcsin(d*x+c)-3/256*(d*x+c)*(2*(d*x+c)^2+3)*(1-(d*x+c)^2)^(1/2)-27/256*arcsin(d*x+c)-9/32*arcsin(d*x+c)*((d*x+c)^2-1)-9/64*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3/16*arcsin(d*x+c)^3)+6*e^3*a^2*b^2*(1/4*arcsin(d*x+c)^2*(d*x+c)^4-1/16*arcsin(d*x+c)*(-2*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-3*(d*x+c)*(1-(d*x+c)^2)^(1/2)+3*arcsin(d*x+c))+3/32*arcsin(d*x+c)^2-1/32*(d*x+c)^4-3/32*(d*x+c)^2)+4*e^3*a^3*b*(1/4*(d*x+c)^4*arcsin(d*x+c)+1/16*(d*x+c)^3*(1-(d*x+c)^2)^(1/2)+3/32*(d*x+c)*(1-(d*x+c)^2)^(1/2)-3/32*arcsin(d*x+c)))","A"
207,1,440,263,0.046000," ","int((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^4,x)","\frac{\frac{e^{2} \left(d x +c \right)^{3} a^{4}}{3}+e^{2} b^{4} \left(\frac{\left(d x +c \right)^{3} \arcsin \left(d x +c \right)^{4}}{3}+\frac{4 \arcsin \left(d x +c \right)^{3} \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{9}-\frac{8 \arcsin \left(d x +c \right)^{2} \left(d x +c \right)}{3}+\frac{160 d x}{27}+\frac{160 c}{27}-\frac{16 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{3}-\frac{4 \arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{3}}{9}-\frac{8 \arcsin \left(d x +c \right) \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{27}+\frac{8 \left(d x +c \right)^{3}}{81}\right)+4 e^{2} a \,b^{3} \left(\frac{\left(d x +c \right)^{3} \arcsin \left(d x +c \right)^{3}}{3}+\frac{\arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{3}-\frac{4 \sqrt{1-\left(d x +c \right)^{2}}}{3}-\frac{4 \left(d x +c \right) \arcsin \left(d x +c \right)}{3}-\frac{2 \arcsin \left(d x +c \right) \left(d x +c \right)^{3}}{9}-\frac{2 \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{27}\right)+6 e^{2} a^{2} b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(d x +c \right)^{3}}{3}+\frac{2 \arcsin \left(d x +c \right) \left(\left(d x +c \right)^{2}+2\right) \sqrt{1-\left(d x +c \right)^{2}}}{9}-\frac{2 \left(d x +c \right)^{3}}{27}-\frac{4 d x}{9}-\frac{4 c}{9}\right)+4 e^{2} a^{3} b \left(\frac{\arcsin \left(d x +c \right) \left(d x +c \right)^{3}}{3}+\frac{\left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{9}+\frac{2 \sqrt{1-\left(d x +c \right)^{2}}}{9}\right)}{d}"," ",0,"1/d*(1/3*e^2*(d*x+c)^3*a^4+e^2*b^4*(1/3*(d*x+c)^3*arcsin(d*x+c)^4+4/9*arcsin(d*x+c)^3*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2)-8/3*arcsin(d*x+c)^2*(d*x+c)+160/27*d*x+160/27*c-16/3*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2)-4/9*arcsin(d*x+c)^2*(d*x+c)^3-8/27*arcsin(d*x+c)*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2)+8/81*(d*x+c)^3)+4*e^2*a*b^3*(1/3*(d*x+c)^3*arcsin(d*x+c)^3+1/3*arcsin(d*x+c)^2*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2)-4/3*(1-(d*x+c)^2)^(1/2)-4/3*(d*x+c)*arcsin(d*x+c)-2/9*arcsin(d*x+c)*(d*x+c)^3-2/27*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2))+6*e^2*a^2*b^2*(1/3*arcsin(d*x+c)^2*(d*x+c)^3+2/9*arcsin(d*x+c)*((d*x+c)^2+2)*(1-(d*x+c)^2)^(1/2)-2/27*(d*x+c)^3-4/9*d*x-4/9*c)+4*e^2*a^3*b*(1/3*arcsin(d*x+c)*(d*x+c)^3+1/9*(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+2/9*(1-(d*x+c)^2)^(1/2)))","A"
208,1,412,182,0.060000," ","int((d*e*x+c*e)*(a+b*arcsin(d*x+c))^4,x)","\frac{\frac{e \left(d x +c \right)^{2} a^{4}}{2}+e \,b^{4} \left(\frac{\left(\left(d x +c \right)^{2}-1\right) \arcsin \left(d x +c \right)^{4}}{2}+\arcsin \left(d x +c \right)^{3} \left(\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+\arcsin \left(d x +c \right)\right)-\frac{3 \arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right)^{2}-1\right)}{2}-\frac{3 \arcsin \left(d x +c \right) \left(\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+\arcsin \left(d x +c \right)\right)}{2}+\frac{3 \arcsin \left(d x +c \right)^{2}}{4}+\frac{3 \left(d x +c \right)^{2}}{4}-\frac{3 \arcsin \left(d x +c \right)^{4}}{4}\right)+4 e a \,b^{3} \left(\frac{\arcsin \left(d x +c \right)^{3} \left(\left(d x +c \right)^{2}-1\right)}{2}+\frac{3 \arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+\arcsin \left(d x +c \right)\right)}{4}-\frac{3 \arcsin \left(d x +c \right) \left(\left(d x +c \right)^{2}-1\right)}{4}-\frac{3 \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{8}-\frac{3 \arcsin \left(d x +c \right)}{8}-\frac{\arcsin \left(d x +c \right)^{3}}{2}\right)+6 e \,a^{2} b^{2} \left(\frac{\arcsin \left(d x +c \right)^{2} \left(\left(d x +c \right)^{2}-1\right)}{2}+\frac{\arcsin \left(d x +c \right) \left(\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}+\arcsin \left(d x +c \right)\right)}{2}-\frac{\arcsin \left(d x +c \right)^{2}}{4}-\frac{\left(d x +c \right)^{2}}{4}\right)+4 e \,a^{3} b \left(\frac{\arcsin \left(d x +c \right) \left(d x +c \right)^{2}}{2}+\frac{\left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{4}-\frac{\arcsin \left(d x +c \right)}{4}\right)}{d}"," ",0,"1/d*(1/2*e*(d*x+c)^2*a^4+e*b^4*(1/2*((d*x+c)^2-1)*arcsin(d*x+c)^4+arcsin(d*x+c)^3*((d*x+c)*(1-(d*x+c)^2)^(1/2)+arcsin(d*x+c))-3/2*arcsin(d*x+c)^2*((d*x+c)^2-1)-3/2*arcsin(d*x+c)*((d*x+c)*(1-(d*x+c)^2)^(1/2)+arcsin(d*x+c))+3/4*arcsin(d*x+c)^2+3/4*(d*x+c)^2-3/4*arcsin(d*x+c)^4)+4*e*a*b^3*(1/2*arcsin(d*x+c)^3*((d*x+c)^2-1)+3/4*arcsin(d*x+c)^2*((d*x+c)*(1-(d*x+c)^2)^(1/2)+arcsin(d*x+c))-3/4*arcsin(d*x+c)*((d*x+c)^2-1)-3/8*(d*x+c)*(1-(d*x+c)^2)^(1/2)-3/8*arcsin(d*x+c)-1/2*arcsin(d*x+c)^3)+6*e*a^2*b^2*(1/2*arcsin(d*x+c)^2*((d*x+c)^2-1)+1/2*arcsin(d*x+c)*((d*x+c)*(1-(d*x+c)^2)^(1/2)+arcsin(d*x+c))-1/4*arcsin(d*x+c)^2-1/4*(d*x+c)^2)+4*e*a^3*b*(1/2*arcsin(d*x+c)*(d*x+c)^2+1/4*(d*x+c)*(1-(d*x+c)^2)^(1/2)-1/4*arcsin(d*x+c)))","B"
209,1,255,115,0.070000," ","int((a+b*arcsin(d*x+c))^4,x)","\frac{a^{4} \left(d x +c \right)+b^{4} \left(\left(d x +c \right) \arcsin \left(d x +c \right)^{4}+4 \arcsin \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-12 \arcsin \left(d x +c \right)^{2} \left(d x +c \right)+24 d x +24 c -24 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\right)+4 a \,b^{3} \left(\left(d x +c \right) \arcsin \left(d x +c \right)^{3}+3 \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}-6 \sqrt{1-\left(d x +c \right)^{2}}-6 \left(d x +c \right) \arcsin \left(d x +c \right)\right)+6 a^{2} b^{2} \left(\arcsin \left(d x +c \right)^{2} \left(d x +c \right)-2 d x -2 c +2 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\right)+4 a^{3} b \left(\left(d x +c \right) \arcsin \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d}"," ",0,"1/d*(a^4*(d*x+c)+b^4*((d*x+c)*arcsin(d*x+c)^4+4*arcsin(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-12*arcsin(d*x+c)^2*(d*x+c)+24*d*x+24*c-24*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2))+4*a*b^3*((d*x+c)*arcsin(d*x+c)^3+3*arcsin(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-6*(1-(d*x+c)^2)^(1/2)-6*(d*x+c)*arcsin(d*x+c))+6*a^2*b^2*(arcsin(d*x+c)^2*(d*x+c)-2*d*x-2*c+2*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2))+4*a^3*b*((d*x+c)*arcsin(d*x+c)+(1-(d*x+c)^2)^(1/2)))","B"
210,1,1295,255,0.099000," ","int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e),x)","\frac{a^{4} \ln \left(d x +c \right)}{d e}-\frac{24 b^{4} \polylog \left(5, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{24 b^{4} \polylog \left(5, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{12 i a \,b^{3} \arcsin \left(d x +c \right)^{2} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{12 i a^{2} b^{2} \arcsin \left(d x +c \right) \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{12 i a^{2} b^{2} \arcsin \left(d x +c \right) \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{12 i a \,b^{3} \arcsin \left(d x +c \right)^{2} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 i b^{4} \arcsin \left(d x +c \right) \polylog \left(4, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{4 i a^{3} b \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 a \,b^{3} \arcsin \left(d x +c \right) \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 a \,b^{3} \arcsin \left(d x +c \right) \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 i b^{4} \arcsin \left(d x +c \right) \polylog \left(4, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{4 i b^{4} \arcsin \left(d x +c \right)^{3} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{4 i a^{3} b \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 a^{2} b^{2} \arcsin \left(d x +c \right)^{2} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 a \,b^{3} \arcsin \left(d x +c \right)^{3} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 i a^{3} b \arcsin \left(d x +c \right)^{2}}{d e}-\frac{i a \,b^{3} \arcsin \left(d x +c \right)^{4}}{d e}+\frac{4 a \,b^{3} \arcsin \left(d x +c \right)^{3} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{6 a^{2} b^{2} \arcsin \left(d x +c \right)^{2} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 a^{3} b \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{4 a^{3} b \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{2 i a^{2} b^{2} \arcsin \left(d x +c \right)^{3}}{d e}+\frac{24 i a \,b^{3} \polylog \left(4, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{24 i a \,b^{3} \polylog \left(4, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{4 i b^{4} \arcsin \left(d x +c \right)^{3} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}-\frac{i b^{4} \arcsin \left(d x +c \right)^{5}}{5 d e}+\frac{b^{4} \arcsin \left(d x +c \right)^{4} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{b^{4} \arcsin \left(d x +c \right)^{4} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{12 b^{4} \arcsin \left(d x +c \right)^{2} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{12 a^{2} b^{2} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{12 a^{2} b^{2} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}+\frac{12 b^{4} \arcsin \left(d x +c \right)^{2} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d e}"," ",0,"12/d*b^4/e*arcsin(d*x+c)^2*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+12/d*a^2*b^2/e*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+12/d*a^2*b^2/e*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-1/5*I/d*b^4/e*arcsin(d*x+c)^5+1/d*b^4/e*arcsin(d*x+c)^4*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+12/d*b^4/e*arcsin(d*x+c)^2*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+1/d*b^4/e*arcsin(d*x+c)^4*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-24/d*b^4/e*polylog(5,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-24/d*b^4/e*polylog(5,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+1/d*a^4/e*ln(d*x+c)+6/d*a^2*b^2/e*arcsin(d*x+c)^2*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+4/d*a*b^3/e*arcsin(d*x+c)^3*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2*I/d*a^3*b/e*arcsin(d*x+c)^2+24*I/d*a*b^3/e*polylog(4,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+24*I/d*a*b^3/e*polylog(4,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-I/d*a*b^3/e*arcsin(d*x+c)^4-4*I/d*b^4/e*arcsin(d*x+c)^3*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+24*I/d*b^4/e*arcsin(d*x+c)*polylog(4,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-4*I/d*a^3*b/e*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+24/d*a*b^3/e*arcsin(d*x+c)*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+24/d*a*b^3/e*arcsin(d*x+c)*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+4/d*a*b^3/e*arcsin(d*x+c)^3*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+6/d*a^2*b^2/e*arcsin(d*x+c)^2*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+4/d*a^3*b/e*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+4/d*a^3*b/e*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+24*I/d*b^4/e*arcsin(d*x+c)*polylog(4,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-4*I/d*b^4/e*arcsin(d*x+c)^3*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-4*I/d*a^3*b/e*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2*I/d*a^2*b^2/e*arcsin(d*x+c)^3-12*I/d*a*b^3/e*arcsin(d*x+c)^2*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-12*I/d*a^2*b^2/e*arcsin(d*x+c)*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-12*I/d*a^2*b^2/e*arcsin(d*x+c)*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-12*I/d*a*b^3/e*arcsin(d*x+c)^2*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))","B"
211,1,911,336,0.229000," ","int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^2,x)","-\frac{a^{4}}{d \,e^{2} \left(d x +c \right)}-\frac{b^{4} \arcsin \left(d x +c \right)^{4}}{d \,e^{2} \left(d x +c \right)}+\frac{4 b^{4} \arcsin \left(d x +c \right)^{3} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{4 b^{4} \arcsin \left(d x +c \right)^{3} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{24 b^{4} \arcsin \left(d x +c \right) \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{24 b^{4} \arcsin \left(d x +c \right) \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{24 i b^{4} \polylog \left(4, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{24 i a \,b^{3} \arcsin \left(d x +c \right) \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{12 i b^{4} \arcsin \left(d x +c \right)^{2} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{12 i b^{4} \arcsin \left(d x +c \right)^{2} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{4 a \,b^{3} \arcsin \left(d x +c \right)^{3}}{d \,e^{2} \left(d x +c \right)}-\frac{12 a \,b^{3} \arcsin \left(d x +c \right)^{2} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{12 i a^{2} b^{2} \dilog \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{24 a \,b^{3} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{12 a \,b^{3} \arcsin \left(d x +c \right)^{2} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{24 i a \,b^{3} \arcsin \left(d x +c \right) \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{24 a \,b^{3} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{6 a^{2} b^{2} \arcsin \left(d x +c \right)^{2}}{d \,e^{2} \left(d x +c \right)}+\frac{12 a^{2} b^{2} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{12 a^{2} b^{2} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}+\frac{24 i b^{4} \polylog \left(4, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{12 i a^{2} b^{2} \dilog \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{2}}-\frac{4 a^{3} b \arcsin \left(d x +c \right)}{d \,e^{2} \left(d x +c \right)}-\frac{4 a^{3} b \arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{d \,e^{2}}"," ",0,"-1/d*a^4/e^2/(d*x+c)-1/d*b^4/e^2/(d*x+c)*arcsin(d*x+c)^4+4/d*b^4/e^2*arcsin(d*x+c)^3*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-4/d*b^4/e^2*arcsin(d*x+c)^3*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+24/d*b^4/e^2*arcsin(d*x+c)*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-24/d*b^4/e^2*arcsin(d*x+c)*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-12*I/d*b^4/e^2*arcsin(d*x+c)^2*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-12*I/d*a^2*b^2/e^2*dilog(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-24*I*b^4*polylog(4,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))/d/e^2+24*I*b^4*polylog(4,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))/d/e^2-4/d*a*b^3/e^2/(d*x+c)*arcsin(d*x+c)^3-12/d*a*b^3/e^2*arcsin(d*x+c)^2*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+12*I/d*b^4/e^2*arcsin(d*x+c)^2*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-24/d*a*b^3/e^2*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+12/d*a*b^3/e^2*arcsin(d*x+c)^2*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-24*I/d*a*b^3/e^2*arcsin(d*x+c)*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+24/d*a*b^3/e^2*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-6/d*a^2*b^2/e^2/(d*x+c)*arcsin(d*x+c)^2+12/d*a^2*b^2/e^2*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-12/d*a^2*b^2/e^2*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+12*I/d*a^2*b^2/e^2*dilog(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+24*I/d*a*b^3/e^2*arcsin(d*x+c)*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-4/d*a^3*b/e^2/(d*x+c)*arcsin(d*x+c)-4/d*a^3*b/e^2*arctanh(1/(1-(d*x+c)^2)^(1/2))","B"
212,1,747,228,0.264000," ","int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^3,x)","-\frac{a^{4}}{2 d \,e^{3} \left(d x +c \right)^{2}}-\frac{12 i a \,b^{3} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{2 b^{4} \arcsin \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}-\frac{b^{4} \arcsin \left(d x +c \right)^{4}}{2 d \,e^{3} \left(d x +c \right)^{2}}+\frac{6 b^{4} \arcsin \left(d x +c \right)^{2} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{12 i b^{4} \arcsin \left(d x +c \right) \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{12 b^{4} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{6 b^{4} \arcsin \left(d x +c \right)^{2} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{12 i b^{4} \arcsin \left(d x +c \right) \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{12 b^{4} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{12 i a \,b^{3} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{6 a \,b^{3} \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}-\frac{2 a \,b^{3} \arcsin \left(d x +c \right)^{3}}{d \,e^{3} \left(d x +c \right)^{2}}+\frac{12 a \,b^{3} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}+\frac{12 a \,b^{3} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{3}}-\frac{2 i b^{4} \arcsin \left(d x +c \right)^{3}}{d \,e^{3}}-\frac{6 i a \,b^{3} \arcsin \left(d x +c \right)^{2}}{d \,e^{3}}-\frac{3 a^{2} b^{2} \arcsin \left(d x +c \right)^{2}}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{6 a^{2} b^{2} \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}+\frac{6 a^{2} b^{2} \ln \left(d x +c \right)}{d \,e^{3}}-\frac{2 a^{3} b \arcsin \left(d x +c \right)}{d \,e^{3} \left(d x +c \right)^{2}}-\frac{2 a^{3} b \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{3} \left(d x +c \right)}"," ",0,"-1/2/d*a^4/e^3/(d*x+c)^2-12*I/d*b^4/e^3*arcsin(d*x+c)*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2/d*b^4/e^3*arcsin(d*x+c)^3/(d*x+c)*(1-(d*x+c)^2)^(1/2)-1/2/d*b^4/e^3*arcsin(d*x+c)^4/(d*x+c)^2+6/d*b^4/e^3*arcsin(d*x+c)^2*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-12*I/d*b^4/e^3*arcsin(d*x+c)*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+12/d*b^4/e^3*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+6/d*b^4/e^3*arcsin(d*x+c)^2*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-12*I/d*a*b^3/e^3*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+12/d*b^4/e^3*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2*I/d*b^4/e^3*arcsin(d*x+c)^3-6/d*a*b^3/e^3*arcsin(d*x+c)^2/(d*x+c)*(1-(d*x+c)^2)^(1/2)-2/d*a*b^3/e^3*arcsin(d*x+c)^3/(d*x+c)^2+12/d*a*b^3/e^3*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+12/d*a*b^3/e^3*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-6*I/d*a*b^3/e^3*arcsin(d*x+c)^2-12*I/d*a*b^3/e^3*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-3/d*a^2*b^2/e^3*arcsin(d*x+c)^2/(d*x+c)^2-6/d*a^2*b^2/e^3*arcsin(d*x+c)/(d*x+c)*(1-(d*x+c)^2)^(1/2)+6/d*a^2*b^2/e^3*ln(d*x+c)-2/d*a^3*b/e^3/(d*x+c)^2*arcsin(d*x+c)-2/d*a^3*b/e^3/(d*x+c)*(1-(d*x+c)^2)^(1/2)","B"
213,1,1327,525,0.421000," ","int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^4,x)","-\frac{2 b^{4} \arcsin \left(d x +c \right)^{2}}{d \,e^{4} \left(d x +c \right)}-\frac{2 a^{3} b \arctanh \left(\frac{1}{\sqrt{1-\left(d x +c \right)^{2}}}\right)}{3 d \,e^{4}}-\frac{2 b^{4} \arcsin \left(d x +c \right)^{3} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}-\frac{4 b^{4} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{2 b^{4} \arcsin \left(d x +c \right)^{3} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{3 d \,e^{4}}-\frac{4 b^{4} \arcsin \left(d x +c \right) \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 a \,b^{3} \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 i b^{4} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 i b^{4} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 i b^{4} \polylog \left(4, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 i b^{4} \polylog \left(4, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 a \,b^{3} \polylog \left(3, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 a^{2} b^{2}}{d \,e^{4} \left(d x +c \right)}+\frac{4 b^{4} \arcsin \left(d x +c \right) \polylog \left(3, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{8 a \,b^{3} \arctanh \left(i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 b^{4} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 i b^{4} \arcsin \left(d x +c \right)^{2} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{a^{4}}{3 d \,e^{4} \left(d x +c \right)^{3}}+\frac{2 i b^{4} \arcsin \left(d x +c \right)^{2} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 a \,b^{3} \arcsin \left(d x +c \right)^{2} \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{2 a^{2} b^{2} \arcsin \left(d x +c \right) \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 i a \,b^{3} \arcsin \left(d x +c \right) \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{4 i a \,b^{3} \arcsin \left(d x +c \right) \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 a^{2} b^{2} \arcsin \left(d x +c \right)^{2}}{d \,e^{4} \left(d x +c \right)^{3}}-\frac{2 a^{3} b \sqrt{1-\left(d x +c \right)^{2}}}{3 d \,e^{4} \left(d x +c \right)^{2}}-\frac{2 b^{4} \arcsin \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}}{3 d \,e^{4} \left(d x +c \right)^{2}}+\frac{2 a \,b^{3} \arcsin \left(d x +c \right)^{2} \ln \left(1-i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 a \,b^{3} \arcsin \left(d x +c \right)^{3}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{2 a^{2} b^{2} \arcsin \left(d x +c \right) \ln \left(1+i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{2 i a^{2} b^{2} \polylog \left(2, i \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}+\frac{2 i a^{2} b^{2} \polylog \left(2, -i \left(d x +c \right)-\sqrt{1-\left(d x +c \right)^{2}}\right)}{d \,e^{4}}-\frac{4 a^{3} b \arcsin \left(d x +c \right)}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{4 a \,b^{3} \arcsin \left(d x +c \right)}{d \,e^{4} \left(d x +c \right)}-\frac{b^{4} \arcsin \left(d x +c \right)^{4}}{3 d \,e^{4} \left(d x +c \right)^{3}}-\frac{2 a^{2} b^{2} \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{4} \left(d x +c \right)^{2}}-\frac{2 a \,b^{3} \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}}{d \,e^{4} \left(d x +c \right)^{2}}"," ",0,"-2/d*a*b^3/e^4*arcsin(d*x+c)^2*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2*I/d*a^2*b^2/e^4*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2/3/d*b^4/e^4*arcsin(d*x+c)^3*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-4/d*b^4/e^4*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+2/3/d*b^4/e^4*arcsin(d*x+c)^3*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2/d*b^4/e^4/(d*x+c)*arcsin(d*x+c)^2-4/d*b^4/e^4*arcsin(d*x+c)*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+4/d*a*b^3/e^4*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2/d*a^2*b^2/e^4/(d*x+c)-1/3/d*a^4/e^4/(d*x+c)^3-2/d*a^2*b^2/e^4*arcsin(d*x+c)*ln(1+I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-2/d*a^2*b^2/e^4/(d*x+c)^3*arcsin(d*x+c)^2-2/3/d*a^3*b/e^4/(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-2/3/d*b^4/e^4/(d*x+c)^2*arcsin(d*x+c)^3*(1-(d*x+c)^2)^(1/2)+2*I/d*b^4/e^4*arcsin(d*x+c)^2*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+2*I/d*a^2*b^2/e^4*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-4/3/d*a*b^3/e^4/(d*x+c)^3*arcsin(d*x+c)^3+4*I*b^4*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))/d/e^4-4*I*b^4*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))/d/e^4+2/d*a^2*b^2/e^4*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2*I/d*b^4/e^4*arcsin(d*x+c)^2*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-4*I*b^4*polylog(4,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))/d/e^4+4*I*b^4*polylog(4,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))/d/e^4-4/3/d*a^3*b/e^4/(d*x+c)^3*arcsin(d*x+c)-4/d*a*b^3/e^4/(d*x+c)*arcsin(d*x+c)-1/3/d*b^4/e^4/(d*x+c)^3*arcsin(d*x+c)^4-2/3/d*a^3*b/e^4*arctanh(1/(1-(d*x+c)^2)^(1/2))-4/d*a*b^3/e^4*polylog(3,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+4/d*b^4/e^4*arcsin(d*x+c)*polylog(3,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))-8/d*a*b^3/e^4*arctanh(I*(d*x+c)+(1-(d*x+c)^2)^(1/2))+4/d*b^4/e^4*arcsin(d*x+c)*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))+2/d*a*b^3/e^4*arcsin(d*x+c)^2*ln(1-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-2/d*a^2*b^2/e^4/(d*x+c)^2*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2)-2/d*a*b^3/e^4/(d*x+c)^2*arcsin(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+4*I/d*a*b^3/e^4*arcsin(d*x+c)*polylog(2,-I*(d*x+c)-(1-(d*x+c)^2)^(1/2))-4*I/d*a*b^3/e^4*arcsin(d*x+c)*polylog(2,I*(d*x+c)+(1-(d*x+c)^2)^(1/2))","B"
214,1,367,158,0.071000," ","int((a+b*arcsin(d*x+c))^5,x)","\frac{a^{5} \left(d x +c \right)+b^{5} \left(\arcsin \left(d x +c \right)^{5} \left(d x +c \right)+5 \arcsin \left(d x +c \right)^{4} \sqrt{1-\left(d x +c \right)^{2}}-20 \left(d x +c \right) \arcsin \left(d x +c \right)^{3}-60 \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}+120 \sqrt{1-\left(d x +c \right)^{2}}+120 \left(d x +c \right) \arcsin \left(d x +c \right)\right)+5 a \,b^{4} \left(\left(d x +c \right) \arcsin \left(d x +c \right)^{4}+4 \arcsin \left(d x +c \right)^{3} \sqrt{1-\left(d x +c \right)^{2}}-12 \arcsin \left(d x +c \right)^{2} \left(d x +c \right)+24 d x +24 c -24 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\right)+10 a^{2} b^{3} \left(\left(d x +c \right) \arcsin \left(d x +c \right)^{3}+3 \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}-6 \sqrt{1-\left(d x +c \right)^{2}}-6 \left(d x +c \right) \arcsin \left(d x +c \right)\right)+10 a^{3} b^{2} \left(\arcsin \left(d x +c \right)^{2} \left(d x +c \right)-2 d x -2 c +2 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\right)+5 a^{4} b \left(\left(d x +c \right) \arcsin \left(d x +c \right)+\sqrt{1-\left(d x +c \right)^{2}}\right)}{d}"," ",0,"1/d*(a^5*(d*x+c)+b^5*(arcsin(d*x+c)^5*(d*x+c)+5*arcsin(d*x+c)^4*(1-(d*x+c)^2)^(1/2)-20*(d*x+c)*arcsin(d*x+c)^3-60*arcsin(d*x+c)^2*(1-(d*x+c)^2)^(1/2)+120*(1-(d*x+c)^2)^(1/2)+120*(d*x+c)*arcsin(d*x+c))+5*a*b^4*((d*x+c)*arcsin(d*x+c)^4+4*arcsin(d*x+c)^3*(1-(d*x+c)^2)^(1/2)-12*arcsin(d*x+c)^2*(d*x+c)+24*d*x+24*c-24*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2))+10*a^2*b^3*((d*x+c)*arcsin(d*x+c)^3+3*arcsin(d*x+c)^2*(1-(d*x+c)^2)^(1/2)-6*(1-(d*x+c)^2)^(1/2)-6*(d*x+c)*arcsin(d*x+c))+10*a^3*b^2*(arcsin(d*x+c)^2*(d*x+c)-2*d*x-2*c+2*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2))+5*a^4*b*((d*x+c)*arcsin(d*x+c)+(1-(d*x+c)^2)^(1/2)))","B"
215,1,155,201,0.040000," ","int((d*e*x+c*e)^4/(a+b*arcsin(d*x+c)),x)","-\frac{e^{4} \left(3 \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)+3 \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)-\Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right)-\Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right)-2 \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)-2 \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)\right)}{16 d b}"," ",0,"-1/16/d*e^4*(3*Si(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)+3*Ci(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)-Si(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)-Ci(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)-2*Si(arcsin(d*x+c)+a/b)*sin(a/b)-2*Ci(arcsin(d*x+c)+a/b)*cos(a/b))/b","A"
216,1,112,137,0.049000," ","int((d*e*x+c*e)^3/(a+b*arcsin(d*x+c)),x)","-\frac{e^{3} \left(\Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right)-\Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right)-2 \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)+2 \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)\right)}{8 d b}"," ",0,"-1/8/d*e^3*(Si(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)-Ci(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)-2*Si(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)+2*Ci(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b))/b","A"
217,1,103,133,0.043000," ","int((d*e*x+c*e)^2/(a+b*arcsin(d*x+c)),x)","\frac{e^{2} \left(\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)+\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-\Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right)-\Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right)\right)}{4 d b}"," ",0,"1/4/d*e^2*(Si(arcsin(d*x+c)+a/b)*sin(a/b)+Ci(arcsin(d*x+c)+a/b)*cos(a/b)-Si(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)-Ci(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b))/b","A"
218,1,60,65,0.034000," ","int((d*e*x+c*e)/(a+b*arcsin(d*x+c)),x)","\frac{e \left(\Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right)-\Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right)\right)}{2 d b}"," ",0,"1/2/d*e*(Si(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)-Ci(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b))/b","A"
219,1,52,57,0.074000," ","int(1/(a+b*arcsin(d*x+c)),x)","\frac{\frac{\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{b}+\frac{\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)}{b}}{d}"," ",0,"1/d*(Si(arcsin(d*x+c)+a/b)*sin(a/b)/b+Ci(arcsin(d*x+c)+a/b)*cos(a/b)/b)","A"
220,0,0,26,0.170000," ","int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c)),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsin \left(d x +c \right)\right)}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c)),x)","F"
221,1,397,244,0.227000," ","int((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^2,x)","\frac{e^{4} \left(9 \arcsin \left(d x +c \right) \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b -9 \arcsin \left(d x +c \right) \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b -5 \arcsin \left(d x +c \right) \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) b +5 \arcsin \left(d x +c \right) \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b -2 \arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +2 \arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +9 \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a -9 \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a -5 \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a +5 \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a -2 \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a +2 \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +3 \cos \left(3 \arcsin \left(d x +c \right)\right) b -\cos \left(5 \arcsin \left(d x +c \right)\right) b -2 \sqrt{1-\left(d x +c \right)^{2}}\, b \right)}{16 d \left(a +b \arcsin \left(d x +c \right)\right) b^{2}}"," ",0,"1/16/d*e^4*(9*arcsin(d*x+c)*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*b-9*arcsin(d*x+c)*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*b-5*arcsin(d*x+c)*Si(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*b+5*arcsin(d*x+c)*Ci(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*b-2*arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*cos(a/b)*b+2*arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*b+9*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a-9*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a-5*Si(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*a+5*Ci(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*a-2*Si(arcsin(d*x+c)+a/b)*cos(a/b)*a+2*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a+3*cos(3*arcsin(d*x+c))*b-cos(5*arcsin(d*x+c))*b-2*(1-(d*x+c)^2)^(1/2)*b)/(a+b*arcsin(d*x+c))/b^2","A"
222,1,281,180,0.047000," ","int((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^2,x)","-\frac{e^{3} \left(4 \arcsin \left(d x +c \right) \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b +4 \arcsin \left(d x +c \right) \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b -4 \arcsin \left(d x +c \right) \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) b -4 \arcsin \left(d x +c \right) \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) b +4 \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a +4 \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a -4 \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a -4 \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a -\sin \left(4 \arcsin \left(d x +c \right)\right) b +2 \sin \left(2 \arcsin \left(d x +c \right)\right) b \right)}{8 d \left(a +b \arcsin \left(d x +c \right)\right) b^{2}}"," ",0,"-1/8/d*e^3*(4*arcsin(d*x+c)*Si(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*b+4*arcsin(d*x+c)*Ci(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*b-4*arcsin(d*x+c)*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*b-4*arcsin(d*x+c)*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*b+4*Si(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*a+4*Ci(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*a-4*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a-4*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a-sin(4*arcsin(d*x+c))*b+2*sin(2*arcsin(d*x+c))*b)/(a+b*arcsin(d*x+c))/b^2","A"
223,1,266,176,0.168000," ","int((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^2,x)","-\frac{e^{2} \left(\arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b -\arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b -3 \arcsin \left(d x +c \right) \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b +3 \arcsin \left(d x +c \right) \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b +\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a -\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a -3 \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a +3 \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a -\cos \left(3 \arcsin \left(d x +c \right)\right) b +\sqrt{1-\left(d x +c \right)^{2}}\, b \right)}{4 d \left(a +b \arcsin \left(d x +c \right)\right) b^{2}}"," ",0,"-1/4/d*e^2*(arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*cos(a/b)*b-arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*b-3*arcsin(d*x+c)*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*b+3*arcsin(d*x+c)*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*b+Si(arcsin(d*x+c)+a/b)*cos(a/b)*a-Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a-3*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a+3*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a-cos(3*arcsin(d*x+c))*b+(1-(d*x+c)^2)^(1/2)*b)/(a+b*arcsin(d*x+c))/b^2","A"
224,1,151,102,0.045000," ","int((d*e*x+c*e)/(a+b*arcsin(d*x+c))^2,x)","\frac{e \left(2 \arcsin \left(d x +c \right) \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) b +2 \arcsin \left(d x +c \right) \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) b +2 \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a +2 \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a -\sin \left(2 \arcsin \left(d x +c \right)\right) b \right)}{2 d \left(a +b \arcsin \left(d x +c \right)\right) b^{2}}"," ",0,"1/2/d*e*(2*arcsin(d*x+c)*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*b+2*arcsin(d*x+c)*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*b+2*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a+2*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a-sin(2*arcsin(d*x+c))*b)/(a+b*arcsin(d*x+c))/b^2","A"
225,1,83,91,0.085000," ","int(1/(a+b*arcsin(d*x+c))^2,x)","\frac{-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{\left(a +b \arcsin \left(d x +c \right)\right) b}-\frac{\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right)-\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right)}{b^{2}}}{d}"," ",0,"1/d*(-(1-(d*x+c)^2)^(1/2)/(a+b*arcsin(d*x+c))/b-(Si(arcsin(d*x+c)+a/b)*cos(a/b)-Ci(arcsin(d*x+c)+a/b)*sin(a/b))/b^2)","A"
226,0,0,26,0.163000," ","int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^2,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^2,x)","F"
227,1,720,304,0.261000," ","int((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^3,x)","\frac{e^{4} \left(27 \arcsin \left(d x +c \right)^{2} \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b^{2}-25 \arcsin \left(d x +c \right)^{2} \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b^{2}-25 \arcsin \left(d x +c \right)^{2} \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) b^{2}-2 \arcsin \left(d x +c \right)^{2} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b^{2}-2 \arcsin \left(d x +c \right)^{2} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b^{2}+27 \arcsin \left(d x +c \right)^{2} \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b^{2}-4 \arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a b -4 \arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a b +54 \arcsin \left(d x +c \right) \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a b +54 \arcsin \left(d x +c \right) \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a b -50 \arcsin \left(d x +c \right) \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a b -9 \sin \left(3 \arcsin \left(d x +c \right)\right) \arcsin \left(d x +c \right) b^{2}-2 \sqrt{1-\left(d x +c \right)^{2}}\, b^{2}+3 \cos \left(3 \arcsin \left(d x +c \right)\right) b^{2}-\cos \left(5 \arcsin \left(d x +c \right)\right) b^{2}-50 \arcsin \left(d x +c \right) \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a b -25 \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a^{2}-25 \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a^{2}-2 \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{2}-2 \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{2}+27 \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a^{2}+27 \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a^{2}+5 \arcsin \left(d x +c \right) \sin \left(5 \arcsin \left(d x +c \right)\right) b^{2}+5 \sin \left(5 \arcsin \left(d x +c \right)\right) a b +2 \arcsin \left(d x +c \right) \left(d x +c \right) b^{2}+2 \left(d x +c \right) a b -9 \sin \left(3 \arcsin \left(d x +c \right)\right) a b \right)}{32 d \left(a +b \arcsin \left(d x +c \right)\right)^{2} b^{3}}"," ",0,"1/32/d*e^4*(27*arcsin(d*x+c)^2*Ci(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*b^2-25*arcsin(d*x+c)^2*Si(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*b^2-25*arcsin(d*x+c)^2*Ci(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*b^2-2*arcsin(d*x+c)^2*Si(arcsin(d*x+c)+a/b)*sin(a/b)*b^2-2*arcsin(d*x+c)^2*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*b^2+27*arcsin(d*x+c)^2*Si(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*b^2-9*sin(3*arcsin(d*x+c))*arcsin(d*x+c)*b^2-50*arcsin(d*x+c)*Ci(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*a*b-4*arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*sin(a/b)*a*b-4*arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*a*b+54*arcsin(d*x+c)*Si(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a*b+54*arcsin(d*x+c)*Ci(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a*b-50*arcsin(d*x+c)*Si(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*a*b-2*(1-(d*x+c)^2)^(1/2)*b^2+3*cos(3*arcsin(d*x+c))*b^2-cos(5*arcsin(d*x+c))*b^2+5*arcsin(d*x+c)*sin(5*arcsin(d*x+c))*b^2-25*Si(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*a^2-25*Ci(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*a^2+5*sin(5*arcsin(d*x+c))*a*b+2*arcsin(d*x+c)*(d*x+c)*b^2-2*Si(arcsin(d*x+c)+a/b)*sin(a/b)*a^2-2*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*a^2+2*(d*x+c)*a*b+27*Si(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a^2+27*Ci(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a^2-9*sin(3*arcsin(d*x+c))*a*b)/(a+b*arcsin(d*x+c))^2/b^3","B"
228,1,506,239,0.051000," ","int((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^3,x)","\frac{e^{3} \left(16 \arcsin \left(d x +c \right)^{2} \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b^{2}-16 \arcsin \left(d x +c \right)^{2} \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b^{2}-8 \arcsin \left(d x +c \right)^{2} \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) b^{2}+8 \arcsin \left(d x +c \right)^{2} \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) b^{2}+32 \arcsin \left(d x +c \right) \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a b -32 \arcsin \left(d x +c \right) \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a b -16 \arcsin \left(d x +c \right) \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a b +16 \arcsin \left(d x +c \right) \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a b +4 \arcsin \left(d x +c \right) \cos \left(4 \arcsin \left(d x +c \right)\right) b^{2}-4 \arcsin \left(d x +c \right) \cos \left(2 \arcsin \left(d x +c \right)\right) b^{2}+16 \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a^{2}-16 \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a^{2}-8 \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a^{2}+8 \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a^{2}+\sin \left(4 \arcsin \left(d x +c \right)\right) b^{2}+4 \cos \left(4 \arcsin \left(d x +c \right)\right) a b -2 \sin \left(2 \arcsin \left(d x +c \right)\right) b^{2}-4 \cos \left(2 \arcsin \left(d x +c \right)\right) a b \right)}{16 d \left(a +b \arcsin \left(d x +c \right)\right)^{2} b^{3}}"," ",0,"1/16/d*e^3*(16*arcsin(d*x+c)^2*Si(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*b^2-16*arcsin(d*x+c)^2*Ci(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*b^2-8*arcsin(d*x+c)^2*Si(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*b^2+8*arcsin(d*x+c)^2*Ci(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*b^2+32*arcsin(d*x+c)*Si(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*a*b-32*arcsin(d*x+c)*Ci(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*a*b-16*arcsin(d*x+c)*Si(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a*b+16*arcsin(d*x+c)*Ci(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a*b+4*arcsin(d*x+c)*cos(4*arcsin(d*x+c))*b^2-4*arcsin(d*x+c)*cos(2*arcsin(d*x+c))*b^2+16*Si(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*a^2-16*Ci(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*a^2-8*Si(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a^2+8*Ci(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a^2+sin(4*arcsin(d*x+c))*b^2+4*cos(4*arcsin(d*x+c))*a*b-2*sin(2*arcsin(d*x+c))*b^2-4*cos(2*arcsin(d*x+c))*a*b)/(a+b*arcsin(d*x+c))^2/b^3","B"
229,1,474,234,0.201000," ","int((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^3,x)","-\frac{e^{2} \left(\arcsin \left(d x +c \right)^{2} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b^{2}+\arcsin \left(d x +c \right)^{2} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b^{2}-9 \arcsin \left(d x +c \right)^{2} \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b^{2}-9 \arcsin \left(d x +c \right)^{2} \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b^{2}+2 \arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a b +2 \arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a b -18 \arcsin \left(d x +c \right) \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a b -18 \arcsin \left(d x +c \right) \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a b +3 \sin \left(3 \arcsin \left(d x +c \right)\right) \arcsin \left(d x +c \right) b^{2}-\arcsin \left(d x +c \right) \left(d x +c \right) b^{2}+\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{2}+\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{2}-9 \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a^{2}-9 \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a^{2}+\sqrt{1-\left(d x +c \right)^{2}}\, b^{2}-\cos \left(3 \arcsin \left(d x +c \right)\right) b^{2}+3 \sin \left(3 \arcsin \left(d x +c \right)\right) a b -\left(d x +c \right) a b \right)}{8 d \left(a +b \arcsin \left(d x +c \right)\right)^{2} b^{3}}"," ",0,"-1/8/d*e^2*(arcsin(d*x+c)^2*Si(arcsin(d*x+c)+a/b)*sin(a/b)*b^2+arcsin(d*x+c)^2*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*b^2-9*arcsin(d*x+c)^2*Si(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*b^2-9*arcsin(d*x+c)^2*Ci(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*b^2+2*arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*sin(a/b)*a*b+2*arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*a*b-18*arcsin(d*x+c)*Si(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a*b-18*arcsin(d*x+c)*Ci(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a*b+3*sin(3*arcsin(d*x+c))*arcsin(d*x+c)*b^2-arcsin(d*x+c)*(d*x+c)*b^2+Si(arcsin(d*x+c)+a/b)*sin(a/b)*a^2+Ci(arcsin(d*x+c)+a/b)*cos(a/b)*a^2-9*Si(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a^2-9*Ci(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a^2+(1-(d*x+c)^2)^(1/2)*b^2-cos(3*arcsin(d*x+c))*b^2+3*sin(3*arcsin(d*x+c))*a*b-(d*x+c)*a*b)/(a+b*arcsin(d*x+c))^2/b^3","B"
230,1,263,151,0.046000," ","int((d*e*x+c*e)/(a+b*arcsin(d*x+c))^3,x)","-\frac{e \left(4 \arcsin \left(d x +c \right)^{2} \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) b^{2}-4 \arcsin \left(d x +c \right)^{2} \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) b^{2}+8 \arcsin \left(d x +c \right) \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a b -8 \arcsin \left(d x +c \right) \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a b +2 \arcsin \left(d x +c \right) \cos \left(2 \arcsin \left(d x +c \right)\right) b^{2}+4 \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a^{2}-4 \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a^{2}+\sin \left(2 \arcsin \left(d x +c \right)\right) b^{2}+2 \cos \left(2 \arcsin \left(d x +c \right)\right) a b \right)}{4 d \left(a +b \arcsin \left(d x +c \right)\right)^{2} b^{3}}"," ",0,"-1/4/d*e*(4*arcsin(d*x+c)^2*Si(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*b^2-4*arcsin(d*x+c)^2*Ci(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*b^2+8*arcsin(d*x+c)*Si(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a*b-8*arcsin(d*x+c)*Ci(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a*b+2*arcsin(d*x+c)*cos(2*arcsin(d*x+c))*b^2+4*Si(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a^2-4*Ci(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a^2+sin(2*arcsin(d*x+c))*b^2+2*cos(2*arcsin(d*x+c))*a*b)/(a+b*arcsin(d*x+c))^2/b^3","A"
231,1,158,117,0.069000," ","int(1/(a+b*arcsin(d*x+c))^3,x)","\frac{-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{2 \left(a +b \arcsin \left(d x +c \right)\right)^{2} b}-\frac{\arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b +\arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b +\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a +\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a -b \left(d x +c \right)}{2 \left(a +b \arcsin \left(d x +c \right)\right) b^{3}}}{d}"," ",0,"1/d*(-1/2*(1-(d*x+c)^2)^(1/2)/(a+b*arcsin(d*x+c))^2/b-1/2*(arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*sin(a/b)*b+arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*b+Si(arcsin(d*x+c)+a/b)*sin(a/b)*a+Ci(arcsin(d*x+c)+a/b)*cos(a/b)*a-b*(d*x+c))/(a+b*arcsin(d*x+c))/b^3)","A"
232,0,0,26,0.177000," ","int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^3,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^3,x)","F"
233,1,1138,390,0.297000," ","int((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^4,x)","-\frac{e^{4} \left(-2 \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{3}+2 \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{3}+81 \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a^{3}-81 \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a^{3}-125 \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a^{3}+125 \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a^{3}-25 \cos \left(5 \arcsin \left(d x +c \right)\right) a^{2} b -5 \sin \left(5 \arcsin \left(d x +c \right)\right) a \,b^{2}-2 \arcsin \left(d x +c \right) \left(d x +c \right) b^{3}-2 \arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}\, b^{3}-2 \sqrt{1-\left(d x +c \right)^{2}}\, a^{2} b -2 \left(d x +c \right) a \,b^{2}+9 \arcsin \left(d x +c \right) \sin \left(3 \arcsin \left(d x +c \right)\right) b^{3}+27 \cos \left(3 \arcsin \left(d x +c \right)\right) a^{2} b +9 \sin \left(3 \arcsin \left(d x +c \right)\right) a \,b^{2}-25 \arcsin \left(d x +c \right)^{2} \cos \left(5 \arcsin \left(d x +c \right)\right) b^{3}-5 \arcsin \left(d x +c \right) \sin \left(5 \arcsin \left(d x +c \right)\right) b^{3}+27 \arcsin \left(d x +c \right)^{2} \cos \left(3 \arcsin \left(d x +c \right)\right) b^{3}-243 \arcsin \left(d x +c \right) \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a^{2} b -375 \arcsin \left(d x +c \right)^{2} \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a \,b^{2}+375 \arcsin \left(d x +c \right)^{2} \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a \,b^{2}-375 \arcsin \left(d x +c \right) \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) a^{2} b +375 \arcsin \left(d x +c \right) \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) a^{2} b -6 \arcsin \left(d x +c \right)^{2} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,b^{2}+6 \arcsin \left(d x +c \right)^{2} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,b^{2}-6 \arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{2} b +6 \arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{2} b +243 \arcsin \left(d x +c \right)^{2} \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a \,b^{2}-243 \arcsin \left(d x +c \right)^{2} \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a \,b^{2}+243 \arcsin \left(d x +c \right) \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a^{2} b -6 \cos \left(3 \arcsin \left(d x +c \right)\right) b^{3}+2 \cos \left(5 \arcsin \left(d x +c \right)\right) b^{3}+4 \sqrt{1-\left(d x +c \right)^{2}}\, b^{3}-4 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\, a \,b^{2}+54 \arcsin \left(d x +c \right) \cos \left(3 \arcsin \left(d x +c \right)\right) a \,b^{2}-50 \arcsin \left(d x +c \right) \cos \left(5 \arcsin \left(d x +c \right)\right) a \,b^{2}+81 \arcsin \left(d x +c \right)^{3} \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b^{3}-81 \arcsin \left(d x +c \right)^{3} \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b^{3}-125 \arcsin \left(d x +c \right)^{3} \Si \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \cos \left(\frac{5 a}{b}\right) b^{3}+125 \arcsin \left(d x +c \right)^{3} \Ci \left(5 \arcsin \left(d x +c \right)+\frac{5 a}{b}\right) \sin \left(\frac{5 a}{b}\right) b^{3}-2 \arcsin \left(d x +c \right)^{3} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b^{3}+2 \arcsin \left(d x +c \right)^{3} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b^{3}\right)}{96 d \left(a +b \arcsin \left(d x +c \right)\right)^{3} b^{4}}"," ",0,"-1/96/d*e^4*(-25*cos(5*arcsin(d*x+c))*a^2*b-5*sin(5*arcsin(d*x+c))*a*b^2-2*arcsin(d*x+c)*(d*x+c)*b^3-2*Si(arcsin(d*x+c)+a/b)*cos(a/b)*a^3+2*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a^3-2*arcsin(d*x+c)^2*(1-(d*x+c)^2)^(1/2)*b^3-2*(1-(d*x+c)^2)^(1/2)*a^2*b-2*(d*x+c)*a*b^2+9*arcsin(d*x+c)*sin(3*arcsin(d*x+c))*b^3+81*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a^3-81*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a^3+27*cos(3*arcsin(d*x+c))*a^2*b+9*sin(3*arcsin(d*x+c))*a*b^2-25*arcsin(d*x+c)^2*cos(5*arcsin(d*x+c))*b^3-5*arcsin(d*x+c)*sin(5*arcsin(d*x+c))*b^3-125*Si(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*a^3+27*arcsin(d*x+c)^2*cos(3*arcsin(d*x+c))*b^3-243*arcsin(d*x+c)*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a^2*b-375*arcsin(d*x+c)^2*Si(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*a*b^2+375*arcsin(d*x+c)^2*Ci(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*a*b^2-375*arcsin(d*x+c)*Si(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*a^2*b+375*arcsin(d*x+c)*Ci(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*a^2*b-6*arcsin(d*x+c)^2*Si(arcsin(d*x+c)+a/b)*cos(a/b)*a*b^2+6*arcsin(d*x+c)^2*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a*b^2-6*arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*cos(a/b)*a^2*b+6*arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a^2*b+243*arcsin(d*x+c)^2*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a*b^2-243*arcsin(d*x+c)^2*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a*b^2+243*arcsin(d*x+c)*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a^2*b-6*cos(3*arcsin(d*x+c))*b^3+2*cos(5*arcsin(d*x+c))*b^3+4*(1-(d*x+c)^2)^(1/2)*b^3+125*Ci(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*a^3-4*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2)*a*b^2+81*arcsin(d*x+c)^3*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*b^3-81*arcsin(d*x+c)^3*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*b^3+54*arcsin(d*x+c)*cos(3*arcsin(d*x+c))*a*b^2-125*arcsin(d*x+c)^3*Si(5*arcsin(d*x+c)+5*a/b)*cos(5*a/b)*b^3+125*arcsin(d*x+c)^3*Ci(5*arcsin(d*x+c)+5*a/b)*sin(5*a/b)*b^3-50*arcsin(d*x+c)*cos(5*arcsin(d*x+c))*a*b^2-2*arcsin(d*x+c)^3*Si(arcsin(d*x+c)+a/b)*cos(a/b)*b^3+2*arcsin(d*x+c)^3*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*b^3)/(a+b*arcsin(d*x+c))^3/b^4","B"
234,1,782,324,0.060000," ","int((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^4,x)","\frac{e^{3} \left(32 \arcsin \left(d x +c \right)^{3} \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) b^{3}+32 \arcsin \left(d x +c \right)^{3} \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) b^{3}-8 \arcsin \left(d x +c \right)^{3} \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) b^{3}-8 \arcsin \left(d x +c \right)^{3} \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) b^{3}-16 \arcsin \left(d x +c \right) \sin \left(4 \arcsin \left(d x +c \right)\right) a \,b^{2}+8 \arcsin \left(d x +c \right) \sin \left(2 \arcsin \left(d x +c \right)\right) a \,b^{2}-8 \arcsin \left(d x +c \right)^{2} \sin \left(4 \arcsin \left(d x +c \right)\right) b^{3}-24 \arcsin \left(d x +c \right)^{2} \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a \,b^{2}-24 \arcsin \left(d x +c \right)^{2} \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a \,b^{2}+96 \arcsin \left(d x +c \right) \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a^{2} b +96 \arcsin \left(d x +c \right) \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a^{2} b -24 \arcsin \left(d x +c \right) \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a^{2} b -24 \arcsin \left(d x +c \right) \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a^{2} b +96 \arcsin \left(d x +c \right)^{2} \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a \,b^{2}+96 \arcsin \left(d x +c \right)^{2} \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a \,b^{2}+\sin \left(4 \arcsin \left(d x +c \right)\right) b^{3}-2 \sin \left(2 \arcsin \left(d x +c \right)\right) b^{3}+32 \Si \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \sin \left(\frac{4 a}{b}\right) a^{3}+32 \Ci \left(4 \arcsin \left(d x +c \right)+\frac{4 a}{b}\right) \cos \left(\frac{4 a}{b}\right) a^{3}-8 \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a^{3}-8 \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a^{3}+4 \arcsin \left(d x +c \right)^{2} \sin \left(2 \arcsin \left(d x +c \right)\right) b^{3}+2 \arcsin \left(d x +c \right) \cos \left(4 \arcsin \left(d x +c \right)\right) b^{3}-2 \arcsin \left(d x +c \right) \cos \left(2 \arcsin \left(d x +c \right)\right) b^{3}-8 \sin \left(4 \arcsin \left(d x +c \right)\right) a^{2} b +2 \cos \left(4 \arcsin \left(d x +c \right)\right) a \,b^{2}+4 \sin \left(2 \arcsin \left(d x +c \right)\right) a^{2} b -2 \cos \left(2 \arcsin \left(d x +c \right)\right) a \,b^{2}\right)}{24 d \left(a +b \arcsin \left(d x +c \right)\right)^{3} b^{4}}"," ",0,"1/24/d*e^3*(32*arcsin(d*x+c)^3*Si(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*b^3+32*arcsin(d*x+c)^3*Ci(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*b^3-8*arcsin(d*x+c)^3*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*b^3-8*arcsin(d*x+c)^3*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*b^3-16*arcsin(d*x+c)*sin(4*arcsin(d*x+c))*a*b^2+8*arcsin(d*x+c)*sin(2*arcsin(d*x+c))*a*b^2-8*arcsin(d*x+c)^2*sin(4*arcsin(d*x+c))*b^3-24*arcsin(d*x+c)^2*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a*b^2-24*arcsin(d*x+c)^2*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a*b^2+96*arcsin(d*x+c)*Si(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*a^2*b+96*arcsin(d*x+c)*Ci(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*a^2*b-24*arcsin(d*x+c)*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a^2*b-24*arcsin(d*x+c)*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a^2*b+96*arcsin(d*x+c)^2*Si(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*a*b^2+96*arcsin(d*x+c)^2*Ci(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*a*b^2+sin(4*arcsin(d*x+c))*b^3-2*sin(2*arcsin(d*x+c))*b^3+4*arcsin(d*x+c)^2*sin(2*arcsin(d*x+c))*b^3+2*arcsin(d*x+c)*cos(4*arcsin(d*x+c))*b^3-2*arcsin(d*x+c)*cos(2*arcsin(d*x+c))*b^3+32*Si(4*arcsin(d*x+c)+4*a/b)*sin(4*a/b)*a^3+32*Ci(4*arcsin(d*x+c)+4*a/b)*cos(4*a/b)*a^3-8*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a^3-8*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a^3-8*sin(4*arcsin(d*x+c))*a^2*b+2*cos(4*arcsin(d*x+c))*a*b^2+4*sin(2*arcsin(d*x+c))*a^2*b-2*cos(2*arcsin(d*x+c))*a*b^2)/(a+b*arcsin(d*x+c))^3/b^4","B"
235,1,753,313,0.224000," ","int((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^4,x)","\frac{e^{2} \left(\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{3}-\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{3}-27 \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a^{3}+27 \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a^{3}+\arcsin \left(d x +c \right) \left(d x +c \right) b^{3}+\arcsin \left(d x +c \right)^{2} \sqrt{1-\left(d x +c \right)^{2}}\, b^{3}+\sqrt{1-\left(d x +c \right)^{2}}\, a^{2} b +\left(d x +c \right) a \,b^{2}-3 \arcsin \left(d x +c \right) \sin \left(3 \arcsin \left(d x +c \right)\right) b^{3}-9 \cos \left(3 \arcsin \left(d x +c \right)\right) a^{2} b -3 \sin \left(3 \arcsin \left(d x +c \right)\right) a \,b^{2}-9 \arcsin \left(d x +c \right)^{2} \cos \left(3 \arcsin \left(d x +c \right)\right) b^{3}+81 \arcsin \left(d x +c \right) \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a^{2} b +3 \arcsin \left(d x +c \right)^{2} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,b^{2}-3 \arcsin \left(d x +c \right)^{2} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,b^{2}+3 \arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{2} b -3 \arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{2} b -81 \arcsin \left(d x +c \right)^{2} \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a \,b^{2}+81 \arcsin \left(d x +c \right)^{2} \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) a \,b^{2}-81 \arcsin \left(d x +c \right) \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) a^{2} b +2 \cos \left(3 \arcsin \left(d x +c \right)\right) b^{3}-2 \sqrt{1-\left(d x +c \right)^{2}}\, b^{3}+2 \arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\, a \,b^{2}-18 \arcsin \left(d x +c \right) \cos \left(3 \arcsin \left(d x +c \right)\right) a \,b^{2}-27 \arcsin \left(d x +c \right)^{3} \Si \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \cos \left(\frac{3 a}{b}\right) b^{3}+27 \arcsin \left(d x +c \right)^{3} \Ci \left(3 \arcsin \left(d x +c \right)+\frac{3 a}{b}\right) \sin \left(\frac{3 a}{b}\right) b^{3}+\arcsin \left(d x +c \right)^{3} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b^{3}-\arcsin \left(d x +c \right)^{3} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b^{3}\right)}{24 d \left(a +b \arcsin \left(d x +c \right)\right)^{3} b^{4}}"," ",0,"1/24/d*e^2*(arcsin(d*x+c)*(d*x+c)*b^3+Si(arcsin(d*x+c)+a/b)*cos(a/b)*a^3-Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a^3+arcsin(d*x+c)^2*(1-(d*x+c)^2)^(1/2)*b^3+(1-(d*x+c)^2)^(1/2)*a^2*b+(d*x+c)*a*b^2-3*arcsin(d*x+c)*sin(3*arcsin(d*x+c))*b^3-27*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a^3+27*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a^3-9*cos(3*arcsin(d*x+c))*a^2*b-3*sin(3*arcsin(d*x+c))*a*b^2-9*arcsin(d*x+c)^2*cos(3*arcsin(d*x+c))*b^3+81*arcsin(d*x+c)*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a^2*b+3*arcsin(d*x+c)^2*Si(arcsin(d*x+c)+a/b)*cos(a/b)*a*b^2-3*arcsin(d*x+c)^2*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a*b^2+3*arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*cos(a/b)*a^2*b-3*arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a^2*b-81*arcsin(d*x+c)^2*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a*b^2+81*arcsin(d*x+c)^2*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*a*b^2-81*arcsin(d*x+c)*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*a^2*b+2*cos(3*arcsin(d*x+c))*b^3-2*(1-(d*x+c)^2)^(1/2)*b^3+2*arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2)*a*b^2-27*arcsin(d*x+c)^3*Si(3*arcsin(d*x+c)+3*a/b)*cos(3*a/b)*b^3+27*arcsin(d*x+c)^3*Ci(3*arcsin(d*x+c)+3*a/b)*sin(3*a/b)*b^3-18*arcsin(d*x+c)*cos(3*arcsin(d*x+c))*a*b^2+arcsin(d*x+c)^3*Si(arcsin(d*x+c)+a/b)*cos(a/b)*b^3-arcsin(d*x+c)^3*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*b^3)/(a+b*arcsin(d*x+c))^3/b^4","B"
236,1,399,192,0.048000," ","int((d*e*x+c*e)/(a+b*arcsin(d*x+c))^4,x)","-\frac{e \left(4 \arcsin \left(d x +c \right)^{3} \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) b^{3}+4 \arcsin \left(d x +c \right)^{3} \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) b^{3}+12 \arcsin \left(d x +c \right)^{2} \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a \,b^{2}+12 \arcsin \left(d x +c \right)^{2} \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a \,b^{2}-2 \arcsin \left(d x +c \right)^{2} \sin \left(2 \arcsin \left(d x +c \right)\right) b^{3}+12 \arcsin \left(d x +c \right) \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a^{2} b +12 \arcsin \left(d x +c \right) \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a^{2} b -4 \arcsin \left(d x +c \right) \sin \left(2 \arcsin \left(d x +c \right)\right) a \,b^{2}+\arcsin \left(d x +c \right) \cos \left(2 \arcsin \left(d x +c \right)\right) b^{3}+4 \Ci \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \cos \left(\frac{2 a}{b}\right) a^{3}+4 \Si \left(2 \arcsin \left(d x +c \right)+\frac{2 a}{b}\right) \sin \left(\frac{2 a}{b}\right) a^{3}-2 \sin \left(2 \arcsin \left(d x +c \right)\right) a^{2} b +\sin \left(2 \arcsin \left(d x +c \right)\right) b^{3}+\cos \left(2 \arcsin \left(d x +c \right)\right) a \,b^{2}\right)}{6 d \left(a +b \arcsin \left(d x +c \right)\right)^{3} b^{4}}"," ",0,"-1/6/d*e*(4*arcsin(d*x+c)^3*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*b^3+4*arcsin(d*x+c)^3*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*b^3+12*arcsin(d*x+c)^2*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a*b^2+12*arcsin(d*x+c)^2*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a*b^2-2*arcsin(d*x+c)^2*sin(2*arcsin(d*x+c))*b^3+12*arcsin(d*x+c)*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a^2*b+12*arcsin(d*x+c)*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a^2*b-4*arcsin(d*x+c)*sin(2*arcsin(d*x+c))*a*b^2+arcsin(d*x+c)*cos(2*arcsin(d*x+c))*b^3+4*Ci(2*arcsin(d*x+c)+2*a/b)*cos(2*a/b)*a^3+4*Si(2*arcsin(d*x+c)+2*a/b)*sin(2*a/b)*a^3-2*sin(2*arcsin(d*x+c))*a^2*b+sin(2*arcsin(d*x+c))*b^3+cos(2*arcsin(d*x+c))*a*b^2)/(a+b*arcsin(d*x+c))^3/b^4","B"
237,1,270,150,0.171000," ","int(1/(a+b*arcsin(d*x+c))^4,x)","\frac{-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{3 \left(a +b \arcsin \left(d x +c \right)\right)^{3} b}+\frac{\arcsin \left(d x +c \right)^{2} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b^{2}-\arcsin \left(d x +c \right)^{2} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b^{2}+2 \arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a b -2 \arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a b +\arcsin \left(d x +c \right) \sqrt{1-\left(d x +c \right)^{2}}\, b^{2}+\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{2}-\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{2}+\sqrt{1-\left(d x +c \right)^{2}}\, a b +\left(d x +c \right) b^{2}}{6 \left(a +b \arcsin \left(d x +c \right)\right)^{2} b^{4}}}{d}"," ",0,"1/d*(-1/3*(1-(d*x+c)^2)^(1/2)/(a+b*arcsin(d*x+c))^3/b+1/6*(arcsin(d*x+c)^2*Si(arcsin(d*x+c)+a/b)*cos(a/b)*b^2-arcsin(d*x+c)^2*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*b^2+2*arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*cos(a/b)*a*b-2*arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a*b+arcsin(d*x+c)*(1-(d*x+c)^2)^(1/2)*b^2+Si(arcsin(d*x+c)+a/b)*cos(a/b)*a^2-Ci(arcsin(d*x+c)+a/b)*sin(a/b)*a^2+(1-(d*x+c)^2)^(1/2)*a*b+(d*x+c)*b^2)/(a+b*arcsin(d*x+c))^2/b^4)","A"
238,0,0,26,0.875000," ","int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^4,x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsin \left(d x +c \right)\right)^{4}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^4,x)","F"
239,1,387,178,0.169000," ","int(1/(a+b*arcsin(d*x+c))^5,x)","\frac{-\frac{\sqrt{1-\left(d x +c \right)^{2}}}{4 \left(a +b \arcsin \left(d x +c \right)\right)^{4} b}+\frac{\arcsin \left(d x +c \right)^{3} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) b^{3}+\arcsin \left(d x +c \right)^{3} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) b^{3}+3 \arcsin \left(d x +c \right)^{2} \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a \,b^{2}+3 \arcsin \left(d x +c \right)^{2} \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a \,b^{2}-\arcsin \left(d x +c \right)^{2} \left(d x +c \right) b^{3}+3 \arcsin \left(d x +c \right) \Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{2} b +3 \arcsin \left(d x +c \right) \Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{2} b +\sqrt{1-\left(d x +c \right)^{2}}\, \arcsin \left(d x +c \right) b^{3}-2 \arcsin \left(d x +c \right) \left(d x +c \right) a \,b^{2}+\Si \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \sin \left(\frac{a}{b}\right) a^{3}+\Ci \left(\arcsin \left(d x +c \right)+\frac{a}{b}\right) \cos \left(\frac{a}{b}\right) a^{3}+\sqrt{1-\left(d x +c \right)^{2}}\, a \,b^{2}-\left(d x +c \right) a^{2} b +2 \left(d x +c \right) b^{3}}{24 \left(a +b \arcsin \left(d x +c \right)\right)^{3} b^{5}}}{d}"," ",0,"1/d*(-1/4*(1-(d*x+c)^2)^(1/2)/(a+b*arcsin(d*x+c))^4/b+1/24*(arcsin(d*x+c)^3*Si(arcsin(d*x+c)+a/b)*sin(a/b)*b^3+arcsin(d*x+c)^3*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*b^3+3*arcsin(d*x+c)^2*Si(arcsin(d*x+c)+a/b)*sin(a/b)*a*b^2+3*arcsin(d*x+c)^2*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*a*b^2-arcsin(d*x+c)^2*(d*x+c)*b^3+3*arcsin(d*x+c)*Si(arcsin(d*x+c)+a/b)*sin(a/b)*a^2*b+3*arcsin(d*x+c)*Ci(arcsin(d*x+c)+a/b)*cos(a/b)*a^2*b+(1-(d*x+c)^2)^(1/2)*arcsin(d*x+c)*b^3-2*arcsin(d*x+c)*(d*x+c)*a*b^2+Si(arcsin(d*x+c)+a/b)*sin(a/b)*a^3+Ci(arcsin(d*x+c)+a/b)*cos(a/b)*a^3+(1-(d*x+c)^2)^(1/2)*a*b^2-(d*x+c)*a^2*b+2*(d*x+c)*b^3)/(a+b*arcsin(d*x+c))^3/b^5)","B"
240,1,372,228,0.388000," ","int((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(1/2),x)","-\frac{e^{3} \left(\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b +\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b -8 \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b -8 \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b +16 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b +16 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a -4 \arcsin \left(d x +c \right) \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b -4 \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a \right)}{128 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/128/d*e^3/(a+b*arcsin(d*x+c))^(1/2)*(2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b+2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b-8*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*Pi^(1/2)*b-8*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*Pi^(1/2)*b+16*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b+16*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a-4*arcsin(d*x+c)*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b-4*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a)","A"
241,1,389,214,0.316000," ","int((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(1/2),x)","-\frac{e^{2} \left(\sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, b -\sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, b +9 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b -9 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sin \left(\frac{a}{b}\right) b +6 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) \arcsin \left(d x +c \right) b +6 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a -18 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b -18 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \right)}{72 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/72/d*e^2/(a+b*arcsin(d*x+c))^(1/2)*((1/b)^(1/2)*2^(1/2)*Pi^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*3^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*b-(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*3^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*b+9*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b-9*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*sin(a/b)*b+6*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*arcsin(d*x+c)*b+6*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a-18*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b-18*sin((a+b*arcsin(d*x+c))/b-a/b)*a)","A"
242,1,190,124,0.210000," ","int((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(1/2),x)","-\frac{e \left(-\cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b -\sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b +2 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b +2 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \right)}{8 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/8*e/d/(a+b*arcsin(d*x+c))^(1/2)*(-cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*Pi^(1/2)*b-sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*Pi^(1/2)*b+2*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b+2*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a)","A"
243,1,194,108,0.000000," ","int((a+b*arcsin(d*x+c))^(1/2),x)","\frac{-\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b +\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sin \left(\frac{a}{b}\right) b +2 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b +2 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a}{2 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/2/d/(a+b*arcsin(d*x+c))^(1/2)*(-2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b+2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*sin(a/b)*b+2*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b+2*sin((a+b*arcsin(d*x+c))/b-a/b)*a)","A"
244,0,0,26,0.248000," ","int((a+b*arcsin(d*x+c))^(1/2)/(d*e*x+c*e),x)","\int \frac{\sqrt{a +b \arcsin \left(d x +c \right)}}{d e x +c e}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^(1/2)/(d*e*x+c*e),x)","F"
245,1,582,308,0.344000," ","int((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{e^{3} \left(-3 \sqrt{2}\, \sqrt{\pi}\, \cos \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, b^{2}+3 \sqrt{2}\, \sqrt{\pi}\, \sin \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, b^{2}+48 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-48 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}+128 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-32 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b^{2}+256 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b -96 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-64 \arcsin \left(d x +c \right) \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a b +12 \arcsin \left(d x +c \right) \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b^{2}+128 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2}-96 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b -32 \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a^{2}+12 \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a b \right)}{1024 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/1024/d*e^3*(-3*2^(1/2)*Pi^(1/2)*cos(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*b^2+3*2^(1/2)*Pi^(1/2)*sin(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*b^2+48*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-48*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2+128*arcsin(d*x+c)^2*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-32*arcsin(d*x+c)^2*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b^2+256*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b-96*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-64*arcsin(d*x+c)*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a*b+12*arcsin(d*x+c)*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b^2+128*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2-96*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b-32*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a^2+12*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a*b)/(a+b*arcsin(d*x+c))^(1/2)","A"
246,1,593,289,0.419000," ","int((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(3/2),x)","\frac{e^{2} \left(\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}+\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-27 \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-27 \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}+36 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}-12 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{2}+72 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b +54 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}-24 \arcsin \left(d x +c \right) \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a b -6 \arcsin \left(d x +c \right) \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{2}+36 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2}+54 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b -12 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{2}-6 \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a b \right)}{144 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/144/d*e^2/(a+b*arcsin(d*x+c))^(1/2)*(3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2+3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-27*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-27*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2+36*arcsin(d*x+c)^2*sin((a+b*arcsin(d*x+c))/b-a/b)*b^2-12*arcsin(d*x+c)^2*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^2+72*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b+54*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2-24*arcsin(d*x+c)*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b-6*arcsin(d*x+c)*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^2+36*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2+54*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b-12*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^2-6*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b)","B"
247,1,294,161,0.215000," ","int((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{e \left(3 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-3 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}+8 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}+16 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b -6 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}+8 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2}-6 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b \right)}{32 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/32*e/d*(3*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-3*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2+8*arcsin(d*x+c)^2*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2+16*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b-6*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2+8*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2-6*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b)/(a+b*arcsin(d*x+c))^(1/2)","A"
248,1,296,139,0.001000," ","int((a+b*arcsin(d*x+c))^(3/2),x)","\frac{-3 \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-3 \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}+4 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}+8 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b +6 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}+4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2}+6 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b}{4 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/4/d/(a+b*arcsin(d*x+c))^(1/2)*(-3*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-3*(1/b)^(1/2)*2^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2+4*arcsin(d*x+c)^2*sin((a+b*arcsin(d*x+c))/b-a/b)*b^2+8*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b+6*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2+4*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2+6*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b)","B"
249,0,0,26,0.259000," ","int((a+b*arcsin(d*x+c))^(3/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{\frac{3}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^(3/2)/(d*e*x+c*e),x)","F"
250,1,864,391,0.391000," ","int((d*e*x+c*e)^3*(a+b*arcsin(d*x+c))^(5/2),x)","-\frac{e^{3} \left(-15 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b^{3}-15 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b^{3}+480 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{3}+480 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{3}+1024 \arcsin \left(d x +c \right)^{3} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}-256 \arcsin \left(d x +c \right)^{3} \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b^{3}+3072 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}-1280 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}-768 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a \,b^{2}+160 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b^{3}+3072 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2} b -960 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}-2560 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}-768 \arcsin \left(d x +c \right) \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a^{2} b +60 \arcsin \left(d x +c \right) \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b^{3}+320 \arcsin \left(d x +c \right) \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a \,b^{2}+1024 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{3}-960 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}-1280 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2} b -256 \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a^{3}+60 \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a \,b^{2}+160 \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a^{2} b \right)}{8192 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/8192/d*e^3*(-15*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b^3-15*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b^3+480*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^3+480*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^3+1024*arcsin(d*x+c)^3*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3-256*arcsin(d*x+c)^3*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b^3+3072*arcsin(d*x+c)^2*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2-1280*arcsin(d*x+c)^2*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3-768*arcsin(d*x+c)^2*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a*b^2+160*arcsin(d*x+c)^2*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b^3+3072*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2*b-960*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3-2560*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2-768*arcsin(d*x+c)*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a^2*b+60*arcsin(d*x+c)*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b^3+320*arcsin(d*x+c)*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a*b^2+1024*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^3-960*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2-1280*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2*b-256*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a^3+60*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a*b^2+160*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a^2*b)/(a+b*arcsin(d*x+c))^(1/2)","B"
251,1,873,347,0.431000," ","int((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(5/2),x)","\frac{e^{2} \left(-5 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, b^{3}+5 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, b^{3}+405 \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, b^{3}-405 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, b^{3}+216 \arcsin \left(d x +c \right)^{3} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}-72 \arcsin \left(d x +c \right)^{3} \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{3}+648 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}+540 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}-216 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a \,b^{2}-60 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{3}+648 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b -810 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}+1080 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}-216 \arcsin \left(d x +c \right) \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{2} b +30 \arcsin \left(d x +c \right) \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{3}-120 \arcsin \left(d x +c \right) \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a \,b^{2}+216 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{3}-810 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}+540 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b -72 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{3}+30 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a \,b^{2}-60 \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{2} b \right)}{864 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/864/d*e^2/(a+b*arcsin(d*x+c))^(1/2)*(-5*3^(1/2)*(1/b)^(1/2)*2^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*b^3+5*3^(1/2)*(1/b)^(1/2)*2^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*b^3+405*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*b^3-405*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*b^3+216*arcsin(d*x+c)^3*sin((a+b*arcsin(d*x+c))/b-a/b)*b^3-72*arcsin(d*x+c)^3*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^3+648*arcsin(d*x+c)^2*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b^2+540*arcsin(d*x+c)^2*cos((a+b*arcsin(d*x+c))/b-a/b)*b^3-216*arcsin(d*x+c)^2*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b^2-60*arcsin(d*x+c)^2*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^3+648*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2*b-810*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b^3+1080*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b^2-216*arcsin(d*x+c)*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^2*b+30*arcsin(d*x+c)*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^3-120*arcsin(d*x+c)*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b^2+216*sin((a+b*arcsin(d*x+c))/b-a/b)*a^3-810*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b^2+540*cos((a+b*arcsin(d*x+c))/b-a/b)*a^2*b-72*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^3+30*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b^2-60*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^2*b)","B"
252,1,435,210,0.242000," ","int((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(5/2),x)","-\frac{e \left(15 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{3}+15 \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{3}+32 \arcsin \left(d x +c \right)^{3} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}+96 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}-40 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}+96 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2} b -30 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{3}-80 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}+32 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{3}-30 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \,b^{2}-40 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2} b \right)}{128 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/128*e/d*(15*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^3+15*(1/b)^(1/2)*Pi^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^3+32*arcsin(d*x+c)^3*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3+96*arcsin(d*x+c)^2*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2-40*arcsin(d*x+c)^2*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3+96*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2*b-30*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^3-80*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2+32*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^3-30*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b^2-40*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2*b)/(a+b*arcsin(d*x+c))^(1/2)","B"
253,1,433,164,0.003000," ","int((a+b*arcsin(d*x+c))^(5/2),x)","\frac{15 \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, b^{3}-15 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, b^{3}+8 \arcsin \left(d x +c \right)^{3} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}+24 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}+20 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}+24 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b -30 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{3}+40 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}+8 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{3}-30 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{2}+20 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b}{8 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/8/d/(a+b*arcsin(d*x+c))^(1/2)*(15*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*b^3-15*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*b^3+8*arcsin(d*x+c)^3*sin((a+b*arcsin(d*x+c))/b-a/b)*b^3+24*arcsin(d*x+c)^2*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b^2+20*arcsin(d*x+c)^2*cos((a+b*arcsin(d*x+c))/b-a/b)*b^3+24*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2*b-30*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b^3+40*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b^2+8*sin((a+b*arcsin(d*x+c))/b-a/b)*a^3-30*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b^2+20*cos((a+b*arcsin(d*x+c))/b-a/b)*a^2*b)","B"
254,0,0,26,0.263000," ","int((a+b*arcsin(d*x+c))^(5/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{\frac{5}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^(5/2)/(d*e*x+c*e),x)","F"
255,1,1228,426,0.497000," ","int((d*e*x+c*e)^2*(a+b*arcsin(d*x+c))^(7/2),x)","\frac{e^{2} \left(5184 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{3} a \,b^{3}+7776 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} a^{2} b^{2}+13608 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} a \,b^{3}+5184 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a^{3} b -22680 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a \,b^{3}+13608 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a^{2} b^{2}-35 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{4}-35 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{4}+4536 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{3} b -17010 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{3}+1296 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{4} b^{4}+4536 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{3} b^{4}-11340 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} b^{4}-17010 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b^{4}-11340 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b^{2}-2592 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{2} b^{2}-1728 \arcsin \left(d x +c \right) \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{3} b +8505 \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{2}\, b^{4}+8505 \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{2}\, b^{4}-1512 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a \,b^{3}+840 \arcsin \left(d x +c \right) \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a \,b^{3}-1512 \arcsin \left(d x +c \right) \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{2} b^{2}-1728 \arcsin \left(d x +c \right)^{3} \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a \,b^{3}+1296 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{4}-432 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{4}+210 \arcsin \left(d x +c \right) \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{4}+420 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{2} b^{2}-504 \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{3} b +210 \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a \,b^{3}-432 \arcsin \left(d x +c \right)^{4} \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{4}+420 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{4}-504 \arcsin \left(d x +c \right)^{3} \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{4}\right)}{5184 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/5184/d*e^2/(a+b*arcsin(d*x+c))^(1/2)*(5184*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^3*a*b^3+7776*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*a^2*b^2+13608*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*a*b^3+5184*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a^3*b-22680*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a*b^3+13608*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a^2*b^2-35*3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^4-35*3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^4+4536*cos((a+b*arcsin(d*x+c))/b-a/b)*a^3*b-17010*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b^3+1296*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^4*b^4+4536*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^3*b^4-11340*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*b^4-17010*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b^4-11340*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2*b^2-2592*arcsin(d*x+c)^2*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^2*b^2-1728*arcsin(d*x+c)*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^3*b-1512*arcsin(d*x+c)^2*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b^3+840*arcsin(d*x+c)*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b^3-1512*arcsin(d*x+c)*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^2*b^2+8505*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*2^(1/2)*b^4+8505*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*2^(1/2)*b^4-1728*arcsin(d*x+c)^3*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b^3+210*arcsin(d*x+c)*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^4+420*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^2*b^2-504*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^3*b+210*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b^3-432*arcsin(d*x+c)^4*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^4+420*arcsin(d*x+c)^2*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^4+1296*sin((a+b*arcsin(d*x+c))/b-a/b)*a^4-504*arcsin(d*x+c)^3*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^4-432*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^4)","B"
256,1,622,249,0.274000," ","int((d*e*x+c*e)*(a+b*arcsin(d*x+c))^(7/2),x)","-\frac{e b \left(128 \arcsin \left(d x +c \right)^{3} \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b^{3}+384 \arcsin \left(d x +c \right)^{2} \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, a \,b^{2}-224 \arcsin \left(d x +c \right)^{2} \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b^{3}+384 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, a^{2} b -280 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b^{3}-448 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, a \,b^{2}+128 \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, a^{3}-280 \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, a \,b^{2}-224 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, a^{2} b +210 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, b^{3}-105 \pi  \,b^{3} \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+105 \pi  \,b^{3} \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right) \sqrt{\frac{1}{b}}}{512 d \sqrt{\pi}}"," ",0,"-1/512*e/d*b*(128*arcsin(d*x+c)^3*(a+b*arcsin(d*x+c))^(1/2)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*b^3+384*arcsin(d*x+c)^2*(a+b*arcsin(d*x+c))^(1/2)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*a*b^2-224*arcsin(d*x+c)^2*(a+b*arcsin(d*x+c))^(1/2)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*b^3+384*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*a^2*b-280*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*b^3-448*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*a*b^2+128*(a+b*arcsin(d*x+c))^(1/2)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*a^3-280*(a+b*arcsin(d*x+c))^(1/2)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*a*b^2-224*(a+b*arcsin(d*x+c))^(1/2)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*a^2*b+210*(a+b*arcsin(d*x+c))^(1/2)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*(1/b)^(1/2)*Pi^(1/2)*b^3-105*Pi*b^3*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+105*Pi*b^3*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b))*(1/b)^(1/2)/Pi^(1/2)","B"
257,1,608,197,0.000000," ","int((a+b*arcsin(d*x+c))^(7/2),x)","\frac{105 \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{2}\, b^{4}+105 \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{2}\, b^{4}+16 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{4} b^{4}+64 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{3} a \,b^{3}+56 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{3} b^{4}+96 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} a^{2} b^{2}-140 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} b^{4}+168 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right)^{2} a \,b^{3}+64 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a^{3} b -280 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a \,b^{3}+168 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) a^{2} b^{2}-210 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b^{4}+16 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{4}-140 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2} b^{2}+56 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{3} b -210 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a \,b^{3}}{16 d \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"1/16/d/(a+b*arcsin(d*x+c))^(1/2)*(105*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*2^(1/2)*b^4+105*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*2^(1/2)*b^4+16*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^4*b^4+64*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^3*a*b^3+56*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^3*b^4+96*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*a^2*b^2-140*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*b^4+168*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)^2*a*b^3+64*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a^3*b-280*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a*b^3+168*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*a^2*b^2-210*cos((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b^4+16*sin((a+b*arcsin(d*x+c))/b-a/b)*a^4-140*sin((a+b*arcsin(d*x+c))/b-a/b)*a^2*b^2+56*cos((a+b*arcsin(d*x+c))/b-a/b)*a^3*b-210*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b^3)","B"
258,0,0,26,0.385000," ","int((a+b*arcsin(d*x+c))^(7/2)/(d*e*x+c*e),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{\frac{7}{2}}}{d e x +c e}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^(7/2)/(d*e*x+c*e),x)","F"
259,1,263,281,0.477000," ","int((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^(1/2),x)","\frac{e^{4} \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \left(-5 \sqrt{3}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-5 \sqrt{3}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{5}\, \cos \left(\frac{5 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{5}\, \sin \left(\frac{5 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+10 \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+10 \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right)}{80 d}"," ",0,"1/80/d*e^4*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(-5*3^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)-5*3^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+5^(1/2)*cos(5*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+5^(1/2)*sin(5*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+10*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+10*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b))","A"
260,1,169,181,0.248000," ","int((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(1/2),x)","\frac{e^{3} \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \left(-\sqrt{2}\, \cos \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{2}\, \sin \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+4 \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-4 \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right)}{16 d}"," ",0,"1/16/d*e^3*Pi^(1/2)*(1/b)^(1/2)*(-2^(1/2)*cos(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+2^(1/2)*sin(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+4*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)-4*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b))","A"
261,1,179,187,0.241000," ","int((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(1/2),x)","\frac{e^{2} \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \left(-\sqrt{3}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sqrt{3}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+3 \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+3 \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right)}{12 d}"," ",0,"1/12/d*e^2*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(-3^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)-3^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+3*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+3*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b))","A"
262,1,85,81,0.094000," ","int((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(1/2),x)","\frac{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, e \left(\cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right)}{2 d}"," ",0,"1/2*Pi^(1/2)*(1/b)^(1/2)*e*(cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)-sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b))/d","A"
263,1,87,85,0.001000," ","int(1/(a+b*arcsin(d*x+c))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \left(\cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)\right)}{d}"," ",0,"2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*(cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b))/d","A"
264,0,0,26,0.251000," ","int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(1/2),x)","\int \frac{1}{\left(d e x +c e \right) \sqrt{a +b \arcsin \left(d x +c \right)}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(1/2),x)","F"
265,1,478,324,0.407000," ","int((d*e*x+c*e)^4/(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{e^{4} \left(\sqrt{5}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{5 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-\sqrt{5}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{5 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{5}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)-3 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+3 \sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+2 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-2 \sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+2 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right)-3 \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right)+\cos \left(\frac{5 a +5 b \arcsin \left(d x +c \right)}{b}-\frac{5 a}{b}\right)\right)}{8 d b \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/8/d*e^4/b*(5^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(5*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)-5^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(5*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*5^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)-3*3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+3*3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+2*2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)-2*2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)+2*cos((a+b*arcsin(d*x+c))/b-a/b)-3*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)+cos(5*(a+b*arcsin(d*x+c))/b-5*a/b))/(a+b*arcsin(d*x+c))^(1/2)","A"
266,1,307,222,0.233000," ","int((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{e^{3} \left(2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}+2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}-4 \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-4 \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+2 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right)-\sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right)\right)}{4 d b \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/4/d*e^3/b*(2*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)*(1/b)^(1/2)+2*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)*(1/b)^(1/2)-4*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)-4*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)+2*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)-sin(4*(a+b*arcsin(d*x+c))/b-4*a/b))/(a+b*arcsin(d*x+c))^(1/2)","A"
267,1,320,230,0.216000," ","int((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{e^{2} \left(-\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{3}\, \sqrt{\frac{1}{b}}\, \sqrt{\pi}\, \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right)+\sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-\sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+\cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right)-\cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right)\right)}{2 d b \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-1/2/d*e^2/b*(-3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+3^(1/2)*(1/b)^(1/2)*Pi^(1/2)*2^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)+2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)-2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)+cos((a+b*arcsin(d*x+c))/b-a/b)-cos(3*(a+b*arcsin(d*x+c))/b-3*a/b))/(a+b*arcsin(d*x+c))^(1/2)","A"
268,1,156,120,0.155000," ","int((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{e \left(-2 \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-2 \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+\sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right)\right)}{d b \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-e/d/b/(a+b*arcsin(d*x+c))^(1/2)*(-2*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)-2*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)+sin(2*(a+b*arcsin(d*x+c))/b-2*a/b))","A"
269,1,161,120,0.001000," ","int(1/(a+b*arcsin(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}-\sqrt{2}\, \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\pi}+\cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right)\right)}{d b \sqrt{a +b \arcsin \left(d x +c \right)}}"," ",0,"-2/d/b*(2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)-2^(1/2)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*Pi^(1/2)+cos((a+b*arcsin(d*x+c))/b-a/b))/(a+b*arcsin(d*x+c))^(1/2)","A"
270,0,0,26,0.326000," ","int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(3/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(3/2),x)","F"
271,1,689,284,0.275000," ","int((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(5/2),x)","-\frac{e^{3} \left(-16 \arcsin \left(d x +c \right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b +16 \arcsin \left(d x +c \right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b +16 \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b -16 \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b -16 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a +16 \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a +16 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a -16 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a +8 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b -8 \arcsin \left(d x +c \right) \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b +2 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b +8 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a -\sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b -8 \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a \right)}{12 d \,b^{2} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-1/12/d*e^3/b^2*(-16*arcsin(d*x+c)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b+16*arcsin(d*x+c)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b+16*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b-16*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b-16*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a+16*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a+16*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a-16*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a+8*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b-8*arcsin(d*x+c)*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b+2*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b+8*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a-sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b-8*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a)/(a+b*arcsin(d*x+c))^(3/2)","B"
272,1,721,286,0.345000," ","int((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(5/2),x)","\frac{e^{2} \left(6 \arcsin \left(d x +c \right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, b +6 \arcsin \left(d x +c \right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, b -2 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, b -2 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, b +6 \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \cos \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, a +6 \sqrt{2}\, \sqrt{\pi}\, \sqrt{3}\, \sin \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{\frac{1}{b}}\, \sqrt{a +b \arcsin \left(d x +c \right)}\, a -2 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, a -2 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, a +2 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b -6 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) \arcsin \left(d x +c \right) b -\cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b +2 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a +\cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b -6 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a \right)}{6 d \,b^{2} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"1/6/d*e^2/b^2*(6*arcsin(d*x+c)*2^(1/2)*Pi^(1/2)*3^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*b+6*arcsin(d*x+c)*2^(1/2)*Pi^(1/2)*3^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*b-2*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*b-2*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*b+6*2^(1/2)*Pi^(1/2)*3^(1/2)*cos(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*a+6*2^(1/2)*Pi^(1/2)*3^(1/2)*sin(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)*a-2*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*a-2*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*a+2*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b-6*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*arcsin(d*x+c)*b-cos((a+b*arcsin(d*x+c))/b-a/b)*b+2*sin((a+b*arcsin(d*x+c))/b-a/b)*a+cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b-6*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a)/(a+b*arcsin(d*x+c))^(3/2)","B"
273,1,342,169,0.181000," ","int((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(5/2),x)","-\frac{e \left(8 \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b -8 \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b +8 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a -8 \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a +4 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b +\sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b +4 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a \right)}{3 d \,b^{2} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-1/3*e/d/b^2*(8*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b-8*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b+8*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a-8*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a+4*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b+sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b+4*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a)/(a+b*arcsin(d*x+c))^(3/2)","B"
274,1,355,145,0.001000," ","int(1/(a+b*arcsin(d*x+c))^(5/2),x)","\frac{-\frac{4 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, b}{3}-\frac{4 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, b}{3}-\frac{4 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, a}{3}-\frac{4 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, a}{3}+\frac{4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) \arcsin \left(d x +c \right) b}{3}-\frac{2 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b}{3}+\frac{4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a}{3}}{d \,b^{2} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"2/3/d/b^2*(-2*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*b-2*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*b-2*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*cos(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*a-2*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*sin(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*a+2*sin((a+b*arcsin(d*x+c))/b-a/b)*arcsin(d*x+c)*b-cos((a+b*arcsin(d*x+c))/b-a/b)*b+2*sin((a+b*arcsin(d*x+c))/b-a/b)*a)/(a+b*arcsin(d*x+c))^(3/2)","B"
275,0,0,26,0.308000," ","int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(5/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(5/2),x)","F"
276,1,1181,368,0.310000," ","int((d*e*x+c*e)^3/(a+b*arcsin(d*x+c))^(7/2),x)","\frac{e^{3} \left(128 \arcsin \left(d x +c \right)^{2} \sqrt{\pi}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, b^{2}+128 \arcsin \left(d x +c \right)^{2} \sqrt{\pi}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, b^{2}+256 \arcsin \left(d x +c \right) \sqrt{\pi}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, a b +256 \arcsin \left(d x +c \right) \sqrt{\pi}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, a b -64 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right)^{2} \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-64 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right)^{2} \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}+128 \sqrt{\pi}\, \cos \left(\frac{4 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, a^{2}+128 \sqrt{\pi}\, \sin \left(\frac{4 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\frac{1}{b}}\, \sqrt{2}\, a^{2}-128 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a b -128 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a b -64 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a^{2}-64 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a^{2}+32 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-64 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b^{2}+64 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b -8 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-128 \arcsin \left(d x +c \right) \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a b +8 \arcsin \left(d x +c \right) \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b^{2}+32 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2}-6 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-8 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b -64 \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a^{2}+3 \sin \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) b^{2}+8 \cos \left(\frac{4 a +4 b \arcsin \left(d x +c \right)}{b}-\frac{4 a}{b}\right) a b \right)}{60 d \,b^{3} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/60/d*e^3/b^3*(128*arcsin(d*x+c)^2*Pi^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*2^(1/2)*b^2+128*arcsin(d*x+c)^2*Pi^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*2^(1/2)*b^2+256*arcsin(d*x+c)*Pi^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*2^(1/2)*a*b+256*arcsin(d*x+c)*Pi^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*2^(1/2)*a*b-64*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)^2*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-64*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)^2*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2+128*Pi^(1/2)*cos(4*a/b)*FresnelC(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*2^(1/2)*a^2+128*Pi^(1/2)*sin(4*a/b)*FresnelS(2*2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*(1/b)^(1/2)*2^(1/2)*a^2-128*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*b-128*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*b-64*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a^2-64*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a^2+32*arcsin(d*x+c)^2*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-64*arcsin(d*x+c)^2*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b^2+64*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b-8*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-128*arcsin(d*x+c)*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a*b+8*arcsin(d*x+c)*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b^2+32*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2-6*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-8*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b-64*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a^2+3*sin(4*(a+b*arcsin(d*x+c))/b-4*a/b)*b^2+8*cos(4*(a+b*arcsin(d*x+c))/b-4*a/b)*a*b)/(a+b*arcsin(d*x+c))^(5/2)","B"
277,1,1229,367,0.390000," ","int((d*e*x+c*e)^2/(a+b*arcsin(d*x+c))^(7/2),x)","\frac{e^{2} \left(-36 \sqrt{3}\, \arcsin \left(d x +c \right)^{2} \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b^{2}+36 \sqrt{3}\, \arcsin \left(d x +c \right)^{2} \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, b^{2}-72 \sqrt{3}\, \arcsin \left(d x +c \right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a b +72 \sqrt{3}\, \arcsin \left(d x +c \right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a b +4 \arcsin \left(d x +c \right)^{2} \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b^{2}-4 \arcsin \left(d x +c \right)^{2} \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b^{2}-36 \sqrt{3}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{3 a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a^{2}+36 \sqrt{3}\, \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{3 a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{a +b \arcsin \left(d x +c \right)}\, a^{2}+8 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a b -8 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a b +4 \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a^{2}-4 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a^{2}+4 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}-36 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{2}+8 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b +2 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}-72 \arcsin \left(d x +c \right) \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a b -6 \arcsin \left(d x +c \right) \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{2}+4 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2}-3 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}+2 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b -36 \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a^{2}+3 \cos \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) b^{2}-6 \sin \left(\frac{3 a +3 b \arcsin \left(d x +c \right)}{b}-\frac{3 a}{b}\right) a b \right)}{30 d \,b^{3} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/30/d*e^2/b^3*(-36*3^(1/2)*arcsin(d*x+c)^2*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b^2+36*3^(1/2)*arcsin(d*x+c)^2*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*b^2-72*3^(1/2)*arcsin(d*x+c)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a*b+72*3^(1/2)*arcsin(d*x+c)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a*b+4*arcsin(d*x+c)^2*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*b^2-4*arcsin(d*x+c)^2*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*b^2-36*3^(1/2)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(3*a/b)*FresnelS(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a^2+36*3^(1/2)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(3*a/b)*FresnelC(2^(1/2)/Pi^(1/2)*3^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*(a+b*arcsin(d*x+c))^(1/2)*a^2+8*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a*b-8*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a*b+4*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a^2-4*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a^2+4*arcsin(d*x+c)^2*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2-36*arcsin(d*x+c)^2*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^2+8*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b+2*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b^2-72*arcsin(d*x+c)*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b-6*arcsin(d*x+c)*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^2+4*cos((a+b*arcsin(d*x+c))/b-a/b)*a^2-3*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2+2*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b-36*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a^2+3*cos(3*(a+b*arcsin(d*x+c))/b-3*a/b)*b^2-6*sin(3*(a+b*arcsin(d*x+c))/b-3*a/b)*a*b)/(a+b*arcsin(d*x+c))^(5/2)","B"
278,1,583,208,0.200000," ","int((d*e*x+c*e)/(a+b*arcsin(d*x+c))^(7/2),x)","\frac{e \left(-32 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right)^{2} \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-32 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right)^{2} \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) b^{2}-64 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a b -64 \sqrt{a +b \arcsin \left(d x +c \right)}\, \arcsin \left(d x +c \right) \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a b -32 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \cos \left(\frac{2 a}{b}\right) \FresnelC \left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a^{2}-32 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, \sin \left(\frac{2 a}{b}\right) \mathrm{S}\left(\frac{2 \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) a^{2}+16 \arcsin \left(d x +c \right)^{2} \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}+32 \arcsin \left(d x +c \right) \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b -4 \arcsin \left(d x +c \right) \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}+16 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a^{2}-3 \sin \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) b^{2}-4 \cos \left(\frac{2 a +2 b \arcsin \left(d x +c \right)}{b}-\frac{2 a}{b}\right) a b \right)}{15 d \,b^{3} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"1/15*e/d/b^3*(-32*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)^2*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-32*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)^2*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*b^2-64*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*b-64*(a+b*arcsin(d*x+c))^(1/2)*arcsin(d*x+c)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a*b-32*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*(1/b)^(1/2)*cos(2*a/b)*FresnelC(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a^2-32*(a+b*arcsin(d*x+c))^(1/2)*Pi^(1/2)*(1/b)^(1/2)*sin(2*a/b)*FresnelS(2/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*a^2+16*arcsin(d*x+c)^2*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2+32*arcsin(d*x+c)*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b-4*arcsin(d*x+c)*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2+16*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a^2-3*sin(2*(a+b*arcsin(d*x+c))/b-2*a/b)*b^2-4*cos(2*(a+b*arcsin(d*x+c))/b-2*a/b)*a*b)/(a+b*arcsin(d*x+c))^(5/2)","B"
279,1,600,178,0.000000," ","int(1/(a+b*arcsin(d*x+c))^(7/2),x)","\frac{\frac{8 \arcsin \left(d x +c \right)^{2} \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b^{2}}{15}-\frac{8 \arcsin \left(d x +c \right)^{2} \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b^{2}}{15}+\frac{16 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a b}{15}-\frac{16 \arcsin \left(d x +c \right) \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a b}{15}+\frac{8 \sqrt{a +b \arcsin \left(d x +c \right)}\, \cos \left(\frac{a}{b}\right) \mathrm{S}\left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a^{2}}{15}-\frac{8 \sqrt{a +b \arcsin \left(d x +c \right)}\, \sin \left(\frac{a}{b}\right) \FresnelC \left(\frac{\sqrt{2}\, \sqrt{a +b \arcsin \left(d x +c \right)}}{\sqrt{\pi}\, \sqrt{\frac{1}{b}}\, b}\right) \sqrt{2}\, \sqrt{\pi}\, \sqrt{\frac{1}{b}}\, a^{2}}{15}+\frac{8 \arcsin \left(d x +c \right)^{2} \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}}{15}+\frac{16 \arcsin \left(d x +c \right) \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b}{15}+\frac{4 \arcsin \left(d x +c \right) \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}}{15}+\frac{8 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a^{2}}{15}-\frac{2 \cos \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) b^{2}}{5}+\frac{4 \sin \left(\frac{a +b \arcsin \left(d x +c \right)}{b}-\frac{a}{b}\right) a b}{15}}{d \,b^{3} \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"2/15/d/b^3*(4*arcsin(d*x+c)^2*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*b^2-4*arcsin(d*x+c)^2*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*b^2+8*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a*b-8*arcsin(d*x+c)*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a*b+4*(a+b*arcsin(d*x+c))^(1/2)*cos(a/b)*FresnelS(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a^2-4*(a+b*arcsin(d*x+c))^(1/2)*sin(a/b)*FresnelC(2^(1/2)/Pi^(1/2)/(1/b)^(1/2)*(a+b*arcsin(d*x+c))^(1/2)/b)*2^(1/2)*Pi^(1/2)*(1/b)^(1/2)*a^2+4*arcsin(d*x+c)^2*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2+8*arcsin(d*x+c)*cos((a+b*arcsin(d*x+c))/b-a/b)*a*b+2*arcsin(d*x+c)*sin((a+b*arcsin(d*x+c))/b-a/b)*b^2+4*cos((a+b*arcsin(d*x+c))/b-a/b)*a^2-3*cos((a+b*arcsin(d*x+c))/b-a/b)*b^2+2*sin((a+b*arcsin(d*x+c))/b-a/b)*a*b)/(a+b*arcsin(d*x+c))^(5/2)","B"
280,0,0,26,0.298000," ","int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(7/2),x)","\int \frac{1}{\left(d e x +c e \right) \left(a +b \arcsin \left(d x +c \right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(d*e*x+c*e)/(a+b*arcsin(d*x+c))^(7/2),x)","F"
281,1,228,132,0.037000," ","int((d*e*x+c*e)^(7/2)*(a+b*arcsin(d*x+c)),x)","\frac{\frac{2 \left(d e x +c e \right)^{\frac{9}{2}} a}{9}+2 b \left(\frac{\left(d e x +c e \right)^{\frac{9}{2}} \arcsin \left(\frac{d e x +c e}{e}\right)}{9}-\frac{2 \left(-\frac{e^{2} \left(d e x +c e \right)^{\frac{7}{2}} \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{9}-\frac{7 e^{4} \left(d e x +c e \right)^{\frac{3}{2}} \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{45}-\frac{7 e^{5} \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)\right)}{15 \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{9 e}\right)}{d e}"," ",0,"2/d/e*(1/9*(d*e*x+c*e)^(9/2)*a+b*(1/9*(d*e*x+c*e)^(9/2)*arcsin((d*e*x+c*e)/e)-2/9/e*(-1/9*e^2*(d*e*x+c*e)^(7/2)*(-(d*e*x+c*e)^2/e^2+1)^(1/2)-7/45*e^4*(d*e*x+c*e)^(3/2)*(-(d*e*x+c*e)^2/e^2+1)^(1/2)-7/15*e^5/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)))))","C"
282,1,206,112,0.012000," ","int((d*e*x+c*e)^(5/2)*(a+b*arcsin(d*x+c)),x)","\frac{\frac{2 \left(d e x +c e \right)^{\frac{7}{2}} a}{7}+2 b \left(\frac{\left(d e x +c e \right)^{\frac{7}{2}} \arcsin \left(\frac{d e x +c e}{e}\right)}{7}-\frac{2 \left(-\frac{e^{2} \left(d e x +c e \right)^{\frac{5}{2}} \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{7}-\frac{5 e^{4} \sqrt{d e x +c e}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{21}+\frac{5 e^{4} \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)}{21 \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{7 e}\right)}{d e}"," ",0,"2/d/e*(1/7*(d*e*x+c*e)^(7/2)*a+b*(1/7*(d*e*x+c*e)^(7/2)*arcsin((d*e*x+c*e)/e)-2/7/e*(-1/7*e^2*(d*e*x+c*e)^(5/2)*(-(d*e*x+c*e)^2/e^2+1)^(1/2)-5/21*e^4*(d*e*x+c*e)^(1/2)*(-(d*e*x+c*e)^2/e^2+1)^(1/2)+5/21*e^4/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I))))","A"
283,1,194,99,0.015000," ","int((d*e*x+c*e)^(3/2)*(a+b*arcsin(d*x+c)),x)","\frac{\frac{2 \left(d e x +c e \right)^{\frac{5}{2}} a}{5}+2 b \left(\frac{\left(d e x +c e \right)^{\frac{5}{2}} \arcsin \left(\frac{d e x +c e}{e}\right)}{5}-\frac{2 \left(-\frac{e^{2} \left(d e x +c e \right)^{\frac{3}{2}} \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{5}-\frac{3 e^{3} \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)\right)}{5 \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{5 e}\right)}{d e}"," ",0,"2/d/e*(1/5*(d*e*x+c*e)^(5/2)*a+b*(1/5*(d*e*x+c*e)^(5/2)*arcsin((d*e*x+c*e)/e)-2/5/e*(-1/5*e^2*(d*e*x+c*e)^(3/2)*(-(d*e*x+c*e)^2/e^2+1)^(1/2)-3/5*e^3/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)))))","C"
284,1,172,81,0.012000," ","int((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c)),x)","\frac{\frac{2 \left(d e x +c e \right)^{\frac{3}{2}} a}{3}+2 b \left(\frac{\left(d e x +c e \right)^{\frac{3}{2}} \arcsin \left(\frac{d e x +c e}{e}\right)}{3}-\frac{2 \left(-\frac{e^{2} \sqrt{d e x +c e}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{3}+\frac{e^{2} \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)}{3 \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{3 e}\right)}{d e}"," ",0,"2/d/e*(1/3*(d*e*x+c*e)^(3/2)*a+b*(1/3*(d*e*x+c*e)^(3/2)*arcsin((d*e*x+c*e)/e)-2/3/e*(-1/3*e^2*(d*e*x+c*e)^(1/2)*(-(d*e*x+c*e)^2/e^2+1)^(1/2)+1/3*e^2/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I))))","B"
285,1,149,73,0.011000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(1/2),x)","\frac{2 a \sqrt{d e x +c e}+2 b \left(\sqrt{d e x +c e}\, \arcsin \left(\frac{d e x +c e}{e}\right)+\frac{2 \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)\right)}{\sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{d e}"," ",0,"2/d/e*(a*(d*e*x+c*e)^(1/2)+b*((d*e*x+c*e)^(1/2)*arcsin((d*e*x+c*e)/e)+2/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I))))","C"
286,1,132,53,0.011000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(3/2),x)","\frac{-\frac{2 a}{\sqrt{d e x +c e}}+2 b \left(-\frac{\arcsin \left(\frac{d e x +c e}{e}\right)}{\sqrt{d e x +c e}}+\frac{2 \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)}{e \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}\right)}{d e}"," ",0,"2/d/e*(-1/(d*e*x+c*e)^(1/2)*a+b*(-1/(d*e*x+c*e)^(1/2)*arcsin((d*e*x+c*e)/e)+2/e/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)))","B"
287,1,190,104,0.024000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(5/2),x)","\frac{-\frac{2 a}{3 \left(d e x +c e \right)^{\frac{3}{2}}}+2 b \left(-\frac{\arcsin \left(\frac{d e x +c e}{e}\right)}{3 \left(d e x +c e \right)^{\frac{3}{2}}}+\frac{-\frac{2 \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{3 \sqrt{d e x +c e}}+\frac{2 \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)\right)}{3 e \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}}{e}\right)}{d e}"," ",0,"2/d/e*(-1/3*a/(d*e*x+c*e)^(3/2)+b*(-1/3/(d*e*x+c*e)^(3/2)*arcsin((d*e*x+c*e)/e)+2/3/e*(-(-(d*e*x+c*e)^2/e^2+1)^(1/2)/(d*e*x+c*e)^(1/2)+1/e/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)))))","C"
288,1,169,84,0.016000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(7/2),x)","\frac{-\frac{2 a}{5 \left(d e x +c e \right)^{\frac{5}{2}}}+2 b \left(-\frac{\arcsin \left(\frac{d e x +c e}{e}\right)}{5 \left(d e x +c e \right)^{\frac{5}{2}}}+\frac{-\frac{2 \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{15 \left(d e x +c e \right)^{\frac{3}{2}}}+\frac{2 \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)}{15 e^{2} \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}}{e}\right)}{d e}"," ",0,"2/d/e*(-1/5*a/(d*e*x+c*e)^(5/2)+b*(-1/5/(d*e*x+c*e)^(5/2)*arcsin((d*e*x+c*e)/e)+2/5/e*(-1/3*(-(d*e*x+c*e)^2/e^2+1)^(1/2)/(d*e*x+c*e)^(3/2)+1/3/e^2/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I))))","A"
289,1,225,135,0.023000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(9/2),x)","\frac{-\frac{2 a}{7 \left(d e x +c e \right)^{\frac{7}{2}}}+2 b \left(-\frac{\arcsin \left(\frac{d e x +c e}{e}\right)}{7 \left(d e x +c e \right)^{\frac{7}{2}}}+\frac{-\frac{2 \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{35 \left(d e x +c e \right)^{\frac{5}{2}}}-\frac{6 \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{35 e^{2} \sqrt{d e x +c e}}+\frac{6 \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \left(\EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)-\EllipticE \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)\right)}{35 e^{3} \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}}{e}\right)}{d e}"," ",0,"2/d/e*(-1/7*a/(d*e*x+c*e)^(7/2)+b*(-1/7/(d*e*x+c*e)^(7/2)*arcsin((d*e*x+c*e)/e)+2/7/e*(-1/5*(-(d*e*x+c*e)^2/e^2+1)^(1/2)/(d*e*x+c*e)^(5/2)-3/5/e^2*(-(d*e*x+c*e)^2/e^2+1)^(1/2)/(d*e*x+c*e)^(1/2)+3/5/e^3/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*(EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)-EllipticE((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I)))))","C"
290,1,203,115,0.020000," ","int((a+b*arcsin(d*x+c))/(d*e*x+c*e)^(11/2),x)","\frac{-\frac{2 a}{9 \left(d e x +c e \right)^{\frac{9}{2}}}+2 b \left(-\frac{\arcsin \left(\frac{d e x +c e}{e}\right)}{9 \left(d e x +c e \right)^{\frac{9}{2}}}+\frac{-\frac{2 \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{63 \left(d e x +c e \right)^{\frac{7}{2}}}-\frac{10 \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}{189 e^{2} \left(d e x +c e \right)^{\frac{3}{2}}}+\frac{10 \sqrt{1-\frac{d e x +c e}{e}}\, \sqrt{\frac{d e x +c e}{e}+1}\, \EllipticF \left(\sqrt{d e x +c e}\, \sqrt{\frac{1}{e}}, i\right)}{189 e^{4} \sqrt{\frac{1}{e}}\, \sqrt{-\frac{\left(d e x +c e \right)^{2}}{e^{2}}+1}}}{e}\right)}{d e}"," ",0,"2/d/e*(-1/9*a/(d*e*x+c*e)^(9/2)+b*(-1/9/(d*e*x+c*e)^(9/2)*arcsin((d*e*x+c*e)/e)+2/9/e*(-1/7*(-(d*e*x+c*e)^2/e^2+1)^(1/2)/(d*e*x+c*e)^(7/2)-5/21/e^2*(-(d*e*x+c*e)^2/e^2+1)^(1/2)/(d*e*x+c*e)^(3/2)+5/21/e^4/(1/e)^(1/2)*(1-(d*e*x+c*e)/e)^(1/2)*((d*e*x+c*e)/e+1)^(1/2)/(-(d*e*x+c*e)^2/e^2+1)^(1/2)*EllipticF((d*e*x+c*e)^(1/2)*(1/e)^(1/2),I))))","A"
291,0,0,106,0.352000," ","int((d*e*x+c*e)^(7/2)*(a+b*arcsin(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{7}{2}} \left(a +b \arcsin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(7/2)*(a+b*arcsin(d*x+c))^2,x)","F"
292,0,0,106,0.334000," ","int((d*e*x+c*e)^(5/2)*(a+b*arcsin(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{5}{2}} \left(a +b \arcsin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(5/2)*(a+b*arcsin(d*x+c))^2,x)","F"
293,0,0,106,0.343000," ","int((d*e*x+c*e)^(3/2)*(a+b*arcsin(d*x+c))^2,x)","\int \left(d e x +c e \right)^{\frac{3}{2}} \left(a +b \arcsin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(3/2)*(a+b*arcsin(d*x+c))^2,x)","F"
294,0,0,106,0.362000," ","int((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^2,x)","\int \sqrt{d e x +c e}\, \left(a +b \arcsin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^2,x)","F"
295,-2,0,106,180.000000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{2}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(1/2),x)","F"
296,0,0,106,0.386000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(3/2),x)","F"
297,0,0,106,0.377000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(5/2),x)","F"
298,0,0,106,0.378000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(7/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{7}{2}}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(7/2),x)","F"
299,0,0,106,0.393000," ","int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(9/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{2}}{\left(d e x +c e \right)^{\frac{9}{2}}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^2/(d*e*x+c*e)^(9/2),x)","F"
300,0,0,73,0.359000," ","int((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^3,x)","\int \sqrt{d e x +c e}\, \left(a +b \arcsin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^3,x)","F"
301,-2,0,73,180.000000," ","int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{3}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(1/2),x)","F"
302,0,0,73,0.387000," ","int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(3/2),x)","F"
303,0,0,73,0.378000," ","int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{3}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^3/(d*e*x+c*e)^(5/2),x)","F"
304,0,0,73,0.358000," ","int((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^4,x)","\int \sqrt{d e x +c e}\, \left(a +b \arcsin \left(d x +c \right)\right)^{4}\, dx"," ",0,"int((d*e*x+c*e)^(1/2)*(a+b*arcsin(d*x+c))^4,x)","F"
305,-2,0,73,180.000000," ","int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(1/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{4}}{\sqrt{d e x +c e}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(1/2),x)","F"
306,0,0,73,0.395000," ","int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(3/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(3/2),x)","F"
307,0,0,73,0.405000," ","int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(5/2),x)","\int \frac{\left(a +b \arcsin \left(d x +c \right)\right)^{4}}{\left(d e x +c e \right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*arcsin(d*x+c))^4/(d*e*x+c*e)^(5/2),x)","F"
308,0,0,86,2.199000," ","int((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^4,x)","\int \left(d e x +c e \right)^{m} \left(a +b \arcsin \left(d x +c \right)\right)^{4}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^4,x)","F"
309,0,0,86,1.809000," ","int((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^3,x)","\int \left(d e x +c e \right)^{m} \left(a +b \arcsin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^3,x)","F"
310,0,0,165,1.582000," ","int((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^2,x)","\int \left(d e x +c e \right)^{m} \left(a +b \arcsin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arcsin(d*x+c))^2,x)","F"
311,0,0,85,1.801000," ","int((d*e*x+c*e)^m*(a+b*arcsin(d*x+c)),x)","\int \left(d e x +c e \right)^{m} \left(a +b \arcsin \left(d x +c \right)\right)\, dx"," ",0,"int((d*e*x+c*e)^m*(a+b*arcsin(d*x+c)),x)","F"
312,0,0,24,1.005000," ","int((d*e*x+c*e)^m/(a+b*arcsin(d*x+c)),x)","\int \frac{\left(d e x +c e \right)^{m}}{a +b \arcsin \left(d x +c \right)}\, dx"," ",0,"int((d*e*x+c*e)^m/(a+b*arcsin(d*x+c)),x)","F"
313,1,215,119,0.177000," ","int(arcsin(b*x+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","\frac{4 \arcsin \left(b x +a \right)^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -6 \arcsin \left(b x +a \right)^{2} x^{2} b^{2}+4 \arcsin \left(b x +a \right)^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a -12 \arcsin \left(b x +a \right)^{2} x a b +\arcsin \left(b x +a \right)^{4}-6 \arcsin \left(b x +a \right)^{2} a^{2}-6 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b +3 b^{2} x^{2}-6 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a +6 a b x +3 \arcsin \left(b x +a \right)^{2}+3 a^{2}}{8 b}"," ",0,"1/8*(4*arcsin(b*x+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-6*arcsin(b*x+a)^2*x^2*b^2+4*arcsin(b*x+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a-12*arcsin(b*x+a)^2*x*a*b+arcsin(b*x+a)^4-6*arcsin(b*x+a)^2*a^2-6*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b+3*b^2*x^2-6*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+6*a*b*x+3*arcsin(b*x+a)^2+3*a^2)/b","A"
314,1,179,97,0.140000," ","int(arcsin(b*x+a)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","\frac{6 \arcsin \left(b x +a \right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -6 \arcsin \left(b x +a \right) x^{2} b^{2}+6 \arcsin \left(b x +a \right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a -12 \arcsin \left(b x +a \right) x a b +2 \arcsin \left(b x +a \right)^{3}-6 \arcsin \left(b x +a \right) a^{2}-3 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -3 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a +3 \arcsin \left(b x +a \right)}{12 b}"," ",0,"1/12*(6*arcsin(b*x+a)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-6*arcsin(b*x+a)*x^2*b^2+6*arcsin(b*x+a)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a-12*arcsin(b*x+a)*x*a*b+2*arcsin(b*x+a)^3-6*arcsin(b*x+a)*a^2-3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+3*arcsin(b*x+a))/b","A"
315,1,96,55,0.132000," ","int(arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","\frac{2 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -b^{2} x^{2}+2 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a -2 a b x +\arcsin \left(b x +a \right)^{2}-a^{2}}{4 b}"," ",0,"1/4*(2*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-b^2*x^2+2*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a-2*a*b*x+arcsin(b*x+a)^2-a^2)/b","A"
316,1,28,27,0.179000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a),x)","\frac{\Ci \left(2 \arcsin \left(b x +a \right)\right)}{2 b}+\frac{\ln \left(\arcsin \left(b x +a \right)\right)}{2 b}"," ",0,"1/2*Ci(2*arcsin(b*x+a))/b+1/2*ln(arcsin(b*x+a))/b","A"
317,1,42,36,0.182000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^2,x)","-\frac{2 \Si \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+\cos \left(2 \arcsin \left(b x +a \right)\right)+1}{2 b \arcsin \left(b x +a \right)}"," ",0,"-1/2/b*(2*Si(2*arcsin(b*x+a))*arcsin(b*x+a)+cos(2*arcsin(b*x+a))+1)/arcsin(b*x+a)","A"
318,1,61,67,0.170000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^3,x)","-\frac{4 \Ci \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}-2 \sin \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+\cos \left(2 \arcsin \left(b x +a \right)\right)+1}{4 b \arcsin \left(b x +a \right)^{2}}"," ",0,"-1/4/b*(4*Ci(2*arcsin(b*x+a))*arcsin(b*x+a)^2-2*sin(2*arcsin(b*x+a))*arcsin(b*x+a)+cos(2*arcsin(b*x+a))+1)/arcsin(b*x+a)^2","A"
319,1,81,101,0.165000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/arcsin(b*x+a)^4,x)","\frac{4 \Si \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{3}+2 \cos \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}+\sin \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)-\cos \left(2 \arcsin \left(b x +a \right)\right)-1}{6 b \arcsin \left(b x +a \right)^{3}}"," ",0,"1/6/b*(4*Si(2*arcsin(b*x+a))*arcsin(b*x+a)^3+2*cos(2*arcsin(b*x+a))*arcsin(b*x+a)^2+sin(2*arcsin(b*x+a))*arcsin(b*x+a)-cos(2*arcsin(b*x+a))-1)/arcsin(b*x+a)^3","A"
320,1,628,217,0.311000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a)^3,x)","\frac{-12+80 \arcsin \left(b x +a \right)^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -240 \arcsin \left(b x +a \right)^{2} x a b -102 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -32 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{3} a^{3}+12 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right) a^{3}-12 x^{3} a \,b^{3}-18 x^{2} a^{2} b^{2}-12 x \,a^{3} b -96 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{3} x \,a^{2} b +36 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right) x^{2} a \,b^{2}+36 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right) x \,a^{2} b -120 \arcsin \left(b x +a \right)^{2} a^{2}+51 \arcsin \left(b x +a \right)^{2}+51 b^{2} x^{2}+102 a b x -96 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{3} x^{2} a \,b^{2}+51 a^{2}-120 \arcsin \left(b x +a \right)^{2} x^{2} b^{2}+12 \arcsin \left(b x +a \right)^{4}+24 \arcsin \left(b x +a \right)^{2} x^{4} b^{4}+96 \arcsin \left(b x +a \right)^{2} x^{3} a \,b^{3}+144 \arcsin \left(b x +a \right)^{2} x^{2} a^{2} b^{2}+96 \arcsin \left(b x +a \right)^{2} x \,a^{3} b -32 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{3} x^{3} b^{3}+12 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right) x^{3} b^{3}+80 \arcsin \left(b x +a \right)^{3} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a -102 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a -3 x^{4} b^{4}+24 \arcsin \left(b x +a \right)^{2} a^{4}-3 a^{4}}{128 b}"," ",0,"1/128*(-12+80*arcsin(b*x+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-240*arcsin(b*x+a)^2*x*a*b-102*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-32*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)^3*a^3+12*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)*a^3-12*x^3*a*b^3-18*x^2*a^2*b^2-12*x*a^3*b-96*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)^3*x*a^2*b+36*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)*x^2*a*b^2+36*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)*x*a^2*b-120*arcsin(b*x+a)^2*a^2+51*arcsin(b*x+a)^2+51*b^2*x^2+102*a*b*x-96*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)^3*x^2*a*b^2+51*a^2-120*arcsin(b*x+a)^2*x^2*b^2+12*arcsin(b*x+a)^4+24*arcsin(b*x+a)^2*x^4*b^4+96*arcsin(b*x+a)^2*x^3*a*b^3+144*arcsin(b*x+a)^2*x^2*a^2*b^2+96*arcsin(b*x+a)^2*x*a^3*b-32*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)^3*x^3*b^3+12*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)*x^3*b^3+80*arcsin(b*x+a)^3*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a-102*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a-3*x^4*b^4+24*arcsin(b*x+a)^2*a^4-3*a^4)/b","B"
321,1,515,175,0.220000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a)^2,x)","\frac{-16 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{2} x^{3} b^{3}+8 \arcsin \left(b x +a \right) x^{4} b^{4}-48 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{2} x^{2} a \,b^{2}+32 \arcsin \left(b x +a \right) x^{3} a \,b^{3}-48 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{2} x \,a^{2} b +48 \arcsin \left(b x +a \right) x^{2} a^{2} b^{2}+2 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x^{3} b^{3}-16 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{2} a^{3}+32 \arcsin \left(b x +a \right) x \,a^{3} b +6 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x^{2} a \,b^{2}+40 \arcsin \left(b x +a \right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -40 \arcsin \left(b x +a \right) x^{2} b^{2}+8 \arcsin \left(b x +a \right) a^{4}+6 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x \,a^{2} b +40 \arcsin \left(b x +a \right)^{2} \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a -80 \arcsin \left(b x +a \right) x a b +2 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a^{3}+8 \arcsin \left(b x +a \right)^{3}-40 \arcsin \left(b x +a \right) a^{2}-17 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -17 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a +17 \arcsin \left(b x +a \right)}{64 b}"," ",0,"1/64*(-16*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)^2*x^3*b^3+8*arcsin(b*x+a)*x^4*b^4-48*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)^2*x^2*a*b^2+32*arcsin(b*x+a)*x^3*a*b^3-48*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)^2*x*a^2*b+48*arcsin(b*x+a)*x^2*a^2*b^2+2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x^3*b^3-16*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)^2*a^3+32*arcsin(b*x+a)*x*a^3*b+6*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x^2*a*b^2+40*arcsin(b*x+a)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-40*arcsin(b*x+a)*x^2*b^2+8*arcsin(b*x+a)*a^4+6*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*a^2*b+40*arcsin(b*x+a)^2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a-80*arcsin(b*x+a)*x*a*b+2*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a^3+8*arcsin(b*x+a)^3-40*arcsin(b*x+a)*a^2-17*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-17*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+17*arcsin(b*x+a))/b","B"
322,1,277,96,0.145000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)*arcsin(b*x+a),x)","\frac{-4 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right) x^{3} b^{3}+x^{4} b^{4}-12 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right) x^{2} a \,b^{2}+4 x^{3} a \,b^{3}-12 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right) x \,a^{2} b +6 x^{2} a^{2} b^{2}-4 \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right) a^{3}+4 x \,a^{3} b +10 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -5 b^{2} x^{2}+a^{4}+10 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a -10 a b x +3 \arcsin \left(b x +a \right)^{2}-5 a^{2}+4}{16 b}"," ",0,"1/16*(-4*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)*x^3*b^3+x^4*b^4-12*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)*x^2*a*b^2+4*x^3*a*b^3-12*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)*x*a^2*b+6*x^2*a^2*b^2-4*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*arcsin(b*x+a)*a^3+4*x*a^3*b+10*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-5*b^2*x^2+a^4+10*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a-10*a*b*x+3*arcsin(b*x+a)^2-5*a^2+4)/b","B"
323,1,42,41,0.168000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a),x)","\frac{\Ci \left(2 \arcsin \left(b x +a \right)\right)}{2 b}+\frac{\Ci \left(4 \arcsin \left(b x +a \right)\right)}{8 b}+\frac{3 \ln \left(\arcsin \left(b x +a \right)\right)}{8 b}"," ",0,"1/2*Ci(2*arcsin(b*x+a))/b+1/8*Ci(4*arcsin(b*x+a))/b+3/8*ln(arcsin(b*x+a))/b","A"
324,1,70,55,0.171000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^2,x)","-\frac{8 \Si \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+4 \Si \left(4 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+4 \cos \left(2 \arcsin \left(b x +a \right)\right)+\cos \left(4 \arcsin \left(b x +a \right)\right)+3}{8 b \arcsin \left(b x +a \right)}"," ",0,"-1/8/b*(8*Si(2*arcsin(b*x+a))*arcsin(b*x+a)+4*Si(4*arcsin(b*x+a))*arcsin(b*x+a)+4*cos(2*arcsin(b*x+a))+cos(4*arcsin(b*x+a))+3)/arcsin(b*x+a)","A"
325,1,108,86,0.163000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^3,x)","-\frac{16 \Ci \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}+16 \Ci \left(4 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}-8 \sin \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)-4 \sin \left(4 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+4 \cos \left(2 \arcsin \left(b x +a \right)\right)+\cos \left(4 \arcsin \left(b x +a \right)\right)+3}{16 b \arcsin \left(b x +a \right)^{2}}"," ",0,"-1/16/b*(16*Ci(2*arcsin(b*x+a))*arcsin(b*x+a)^2+16*Ci(4*arcsin(b*x+a))*arcsin(b*x+a)^2-8*sin(2*arcsin(b*x+a))*arcsin(b*x+a)-4*sin(4*arcsin(b*x+a))*arcsin(b*x+a)+4*cos(2*arcsin(b*x+a))+cos(4*arcsin(b*x+a))+3)/arcsin(b*x+a)^2","A"
326,1,148,141,0.171000," ","int((-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^4,x)","\frac{16 \Si \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{3}+32 \Si \left(4 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{3}+8 \cos \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}+8 \cos \left(4 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)^{2}+4 \sin \left(2 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)+2 \sin \left(4 \arcsin \left(b x +a \right)\right) \arcsin \left(b x +a \right)-4 \cos \left(2 \arcsin \left(b x +a \right)\right)-\cos \left(4 \arcsin \left(b x +a \right)\right)-3}{24 b \arcsin \left(b x +a \right)^{3}}"," ",0,"1/24/b*(16*Si(2*arcsin(b*x+a))*arcsin(b*x+a)^3+32*Si(4*arcsin(b*x+a))*arcsin(b*x+a)^3+8*cos(2*arcsin(b*x+a))*arcsin(b*x+a)^2+8*cos(4*arcsin(b*x+a))*arcsin(b*x+a)^2+4*sin(2*arcsin(b*x+a))*arcsin(b*x+a)+2*sin(4*arcsin(b*x+a))*arcsin(b*x+a)-4*cos(2*arcsin(b*x+a))-cos(4*arcsin(b*x+a))-3)/arcsin(b*x+a)^3","A"
327,1,20,19,0.113000," ","int(arcsin(b*x+a)^n/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","\frac{\arcsin \left(b x +a \right)^{1+n}}{b \left(1+n \right)}"," ",0,"arcsin(b*x+a)^(1+n)/b/(1+n)","A"
328,1,14,13,0.096000," ","int(arcsin(b*x+a)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","\frac{\arcsin \left(b x +a \right)^{3}}{3 b}"," ",0,"1/3*arcsin(b*x+a)^3/b","A"
329,1,14,13,0.095000," ","int(arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","\frac{\arcsin \left(b x +a \right)^{2}}{2 b}"," ",0,"1/2*arcsin(b*x+a)^2/b","A"
330,1,12,11,0.096000," ","int(1/arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","\frac{\ln \left(\arcsin \left(b x +a \right)\right)}{b}"," ",0,"ln(arcsin(b*x+a))/b","A"
331,1,14,13,0.095000," ","int(1/arcsin(b*x+a)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","-\frac{1}{b \arcsin \left(b x +a \right)}"," ",0,"-1/b/arcsin(b*x+a)","A"
332,1,14,13,0.095000," ","int(1/arcsin(b*x+a)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(1/2),x)","-\frac{1}{2 b \arcsin \left(b x +a \right)^{2}}"," ",0,"-1/2/b/arcsin(b*x+a)^2","A"
333,1,235,158,0.404000," ","int(arcsin(b*x+a)^3/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2),x)","\frac{\left(-\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b +i x^{2} b^{2}-\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a +2 i x a b +i a^{2}-i\right) \arcsin \left(b x +a \right)^{3}}{b \left(b^{2} x^{2}+2 a b x +a^{2}-1\right)}-\frac{2 i \arcsin \left(b x +a \right)^{3}}{b}-\frac{3 i \arcsin \left(b x +a \right) \polylog \left(2, -\left(i \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)^{2}\right)}{b}+\frac{3 \arcsin \left(b x +a \right)^{2} \ln \left(1+\left(i \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)^{2}\right)}{b}+\frac{3 \polylog \left(3, -\left(i \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)^{2}\right)}{2 b}"," ",0,"(-(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b+I*x^2*b^2-(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+2*I*x*a*b+I*a^2-I)/b/(b^2*x^2+2*a*b*x+a^2-1)*arcsin(b*x+a)^3-2*I/b*arcsin(b*x+a)^3-3*I*arcsin(b*x+a)*polylog(2,-(I*(b*x+a)+(1-(b*x+a)^2)^(1/2))^2)/b+3*arcsin(b*x+a)^2*ln(1+(I*(b*x+a)+(1-(b*x+a)^2)^(1/2))^2)/b+3/2*polylog(3,-(I*(b*x+a)+(1-(b*x+a)^2)^(1/2))^2)/b","A"
334,1,194,117,0.314000," ","int(arcsin(b*x+a)^2/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2),x)","\frac{\left(-\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b +i x^{2} b^{2}-\sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a +2 i x a b +i a^{2}-i\right) \arcsin \left(b x +a \right)^{2}}{b \left(b^{2} x^{2}+2 a b x +a^{2}-1\right)}+\frac{2 \arcsin \left(b x +a \right) \ln \left(1+\left(i \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)^{2}\right)}{b}-\frac{2 i \arcsin \left(b x +a \right)^{2}}{b}-\frac{i \polylog \left(2, -\left(i \left(b x +a \right)+\sqrt{1-\left(b x +a \right)^{2}}\right)^{2}\right)}{b}"," ",0,"(-(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b+I*x^2*b^2-(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a+2*I*x*a*b+I*a^2-I)/b/(b^2*x^2+2*a*b*x+a^2-1)*arcsin(b*x+a)^2+2*arcsin(b*x+a)*ln(1+(I*(b*x+a)+(1-(b*x+a)^2)^(1/2))^2)/b-2*I/b*arcsin(b*x+a)^2-I*polylog(2,-(I*(b*x+a)+(1-(b*x+a)^2)^(1/2))^2)/b","A"
335,1,155,46,0.168000," ","int(arcsin(b*x+a)/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2),x)","-\frac{-\ln \left(1-\left(b x +a \right)^{2}\right) x^{2} b^{2}+2 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, x b -2 \ln \left(1-\left(b x +a \right)^{2}\right) x a b +2 \arcsin \left(b x +a \right) \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, a -\ln \left(1-\left(b x +a \right)^{2}\right) a^{2}+\ln \left(1-\left(b x +a \right)^{2}\right)}{2 b \left(b^{2} x^{2}+2 a b x +a^{2}-1\right)}"," ",0,"-1/2/b*(-ln(1-(b*x+a)^2)*x^2*b^2+2*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*x*b-2*ln(1-(b*x+a)^2)*x*a*b+2*arcsin(b*x+a)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)*a-ln(1-(b*x+a)^2)*a^2+ln(1-(b*x+a)^2))/(b^2*x^2+2*a*b*x+a^2-1)","B"
336,0,0,24,0.472000," ","int(1/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a),x)","\int \frac{1}{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}} \arcsin \left(b x +a \right)}\, dx"," ",0,"int(1/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a),x)","F"
337,0,0,58,0.374000," ","int(1/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^2,x)","\int \frac{1}{\left(-b^{2} x^{2}-2 a b x -a^{2}+1\right)^{\frac{3}{2}} \arcsin \left(b x +a \right)^{2}}\, dx"," ",0,"int(1/(-b^2*x^2-2*a*b*x-a^2+1)^(3/2)/arcsin(b*x+a)^2,x)","F"
338,1,80,40,0.084000," ","int(arcsin(b*x+a)/(c-c*(b*x+a)^2)^(1/2),x)","-\frac{\sqrt{-c \left(b^{2} x^{2}+2 a b x +a^{2}-1\right)}\, \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{2}}{2 b \left(b^{2} x^{2}+2 a b x +a^{2}-1\right) c}"," ",0,"-1/2*(-c*(b^2*x^2+2*a*b*x+a^2-1))^(1/2)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/b/(b^2*x^2+2*a*b*x+a^2-1)/c*arcsin(b*x+a)^2","A"
339,1,80,40,0.058000," ","int(arcsin(b*x+a)/((-a^2+1)*c-2*a*b*c*x-b^2*c*x^2)^(1/2),x)","-\frac{\sqrt{-c \left(b^{2} x^{2}+2 a b x +a^{2}-1\right)}\, \sqrt{-b^{2} x^{2}-2 a b x -a^{2}+1}\, \arcsin \left(b x +a \right)^{2}}{2 b \left(b^{2} x^{2}+2 a b x +a^{2}-1\right) c}"," ",0,"-1/2*(-c*(b^2*x^2+2*a*b*x+a^2-1))^(1/2)*(-b^2*x^2-2*a*b*x-a^2+1)^(1/2)/b/(b^2*x^2+2*a*b*x+a^2-1)/c*arcsin(b*x+a)^2","A"
340,1,71,70,0.037000," ","int(x^9*(a+b*arcsin(c*x^2)),x)","\frac{x^{10} a}{10}+b \left(\frac{x^{10} \arcsin \left(c \,x^{2}\right)}{10}-\frac{\left(c \,x^{2}-1\right) \left(c \,x^{2}+1\right) \left(3 c^{4} x^{8}+4 c^{2} x^{4}+8\right)}{150 c^{5} \sqrt{-c^{2} x^{4}+1}}\right)"," ",0,"1/10*x^10*a+b*(1/10*x^10*arcsin(c*x^2)-1/150/c^5*(c*x^2-1)*(c*x^2+1)*(3*c^4*x^8+4*c^2*x^4+8)/(-c^2*x^4+1)^(1/2))","A"
341,1,95,70,0.028000," ","int(x^7*(a+b*arcsin(c*x^2)),x)","\frac{x^{8} a}{8}+\frac{b \,x^{8} \arcsin \left(c \,x^{2}\right)}{8}+\frac{b \,x^{6} \sqrt{-c^{2} x^{4}+1}}{32 c}+\frac{3 b \,x^{2} \sqrt{-c^{2} x^{4}+1}}{64 c^{3}}-\frac{3 b \arctan \left(\frac{\sqrt{c^{2}}\, x^{2}}{\sqrt{-c^{2} x^{4}+1}}\right)}{64 c^{3} \sqrt{c^{2}}}"," ",0,"1/8*x^8*a+1/8*b*x^8*arcsin(c*x^2)+1/32*b*x^6*(-c^2*x^4+1)^(1/2)/c+3/64*b*x^2*(-c^2*x^4+1)^(1/2)/c^3-3/64*b/c^3/(c^2)^(1/2)*arctan((c^2)^(1/2)*x^2/(-c^2*x^4+1)^(1/2))","A"
342,1,62,52,0.018000," ","int(x^5*(a+b*arcsin(c*x^2)),x)","\frac{x^{6} a}{6}+b \left(\frac{x^{6} \arcsin \left(c \,x^{2}\right)}{6}-\frac{\left(c \,x^{2}-1\right) \left(c \,x^{2}+1\right) \left(c^{2} x^{4}+2\right)}{18 c^{3} \sqrt{-c^{2} x^{4}+1}}\right)"," ",0,"1/6*x^6*a+b*(1/6*x^6*arcsin(c*x^2)-1/18/c^3*(c*x^2-1)*(c*x^2+1)*(c^2*x^4+2)/(-c^2*x^4+1)^(1/2))","A"
343,1,74,49,0.016000," ","int(x^3*(a+b*arcsin(c*x^2)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arcsin \left(c \,x^{2}\right)}{4}+\frac{b \,x^{2} \sqrt{-c^{2} x^{4}+1}}{8 c}-\frac{b \arctan \left(\frac{\sqrt{c^{2}}\, x^{2}}{\sqrt{-c^{2} x^{4}+1}}\right)}{8 c \sqrt{c^{2}}}"," ",0,"1/4*x^4*a+1/4*b*x^4*arcsin(c*x^2)+1/8*b*x^2*(-c^2*x^4+1)^(1/2)/c-1/8*b/c/(c^2)^(1/2)*arctan((c^2)^(1/2)*x^2/(-c^2*x^4+1)^(1/2))","A"
344,1,39,37,0.004000," ","int(x*(a+b*arcsin(c*x^2)),x)","\frac{a \,x^{2} c +b \left(x^{2} c \arcsin \left(c \,x^{2}\right)+\sqrt{-c^{2} x^{4}+1}\right)}{2 c}"," ",0,"1/2/c*(a*x^2*c+b*(x^2*c*arcsin(c*x^2)+(-c^2*x^4+1)^(1/2)))","A"
345,0,0,81,0.112000," ","int((a+b*arcsin(c*x^2))/x,x)","\int \frac{a +b \arcsin \left(c \,x^{2}\right)}{x}\, dx"," ",0,"int((a+b*arcsin(c*x^2))/x,x)","F"
346,1,38,36,0.015000," ","int((a+b*arcsin(c*x^2))/x^3,x)","-\frac{a}{2 x^{2}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{2 x^{2}}-\frac{c \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{4}+1}}\right)}{2}\right)"," ",0,"-1/2*a/x^2+b*(-1/2/x^2*arcsin(c*x^2)-1/2*c*arctanh(1/(-c^2*x^4+1)^(1/2)))","A"
347,1,54,38,0.013000," ","int((a+b*arcsin(c*x^2))/x^5,x)","-\frac{a}{4 x^{4}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{4 x^{4}}+\frac{c \left(c \,x^{2}-1\right) \left(c \,x^{2}+1\right)}{4 x^{2} \sqrt{-c^{2} x^{4}+1}}\right)"," ",0,"-1/4*a/x^4+b*(-1/4/x^4*arcsin(c*x^2)+1/4*c/x^2*(c*x^2-1)*(c*x^2+1)/(-c^2*x^4+1)^(1/2))","A"
348,1,61,57,0.023000," ","int((a+b*arcsin(c*x^2))/x^7,x)","-\frac{a}{6 x^{6}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{6 x^{6}}+\frac{c \left(-\frac{\sqrt{-c^{2} x^{4}+1}}{4 x^{4}}-\frac{c^{2} \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{4}+1}}\right)}{4}\right)}{3}\right)"," ",0,"-1/6*a/x^6+b*(-1/6/x^6*arcsin(c*x^2)+1/3*c*(-1/4/x^4*(-c^2*x^4+1)^(1/2)-1/4*c^2*arctanh(1/(-c^2*x^4+1)^(1/2))))","A"
349,1,64,59,0.018000," ","int((a+b*arcsin(c*x^2))/x^9,x)","-\frac{a}{8 x^{8}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{8 x^{8}}+\frac{c \left(c \,x^{2}-1\right) \left(c \,x^{2}+1\right) \left(2 c^{2} x^{4}+1\right)}{24 x^{6} \sqrt{-c^{2} x^{4}+1}}\right)"," ",0,"-1/8*a/x^8+b*(-1/8/x^8*arcsin(c*x^2)+1/24*c*(c*x^2-1)*(c*x^2+1)*(2*c^2*x^4+1)/x^6/(-c^2*x^4+1)^(1/2))","A"
350,1,84,78,0.017000," ","int((a+b*arcsin(c*x^2))/x^11,x)","-\frac{a}{10 x^{10}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{10 x^{10}}+\frac{c \left(-\frac{\sqrt{-c^{2} x^{4}+1}}{8 x^{8}}+\frac{3 c^{2} \left(-\frac{\sqrt{-c^{2} x^{4}+1}}{2 x^{4}}-\frac{c^{2} \arctanh \left(\frac{1}{\sqrt{-c^{2} x^{4}+1}}\right)}{2}\right)}{8}\right)}{5}\right)"," ",0,"-1/10*a/x^10+b*(-1/10/x^10*arcsin(c*x^2)+1/5*c*(-1/8/x^8*(-c^2*x^4+1)^(1/2)+3/8*c^2*(-1/2/x^4*(-c^2*x^4+1)^(1/2)-1/2*c^2*arctanh(1/(-c^2*x^4+1)^(1/2)))))","A"
351,1,72,80,0.017000," ","int((a+b*arcsin(c*x^2))/x^13,x)","-\frac{a}{12 x^{12}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{12 x^{12}}+\frac{c \left(c \,x^{2}-1\right) \left(c \,x^{2}+1\right) \left(8 c^{4} x^{8}+4 c^{2} x^{4}+3\right)}{180 x^{10} \sqrt{-c^{2} x^{4}+1}}\right)"," ",0,"-1/12*a/x^12+b*(-1/12/x^12*arcsin(c*x^2)+1/180*c*(c*x^2-1)*(c*x^2+1)*(8*c^4*x^8+4*c^2*x^4+3)/x^10/(-c^2*x^4+1)^(1/2))","A"
352,1,108,70,0.010000," ","int(x^6*(a+b*arcsin(c*x^2)),x)","\frac{x^{7} a}{7}+b \left(\frac{x^{7} \arcsin \left(c \,x^{2}\right)}{7}-\frac{2 c \left(-\frac{x^{5} \sqrt{-c^{2} x^{4}+1}}{7 c^{2}}-\frac{5 x \sqrt{-c^{2} x^{4}+1}}{21 c^{4}}+\frac{5 \sqrt{-c \,x^{2}+1}\, \sqrt{c \,x^{2}+1}\, \EllipticF \left(x \sqrt{c}, i\right)}{21 c^{\frac{9}{2}} \sqrt{-c^{2} x^{4}+1}}\right)}{7}\right)"," ",0,"1/7*x^7*a+b*(1/7*x^7*arcsin(c*x^2)-2/7*c*(-1/7/c^2*x^5*(-c^2*x^4+1)^(1/2)-5/21/c^4*x*(-c^2*x^4+1)^(1/2)+5/21/c^(9/2)*(-c*x^2+1)^(1/2)*(c*x^2+1)^(1/2)/(-c^2*x^4+1)^(1/2)*EllipticF(x*c^(1/2),I)))","A"
353,1,101,65,0.008000," ","int(x^4*(a+b*arcsin(c*x^2)),x)","\frac{a \,x^{5}}{5}+b \left(\frac{x^{5} \arcsin \left(c \,x^{2}\right)}{5}-\frac{2 c \left(-\frac{x^{3} \sqrt{-c^{2} x^{4}+1}}{5 c^{2}}-\frac{3 \sqrt{-c \,x^{2}+1}\, \sqrt{c \,x^{2}+1}\, \left(\EllipticF \left(x \sqrt{c}, i\right)-\EllipticE \left(x \sqrt{c}, i\right)\right)}{5 c^{\frac{7}{2}} \sqrt{-c^{2} x^{4}+1}}\right)}{5}\right)"," ",0,"1/5*a*x^5+b*(1/5*x^5*arcsin(c*x^2)-2/5*c*(-1/5/c^2*x^3*(-c^2*x^4+1)^(1/2)-3/5/c^(7/2)*(-c*x^2+1)^(1/2)*(c*x^2+1)^(1/2)/(-c^2*x^4+1)^(1/2)*(EllipticF(x*c^(1/2),I)-EllipticE(x*c^(1/2),I))))","A"
354,1,88,49,0.009000," ","int(x^2*(a+b*arcsin(c*x^2)),x)","\frac{x^{3} a}{3}+b \left(\frac{x^{3} \arcsin \left(c \,x^{2}\right)}{3}-\frac{2 c \left(-\frac{x \sqrt{-c^{2} x^{4}+1}}{3 c^{2}}+\frac{\sqrt{-c \,x^{2}+1}\, \sqrt{c \,x^{2}+1}\, \EllipticF \left(x \sqrt{c}, i\right)}{3 c^{\frac{5}{2}} \sqrt{-c^{2} x^{4}+1}}\right)}{3}\right)"," ",0,"1/3*x^3*a+b*(1/3*x^3*arcsin(c*x^2)-2/3*c*(-1/3/c^2*x*(-c^2*x^4+1)^(1/2)+1/3/c^(5/2)*(-c*x^2+1)^(1/2)*(c*x^2+1)^(1/2)/(-c^2*x^4+1)^(1/2)*EllipticF(x*c^(1/2),I)))","A"
355,1,71,41,0.008000," ","int(a+b*arcsin(c*x^2),x)","a x +b \left(x \arcsin \left(c \,x^{2}\right)+\frac{2 \sqrt{-c \,x^{2}+1}\, \sqrt{c \,x^{2}+1}\, \left(\EllipticF \left(x \sqrt{c}, i\right)-\EllipticE \left(x \sqrt{c}, i\right)\right)}{\sqrt{c}\, \sqrt{-c^{2} x^{4}+1}}\right)"," ",0,"a*x+b*(x*arcsin(c*x^2)+2/c^(1/2)*(-c*x^2+1)^(1/2)*(c*x^2+1)^(1/2)/(-c^2*x^4+1)^(1/2)*(EllipticF(x*c^(1/2),I)-EllipticE(x*c^(1/2),I)))","A"
356,1,66,32,0.008000," ","int((a+b*arcsin(c*x^2))/x^2,x)","-\frac{a}{x}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{x}+\frac{2 \sqrt{c}\, \sqrt{-c \,x^{2}+1}\, \sqrt{c \,x^{2}+1}\, \EllipticF \left(x \sqrt{c}, i\right)}{\sqrt{-c^{2} x^{4}+1}}\right)"," ",0,"-a/x+b*(-1/x*arcsin(c*x^2)+2*c^(1/2)*(-c*x^2+1)^(1/2)*(c*x^2+1)^(1/2)/(-c^2*x^4+1)^(1/2)*EllipticF(x*c^(1/2),I))","B"
357,1,97,66,0.016000," ","int((a+b*arcsin(c*x^2))/x^4,x)","-\frac{a}{3 x^{3}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{3 x^{3}}+\frac{2 c \left(-\frac{\sqrt{-c^{2} x^{4}+1}}{x}+\frac{\sqrt{c}\, \sqrt{-c \,x^{2}+1}\, \sqrt{c \,x^{2}+1}\, \left(\EllipticF \left(x \sqrt{c}, i\right)-\EllipticE \left(x \sqrt{c}, i\right)\right)}{\sqrt{-c^{2} x^{4}+1}}\right)}{3}\right)"," ",0,"-1/3*a/x^3+b*(-1/3/x^3*arcsin(c*x^2)+2/3*c*(-(-c^2*x^4+1)^(1/2)/x+c^(1/2)*(-c*x^2+1)^(1/2)*(c*x^2+1)^(1/2)/(-c^2*x^4+1)^(1/2)*(EllipticF(x*c^(1/2),I)-EllipticE(x*c^(1/2),I))))","A"
358,1,87,52,0.013000," ","int((a+b*arcsin(c*x^2))/x^6,x)","-\frac{a}{5 x^{5}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{5 x^{5}}+\frac{2 c \left(-\frac{\sqrt{-c^{2} x^{4}+1}}{3 x^{3}}+\frac{c^{\frac{3}{2}} \sqrt{-c \,x^{2}+1}\, \sqrt{c \,x^{2}+1}\, \EllipticF \left(x \sqrt{c}, i\right)}{3 \sqrt{-c^{2} x^{4}+1}}\right)}{5}\right)"," ",0,"-1/5*a/x^5+b*(-1/5/x^5*arcsin(c*x^2)+2/5*c*(-1/3*(-c^2*x^4+1)^(1/2)/x^3+1/3*c^(3/2)*(-c*x^2+1)^(1/2)*(c*x^2+1)^(1/2)/(-c^2*x^4+1)^(1/2)*EllipticF(x*c^(1/2),I)))","A"
359,1,118,87,0.014000," ","int((a+b*arcsin(c*x^2))/x^8,x)","-\frac{a}{7 x^{7}}+b \left(-\frac{\arcsin \left(c \,x^{2}\right)}{7 x^{7}}+\frac{2 c \left(-\frac{\sqrt{-c^{2} x^{4}+1}}{5 x^{5}}-\frac{3 c^{2} \sqrt{-c^{2} x^{4}+1}}{5 x}+\frac{3 c^{\frac{5}{2}} \sqrt{-c \,x^{2}+1}\, \sqrt{c \,x^{2}+1}\, \left(\EllipticF \left(x \sqrt{c}, i\right)-\EllipticE \left(x \sqrt{c}, i\right)\right)}{5 \sqrt{-c^{2} x^{4}+1}}\right)}{7}\right)"," ",0,"-1/7*a/x^7+b*(-1/7/x^7*arcsin(c*x^2)+2/7*c*(-1/5*(-c^2*x^4+1)^(1/2)/x^5-3/5*c^2*(-c^2*x^4+1)^(1/2)/x+3/5*c^(5/2)*(-c*x^2+1)^(1/2)*(c*x^2+1)^(1/2)/(-c^2*x^4+1)^(1/2)*(EllipticF(x*c^(1/2),I)-EllipticE(x*c^(1/2),I))))","A"
360,0,0,74,0.079000," ","int(arcsin(a*x^5)/x,x)","\int \frac{\arcsin \left(a \,x^{5}\right)}{x}\, dx"," ",0,"int(arcsin(a*x^5)/x,x)","F"
361,1,53,54,0.019000," ","int(x^2*arcsin(x^(1/2)),x)","\frac{x^{3} \arcsin \left(\sqrt{x}\right)}{3}+\frac{x^{\frac{5}{2}} \sqrt{1-x}}{18}+\frac{5 x^{\frac{3}{2}} \sqrt{1-x}}{72}+\frac{5 \sqrt{1-x}\, \sqrt{x}}{48}-\frac{5 \arcsin \left(\sqrt{x}\right)}{48}"," ",0,"1/3*x^3*arcsin(x^(1/2))+1/18*x^(5/2)*(1-x)^(1/2)+5/72*x^(3/2)*(1-x)^(1/2)+5/48*(1-x)^(1/2)*x^(1/2)-5/48*arcsin(x^(1/2))","A"
362,1,41,42,0.004000," ","int(x*arcsin(x^(1/2)),x)","\frac{x^{2} \arcsin \left(\sqrt{x}\right)}{2}+\frac{x^{\frac{3}{2}} \sqrt{1-x}}{8}+\frac{3 \sqrt{1-x}\, \sqrt{x}}{16}-\frac{3 \arcsin \left(\sqrt{x}\right)}{16}"," ",0,"1/2*x^2*arcsin(x^(1/2))+1/8*x^(3/2)*(1-x)^(1/2)+3/16*(1-x)^(1/2)*x^(1/2)-3/16*arcsin(x^(1/2))","A"
363,1,26,27,0.007000," ","int(arcsin(x^(1/2)),x)","x \arcsin \left(\sqrt{x}\right)+\frac{\sqrt{1-x}\, \sqrt{x}}{2}-\frac{\arcsin \left(\sqrt{x}\right)}{2}"," ",0,"x*arcsin(x^(1/2))+1/2*(1-x)^(1/2)*x^(1/2)-1/2*arcsin(x^(1/2))","A"
364,1,97,58,0.093000," ","int(arcsin(x^(1/2))/x,x)","-i \arcsin \left(\sqrt{x}\right)^{2}+2 \arcsin \left(\sqrt{x}\right) \ln \left(1+i \sqrt{x}+\sqrt{1-x}\right)+2 \arcsin \left(\sqrt{x}\right) \ln \left(1-i \sqrt{x}-\sqrt{1-x}\right)-2 i \polylog \left(2, -i \sqrt{x}-\sqrt{1-x}\right)-2 i \polylog \left(2, i \sqrt{x}+\sqrt{1-x}\right)"," ",0,"-I*arcsin(x^(1/2))^2+2*arcsin(x^(1/2))*ln(1+I*x^(1/2)+(1-x)^(1/2))+2*arcsin(x^(1/2))*ln(1-I*x^(1/2)-(1-x)^(1/2))-2*I*polylog(2,-I*x^(1/2)-(1-x)^(1/2))-2*I*polylog(2,I*x^(1/2)+(1-x)^(1/2))","A"
365,1,23,22,0.005000," ","int(arcsin(x^(1/2))/x^2,x)","-\frac{\arcsin \left(\sqrt{x}\right)}{x}-\frac{\sqrt{1-x}}{\sqrt{x}}"," ",0,"-arcsin(x^(1/2))/x-(1-x)^(1/2)/x^(1/2)","A"
366,1,35,34,0.005000," ","int(arcsin(x^(1/2))/x^3,x)","-\frac{\arcsin \left(\sqrt{x}\right)}{2 x^{2}}-\frac{\sqrt{1-x}}{6 x^{\frac{3}{2}}}-\frac{\sqrt{1-x}}{3 \sqrt{x}}"," ",0,"-1/2*arcsin(x^(1/2))/x^2-1/6*(1-x)^(1/2)/x^(3/2)-1/3*(1-x)^(1/2)/x^(1/2)","A"
367,1,47,46,0.006000," ","int(arcsin(x^(1/2))/x^4,x)","-\frac{\arcsin \left(\sqrt{x}\right)}{3 x^{3}}-\frac{\sqrt{1-x}}{15 x^{\frac{5}{2}}}-\frac{4 \sqrt{1-x}}{45 x^{\frac{3}{2}}}-\frac{8 \sqrt{1-x}}{45 \sqrt{x}}"," ",0,"-1/3*arcsin(x^(1/2))/x^3-1/15*(1-x)^(1/2)/x^(5/2)-4/45*(1-x)^(1/2)/x^(3/2)-8/45*(1-x)^(1/2)/x^(1/2)","A"
368,1,59,58,0.008000," ","int(arcsin(x^(1/2))/x^5,x)","-\frac{\arcsin \left(\sqrt{x}\right)}{4 x^{4}}-\frac{\sqrt{1-x}}{28 x^{\frac{7}{2}}}-\frac{3 \sqrt{1-x}}{70 x^{\frac{5}{2}}}-\frac{2 \sqrt{1-x}}{35 x^{\frac{3}{2}}}-\frac{4 \sqrt{1-x}}{35 \sqrt{x}}"," ",0,"-1/4*arcsin(x^(1/2))/x^4-1/28*(1-x)^(1/2)/x^(7/2)-3/70*(1-x)^(1/2)/x^(5/2)-2/35*(1-x)^(1/2)/x^(3/2)-4/35*(1-x)^(1/2)/x^(1/2)","A"
369,1,88,75,0.019000," ","int(x^4*(a+b*arcsin(c/x)),x)","-c^{5} \left(-\frac{a \,x^{5}}{5 c^{5}}+b \left(-\frac{\arcsin \left(\frac{c}{x}\right) x^{5}}{5 c^{5}}-\frac{x^{4} \sqrt{1-\frac{c^{2}}{x^{2}}}}{20 c^{4}}-\frac{3 x^{2} \sqrt{1-\frac{c^{2}}{x^{2}}}}{40 c^{2}}-\frac{3 \arctanh \left(\frac{1}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)}{40}\right)\right)"," ",0,"-c^5*(-1/5*a/c^5*x^5+b*(-1/5*arcsin(c/x)/c^5*x^5-1/20/c^4*x^4*(1-c^2/x^2)^(1/2)-3/40/c^2*x^2*(1-c^2/x^2)^(1/2)-3/40*arctanh(1/(1-c^2/x^2)^(1/2))))","A"
370,1,71,54,0.007000," ","int(x^3*(a+b*arcsin(c/x)),x)","-c^{4} \left(-\frac{a \,x^{4}}{4 c^{4}}+b \left(-\frac{x^{4} \arcsin \left(\frac{c}{x}\right)}{4 c^{4}}-\frac{x^{3} \sqrt{1-\frac{c^{2}}{x^{2}}}}{12 c^{3}}-\frac{x \sqrt{1-\frac{c^{2}}{x^{2}}}}{6 c}\right)\right)"," ",0,"-c^4*(-1/4*a/c^4*x^4+b*(-1/4/c^4*x^4*arcsin(c/x)-1/12/c^3*x^3*(1-c^2/x^2)^(1/2)-1/6/c*x*(1-c^2/x^2)^(1/2)))","A"
371,1,68,54,0.009000," ","int(x^2*(a+b*arcsin(c/x)),x)","-c^{3} \left(-\frac{a \,x^{3}}{3 c^{3}}+b \left(-\frac{x^{3} \arcsin \left(\frac{c}{x}\right)}{3 c^{3}}-\frac{x^{2} \sqrt{1-\frac{c^{2}}{x^{2}}}}{6 c^{2}}-\frac{\arctanh \left(\frac{1}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)}{6}\right)\right)"," ",0,"-c^3*(-1/3*a/c^3*x^3+b*(-1/3/c^3*x^3*arcsin(c/x)-1/6/c^2*x^2*(1-c^2/x^2)^(1/2)-1/6*arctanh(1/(1-c^2/x^2)^(1/2))))","A"
372,1,51,33,0.008000," ","int(x*(a+b*arcsin(c/x)),x)","-c^{2} \left(-\frac{a \,x^{2}}{2 c^{2}}+b \left(-\frac{x^{2} \arcsin \left(\frac{c}{x}\right)}{2 c^{2}}-\frac{x \sqrt{1-\frac{c^{2}}{x^{2}}}}{2 c}\right)\right)"," ",0,"-c^2*(-1/2*a/c^2*x^2+b*(-1/2/c^2*x^2*arcsin(c/x)-1/2/c*x*(1-c^2/x^2)^(1/2)))","A"
373,1,37,29,0.009000," ","int(a+b*arcsin(c/x),x)","a x -b c \left(-\frac{\arcsin \left(\frac{c}{x}\right) x}{c}-\arctanh \left(\frac{1}{\sqrt{1-\frac{c^{2}}{x^{2}}}}\right)\right)"," ",0,"a*x-b*c*(-arcsin(c/x)/c*x-arctanh(1/(1-c^2/x^2)^(1/2)))","A"
374,1,141,81,0.009000," ","int((a+b*arcsin(c/x))/x,x)","-a \ln \left(\frac{c}{x}\right)+\frac{i b \arcsin \left(\frac{c}{x}\right)^{2}}{2}-b \arcsin \left(\frac{c}{x}\right) \ln \left(1+\frac{i c}{x}+\sqrt{1-\frac{c^{2}}{x^{2}}}\right)-b \arcsin \left(\frac{c}{x}\right) \ln \left(1-\frac{i c}{x}-\sqrt{1-\frac{c^{2}}{x^{2}}}\right)+i b \polylog \left(2, -\frac{i c}{x}-\sqrt{1-\frac{c^{2}}{x^{2}}}\right)+i b \polylog \left(2, \frac{i c}{x}+\sqrt{1-\frac{c^{2}}{x^{2}}}\right)"," ",0,"-a*ln(c/x)+1/2*I*b*arcsin(c/x)^2-b*arcsin(c/x)*ln(1+I*c/x+(1-c^2/x^2)^(1/2))-b*arcsin(c/x)*ln(1-I*c/x-(1-c^2/x^2)^(1/2))+I*b*polylog(2,-I*c/x-(1-c^2/x^2)^(1/2))+I*b*polylog(2,I*c/x+(1-c^2/x^2)^(1/2))","A"
375,1,39,37,0.003000," ","int((a+b*arcsin(c/x))/x^2,x)","-\frac{\frac{a c}{x}+b \left(\frac{c \arcsin \left(\frac{c}{x}\right)}{x}+\sqrt{1-\frac{c^{2}}{x^{2}}}\right)}{c}"," ",0,"-1/c*(a*c/x+b*(c/x*arcsin(c/x)+(1-c^2/x^2)^(1/2)))","A"
376,1,59,52,0.007000," ","int((a+b*arcsin(c/x))/x^3,x)","-\frac{\frac{c^{2} a}{2 x^{2}}+b \left(\frac{\arcsin \left(\frac{c}{x}\right) c^{2}}{2 x^{2}}+\frac{c \sqrt{1-\frac{c^{2}}{x^{2}}}}{4 x}-\frac{\arcsin \left(\frac{c}{x}\right)}{4}\right)}{c^{2}}"," ",0,"-1/c^2*(1/2*c^2/x^2*a+b*(1/2*arcsin(c/x)*c^2/x^2+1/4*c/x*(1-c^2/x^2)^(1/2)-1/4*arcsin(c/x)))","A"
377,1,67,55,0.010000," ","int((a+b*arcsin(c/x))/x^4,x)","-\frac{\frac{c^{3} a}{3 x^{3}}+b \left(\frac{\arcsin \left(\frac{c}{x}\right) c^{3}}{3 x^{3}}+\frac{c^{2} \sqrt{1-\frac{c^{2}}{x^{2}}}}{9 x^{2}}+\frac{2 \sqrt{1-\frac{c^{2}}{x^{2}}}}{9}\right)}{c^{3}}"," ",0,"-1/c^3*(1/3*c^3/x^3*a+b*(1/3*arcsin(c/x)*c^3/x^3+1/9*c^2/x^2*(1-c^2/x^2)^(1/2)+2/9*(1-c^2/x^2)^(1/2)))","A"
378,1,79,73,0.007000," ","int((a+b*arcsin(c/x))/x^5,x)","-\frac{\frac{c^{4} a}{4 x^{4}}+b \left(\frac{c^{4} \arcsin \left(\frac{c}{x}\right)}{4 x^{4}}+\frac{c^{3} \sqrt{1-\frac{c^{2}}{x^{2}}}}{16 x^{3}}+\frac{3 c \sqrt{1-\frac{c^{2}}{x^{2}}}}{32 x}-\frac{3 \arcsin \left(\frac{c}{x}\right)}{32}\right)}{c^{4}}"," ",0,"-1/c^4*(1/4*c^4/x^4*a+b*(1/4*c^4/x^4*arcsin(c/x)+1/16*c^3/x^3*(1-c^2/x^2)^(1/2)+3/32*c/x*(1-c^2/x^2)^(1/2)-3/32*arcsin(c/x)))","A"
379,0,0,77,0.142000," ","int(x^m*(a+b*arcsin(c*x^n)),x)","\int x^{m} \left(a +b \arcsin \left(c \,x^{n}\right)\right)\, dx"," ",0,"int(x^m*(a+b*arcsin(c*x^n)),x)","F"
380,0,0,60,0.043000," ","int(x^2*(a+b*arcsin(c*x^n)),x)","\int x^{2} \left(a +b \arcsin \left(c \,x^{n}\right)\right)\, dx"," ",0,"int(x^2*(a+b*arcsin(c*x^n)),x)","F"
381,0,0,57,0.022000," ","int(x*(a+b*arcsin(c*x^n)),x)","\int x \left(a +b \arcsin \left(c \,x^{n}\right)\right)\, dx"," ",0,"int(x*(a+b*arcsin(c*x^n)),x)","F"
382,0,0,56,0.024000," ","int(a+b*arcsin(c*x^n),x)","\int a +b \arcsin \left(c \,x^{n}\right)\, dx"," ",0,"int(a+b*arcsin(c*x^n),x)","F"
383,1,164,93,0.007000," ","int((a+b*arcsin(c*x^n))/x,x)","\frac{a \ln \left(c \,x^{n}\right)}{n}-\frac{i b \arcsin \left(c \,x^{n}\right)^{2}}{2 n}+\frac{b \arcsin \left(c \,x^{n}\right) \ln \left(1+i c \,x^{n}+\sqrt{1-c^{2} x^{2 n}}\right)}{n}+\frac{b \arcsin \left(c \,x^{n}\right) \ln \left(1-i c \,x^{n}-\sqrt{1-c^{2} x^{2 n}}\right)}{n}-\frac{i b \polylog \left(2, -i c \,x^{n}-\sqrt{1-c^{2} x^{2 n}}\right)}{n}-\frac{i b \polylog \left(2, i c \,x^{n}+\sqrt{1-c^{2} x^{2 n}}\right)}{n}"," ",0,"1/n*a*ln(c*x^n)-1/2*I*b*arcsin(c*x^n)^2/n+1/n*b*arcsin(c*x^n)*ln(1+I*c*x^n+(1-c^2*(x^n)^2)^(1/2))+1/n*b*arcsin(c*x^n)*ln(1-I*c*x^n-(1-c^2*(x^n)^2)^(1/2))-I/n*b*polylog(2,-I*c*x^n-(1-c^2*(x^n)^2)^(1/2))-I/n*b*polylog(2,I*c*x^n+(1-c^2*(x^n)^2)^(1/2))","A"
384,0,0,63,0.019000," ","int((a+b*arcsin(c*x^n))/x^2,x)","\int \frac{a +b \arcsin \left(c \,x^{n}\right)}{x^{2}}\, dx"," ",0,"int((a+b*arcsin(c*x^n))/x^2,x)","F"
385,0,0,63,0.018000," ","int((a+b*arcsin(c*x^n))/x^3,x)","\int \frac{a +b \arcsin \left(c \,x^{n}\right)}{x^{3}}\, dx"," ",0,"int((a+b*arcsin(c*x^n))/x^3,x)","F"
386,1,258,117,0.067000," ","int(x^5*(a+b*arcsin(d*x^2+c)),x)","\frac{x^{6} a}{6}+\frac{b \,x^{6} \arcsin \left(d \,x^{2}+c \right)}{6}+\frac{b \,x^{4} \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{18 d}-\frac{5 b c \,x^{2} \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{36 d^{2}}+\frac{11 b \,c^{2} \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{36 d^{3}}+\frac{b \,c^{3} \arctan \left(\frac{\sqrt{d^{2}}\, \left(x^{2}+\frac{c}{d}\right)}{\sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}\right)}{6 d^{2} \sqrt{d^{2}}}+\frac{b c \arctan \left(\frac{\sqrt{d^{2}}\, \left(x^{2}+\frac{c}{d}\right)}{\sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}\right)}{4 d^{2} \sqrt{d^{2}}}+\frac{b \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{9 d^{3}}"," ",0,"1/6*x^6*a+1/6*b*x^6*arcsin(d*x^2+c)+1/18*b*x^4*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/d-5/36*b*c/d^2*x^2*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)+11/36*b*c^2/d^3*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)+1/6*b*c^3/d^2/(d^2)^(1/2)*arctan((d^2)^(1/2)*(x^2+c/d)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2))+1/4*b*c/d^2/(d^2)^(1/2)*arctan((d^2)^(1/2)*(x^2+c/d)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2))+1/9*b/d^3*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)","B"
387,1,191,103,0.021000," ","int(x^3*(a+b*arcsin(d*x^2+c)),x)","\frac{x^{4} a}{4}+\frac{b \,x^{4} \arcsin \left(d \,x^{2}+c \right)}{4}+\frac{b \,x^{2} \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{8 d}-\frac{3 b c \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{8 d^{2}}-\frac{b \,c^{2} \arctan \left(\frac{\sqrt{d^{2}}\, \left(x^{2}+\frac{c}{d}\right)}{\sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}\right)}{4 d \sqrt{d^{2}}}-\frac{b \arctan \left(\frac{\sqrt{d^{2}}\, \left(x^{2}+\frac{c}{d}\right)}{\sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}\right)}{8 d \sqrt{d^{2}}}"," ",0,"1/4*x^4*a+1/4*b*x^4*arcsin(d*x^2+c)+1/8*b*x^2*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/d-3/8*b*c*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/d^2-1/4*b*c^2/d/(d^2)^(1/2)*arctan((d^2)^(1/2)*(x^2+c/d)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2))-1/8*b/d/(d^2)^(1/2)*arctan((d^2)^(1/2)*(x^2+c/d)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2))","A"
388,1,50,49,0.005000," ","int(x*(a+b*arcsin(d*x^2+c)),x)","\frac{a \left(d \,x^{2}+c \right)+b \left(\left(d \,x^{2}+c \right) \arcsin \left(d \,x^{2}+c \right)+\sqrt{1-\left(d \,x^{2}+c \right)^{2}}\right)}{2 d}"," ",0,"1/2/d*(a*(d*x^2+c)+b*((d*x^2+c)*arcsin(d*x^2+c)+(1-(d*x^2+c)^2)^(1/2)))","A"
389,0,0,237,0.142000," ","int((a+b*arcsin(d*x^2+c))/x,x)","\int \frac{a +b \arcsin \left(d \,x^{2}+c \right)}{x}\, dx"," ",0,"int((a+b*arcsin(d*x^2+c))/x,x)","F"
390,1,89,83,0.020000," ","int((a+b*arcsin(d*x^2+c))/x^3,x)","-\frac{a}{2 x^{2}}-\frac{b \arcsin \left(d \,x^{2}+c \right)}{2 x^{2}}-\frac{b d \ln \left(\frac{-2 c^{2}+2-2 c d \,x^{2}+2 \sqrt{-c^{2}+1}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{x^{2}}\right)}{2 \sqrt{-c^{2}+1}}"," ",0,"-1/2*a/x^2-1/2*b/x^2*arcsin(d*x^2+c)-1/2*b*d/(-c^2+1)^(1/2)*ln((-2*c^2+2-2*c*d*x^2+2*(-c^2+1)^(1/2)*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2))/x^2)","A"
391,1,132,126,0.020000," ","int((a+b*arcsin(d*x^2+c))/x^5,x)","-\frac{a}{4 x^{4}}-\frac{b \arcsin \left(d \,x^{2}+c \right)}{4 x^{4}}-\frac{b d \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{4 \left(-c^{2}+1\right) x^{2}}-\frac{b \,d^{2} c \ln \left(\frac{-2 c^{2}+2-2 c d \,x^{2}+2 \sqrt{-c^{2}+1}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{x^{2}}\right)}{4 \left(-c^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-1/4*a/x^4-1/4*b/x^4*arcsin(d*x^2+c)-1/4*b*d*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/(-c^2+1)/x^2-1/4*b*d^2*c/(-c^2+1)^(3/2)*ln((-2*c^2+2-2*c*d*x^2+2*(-c^2+1)^(1/2)*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2))/x^2)","A"
392,1,246,175,0.022000," ","int((a+b*arcsin(d*x^2+c))/x^7,x)","-\frac{a}{6 x^{6}}-\frac{b \arcsin \left(d \,x^{2}+c \right)}{6 x^{6}}-\frac{b d \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{12 \left(-c^{2}+1\right) x^{4}}-\frac{b c \,d^{2} \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{4 \left(-c^{2}+1\right)^{2} x^{2}}-\frac{b \,d^{3} c^{2} \ln \left(\frac{-2 c^{2}+2-2 c d \,x^{2}+2 \sqrt{-c^{2}+1}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{x^{2}}\right)}{4 \left(-c^{2}+1\right)^{\frac{5}{2}}}-\frac{b \,d^{3} \ln \left(\frac{-2 c^{2}+2-2 c d \,x^{2}+2 \sqrt{-c^{2}+1}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{x^{2}}\right)}{12 \left(-c^{2}+1\right)^{\frac{3}{2}}}"," ",0,"-1/6*a/x^6-1/6*b/x^6*arcsin(d*x^2+c)-1/12*b*d*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/(-c^2+1)/x^4-1/4*b*c*d^2*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/(-c^2+1)^2/x^2-1/4*b*d^3*c^2/(-c^2+1)^(5/2)*ln((-2*c^2+2-2*c*d*x^2+2*(-c^2+1)^(1/2)*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2))/x^2)-1/12*b*d^3/(-c^2+1)^(3/2)*ln((-2*c^2+2-2*c*d*x^2+2*(-c^2+1)^(1/2)*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2))/x^2)","A"
393,1,346,290,0.039000," ","int(x^4*(a+b*arcsin(d*x^2+c)),x)","\frac{a \,x^{5}}{5}+b \left(\frac{x^{5} \arcsin \left(d \,x^{2}+c \right)}{5}-\frac{2 d \left(-\frac{x^{3} \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{5 d^{2}}+\frac{8 c x \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{15 d^{3}}-\frac{8 c \left(-c^{2}+1\right) \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)}{15 d^{3} \sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}-\frac{2 \left(\frac{-3 c^{2}+3}{5 d^{2}}+\frac{32 c^{2}}{15 d^{2}}\right) \left(-c^{2}+1\right) \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \left(\EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)-\EllipticE \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)\right)}{\sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}\, \left(-2 d c +2 d \right)}\right)}{5}\right)"," ",0,"1/5*a*x^5+b*(1/5*x^5*arcsin(d*x^2+c)-2/5*d*(-1/5/d^2*x^3*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)+8/15*c/d^3*x*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)-8/15*c/d^3*(-c^2+1)/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)*EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))-2*(1/5/d^2*(-3*c^2+3)+32/15*c^2/d^2)*(-c^2+1)/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/(-2*c*d+2*d)*(EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))-EllipticE(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2)))))","A"
394,1,295,245,0.011000," ","int(x^2*(a+b*arcsin(d*x^2+c)),x)","\frac{x^{3} a}{3}+b \left(\frac{x^{3} \arcsin \left(d \,x^{2}+c \right)}{3}-\frac{2 d \left(-\frac{x \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{3 d^{2}}+\frac{\left(-c^{2}+1\right) \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)}{3 d^{2} \sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}+\frac{8 c \left(-c^{2}+1\right) \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \left(\EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)-\EllipticE \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)\right)}{3 d \sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}\, \left(-2 d c +2 d \right)}\right)}{3}\right)"," ",0,"1/3*x^3*a+b*(1/3*x^3*arcsin(d*x^2+c)-2/3*d*(-1/3/d^2*x*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)+1/3/d^2*(-c^2+1)/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)*EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))+8/3*c/d*(-c^2+1)/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/(-2*c*d+2*d)*(EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))-EllipticE(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2)))))","A"
395,1,153,205,0.011000," ","int(a+b*arcsin(d*x^2+c),x)","a x +b \left(x \arcsin \left(d \,x^{2}+c \right)+\frac{4 d \left(-c^{2}+1\right) \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \left(\EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)-\EllipticE \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)\right)}{\sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}\, \left(-2 d c +2 d \right)}\right)"," ",0,"a*x+b*(x*arcsin(d*x^2+c)+4*d*(-c^2+1)/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/(-2*c*d+2*d)*(EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))-EllipticE(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))))","A"
396,1,114,112,0.011000," ","int((a+b*arcsin(d*x^2+c))/x^2,x)","-\frac{a}{x}+b \left(-\frac{\arcsin \left(d \,x^{2}+c \right)}{x}+\frac{2 d \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)}{\sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}\right)"," ",0,"-a/x+b*(-1/x*arcsin(d*x^2+c)+2*d/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)*EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2)))","A"
397,1,207,245,0.014000," ","int((a+b*arcsin(d*x^2+c))/x^4,x)","-\frac{a}{3 x^{3}}+b \left(-\frac{\arcsin \left(d \,x^{2}+c \right)}{3 x^{3}}+\frac{2 d \left(\frac{\sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{\left(c^{2}-1\right) x}-\frac{2 d^{2} \left(-c^{2}+1\right) \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \left(\EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)-\EllipticE \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)\right)}{\left(c^{2}-1\right) \sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}\, \left(-2 d c +2 d \right)}\right)}{3}\right)"," ",0,"-1/3*a/x^3+b*(-1/3/x^3*arcsin(d*x^2+c)+2/3*d*(1/(c^2-1)*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/x-2*d^2/(c^2-1)*(-c^2+1)/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/(-2*c*d+2*d)*(EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))-EllipticE(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2)))))","A"
398,1,346,312,0.019000," ","int((a+b*arcsin(d*x^2+c))/x^6,x)","-\frac{a}{5 x^{5}}+b \left(-\frac{\arcsin \left(d \,x^{2}+c \right)}{5 x^{5}}+\frac{2 d \left(\frac{\sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{3 \left(c^{2}-1\right) x^{3}}-\frac{4 c d \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}{3 \left(c^{2}-1\right)^{2} x}-\frac{d^{2} \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)}{3 \left(c^{2}-1\right) \sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}}+\frac{8 c \,d^{3} \left(-c^{2}+1\right) \sqrt{1+\frac{d \,x^{2}}{-1+c}}\, \sqrt{1+\frac{d \,x^{2}}{1+c}}\, \left(\EllipticF \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)-\EllipticE \left(x \sqrt{-\frac{d}{-1+c}}, \sqrt{-1+\frac{2 c}{1+c}}\right)\right)}{3 \left(c^{2}-1\right)^{2} \sqrt{-\frac{d}{-1+c}}\, \sqrt{-d^{2} x^{4}-2 c d \,x^{2}-c^{2}+1}\, \left(-2 d c +2 d \right)}\right)}{5}\right)"," ",0,"-1/5*a/x^5+b*(-1/5/x^5*arcsin(d*x^2+c)+2/5*d*(1/3/(c^2-1)*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/x^3-4/3*c*d/(c^2-1)^2*(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/x-1/3*d^2/(c^2-1)/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)*EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))+8/3*c*d^3/(c^2-1)^2*(-c^2+1)/(-d/(-1+c))^(1/2)*(1+d/(-1+c)*x^2)^(1/2)*(1+d*x^2/(1+c))^(1/2)/(-d^2*x^4-2*c*d*x^2-c^2+1)^(1/2)/(-2*c*d+2*d)*(EllipticF(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2))-EllipticE(x*(-d/(-1+c))^(1/2),(-1+2*c/(1+c))^(1/2)))))","A"
399,1,38,41,0.005000," ","int(x^3*arcsin(b*x^4+a),x)","\frac{\left(b \,x^{4}+a \right) \arcsin \left(b \,x^{4}+a \right)+\sqrt{1-\left(b \,x^{4}+a \right)^{2}}}{4 b}"," ",0,"1/4/b*((b*x^4+a)*arcsin(b*x^4+a)+(1-(b*x^4+a)^2)^(1/2))","A"
400,0,0,45,0.068000," ","int(x^(n-1)*arcsin(a+b*x^n),x)","\int x^{n -1} \arcsin \left(a +b \,x^{n}\right)\, dx"," ",0,"int(x^(n-1)*arcsin(a+b*x^n),x)","F"
401,0,0,123,0.146000," ","int((a+b*arcsin(d*x^2+1))^4,x)","\int \left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{4}\, dx"," ",0,"int((a+b*arcsin(d*x^2+1))^4,x)","F"
402,0,0,106,0.111000," ","int((a+b*arcsin(d*x^2+1))^3,x)","\int \left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{3}\, dx"," ",0,"int((a+b*arcsin(d*x^2+1))^3,x)","F"
403,0,0,61,0.115000," ","int((a+b*arcsin(d*x^2+1))^2,x)","\int \left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{2}\, dx"," ",0,"int((a+b*arcsin(d*x^2+1))^2,x)","F"
404,1,45,41,0.009000," ","int(a+b*arcsin(d*x^2+1),x)","a x +b \left(x \arcsin \left(d \,x^{2}+1\right)-\frac{2 x \left(d \,x^{2}+2\right)}{\sqrt{-d^{2} x^{4}-2 d \,x^{2}}}\right)"," ",0,"a*x+b*(x*arcsin(d*x^2+1)-2/(-d^2*x^4-2*d*x^2)^(1/2)*x*(d*x^2+2))","A"
405,0,0,135,0.085000," ","int(1/(a+b*arcsin(d*x^2+1)),x)","\int \frac{1}{a +b \arcsin \left(d \,x^{2}+1\right)}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2+1)),x)","F"
406,0,0,177,0.069000," ","int(1/(a+b*arcsin(d*x^2+1))^2,x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{2}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2+1))^2,x)","F"
407,0,0,197,0.072000," ","int(1/(a+b*arcsin(d*x^2+1))^3,x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{3}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2+1))^3,x)","F"
408,0,0,123,0.116000," ","int((a+b*arcsin(d*x^2-1))^4,x)","\int \left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{4}\, dx"," ",0,"int((a+b*arcsin(d*x^2-1))^4,x)","F"
409,0,0,106,0.111000," ","int((a+b*arcsin(d*x^2-1))^3,x)","\int \left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{3}\, dx"," ",0,"int((a+b*arcsin(d*x^2-1))^3,x)","F"
410,0,0,61,0.125000," ","int((a+b*arcsin(d*x^2-1))^2,x)","\int \left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{2}\, dx"," ",0,"int((a+b*arcsin(d*x^2-1))^2,x)","F"
411,1,45,41,0.010000," ","int(a+b*arcsin(d*x^2-1),x)","a x +b \left(x \arcsin \left(d \,x^{2}-1\right)-\frac{2 x \left(d \,x^{2}-2\right)}{\sqrt{-d^{2} x^{4}+2 d \,x^{2}}}\right)"," ",0,"a*x+b*(x*arcsin(d*x^2-1)-2/(-d^2*x^4+2*d*x^2)^(1/2)*x*(d*x^2-2))","A"
412,0,0,134,0.067000," ","int(1/(a+b*arcsin(d*x^2-1)),x)","\int \frac{1}{a +b \arcsin \left(d \,x^{2}-1\right)}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2-1)),x)","F"
413,0,0,176,0.069000," ","int(1/(a+b*arcsin(d*x^2-1))^2,x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{2}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2-1))^2,x)","F"
414,0,0,196,0.068000," ","int(1/(a+b*arcsin(d*x^2-1))^3,x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{3}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2-1))^3,x)","F"
415,0,0,38,0.064000," ","int(arcsin(x^2+1)^2,x)","\int \arcsin \left(x^{2}+1\right)^{2}\, dx"," ",0,"int(arcsin(x^2+1)^2,x)","F"
416,0,0,38,0.076000," ","int(arcsin(x^2-1)^2,x)","\int \arcsin \left(x^{2}-1\right)^{2}\, dx"," ",0,"int(arcsin(x^2-1)^2,x)","F"
417,0,0,233,0.078000," ","int((a+b*arcsin(d*x^2+1))^(5/2),x)","\int \left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arcsin(d*x^2+1))^(5/2),x)","F"
418,0,0,205,0.069000," ","int((a+b*arcsin(d*x^2+1))^(3/2),x)","\int \left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arcsin(d*x^2+1))^(3/2),x)","F"
419,0,0,172,0.069000," ","int((a+b*arcsin(d*x^2+1))^(1/2),x)","\int \sqrt{a +b \arcsin \left(d \,x^{2}+1\right)}\, dx"," ",0,"int((a+b*arcsin(d*x^2+1))^(1/2),x)","F"
420,0,0,149,0.069000," ","int(1/(a+b*arcsin(d*x^2+1))^(1/2),x)","\int \frac{1}{\sqrt{a +b \arcsin \left(d \,x^{2}+1\right)}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2+1))^(1/2),x)","F"
421,0,0,198,0.067000," ","int(1/(a+b*arcsin(d*x^2+1))^(3/2),x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2+1))^(3/2),x)","F"
422,0,0,211,0.070000," ","int(1/(a+b*arcsin(d*x^2+1))^(5/2),x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2+1))^(5/2),x)","F"
423,0,0,261,0.082000," ","int(1/(a+b*arcsin(d*x^2+1))^(7/2),x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}+1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2+1))^(7/2),x)","F"
424,0,0,237,0.069000," ","int((a+b*arcsin(d*x^2-1))^(5/2),x)","\int \left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((a+b*arcsin(d*x^2-1))^(5/2),x)","F"
425,0,0,209,0.066000," ","int((a+b*arcsin(d*x^2-1))^(3/2),x)","\int \left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((a+b*arcsin(d*x^2-1))^(3/2),x)","F"
426,0,0,176,0.071000," ","int((a+b*arcsin(d*x^2-1))^(1/2),x)","\int \sqrt{a +b \arcsin \left(d \,x^{2}-1\right)}\, dx"," ",0,"int((a+b*arcsin(d*x^2-1))^(1/2),x)","F"
427,0,0,153,0.069000," ","int(1/(a+b*arcsin(d*x^2-1))^(1/2),x)","\int \frac{1}{\sqrt{a +b \arcsin \left(d \,x^{2}-1\right)}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2-1))^(1/2),x)","F"
428,0,0,202,0.069000," ","int(1/(a+b*arcsin(d*x^2-1))^(3/2),x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2-1))^(3/2),x)","F"
429,0,0,215,0.071000," ","int(1/(a+b*arcsin(d*x^2-1))^(5/2),x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2-1))^(5/2),x)","F"
430,0,0,265,0.067000," ","int(1/(a+b*arcsin(d*x^2-1))^(7/2),x)","\int \frac{1}{\left(a +b \arcsin \left(d \,x^{2}-1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"int(1/(a+b*arcsin(d*x^2-1))^(7/2),x)","F"
431,0,0,38,1.210000," ","int((a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","\int \frac{\left(a +b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{n}}{-c^{2} x^{2}+1}\, dx"," ",0,"int((a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x)","F"
432,1,1232,300,0.828000," ","int((a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x)","-\frac{a^{3} \ln \left(c x -1\right)}{2 c}+\frac{a^{3} \ln \left(c x +1\right)}{2 c}+\frac{i a \,b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3}}{c}-\frac{b^{3} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{3 i a^{2} b \polylog \left(2, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 b^{3} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{3 i b^{3} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{b^{3} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3} \ln \left(1-\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{3 i a^{2} b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{2 c}-\frac{6 b^{3} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(3, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 i b^{3} \polylog \left(4, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{3 i a^{2} b \polylog \left(2, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 a \,b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{6 i a \,b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 a \,b^{2} \polylog \left(3, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 a \,b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1-\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 i b^{3} \polylog \left(4, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{6 a \,b^{2} \polylog \left(3, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{3 i b^{3} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \polylog \left(2, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 a^{2} b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{6 i a \,b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{3 a^{2} b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{i b^{3} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{4}}{4 c}"," ",0,"-1/2*a^3/c*ln(c*x-1)+1/2*a^3/c*ln(c*x+1)+3*I*a^2*b/c*polylog(2,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))-b^3/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+I*a*b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3-6*b^3/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-6*I*b^3/c*polylog(4,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))-b^3/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3*ln(1-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))+3*I*b^3/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-6*b^3/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(3,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+3/2*I*a^2*b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-6*I*b^3/c*polylog(4,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-3*a*b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+6*I*a*b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))-6*a*b^2/c*polylog(3,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-3*a*b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))+6*I*a*b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-6*a*b^2/c*polylog(3,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+3*I*a^2*b/c*polylog(2,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-3*a^2*b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+3*I*b^3/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*polylog(2,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))-3*a^2*b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))+1/4*I*b^3/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^4","B"
433,1,681,226,0.010000," ","int((a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x)","-\frac{a^{2} \ln \left(c x -1\right)}{2 c}+\frac{a^{2} \ln \left(c x +1\right)}{2 c}+\frac{i b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{3}}{3 c}-\frac{b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{2 i b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{2 b^{2} \polylog \left(3, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2} \ln \left(1-\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{2 i b^{2} \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \polylog \left(2, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{2 b^{2} \polylog \left(3, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{i a b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{c}-\frac{2 a b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{2 i a b \polylog \left(2, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{2 a b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{2 i a b \polylog \left(2, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}"," ",0,"-1/2*a^2/c*ln(c*x-1)+1/2*a^2/c*ln(c*x+1)+1/3*I*b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^3-b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+2*I*b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-2*b^2/c*polylog(3,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2*ln(1-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))+2*I*b^2/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*polylog(2,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))-2*b^2/c*polylog(3,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+I*a*b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-2*a*b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+2*I*a*b/c*polylog(2,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-2*a*b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))+2*I*a*b/c*polylog(2,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))","B"
434,1,276,153,0.010000," ","int((a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x)","-\frac{a \ln \left(c x -1\right)}{2 c}+\frac{a \ln \left(c x +1\right)}{2 c}+\frac{i b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)^{2}}{2 c}-\frac{b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1+\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{i b \polylog \left(2, -\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}-\frac{b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right) \ln \left(1-\frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}-\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}+\frac{i b \polylog \left(2, \frac{i \sqrt{-c x +1}}{\sqrt{c x +1}}+\sqrt{1-\frac{-c x +1}{c x +1}}\right)}{c}"," ",0,"-1/2*a/c*ln(c*x-1)+1/2*a/c*ln(c*x+1)+1/2*I*b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))^2-b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1+I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))+I*b/c*polylog(2,-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))-b/c*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))*ln(1-I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)-(1-(-c*x+1)/(c*x+1))^(1/2))+I*b/c*polylog(2,I*(-c*x+1)^(1/2)/(c*x+1)^(1/2)+(1-(-c*x+1)/(c*x+1))^(1/2))","A"
435,0,0,38,0.345000," ","int(1/(-c^2*x^2+1)/(a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right) \left(a +b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x)","F"
436,0,0,38,0.329000," ","int(1/(-c^2*x^2+1)/(a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x)","\int \frac{1}{\left(-c^{2} x^{2}+1\right) \left(a +b \arcsin \left(\frac{\sqrt{-c x +1}}{\sqrt{c x +1}}\right)\right)^{2}}\, dx"," ",0,"int(1/(-c^2*x^2+1)/(a+b*arcsin((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x)","F"
437,1,18,17,0.009000," ","int(exp(x)*arcsin(exp(x)),x)","{\mathrm e}^{x} \arcsin \left({\mathrm e}^{x}\right)+\sqrt{1-{\mathrm e}^{2 x}}"," ",0,"exp(x)*arcsin(exp(x))+(-exp(x)^2+1)^(1/2)","A"
438,1,181,104,0.028000," ","int(arcsin(c*exp(b*x+a)),x)","-\frac{i \arcsin \left(c \,{\mathrm e}^{b x +a}\right)^{2}}{2 b}+\frac{\arcsin \left(c \,{\mathrm e}^{b x +a}\right) \ln \left(1+i c \,{\mathrm e}^{b x +a}+\sqrt{1-c^{2} {\mathrm e}^{2 b x +2 a}}\right)}{b}+\frac{\arcsin \left(c \,{\mathrm e}^{b x +a}\right) \ln \left(1-i c \,{\mathrm e}^{b x +a}-\sqrt{1-c^{2} {\mathrm e}^{2 b x +2 a}}\right)}{b}-\frac{i \polylog \left(2, -i c \,{\mathrm e}^{b x +a}-\sqrt{1-c^{2} {\mathrm e}^{2 b x +2 a}}\right)}{b}-\frac{i \polylog \left(2, i c \,{\mathrm e}^{b x +a}+\sqrt{1-c^{2} {\mathrm e}^{2 b x +2 a}}\right)}{b}"," ",0,"-1/2*I*arcsin(c*exp(b*x+a))^2/b+1/b*arcsin(c*exp(b*x+a))*ln(1+I*c*exp(b*x+a)+(1-c^2*exp(b*x+a)^2)^(1/2))+1/b*arcsin(c*exp(b*x+a))*ln(1-I*c*exp(b*x+a)-(1-c^2*exp(b*x+a)^2)^(1/2))-I/b*polylog(2,-I*c*exp(b*x+a)-(1-c^2*exp(b*x+a)^2)^(1/2))-I/b*polylog(2,I*c*exp(b*x+a)+(1-c^2*exp(b*x+a)^2)^(1/2))","A"
439,0,0,69,0.023000," ","int(exp(arcsin(a*x))*x^3,x)","\int {\mathrm e}^{\arcsin \left(a x \right)} x^{3}\, dx"," ",0,"int(exp(arcsin(a*x))*x^3,x)","F"
440,0,0,68,0.010000," ","int(exp(arcsin(a*x))*x^2,x)","\int {\mathrm e}^{\arcsin \left(a x \right)} x^{2}\, dx"," ",0,"int(exp(arcsin(a*x))*x^2,x)","F"
441,0,0,35,0.012000," ","int(exp(arcsin(a*x))*x,x)","\int {\mathrm e}^{\arcsin \left(a x \right)} x\, dx"," ",0,"int(exp(arcsin(a*x))*x,x)","F"
442,0,0,31,0.006000," ","int(exp(arcsin(a*x)),x)","\int {\mathrm e}^{\arcsin \left(a x \right)}\, dx"," ",0,"int(exp(arcsin(a*x)),x)","F"
443,0,0,46,0.011000," ","int(exp(arcsin(a*x))/x,x)","\int \frac{{\mathrm e}^{\arcsin \left(a x \right)}}{x}\, dx"," ",0,"int(exp(arcsin(a*x))/x,x)","F"
444,0,0,89,0.013000," ","int(exp(arcsin(a*x))/x^2,x)","\int \frac{{\mathrm e}^{\arcsin \left(a x \right)}}{x^{2}}\, dx"," ",0,"int(exp(arcsin(a*x))/x^2,x)","F"
445,0,0,75,0.010000," ","int(exp(arcsin(a*x)^2)*x^3,x)","\int {\mathrm e}^{\arcsin \left(a x \right)^{2}} x^{3}\, dx"," ",0,"int(exp(arcsin(a*x)^2)*x^3,x)","F"
446,0,0,73,0.009000," ","int(exp(arcsin(a*x)^2)*x^2,x)","\int {\mathrm e}^{\arcsin \left(a x \right)^{2}} x^{2}\, dx"," ",0,"int(exp(arcsin(a*x)^2)*x^2,x)","F"
447,0,0,37,0.009000," ","int(exp(arcsin(a*x)^2)*x,x)","\int {\mathrm e}^{\arcsin \left(a x \right)^{2}} x\, dx"," ",0,"int(exp(arcsin(a*x)^2)*x,x)","F"
448,0,0,37,0.005000," ","int(exp(arcsin(a*x)^2),x)","\int {\mathrm e}^{\arcsin \left(a x \right)^{2}}\, dx"," ",0,"int(exp(arcsin(a*x)^2),x)","F"
449,0,0,18,0.009000," ","int(exp(arcsin(a*x)^2)/x,x)","\int \frac{{\mathrm e}^{\arcsin \left(a x \right)^{2}}}{x}\, dx"," ",0,"int(exp(arcsin(a*x)^2)/x,x)","F"
450,0,0,20,0.009000," ","int(exp(arcsin(a*x)^2)/x^2,x)","\int \frac{{\mathrm e}^{\arcsin \left(a x \right)^{2}}}{x^{2}}\, dx"," ",0,"int(exp(arcsin(a*x)^2)/x^2,x)","F"
451,0,0,269,0.014000," ","int(exp(arcsin(b*x+a))*x^3,x)","\int {\mathrm e}^{\arcsin \left(b x +a \right)} x^{3}\, dx"," ",0,"int(exp(arcsin(b*x+a))*x^3,x)","F"
452,0,0,177,0.010000," ","int(exp(arcsin(b*x+a))*x^2,x)","\int {\mathrm e}^{\arcsin \left(b x +a \right)} x^{2}\, dx"," ",0,"int(exp(arcsin(b*x+a))*x^2,x)","F"
453,0,0,87,0.010000," ","int(exp(arcsin(b*x+a))*x,x)","\int {\mathrm e}^{\arcsin \left(b x +a \right)} x\, dx"," ",0,"int(exp(arcsin(b*x+a))*x,x)","F"
454,0,0,43,0.008000," ","int(exp(arcsin(b*x+a)),x)","\int {\mathrm e}^{\arcsin \left(b x +a \right)}\, dx"," ",0,"int(exp(arcsin(b*x+a)),x)","F"
455,0,0,18,0.010000," ","int(exp(arcsin(b*x+a))/x,x)","\int \frac{{\mathrm e}^{\arcsin \left(b x +a \right)}}{x}\, dx"," ",0,"int(exp(arcsin(b*x+a))/x,x)","F"
456,0,0,20,0.013000," ","int(exp(arcsin(b*x+a))/x^2,x)","\int \frac{{\mathrm e}^{\arcsin \left(b x +a \right)}}{x^{2}}\, dx"," ",0,"int(exp(arcsin(b*x+a))/x^2,x)","F"
457,0,0,259,0.011000," ","int(exp(arcsin(b*x+a)^2)*x^3,x)","\int {\mathrm e}^{\arcsin \left(b x +a \right)^{2}} x^{3}\, dx"," ",0,"int(exp(arcsin(b*x+a)^2)*x^3,x)","F"
458,0,0,169,0.010000," ","int(exp(arcsin(b*x+a)^2)*x^2,x)","\int {\mathrm e}^{\arcsin \left(b x +a \right)^{2}} x^{2}\, dx"," ",0,"int(exp(arcsin(b*x+a)^2)*x^2,x)","F"
459,0,0,83,0.008000," ","int(exp(arcsin(b*x+a)^2)*x,x)","\int {\mathrm e}^{\arcsin \left(b x +a \right)^{2}} x\, dx"," ",0,"int(exp(arcsin(b*x+a)^2)*x,x)","F"
460,0,0,41,0.006000," ","int(exp(arcsin(b*x+a)^2),x)","\int {\mathrm e}^{\arcsin \left(b x +a \right)^{2}}\, dx"," ",0,"int(exp(arcsin(b*x+a)^2),x)","F"
461,0,0,20,0.010000," ","int(exp(arcsin(b*x+a)^2)/x,x)","\int \frac{{\mathrm e}^{\arcsin \left(b x +a \right)^{2}}}{x}\, dx"," ",0,"int(exp(arcsin(b*x+a)^2)/x,x)","F"
462,0,0,22,0.012000," ","int(exp(arcsin(b*x+a)^2)/x^2,x)","\int \frac{{\mathrm e}^{\arcsin \left(b x +a \right)^{2}}}{x^{2}}\, dx"," ",0,"int(exp(arcsin(b*x+a)^2)/x^2,x)","F"
463,0,0,135,0.125000," ","int(exp(arcsin(a*x))*(-a^2*x^2+1)^(5/2),x)","\int {\mathrm e}^{\arcsin \left(a x \right)} \left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}\, dx"," ",0,"int(exp(arcsin(a*x))*(-a^2*x^2+1)^(5/2),x)","F"
464,0,0,93,0.164000," ","int(exp(arcsin(a*x))*(-a^2*x^2+1)^(3/2),x)","\int {\mathrm e}^{\arcsin \left(a x \right)} \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}\, dx"," ",0,"int(exp(arcsin(a*x))*(-a^2*x^2+1)^(3/2),x)","F"
465,0,0,51,0.119000," ","int(exp(arcsin(a*x))*(-a^2*x^2+1)^(1/2),x)","\int {\mathrm e}^{\arcsin \left(a x \right)} \sqrt{-a^{2} x^{2}+1}\, dx"," ",0,"int(exp(arcsin(a*x))*(-a^2*x^2+1)^(1/2),x)","F"
466,1,10,9,0.008000," ","int(exp(arcsin(a*x))/(-a^2*x^2+1)^(1/2),x)","\frac{{\mathrm e}^{\arcsin \left(a x \right)}}{a}"," ",0,"exp(arcsin(a*x))/a","A"
467,0,0,48,0.148000," ","int(exp(arcsin(a*x))/(-a^2*x^2+1)^(3/2),x)","\int \frac{{\mathrm e}^{\arcsin \left(a x \right)}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(exp(arcsin(a*x))/(-a^2*x^2+1)^(3/2),x)","F"
468,0,0,91,0.127000," ","int(exp(arcsin(a*x))/(-a^2*x^2+1)^(5/2),x)","\int \frac{{\mathrm e}^{\arcsin \left(a x \right)}}{\left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}\, dx"," ",0,"int(exp(arcsin(a*x))/(-a^2*x^2+1)^(5/2),x)","F"
469,1,47,45,0.021000," ","int(arcsin(c/(b*x+a)),x)","-\frac{c \left(-\frac{\arcsin \left(\frac{c}{b x +a}\right) \left(b x +a \right)}{c}-\arctanh \left(\frac{1}{\sqrt{1-\frac{c^{2}}{\left(b x +a \right)^{2}}}}\right)\right)}{b}"," ",0,"-1/b*c*(-arcsin(c/(b*x+a))/c*(b*x+a)-arctanh(1/(1-c^2/(b*x+a)^2)^(1/2)))","A"
470,0,0,25,0.197000," ","int(x/arcsin(sin(x)),x)","\int \frac{x}{\arcsin \left(\sin \left(x \right)\right)}\, dx"," ",0,"int(x/arcsin(sin(x)),x)","F"
471,0,0,34,0.355000," ","int(arcsin((b*x^2+1)^(1/2))^n/(b*x^2+1)^(1/2),x)","\int \frac{\arcsin \left(\sqrt{b \,x^{2}+1}\right)^{n}}{\sqrt{b \,x^{2}+1}}\, dx"," ",0,"int(arcsin((b*x^2+1)^(1/2))^n/(b*x^2+1)^(1/2),x)","F"
472,0,0,26,0.237000," ","int(1/arcsin((b*x^2+1)^(1/2))/(b*x^2+1)^(1/2),x)","\int \frac{1}{\arcsin \left(\sqrt{b \,x^{2}+1}\right) \sqrt{b \,x^{2}+1}}\, dx"," ",0,"int(1/arcsin((b*x^2+1)^(1/2))/(b*x^2+1)^(1/2),x)","F"
473,1,17,14,0.012000," ","int(x/(-x^2+1)+1/arcsin(x)/(-x^2+1)^(1/2),x)","-\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}+\ln \left(\arcsin \left(x \right)\right)"," ",0,"-1/2*ln(x-1)-1/2*ln(x+1)+ln(arcsin(x))","A"
474,1,17,14,0.009000," ","int((x*arcsin(x)+(-x^2+1)^(1/2))/(arcsin(x)-x^2*arcsin(x)),x)","-\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}+\ln \left(\arcsin \left(x \right)\right)"," ",0,"-1/2*ln(x-1)-1/2*ln(x+1)+ln(arcsin(x))","A"