1,1,316,0,1.365117," ","integrate((e*x+d)**3*(a+b*asin(c*x)),x)","\begin{cases} a d^{3} x + \frac{3 a d^{2} e x^{2}}{2} + a d e^{2} x^{3} + \frac{a e^{3} x^{4}}{4} + b d^{3} x \operatorname{asin}{\left(c x \right)} + \frac{3 b d^{2} e x^{2} \operatorname{asin}{\left(c x \right)}}{2} + b d e^{2} x^{3} \operatorname{asin}{\left(c x \right)} + \frac{b e^{3} x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b d^{3} \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{3 b d^{2} e x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d e^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{b e^{3} x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} - \frac{3 b d^{2} e \operatorname{asin}{\left(c x \right)}}{4 c^{2}} + \frac{2 b d e^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{3 b e^{3} x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} - \frac{3 b e^{3} \operatorname{asin}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\a \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*x + 3*a*d**2*e*x**2/2 + a*d*e**2*x**3 + a*e**3*x**4/4 + b*d**3*x*asin(c*x) + 3*b*d**2*e*x**2*asin(c*x)/2 + b*d*e**2*x**3*asin(c*x) + b*e**3*x**4*asin(c*x)/4 + b*d**3*sqrt(-c**2*x**2 + 1)/c + 3*b*d**2*e*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d*e**2*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + b*e**3*x**3*sqrt(-c**2*x**2 + 1)/(16*c) - 3*b*d**2*e*asin(c*x)/(4*c**2) + 2*b*d*e**2*sqrt(-c**2*x**2 + 1)/(3*c**3) + 3*b*e**3*x*sqrt(-c**2*x**2 + 1)/(32*c**3) - 3*b*e**3*asin(c*x)/(32*c**4), Ne(c, 0)), (a*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4), True))","A",0
2,1,190,0,0.633185," ","integrate((e*x+d)**2*(a+b*asin(c*x)),x)","\begin{cases} a d^{2} x + a d e x^{2} + \frac{a e^{2} x^{3}}{3} + b d^{2} x \operatorname{asin}{\left(c x \right)} + b d e x^{2} \operatorname{asin}{\left(c x \right)} + \frac{b e^{2} x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b d^{2} \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d e x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{b e^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} - \frac{b d e \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + \frac{2 b e^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} & \text{for}\: c \neq 0 \\a \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*x + a*d*e*x**2 + a*e**2*x**3/3 + b*d**2*x*asin(c*x) + b*d*e*x**2*asin(c*x) + b*e**2*x**3*asin(c*x)/3 + b*d**2*sqrt(-c**2*x**2 + 1)/c + b*d*e*x*sqrt(-c**2*x**2 + 1)/(2*c) + b*e**2*x**2*sqrt(-c**2*x**2 + 1)/(9*c) - b*d*e*asin(c*x)/(2*c**2) + 2*b*e**2*sqrt(-c**2*x**2 + 1)/(9*c**3), Ne(c, 0)), (a*(d**2*x + d*e*x**2 + e**2*x**3/3), True))","A",0
3,1,99,0,0.279471," ","integrate((e*x+d)*(a+b*asin(c*x)),x)","\begin{cases} a d x + \frac{a e x^{2}}{2} + b d x \operatorname{asin}{\left(c x \right)} + \frac{b e x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b d \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b e x \sqrt{- c^{2} x^{2} + 1}}{4 c} - \frac{b e \operatorname{asin}{\left(c x \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\a \left(d x + \frac{e x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*x + a*e*x**2/2 + b*d*x*asin(c*x) + b*e*x**2*asin(c*x)/2 + b*d*sqrt(-c**2*x**2 + 1)/c + b*e*x*sqrt(-c**2*x**2 + 1)/(4*c) - b*e*asin(c*x)/(4*c**2), Ne(c, 0)), (a*(d*x + e*x**2/2), True))","A",0
4,1,26,0,0.124270," ","integrate(a+b*asin(c*x),x)","a x + b \left(\begin{cases} x \operatorname{asin}{\left(c x \right)} + \frac{\sqrt{- c^{2} x^{2} + 1}}{c} & \text{for}\: c \neq 0 \\0 & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((x*asin(c*x) + sqrt(-c**2*x**2 + 1)/c, Ne(c, 0)), (0, True))","A",0
5,0,0,0,0.000000," ","integrate((a+b*asin(c*x))/(e*x+d),x)","\int \frac{a + b \operatorname{asin}{\left(c x \right)}}{d + e x}\, dx"," ",0,"Integral((a + b*asin(c*x))/(d + e*x), x)","F",0
6,0,0,0,0.000000," ","integrate((a+b*asin(c*x))/(e*x+d)**2,x)","\int \frac{a + b \operatorname{asin}{\left(c x \right)}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))/(d + e*x)**2, x)","F",0
7,0,0,0,0.000000," ","integrate((a+b*asin(c*x))/(e*x+d)**3,x)","\int \frac{a + b \operatorname{asin}{\left(c x \right)}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(c*x))/(d + e*x)**3, x)","F",0
8,0,0,0,0.000000," ","integrate((a+b*asin(c*x))/(e*x+d)**4,x)","\int \frac{a + b \operatorname{asin}{\left(c x \right)}}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*asin(c*x))/(d + e*x)**4, x)","F",0
9,1,743,0,3.492710," ","integrate((e*x+d)**3*(a+b*asin(c*x))**2,x)","\begin{cases} a^{2} d^{3} x + \frac{3 a^{2} d^{2} e x^{2}}{2} + a^{2} d e^{2} x^{3} + \frac{a^{2} e^{3} x^{4}}{4} + 2 a b d^{3} x \operatorname{asin}{\left(c x \right)} + 3 a b d^{2} e x^{2} \operatorname{asin}{\left(c x \right)} + 2 a b d e^{2} x^{3} \operatorname{asin}{\left(c x \right)} + \frac{a b e^{3} x^{4} \operatorname{asin}{\left(c x \right)}}{2} + \frac{2 a b d^{3} \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{3 a b d^{2} e x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{2 a b d e^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{a b e^{3} x^{3} \sqrt{- c^{2} x^{2} + 1}}{8 c} - \frac{3 a b d^{2} e \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + \frac{4 a b d e^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{3 a b e^{3} x \sqrt{- c^{2} x^{2} + 1}}{16 c^{3}} - \frac{3 a b e^{3} \operatorname{asin}{\left(c x \right)}}{16 c^{4}} + b^{2} d^{3} x \operatorname{asin}^{2}{\left(c x \right)} - 2 b^{2} d^{3} x + \frac{3 b^{2} d^{2} e x^{2} \operatorname{asin}^{2}{\left(c x \right)}}{2} - \frac{3 b^{2} d^{2} e x^{2}}{4} + b^{2} d e^{2} x^{3} \operatorname{asin}^{2}{\left(c x \right)} - \frac{2 b^{2} d e^{2} x^{3}}{9} + \frac{b^{2} e^{3} x^{4} \operatorname{asin}^{2}{\left(c x \right)}}{4} - \frac{b^{2} e^{3} x^{4}}{32} + \frac{2 b^{2} d^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} + \frac{3 b^{2} d^{2} e x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{2 c} + \frac{2 b^{2} d e^{2} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{3 c} + \frac{b^{2} e^{3} x^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{8 c} - \frac{3 b^{2} d^{2} e \operatorname{asin}^{2}{\left(c x \right)}}{4 c^{2}} - \frac{4 b^{2} d e^{2} x}{3 c^{2}} - \frac{3 b^{2} e^{3} x^{2}}{32 c^{2}} + \frac{4 b^{2} d e^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{3 c^{3}} + \frac{3 b^{2} e^{3} x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{16 c^{3}} - \frac{3 b^{2} e^{3} \operatorname{asin}^{2}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\a^{2} \left(d^{3} x + \frac{3 d^{2} e x^{2}}{2} + d e^{2} x^{3} + \frac{e^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**3*x + 3*a**2*d**2*e*x**2/2 + a**2*d*e**2*x**3 + a**2*e**3*x**4/4 + 2*a*b*d**3*x*asin(c*x) + 3*a*b*d**2*e*x**2*asin(c*x) + 2*a*b*d*e**2*x**3*asin(c*x) + a*b*e**3*x**4*asin(c*x)/2 + 2*a*b*d**3*sqrt(-c**2*x**2 + 1)/c + 3*a*b*d**2*e*x*sqrt(-c**2*x**2 + 1)/(2*c) + 2*a*b*d*e**2*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + a*b*e**3*x**3*sqrt(-c**2*x**2 + 1)/(8*c) - 3*a*b*d**2*e*asin(c*x)/(2*c**2) + 4*a*b*d*e**2*sqrt(-c**2*x**2 + 1)/(3*c**3) + 3*a*b*e**3*x*sqrt(-c**2*x**2 + 1)/(16*c**3) - 3*a*b*e**3*asin(c*x)/(16*c**4) + b**2*d**3*x*asin(c*x)**2 - 2*b**2*d**3*x + 3*b**2*d**2*e*x**2*asin(c*x)**2/2 - 3*b**2*d**2*e*x**2/4 + b**2*d*e**2*x**3*asin(c*x)**2 - 2*b**2*d*e**2*x**3/9 + b**2*e**3*x**4*asin(c*x)**2/4 - b**2*e**3*x**4/32 + 2*b**2*d**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/c + 3*b**2*d**2*e*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(2*c) + 2*b**2*d*e**2*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(3*c) + b**2*e**3*x**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(8*c) - 3*b**2*d**2*e*asin(c*x)**2/(4*c**2) - 4*b**2*d*e**2*x/(3*c**2) - 3*b**2*e**3*x**2/(32*c**2) + 4*b**2*d*e**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(3*c**3) + 3*b**2*e**3*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(16*c**3) - 3*b**2*e**3*asin(c*x)**2/(32*c**4), Ne(c, 0)), (a**2*(d**3*x + 3*d**2*e*x**2/2 + d*e**2*x**3 + e**3*x**4/4), True))","A",0
10,1,454,0,1.572286," ","integrate((e*x+d)**2*(a+b*asin(c*x))**2,x)","\begin{cases} a^{2} d^{2} x + a^{2} d e x^{2} + \frac{a^{2} e^{2} x^{3}}{3} + 2 a b d^{2} x \operatorname{asin}{\left(c x \right)} + 2 a b d e x^{2} \operatorname{asin}{\left(c x \right)} + \frac{2 a b e^{2} x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{2 a b d^{2} \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{a b d e x \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{2 a b e^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} - \frac{a b d e \operatorname{asin}{\left(c x \right)}}{c^{2}} + \frac{4 a b e^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + b^{2} d^{2} x \operatorname{asin}^{2}{\left(c x \right)} - 2 b^{2} d^{2} x + b^{2} d e x^{2} \operatorname{asin}^{2}{\left(c x \right)} - \frac{b^{2} d e x^{2}}{2} + \frac{b^{2} e^{2} x^{3} \operatorname{asin}^{2}{\left(c x \right)}}{3} - \frac{2 b^{2} e^{2} x^{3}}{27} + \frac{2 b^{2} d^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} + \frac{b^{2} d e x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} + \frac{2 b^{2} e^{2} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c} - \frac{b^{2} d e \operatorname{asin}^{2}{\left(c x \right)}}{2 c^{2}} - \frac{4 b^{2} e^{2} x}{9 c^{2}} + \frac{4 b^{2} e^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c^{3}} & \text{for}\: c \neq 0 \\a^{2} \left(d^{2} x + d e x^{2} + \frac{e^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d**2*x + a**2*d*e*x**2 + a**2*e**2*x**3/3 + 2*a*b*d**2*x*asin(c*x) + 2*a*b*d*e*x**2*asin(c*x) + 2*a*b*e**2*x**3*asin(c*x)/3 + 2*a*b*d**2*sqrt(-c**2*x**2 + 1)/c + a*b*d*e*x*sqrt(-c**2*x**2 + 1)/c + 2*a*b*e**2*x**2*sqrt(-c**2*x**2 + 1)/(9*c) - a*b*d*e*asin(c*x)/c**2 + 4*a*b*e**2*sqrt(-c**2*x**2 + 1)/(9*c**3) + b**2*d**2*x*asin(c*x)**2 - 2*b**2*d**2*x + b**2*d*e*x**2*asin(c*x)**2 - b**2*d*e*x**2/2 + b**2*e**2*x**3*asin(c*x)**2/3 - 2*b**2*e**2*x**3/27 + 2*b**2*d**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/c + b**2*d*e*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/c + 2*b**2*e**2*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c) - b**2*d*e*asin(c*x)**2/(2*c**2) - 4*b**2*e**2*x/(9*c**2) + 4*b**2*e**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c**3), Ne(c, 0)), (a**2*(d**2*x + d*e*x**2 + e**2*x**3/3), True))","A",0
11,1,233,0,0.672858," ","integrate((e*x+d)*(a+b*asin(c*x))**2,x)","\begin{cases} a^{2} d x + \frac{a^{2} e x^{2}}{2} + 2 a b d x \operatorname{asin}{\left(c x \right)} + a b e x^{2} \operatorname{asin}{\left(c x \right)} + \frac{2 a b d \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{a b e x \sqrt{- c^{2} x^{2} + 1}}{2 c} - \frac{a b e \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + b^{2} d x \operatorname{asin}^{2}{\left(c x \right)} - 2 b^{2} d x + \frac{b^{2} e x^{2} \operatorname{asin}^{2}{\left(c x \right)}}{2} - \frac{b^{2} e x^{2}}{4} + \frac{2 b^{2} d \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} + \frac{b^{2} e x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{2 c} - \frac{b^{2} e \operatorname{asin}^{2}{\left(c x \right)}}{4 c^{2}} & \text{for}\: c \neq 0 \\a^{2} \left(d x + \frac{e x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*x + a**2*e*x**2/2 + 2*a*b*d*x*asin(c*x) + a*b*e*x**2*asin(c*x) + 2*a*b*d*sqrt(-c**2*x**2 + 1)/c + a*b*e*x*sqrt(-c**2*x**2 + 1)/(2*c) - a*b*e*asin(c*x)/(2*c**2) + b**2*d*x*asin(c*x)**2 - 2*b**2*d*x + b**2*e*x**2*asin(c*x)**2/2 - b**2*e*x**2/4 + 2*b**2*d*sqrt(-c**2*x**2 + 1)*asin(c*x)/c + b**2*e*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(2*c) - b**2*e*asin(c*x)**2/(4*c**2), Ne(c, 0)), (a**2*(d*x + e*x**2/2), True))","A",0
12,1,82,0,0.256366," ","integrate((a+b*asin(c*x))**2,x)","\begin{cases} a^{2} x + 2 a b x \operatorname{asin}{\left(c x \right)} + \frac{2 a b \sqrt{- c^{2} x^{2} + 1}}{c} + b^{2} x \operatorname{asin}^{2}{\left(c x \right)} - 2 b^{2} x + \frac{2 b^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} & \text{for}\: c \neq 0 \\a^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*x*asin(c*x) + 2*a*b*sqrt(-c**2*x**2 + 1)/c + b**2*x*asin(c*x)**2 - 2*b**2*x + 2*b**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/c, Ne(c, 0)), (a**2*x, True))","A",0
13,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**2/(e*x+d),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}{d + e x}\, dx"," ",0,"Integral((a + b*asin(c*x))**2/(d + e*x), x)","F",0
14,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**2/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2/(d + e*x)**2, x)","F",0
15,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**2/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2/(d + e*x)**3, x)","F",0
16,0,0,0,0.000000," ","integrate((e*x+d)**3/(a+b*asin(c*x)),x)","\int \frac{\left(d + e x\right)^{3}}{a + b \operatorname{asin}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**3/(a + b*asin(c*x)), x)","F",0
17,0,0,0,0.000000," ","integrate((e*x+d)**2/(a+b*asin(c*x)),x)","\int \frac{\left(d + e x\right)^{2}}{a + b \operatorname{asin}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*asin(c*x)), x)","F",0
18,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*asin(c*x)),x)","\int \frac{d + e x}{a + b \operatorname{asin}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)/(a + b*asin(c*x)), x)","F",0
19,0,0,0,0.000000," ","integrate(1/(a+b*asin(c*x)),x)","\int \frac{1}{a + b \operatorname{asin}{\left(c x \right)}}\, dx"," ",0,"Integral(1/(a + b*asin(c*x)), x)","F",0
20,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*asin(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*asin(c*x))*(d + e*x)), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a+b*asin(c*x)),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*asin(c*x))*(d + e*x)**2), x)","F",0
22,0,0,0,0.000000," ","integrate((e*x+d)**2/(a+b*asin(c*x))**2,x)","\int \frac{\left(d + e x\right)^{2}}{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**2/(a + b*asin(c*x))**2, x)","F",0
23,0,0,0,0.000000," ","integrate((e*x+d)/(a+b*asin(c*x))**2,x)","\int \frac{d + e x}{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)/(a + b*asin(c*x))**2, x)","F",0
24,0,0,0,0.000000," ","integrate(1/(a+b*asin(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))**(-2), x)","F",0
25,0,0,0,0.000000," ","integrate(1/(e*x+d)/(a+b*asin(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(d + e x\right)}\, dx"," ",0,"Integral(1/((a + b*asin(c*x))**2*(d + e*x)), x)","F",0
26,0,0,0,0.000000," ","integrate(1/(e*x+d)**2/(a+b*asin(c*x))**2,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*asin(c*x))**2*(d + e*x)**2), x)","F",0
27,0,0,0,0.000000," ","integrate((e*x+d)**m*(a+b*asin(c*x))**2,x)","\int \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(d + e x\right)^{m}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(d + e*x)**m, x)","F",0
28,0,0,0,0.000000," ","integrate((e*x+d)**m*(a+b*asin(c*x)),x)","\int \left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(d + e x\right)^{m}\, dx"," ",0,"Integral((a + b*asin(c*x))*(d + e*x)**m, x)","F",0
29,0,0,0,0.000000," ","integrate((e*x+d)**m/(a+b*asin(c*x)),x)","\int \frac{\left(d + e x\right)^{m}}{a + b \operatorname{asin}{\left(c x \right)}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*asin(c*x)), x)","F",0
30,0,0,0,0.000000," ","integrate((e*x+d)**m/(a+b*asin(c*x))**2,x)","\int \frac{\left(d + e x\right)^{m}}{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}\, dx"," ",0,"Integral((d + e*x)**m/(a + b*asin(c*x))**2, x)","F",0
31,0,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asin(c*x))*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)^{3}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))*(f + g*x)**3, x)","F",0
32,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)^{2}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))*(f + g*x)**2, x)","F",0
33,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))*(f + g*x), x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*asin(c*x))*(-c**2*d*x**2+d)**(1/2)/(g*x+f),x)","\int \frac{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))/(f + g*x), x)","F",0
35,0,0,0,0.000000," ","integrate((a+b*asin(c*x))*(-c**2*d*x**2+d)**(1/2)/(g*x+f)**2,x)","\int \frac{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right)}{\left(f + g x\right)^{2}}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))/(f + g*x)**2, x)","F",0
36,0,0,0,0.000000," ","integrate((g*x+f)**3*(-c**2*d*x**2+d)**(3/2)*(a+b*asin(c*x)),x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)^{3}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*asin(c*x))*(f + g*x)**3, x)","F",0
37,0,0,0,0.000000," ","integrate((g*x+f)**2*(-c**2*d*x**2+d)**(3/2)*(a+b*asin(c*x)),x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)^{2}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*asin(c*x))*(f + g*x)**2, x)","F",0
38,0,0,0,0.000000," ","integrate((g*x+f)*(-c**2*d*x**2+d)**(3/2)*(a+b*asin(c*x)),x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*asin(c*x))*(f + g*x), x)","F",0
39,0,0,0,0.000000," ","integrate((-c**2*d*x**2+d)**(3/2)*(a+b*asin(c*x))/(g*x+f),x)","\int \frac{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*asin(c*x))/(f + g*x), x)","F",0
40,-1,0,0,0.000000," ","integrate((g*x+f)**3*(-c**2*d*x**2+d)**(5/2)*(a+b*asin(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate((g*x+f)**2*(-c**2*d*x**2+d)**(5/2)*(a+b*asin(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate((g*x+f)*(-c**2*d*x**2+d)**(5/2)*(a+b*asin(c*x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,0,0,0,0.000000," ","integrate((-c**2*d*x**2+d)**(5/2)*(a+b*asin(c*x))/(g*x+f),x)","\int \frac{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{5}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right)}{f + g x}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(5/2)*(a + b*asin(c*x))/(f + g*x), x)","F",0
44,-2,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
45,-2,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
46,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
47,0,0,0,0.000000," ","integrate((a+b*asin(c*x))/(g*x+f)/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asin}{\left(c x \right)}}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*asin(c*x))/(sqrt(-d*(c*x - 1)*(c*x + 1))*(f + g*x)), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*asin(c*x))/(g*x+f)**2/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{a + b \operatorname{asin}{\left(c x \right)}}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))/(sqrt(-d*(c*x - 1)*(c*x + 1))*(f + g*x)**2), x)","F",0
49,-2,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
50,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)^{2}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)**2/(-d*(c*x - 1)*(c*x + 1))**(3/2), x)","F",0
51,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)/(-d*(c*x - 1)*(c*x + 1))**(3/2), x)","F",0
52,0,0,0,0.000000," ","integrate((a+b*asin(c*x))/(g*x+f)/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{a + b \operatorname{asin}{\left(c x \right)}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*asin(c*x))/((-d*(c*x - 1)*(c*x + 1))**(3/2)*(f + g*x)), x)","F",0
53,-2,0,0,0.000000," ","integrate((g*x+f)**4*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
54,-2,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
55,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)^{2}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)**2/(-d*(c*x - 1)*(c*x + 1))**(5/2), x)","F",0
56,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(-c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)/(-d*(c*x - 1)*(c*x + 1))**(5/2), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*asin(c*x))/(g*x+f)/(-c**2*d*x**2+d)**(5/2),x)","\int \frac{a + b \operatorname{asin}{\left(c x \right)}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{5}{2}} \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*asin(c*x))/((-d*(c*x - 1)*(c*x + 1))**(5/2)*(f + g*x)), x)","F",0
58,0,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asin(c*x))**2*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)^{3}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))**2*(f + g*x)**3, x)","F",0
59,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))**2*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)^{2}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))**2*(f + g*x)**2, x)","F",0
60,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))**2*(-c**2*d*x**2+d)**(1/2),x)","\int \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))**2*(f + g*x), x)","F",0
61,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**2*(-c**2*d*x**2+d)**(1/2)/(g*x+f),x)","\int \frac{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}{f + g x}\, dx"," ",0,"Integral(sqrt(-d*(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))**2/(f + g*x), x)","F",0
62,0,0,0,0.000000," ","integrate((g*x+f)**3*(-c**2*d*x**2+d)**(3/2)*(a+b*asin(c*x))**2,x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)^{3}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*asin(c*x))**2*(f + g*x)**3, x)","F",0
63,0,0,0,0.000000," ","integrate((g*x+f)**2*(-c**2*d*x**2+d)**(3/2)*(a+b*asin(c*x))**2,x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)^{2}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*asin(c*x))**2*(f + g*x)**2, x)","F",0
64,0,0,0,0.000000," ","integrate((g*x+f)*(-c**2*d*x**2+d)**(3/2)*(a+b*asin(c*x))**2,x)","\int \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*asin(c*x))**2*(f + g*x), x)","F",0
65,0,0,0,0.000000," ","integrate((-c**2*d*x**2+d)**(3/2)*(a+b*asin(c*x))**2/(g*x+f),x)","\int \frac{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}{f + g x}\, dx"," ",0,"Integral((-d*(c*x - 1)*(c*x + 1))**(3/2)*(a + b*asin(c*x))**2/(f + g*x), x)","F",0
66,-1,0,0,0.000000," ","integrate((g*x+f)**3*(-c**2*d*x**2+d)**(5/2)*(a+b*asin(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-1,0,0,0.000000," ","integrate((g*x+f)**2*(-c**2*d*x**2+d)**(5/2)*(a+b*asin(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate((g*x+f)*(-c**2*d*x**2+d)**(5/2)*(a+b*asin(c*x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate((-c**2*d*x**2+d)**(5/2)*(a+b*asin(c*x))**2/(g*x+f),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-2,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
71,-2,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
72,-2,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
73,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**2/(g*x+f)/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*asin(c*x))**2/(sqrt(-d*(c*x - 1)*(c*x + 1))*(f + g*x)), x)","F",0
74,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**2/(g*x+f)**2/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}{\sqrt{- d \left(c x - 1\right) \left(c x + 1\right)} \left(f + g x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2/(sqrt(-d*(c*x - 1)*(c*x + 1))*(f + g*x)**2), x)","F",0
75,-2,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(3/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
76,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)^{2}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(f + g*x)**2/(-d*(c*x - 1)*(c*x + 1))**(3/2), x)","F",0
77,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(f + g*x)/(-d*(c*x - 1)*(c*x + 1))**(3/2), x)","F",0
78,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**2/(g*x+f)/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \left(f + g x\right)}\, dx"," ",0,"Integral((a + b*asin(c*x))**2/((-d*(c*x - 1)*(c*x + 1))**(3/2)*(f + g*x)), x)","F",0
79,-2,0,0,0.000000," ","integrate((g*x+f)**3*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(5/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
80,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)^{2}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(f + g*x)**2/(-d*(c*x - 1)*(c*x + 1))**(5/2), x)","F",0
81,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))**2/(-c**2*d*x**2+d)**(5/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(f + g*x)/(-d*(c*x - 1)*(c*x + 1))**(5/2), x)","F",0
82,-1,0,0,0.000000," ","integrate((a+b*asin(c*x))**n*ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**3*ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{3} \log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*asin(c*x))**3*log(h*(f + g*x)**m)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
84,0,0,0,0.000000," ","integrate((a+b*asin(c*x))**2*ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*log(h*(f + g*x)**m)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
85,0,0,0,0.000000," ","integrate((a+b*asin(c*x))*ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral((a + b*asin(c*x))*log(h*(f + g*x)**m)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
86,0,0,0,0.000000," ","integrate(ln(h*(g*x+f)**m)/(-c**2*x**2+1)**(1/2),x)","\int \frac{\log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral(log(h*(f + g*x)**m)/sqrt(-(c*x - 1)*(c*x + 1)), x)","F",0
87,0,0,0,0.000000," ","integrate(ln(h*(g*x+f)**m)/(a+b*asin(c*x))/(-c**2*x**2+1)**(1/2),x)","\int \frac{\log{\left(h \left(f + g x\right)^{m} \right)}}{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)} \left(a + b \operatorname{asin}{\left(c x \right)}\right)}\, dx"," ",0,"Integral(log(h*(f + g*x)**m)/(sqrt(-(c*x - 1)*(c*x + 1))*(a + b*asin(c*x))), x)","F",0
88,1,770,0,3.653808," ","integrate((e*x+d)**3*(g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d^{3} f x + \frac{a d^{3} g x^{2}}{2} + \frac{3 a d^{2} e f x^{2}}{2} + a d^{2} e g x^{3} + a d e^{2} f x^{3} + \frac{3 a d e^{2} g x^{4}}{4} + \frac{a e^{3} f x^{4}}{4} + \frac{a e^{3} g x^{5}}{5} + b d^{3} f x \operatorname{asin}{\left(c x \right)} + \frac{b d^{3} g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{3 b d^{2} e f x^{2} \operatorname{asin}{\left(c x \right)}}{2} + b d^{2} e g x^{3} \operatorname{asin}{\left(c x \right)} + b d e^{2} f x^{3} \operatorname{asin}{\left(c x \right)} + \frac{3 b d e^{2} g x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b e^{3} f x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b e^{3} g x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b d^{3} f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d^{3} g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{3 b d^{2} e f x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d^{2} e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{b d e^{2} f x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{3 b d e^{2} g x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b e^{3} f x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b e^{3} g x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} - \frac{b d^{3} g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{3 b d^{2} e f \operatorname{asin}{\left(c x \right)}}{4 c^{2}} + \frac{2 b d^{2} e g \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{2 b d e^{2} f \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{9 b d e^{2} g x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{3 b e^{3} f x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b e^{3} g x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} - \frac{9 b d e^{2} g \operatorname{asin}{\left(c x \right)}}{32 c^{4}} - \frac{3 b e^{3} f \operatorname{asin}{\left(c x \right)}}{32 c^{4}} + \frac{8 b e^{3} g \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} & \text{for}\: c \neq 0 \\a \left(d^{3} f x + \frac{d^{3} g x^{2}}{2} + \frac{3 d^{2} e f x^{2}}{2} + d^{2} e g x^{3} + d e^{2} f x^{3} + \frac{3 d e^{2} g x^{4}}{4} + \frac{e^{3} f x^{4}}{4} + \frac{e^{3} g x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*f*x + a*d**3*g*x**2/2 + 3*a*d**2*e*f*x**2/2 + a*d**2*e*g*x**3 + a*d*e**2*f*x**3 + 3*a*d*e**2*g*x**4/4 + a*e**3*f*x**4/4 + a*e**3*g*x**5/5 + b*d**3*f*x*asin(c*x) + b*d**3*g*x**2*asin(c*x)/2 + 3*b*d**2*e*f*x**2*asin(c*x)/2 + b*d**2*e*g*x**3*asin(c*x) + b*d*e**2*f*x**3*asin(c*x) + 3*b*d*e**2*g*x**4*asin(c*x)/4 + b*e**3*f*x**4*asin(c*x)/4 + b*e**3*g*x**5*asin(c*x)/5 + b*d**3*f*sqrt(-c**2*x**2 + 1)/c + b*d**3*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + 3*b*d**2*e*f*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d**2*e*g*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + b*d*e**2*f*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 3*b*d*e**2*g*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*e**3*f*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*e**3*g*x**4*sqrt(-c**2*x**2 + 1)/(25*c) - b*d**3*g*asin(c*x)/(4*c**2) - 3*b*d**2*e*f*asin(c*x)/(4*c**2) + 2*b*d**2*e*g*sqrt(-c**2*x**2 + 1)/(3*c**3) + 2*b*d*e**2*f*sqrt(-c**2*x**2 + 1)/(3*c**3) + 9*b*d*e**2*g*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 3*b*e**3*f*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*e**3*g*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) - 9*b*d*e**2*g*asin(c*x)/(32*c**4) - 3*b*e**3*f*asin(c*x)/(32*c**4) + 8*b*e**3*g*sqrt(-c**2*x**2 + 1)/(75*c**5), Ne(c, 0)), (a*(d**3*f*x + d**3*g*x**2/2 + 3*d**2*e*f*x**2/2 + d**2*e*g*x**3 + d*e**2*f*x**3 + 3*d*e**2*g*x**4/4 + e**3*f*x**4/4 + e**3*g*x**5/5), True))","A",0
89,1,502,0,1.762413," ","integrate((e*x+d)**2*(g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d^{2} f x + \frac{a d^{2} g x^{2}}{2} + a d e f x^{2} + \frac{2 a d e g x^{3}}{3} + \frac{a e^{2} f x^{3}}{3} + \frac{a e^{2} g x^{4}}{4} + b d^{2} f x \operatorname{asin}{\left(c x \right)} + \frac{b d^{2} g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + b d e f x^{2} \operatorname{asin}{\left(c x \right)} + \frac{2 b d e g x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b e^{2} f x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b e^{2} g x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b d^{2} f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d^{2} g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d e f x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{2 b d e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b e^{2} f x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b e^{2} g x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} - \frac{b d^{2} g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{b d e f \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + \frac{4 b d e g \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{2 b e^{2} f \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b e^{2} g x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} - \frac{3 b e^{2} g \operatorname{asin}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\a \left(d^{2} f x + \frac{d^{2} g x^{2}}{2} + d e f x^{2} + \frac{2 d e g x^{3}}{3} + \frac{e^{2} f x^{3}}{3} + \frac{e^{2} g x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*f*x + a*d**2*g*x**2/2 + a*d*e*f*x**2 + 2*a*d*e*g*x**3/3 + a*e**2*f*x**3/3 + a*e**2*g*x**4/4 + b*d**2*f*x*asin(c*x) + b*d**2*g*x**2*asin(c*x)/2 + b*d*e*f*x**2*asin(c*x) + 2*b*d*e*g*x**3*asin(c*x)/3 + b*e**2*f*x**3*asin(c*x)/3 + b*e**2*g*x**4*asin(c*x)/4 + b*d**2*f*sqrt(-c**2*x**2 + 1)/c + b*d**2*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d*e*f*x*sqrt(-c**2*x**2 + 1)/(2*c) + 2*b*d*e*g*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*e**2*f*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*e**2*g*x**3*sqrt(-c**2*x**2 + 1)/(16*c) - b*d**2*g*asin(c*x)/(4*c**2) - b*d*e*f*asin(c*x)/(2*c**2) + 4*b*d*e*g*sqrt(-c**2*x**2 + 1)/(9*c**3) + 2*b*e**2*f*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*e**2*g*x*sqrt(-c**2*x**2 + 1)/(32*c**3) - 3*b*e**2*g*asin(c*x)/(32*c**4), Ne(c, 0)), (a*(d**2*f*x + d**2*g*x**2/2 + d*e*f*x**2 + 2*d*e*g*x**3/3 + e**2*f*x**3/3 + e**2*g*x**4/4), True))","A",0
90,1,267,0,0.772192," ","integrate((e*x+d)*(g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d f x + \frac{a d g x^{2}}{2} + \frac{a e f x^{2}}{2} + \frac{a e g x^{3}}{3} + b d f x \operatorname{asin}{\left(c x \right)} + \frac{b d g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b e f x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b e g x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b d f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b e f x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} - \frac{b d g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{b e f \operatorname{asin}{\left(c x \right)}}{4 c^{2}} + \frac{2 b e g \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} & \text{for}\: c \neq 0 \\a \left(d f x + \frac{d g x^{2}}{2} + \frac{e f x^{2}}{2} + \frac{e g x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*f*x + a*d*g*x**2/2 + a*e*f*x**2/2 + a*e*g*x**3/3 + b*d*f*x*asin(c*x) + b*d*g*x**2*asin(c*x)/2 + b*e*f*x**2*asin(c*x)/2 + b*e*g*x**3*asin(c*x)/3 + b*d*f*sqrt(-c**2*x**2 + 1)/c + b*d*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*e*f*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*e*g*x**2*sqrt(-c**2*x**2 + 1)/(9*c) - b*d*g*asin(c*x)/(4*c**2) - b*e*f*asin(c*x)/(4*c**2) + 2*b*e*g*sqrt(-c**2*x**2 + 1)/(9*c**3), Ne(c, 0)), (a*(d*f*x + d*g*x**2/2 + e*f*x**2/2 + e*g*x**3/3), True))","A",0
91,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(e*x+d),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)}{d + e x}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)/(d + e*x), x)","F",0
92,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)/(d + e*x)**2, x)","F",0
93,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)/(d + e*x)**3, x)","F",0
94,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(e*x+d)**4,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)/(d + e*x)**4, x)","F",0
95,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(e*x+d)**5,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)/(d + e*x)**5, x)","F",0
96,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))/(e*x+d)**6,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x\right)}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x)/(d + e*x)**6, x)","F",0
97,1,1263,0,7.170078," ","integrate((e*x+d)**3*(h*x**2+g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d^{3} f x + \frac{a d^{3} g x^{2}}{2} + \frac{a d^{3} h x^{3}}{3} + \frac{3 a d^{2} e f x^{2}}{2} + a d^{2} e g x^{3} + \frac{3 a d^{2} e h x^{4}}{4} + a d e^{2} f x^{3} + \frac{3 a d e^{2} g x^{4}}{4} + \frac{3 a d e^{2} h x^{5}}{5} + \frac{a e^{3} f x^{4}}{4} + \frac{a e^{3} g x^{5}}{5} + \frac{a e^{3} h x^{6}}{6} + b d^{3} f x \operatorname{asin}{\left(c x \right)} + \frac{b d^{3} g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b d^{3} h x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{3 b d^{2} e f x^{2} \operatorname{asin}{\left(c x \right)}}{2} + b d^{2} e g x^{3} \operatorname{asin}{\left(c x \right)} + \frac{3 b d^{2} e h x^{4} \operatorname{asin}{\left(c x \right)}}{4} + b d e^{2} f x^{3} \operatorname{asin}{\left(c x \right)} + \frac{3 b d e^{2} g x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{3 b d e^{2} h x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b e^{3} f x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b e^{3} g x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b e^{3} h x^{6} \operatorname{asin}{\left(c x \right)}}{6} + \frac{b d^{3} f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d^{3} g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d^{3} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{3 b d^{2} e f x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d^{2} e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{3 b d^{2} e h x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b d e^{2} f x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{3 b d e^{2} g x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{3 b d e^{2} h x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{b e^{3} f x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b e^{3} g x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{b e^{3} h x^{5} \sqrt{- c^{2} x^{2} + 1}}{36 c} - \frac{b d^{3} g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{3 b d^{2} e f \operatorname{asin}{\left(c x \right)}}{4 c^{2}} + \frac{2 b d^{3} h \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{2 b d^{2} e g \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{9 b d^{2} e h x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{2 b d e^{2} f \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{9 b d e^{2} g x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b d e^{2} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{25 c^{3}} + \frac{3 b e^{3} f x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b e^{3} g x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} + \frac{5 b e^{3} h x^{3} \sqrt{- c^{2} x^{2} + 1}}{144 c^{3}} - \frac{9 b d^{2} e h \operatorname{asin}{\left(c x \right)}}{32 c^{4}} - \frac{9 b d e^{2} g \operatorname{asin}{\left(c x \right)}}{32 c^{4}} - \frac{3 b e^{3} f \operatorname{asin}{\left(c x \right)}}{32 c^{4}} + \frac{8 b d e^{2} h \sqrt{- c^{2} x^{2} + 1}}{25 c^{5}} + \frac{8 b e^{3} g \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} + \frac{5 b e^{3} h x \sqrt{- c^{2} x^{2} + 1}}{96 c^{5}} - \frac{5 b e^{3} h \operatorname{asin}{\left(c x \right)}}{96 c^{6}} & \text{for}\: c \neq 0 \\a \left(d^{3} f x + \frac{d^{3} g x^{2}}{2} + \frac{d^{3} h x^{3}}{3} + \frac{3 d^{2} e f x^{2}}{2} + d^{2} e g x^{3} + \frac{3 d^{2} e h x^{4}}{4} + d e^{2} f x^{3} + \frac{3 d e^{2} g x^{4}}{4} + \frac{3 d e^{2} h x^{5}}{5} + \frac{e^{3} f x^{4}}{4} + \frac{e^{3} g x^{5}}{5} + \frac{e^{3} h x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*f*x + a*d**3*g*x**2/2 + a*d**3*h*x**3/3 + 3*a*d**2*e*f*x**2/2 + a*d**2*e*g*x**3 + 3*a*d**2*e*h*x**4/4 + a*d*e**2*f*x**3 + 3*a*d*e**2*g*x**4/4 + 3*a*d*e**2*h*x**5/5 + a*e**3*f*x**4/4 + a*e**3*g*x**5/5 + a*e**3*h*x**6/6 + b*d**3*f*x*asin(c*x) + b*d**3*g*x**2*asin(c*x)/2 + b*d**3*h*x**3*asin(c*x)/3 + 3*b*d**2*e*f*x**2*asin(c*x)/2 + b*d**2*e*g*x**3*asin(c*x) + 3*b*d**2*e*h*x**4*asin(c*x)/4 + b*d*e**2*f*x**3*asin(c*x) + 3*b*d*e**2*g*x**4*asin(c*x)/4 + 3*b*d*e**2*h*x**5*asin(c*x)/5 + b*e**3*f*x**4*asin(c*x)/4 + b*e**3*g*x**5*asin(c*x)/5 + b*e**3*h*x**6*asin(c*x)/6 + b*d**3*f*sqrt(-c**2*x**2 + 1)/c + b*d**3*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d**3*h*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + 3*b*d**2*e*f*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d**2*e*g*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 3*b*d**2*e*h*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*d*e**2*f*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 3*b*d*e**2*g*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + 3*b*d*e**2*h*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + b*e**3*f*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*e**3*g*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + b*e**3*h*x**5*sqrt(-c**2*x**2 + 1)/(36*c) - b*d**3*g*asin(c*x)/(4*c**2) - 3*b*d**2*e*f*asin(c*x)/(4*c**2) + 2*b*d**3*h*sqrt(-c**2*x**2 + 1)/(9*c**3) + 2*b*d**2*e*g*sqrt(-c**2*x**2 + 1)/(3*c**3) + 9*b*d**2*e*h*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 2*b*d*e**2*f*sqrt(-c**2*x**2 + 1)/(3*c**3) + 9*b*d*e**2*g*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*d*e**2*h*x**2*sqrt(-c**2*x**2 + 1)/(25*c**3) + 3*b*e**3*f*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*e**3*g*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) + 5*b*e**3*h*x**3*sqrt(-c**2*x**2 + 1)/(144*c**3) - 9*b*d**2*e*h*asin(c*x)/(32*c**4) - 9*b*d*e**2*g*asin(c*x)/(32*c**4) - 3*b*e**3*f*asin(c*x)/(32*c**4) + 8*b*d*e**2*h*sqrt(-c**2*x**2 + 1)/(25*c**5) + 8*b*e**3*g*sqrt(-c**2*x**2 + 1)/(75*c**5) + 5*b*e**3*h*x*sqrt(-c**2*x**2 + 1)/(96*c**5) - 5*b*e**3*h*asin(c*x)/(96*c**6), Ne(c, 0)), (a*(d**3*f*x + d**3*g*x**2/2 + d**3*h*x**3/3 + 3*d**2*e*f*x**2/2 + d**2*e*g*x**3 + 3*d**2*e*h*x**4/4 + d*e**2*f*x**3 + 3*d*e**2*g*x**4/4 + 3*d*e**2*h*x**5/5 + e**3*f*x**4/4 + e**3*g*x**5/5 + e**3*h*x**6/6), True))","A",0
98,1,821,0,3.784694," ","integrate((e*x+d)**2*(h*x**2+g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d^{2} f x + \frac{a d^{2} g x^{2}}{2} + \frac{a d^{2} h x^{3}}{3} + a d e f x^{2} + \frac{2 a d e g x^{3}}{3} + \frac{a d e h x^{4}}{2} + \frac{a e^{2} f x^{3}}{3} + \frac{a e^{2} g x^{4}}{4} + \frac{a e^{2} h x^{5}}{5} + b d^{2} f x \operatorname{asin}{\left(c x \right)} + \frac{b d^{2} g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b d^{2} h x^{3} \operatorname{asin}{\left(c x \right)}}{3} + b d e f x^{2} \operatorname{asin}{\left(c x \right)} + \frac{2 b d e g x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b d e h x^{4} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b e^{2} f x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b e^{2} g x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b e^{2} h x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b d^{2} f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d^{2} g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d^{2} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b d e f x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{2 b d e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b d e h x^{3} \sqrt{- c^{2} x^{2} + 1}}{8 c} + \frac{b e^{2} f x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b e^{2} g x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b e^{2} h x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} - \frac{b d^{2} g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{b d e f \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + \frac{2 b d^{2} h \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{4 b d e g \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b d e h x \sqrt{- c^{2} x^{2} + 1}}{16 c^{3}} + \frac{2 b e^{2} f \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b e^{2} g x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b e^{2} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} - \frac{3 b d e h \operatorname{asin}{\left(c x \right)}}{16 c^{4}} - \frac{3 b e^{2} g \operatorname{asin}{\left(c x \right)}}{32 c^{4}} + \frac{8 b e^{2} h \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} & \text{for}\: c \neq 0 \\a \left(d^{2} f x + \frac{d^{2} g x^{2}}{2} + \frac{d^{2} h x^{3}}{3} + d e f x^{2} + \frac{2 d e g x^{3}}{3} + \frac{d e h x^{4}}{2} + \frac{e^{2} f x^{3}}{3} + \frac{e^{2} g x^{4}}{4} + \frac{e^{2} h x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*f*x + a*d**2*g*x**2/2 + a*d**2*h*x**3/3 + a*d*e*f*x**2 + 2*a*d*e*g*x**3/3 + a*d*e*h*x**4/2 + a*e**2*f*x**3/3 + a*e**2*g*x**4/4 + a*e**2*h*x**5/5 + b*d**2*f*x*asin(c*x) + b*d**2*g*x**2*asin(c*x)/2 + b*d**2*h*x**3*asin(c*x)/3 + b*d*e*f*x**2*asin(c*x) + 2*b*d*e*g*x**3*asin(c*x)/3 + b*d*e*h*x**4*asin(c*x)/2 + b*e**2*f*x**3*asin(c*x)/3 + b*e**2*g*x**4*asin(c*x)/4 + b*e**2*h*x**5*asin(c*x)/5 + b*d**2*f*sqrt(-c**2*x**2 + 1)/c + b*d**2*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d**2*h*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*d*e*f*x*sqrt(-c**2*x**2 + 1)/(2*c) + 2*b*d*e*g*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*d*e*h*x**3*sqrt(-c**2*x**2 + 1)/(8*c) + b*e**2*f*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*e**2*g*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*e**2*h*x**4*sqrt(-c**2*x**2 + 1)/(25*c) - b*d**2*g*asin(c*x)/(4*c**2) - b*d*e*f*asin(c*x)/(2*c**2) + 2*b*d**2*h*sqrt(-c**2*x**2 + 1)/(9*c**3) + 4*b*d*e*g*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*d*e*h*x*sqrt(-c**2*x**2 + 1)/(16*c**3) + 2*b*e**2*f*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*e**2*g*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*e**2*h*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) - 3*b*d*e*h*asin(c*x)/(16*c**4) - 3*b*e**2*g*asin(c*x)/(32*c**4) + 8*b*e**2*h*sqrt(-c**2*x**2 + 1)/(75*c**5), Ne(c, 0)), (a*(d**2*f*x + d**2*g*x**2/2 + d**2*h*x**3/3 + d*e*f*x**2 + 2*d*e*g*x**3/3 + d*e*h*x**4/2 + e**2*f*x**3/3 + e**2*g*x**4/4 + e**2*h*x**5/5), True))","A",0
99,1,449,0,1.635501," ","integrate((e*x+d)*(h*x**2+g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d f x + \frac{a d g x^{2}}{2} + \frac{a d h x^{3}}{3} + \frac{a e f x^{2}}{2} + \frac{a e g x^{3}}{3} + \frac{a e h x^{4}}{4} + b d f x \operatorname{asin}{\left(c x \right)} + \frac{b d g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b d h x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b e f x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b e g x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b e h x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b d f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d h x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b e f x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b e h x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} - \frac{b d g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{b e f \operatorname{asin}{\left(c x \right)}}{4 c^{2}} + \frac{2 b d h \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{2 b e g \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b e h x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} - \frac{3 b e h \operatorname{asin}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\a \left(d f x + \frac{d g x^{2}}{2} + \frac{d h x^{3}}{3} + \frac{e f x^{2}}{2} + \frac{e g x^{3}}{3} + \frac{e h x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*f*x + a*d*g*x**2/2 + a*d*h*x**3/3 + a*e*f*x**2/2 + a*e*g*x**3/3 + a*e*h*x**4/4 + b*d*f*x*asin(c*x) + b*d*g*x**2*asin(c*x)/2 + b*d*h*x**3*asin(c*x)/3 + b*e*f*x**2*asin(c*x)/2 + b*e*g*x**3*asin(c*x)/3 + b*e*h*x**4*asin(c*x)/4 + b*d*f*sqrt(-c**2*x**2 + 1)/c + b*d*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d*h*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*e*f*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*e*g*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*e*h*x**3*sqrt(-c**2*x**2 + 1)/(16*c) - b*d*g*asin(c*x)/(4*c**2) - b*e*f*asin(c*x)/(4*c**2) + 2*b*d*h*sqrt(-c**2*x**2 + 1)/(9*c**3) + 2*b*e*g*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*e*h*x*sqrt(-c**2*x**2 + 1)/(32*c**3) - 3*b*e*h*asin(c*x)/(32*c**4), Ne(c, 0)), (a*(d*f*x + d*g*x**2/2 + d*h*x**3/3 + e*f*x**2/2 + e*g*x**3/3 + e*h*x**4/4), True))","A",0
100,0,0,0,0.000000," ","integrate((h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2}\right)}{d + e x}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2)/(d + e*x), x)","F",0
101,0,0,0,0.000000," ","integrate((h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2}\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2)/(d + e*x)**2, x)","F",0
102,0,0,0,0.000000," ","integrate((h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2}\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2)/(d + e*x)**3, x)","F",0
103,0,0,0,0.000000," ","integrate((h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d)**4,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2}\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2)/(d + e*x)**4, x)","F",0
104,0,0,0,0.000000," ","integrate((h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d)**5,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2}\right)}{\left(d + e x\right)^{5}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2)/(d + e*x)**5, x)","F",0
105,0,0,0,0.000000," ","integrate((h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d)**6,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2}\right)}{\left(d + e x\right)^{6}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2)/(d + e*x)**6, x)","F",0
106,1,1809,0,11.976870," ","integrate((e*x+d)**3*(i*x**3+h*x**2+g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d^{3} f x + \frac{a d^{3} g x^{2}}{2} + \frac{a d^{3} h x^{3}}{3} + \frac{a d^{3} i x^{4}}{4} + \frac{3 a d^{2} e f x^{2}}{2} + a d^{2} e g x^{3} + \frac{3 a d^{2} e h x^{4}}{4} + \frac{3 a d^{2} e i x^{5}}{5} + a d e^{2} f x^{3} + \frac{3 a d e^{2} g x^{4}}{4} + \frac{3 a d e^{2} h x^{5}}{5} + \frac{a d e^{2} i x^{6}}{2} + \frac{a e^{3} f x^{4}}{4} + \frac{a e^{3} g x^{5}}{5} + \frac{a e^{3} h x^{6}}{6} + \frac{a e^{3} i x^{7}}{7} + b d^{3} f x \operatorname{asin}{\left(c x \right)} + \frac{b d^{3} g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b d^{3} h x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b d^{3} i x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{3 b d^{2} e f x^{2} \operatorname{asin}{\left(c x \right)}}{2} + b d^{2} e g x^{3} \operatorname{asin}{\left(c x \right)} + \frac{3 b d^{2} e h x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{3 b d^{2} e i x^{5} \operatorname{asin}{\left(c x \right)}}{5} + b d e^{2} f x^{3} \operatorname{asin}{\left(c x \right)} + \frac{3 b d e^{2} g x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{3 b d e^{2} h x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b d e^{2} i x^{6} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b e^{3} f x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b e^{3} g x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b e^{3} h x^{6} \operatorname{asin}{\left(c x \right)}}{6} + \frac{b e^{3} i x^{7} \operatorname{asin}{\left(c x \right)}}{7} + \frac{b d^{3} f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d^{3} g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d^{3} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b d^{3} i x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{3 b d^{2} e f x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d^{2} e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{3 b d^{2} e h x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{3 b d^{2} e i x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{b d e^{2} f x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{3 b d e^{2} g x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{3 b d e^{2} h x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{b d e^{2} i x^{5} \sqrt{- c^{2} x^{2} + 1}}{12 c} + \frac{b e^{3} f x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b e^{3} g x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{b e^{3} h x^{5} \sqrt{- c^{2} x^{2} + 1}}{36 c} + \frac{b e^{3} i x^{6} \sqrt{- c^{2} x^{2} + 1}}{49 c} - \frac{b d^{3} g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{3 b d^{2} e f \operatorname{asin}{\left(c x \right)}}{4 c^{2}} + \frac{2 b d^{3} h \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b d^{3} i x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{2 b d^{2} e g \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{9 b d^{2} e h x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b d^{2} e i x^{2} \sqrt{- c^{2} x^{2} + 1}}{25 c^{3}} + \frac{2 b d e^{2} f \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{9 b d e^{2} g x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b d e^{2} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{25 c^{3}} + \frac{5 b d e^{2} i x^{3} \sqrt{- c^{2} x^{2} + 1}}{48 c^{3}} + \frac{3 b e^{3} f x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b e^{3} g x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} + \frac{5 b e^{3} h x^{3} \sqrt{- c^{2} x^{2} + 1}}{144 c^{3}} + \frac{6 b e^{3} i x^{4} \sqrt{- c^{2} x^{2} + 1}}{245 c^{3}} - \frac{3 b d^{3} i \operatorname{asin}{\left(c x \right)}}{32 c^{4}} - \frac{9 b d^{2} e h \operatorname{asin}{\left(c x \right)}}{32 c^{4}} - \frac{9 b d e^{2} g \operatorname{asin}{\left(c x \right)}}{32 c^{4}} - \frac{3 b e^{3} f \operatorname{asin}{\left(c x \right)}}{32 c^{4}} + \frac{8 b d^{2} e i \sqrt{- c^{2} x^{2} + 1}}{25 c^{5}} + \frac{8 b d e^{2} h \sqrt{- c^{2} x^{2} + 1}}{25 c^{5}} + \frac{5 b d e^{2} i x \sqrt{- c^{2} x^{2} + 1}}{32 c^{5}} + \frac{8 b e^{3} g \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} + \frac{5 b e^{3} h x \sqrt{- c^{2} x^{2} + 1}}{96 c^{5}} + \frac{8 b e^{3} i x^{2} \sqrt{- c^{2} x^{2} + 1}}{245 c^{5}} - \frac{5 b d e^{2} i \operatorname{asin}{\left(c x \right)}}{32 c^{6}} - \frac{5 b e^{3} h \operatorname{asin}{\left(c x \right)}}{96 c^{6}} + \frac{16 b e^{3} i \sqrt{- c^{2} x^{2} + 1}}{245 c^{7}} & \text{for}\: c \neq 0 \\a \left(d^{3} f x + \frac{d^{3} g x^{2}}{2} + \frac{d^{3} h x^{3}}{3} + \frac{d^{3} i x^{4}}{4} + \frac{3 d^{2} e f x^{2}}{2} + d^{2} e g x^{3} + \frac{3 d^{2} e h x^{4}}{4} + \frac{3 d^{2} e i x^{5}}{5} + d e^{2} f x^{3} + \frac{3 d e^{2} g x^{4}}{4} + \frac{3 d e^{2} h x^{5}}{5} + \frac{d e^{2} i x^{6}}{2} + \frac{e^{3} f x^{4}}{4} + \frac{e^{3} g x^{5}}{5} + \frac{e^{3} h x^{6}}{6} + \frac{e^{3} i x^{7}}{7}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**3*f*x + a*d**3*g*x**2/2 + a*d**3*h*x**3/3 + a*d**3*i*x**4/4 + 3*a*d**2*e*f*x**2/2 + a*d**2*e*g*x**3 + 3*a*d**2*e*h*x**4/4 + 3*a*d**2*e*i*x**5/5 + a*d*e**2*f*x**3 + 3*a*d*e**2*g*x**4/4 + 3*a*d*e**2*h*x**5/5 + a*d*e**2*i*x**6/2 + a*e**3*f*x**4/4 + a*e**3*g*x**5/5 + a*e**3*h*x**6/6 + a*e**3*i*x**7/7 + b*d**3*f*x*asin(c*x) + b*d**3*g*x**2*asin(c*x)/2 + b*d**3*h*x**3*asin(c*x)/3 + b*d**3*i*x**4*asin(c*x)/4 + 3*b*d**2*e*f*x**2*asin(c*x)/2 + b*d**2*e*g*x**3*asin(c*x) + 3*b*d**2*e*h*x**4*asin(c*x)/4 + 3*b*d**2*e*i*x**5*asin(c*x)/5 + b*d*e**2*f*x**3*asin(c*x) + 3*b*d*e**2*g*x**4*asin(c*x)/4 + 3*b*d*e**2*h*x**5*asin(c*x)/5 + b*d*e**2*i*x**6*asin(c*x)/2 + b*e**3*f*x**4*asin(c*x)/4 + b*e**3*g*x**5*asin(c*x)/5 + b*e**3*h*x**6*asin(c*x)/6 + b*e**3*i*x**7*asin(c*x)/7 + b*d**3*f*sqrt(-c**2*x**2 + 1)/c + b*d**3*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d**3*h*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*d**3*i*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + 3*b*d**2*e*f*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d**2*e*g*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 3*b*d**2*e*h*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + 3*b*d**2*e*i*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + b*d*e**2*f*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 3*b*d*e**2*g*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + 3*b*d*e**2*h*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + b*d*e**2*i*x**5*sqrt(-c**2*x**2 + 1)/(12*c) + b*e**3*f*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*e**3*g*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + b*e**3*h*x**5*sqrt(-c**2*x**2 + 1)/(36*c) + b*e**3*i*x**6*sqrt(-c**2*x**2 + 1)/(49*c) - b*d**3*g*asin(c*x)/(4*c**2) - 3*b*d**2*e*f*asin(c*x)/(4*c**2) + 2*b*d**3*h*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*d**3*i*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 2*b*d**2*e*g*sqrt(-c**2*x**2 + 1)/(3*c**3) + 9*b*d**2*e*h*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*d**2*e*i*x**2*sqrt(-c**2*x**2 + 1)/(25*c**3) + 2*b*d*e**2*f*sqrt(-c**2*x**2 + 1)/(3*c**3) + 9*b*d*e**2*g*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*d*e**2*h*x**2*sqrt(-c**2*x**2 + 1)/(25*c**3) + 5*b*d*e**2*i*x**3*sqrt(-c**2*x**2 + 1)/(48*c**3) + 3*b*e**3*f*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*e**3*g*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) + 5*b*e**3*h*x**3*sqrt(-c**2*x**2 + 1)/(144*c**3) + 6*b*e**3*i*x**4*sqrt(-c**2*x**2 + 1)/(245*c**3) - 3*b*d**3*i*asin(c*x)/(32*c**4) - 9*b*d**2*e*h*asin(c*x)/(32*c**4) - 9*b*d*e**2*g*asin(c*x)/(32*c**4) - 3*b*e**3*f*asin(c*x)/(32*c**4) + 8*b*d**2*e*i*sqrt(-c**2*x**2 + 1)/(25*c**5) + 8*b*d*e**2*h*sqrt(-c**2*x**2 + 1)/(25*c**5) + 5*b*d*e**2*i*x*sqrt(-c**2*x**2 + 1)/(32*c**5) + 8*b*e**3*g*sqrt(-c**2*x**2 + 1)/(75*c**5) + 5*b*e**3*h*x*sqrt(-c**2*x**2 + 1)/(96*c**5) + 8*b*e**3*i*x**2*sqrt(-c**2*x**2 + 1)/(245*c**5) - 5*b*d*e**2*i*asin(c*x)/(32*c**6) - 5*b*e**3*h*asin(c*x)/(96*c**6) + 16*b*e**3*i*sqrt(-c**2*x**2 + 1)/(245*c**7), Ne(c, 0)), (a*(d**3*f*x + d**3*g*x**2/2 + d**3*h*x**3/3 + d**3*i*x**4/4 + 3*d**2*e*f*x**2/2 + d**2*e*g*x**3 + 3*d**2*e*h*x**4/4 + 3*d**2*e*i*x**5/5 + d*e**2*f*x**3 + 3*d*e**2*g*x**4/4 + 3*d*e**2*h*x**5/5 + d*e**2*i*x**6/2 + e**3*f*x**4/4 + e**3*g*x**5/5 + e**3*h*x**6/6 + e**3*i*x**7/7), True))","A",0
107,1,1197,0,6.849833," ","integrate((e*x+d)**2*(i*x**3+h*x**2+g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d^{2} f x + \frac{a d^{2} g x^{2}}{2} + \frac{a d^{2} h x^{3}}{3} + \frac{a d^{2} i x^{4}}{4} + a d e f x^{2} + \frac{2 a d e g x^{3}}{3} + \frac{a d e h x^{4}}{2} + \frac{2 a d e i x^{5}}{5} + \frac{a e^{2} f x^{3}}{3} + \frac{a e^{2} g x^{4}}{4} + \frac{a e^{2} h x^{5}}{5} + \frac{a e^{2} i x^{6}}{6} + b d^{2} f x \operatorname{asin}{\left(c x \right)} + \frac{b d^{2} g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b d^{2} h x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b d^{2} i x^{4} \operatorname{asin}{\left(c x \right)}}{4} + b d e f x^{2} \operatorname{asin}{\left(c x \right)} + \frac{2 b d e g x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b d e h x^{4} \operatorname{asin}{\left(c x \right)}}{2} + \frac{2 b d e i x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b e^{2} f x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b e^{2} g x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b e^{2} h x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b e^{2} i x^{6} \operatorname{asin}{\left(c x \right)}}{6} + \frac{b d^{2} f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d^{2} g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d^{2} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b d^{2} i x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b d e f x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{2 b d e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b d e h x^{3} \sqrt{- c^{2} x^{2} + 1}}{8 c} + \frac{2 b d e i x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{b e^{2} f x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b e^{2} g x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b e^{2} h x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{b e^{2} i x^{5} \sqrt{- c^{2} x^{2} + 1}}{36 c} - \frac{b d^{2} g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{b d e f \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + \frac{2 b d^{2} h \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b d^{2} i x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b d e g \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b d e h x \sqrt{- c^{2} x^{2} + 1}}{16 c^{3}} + \frac{8 b d e i x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} + \frac{2 b e^{2} f \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b e^{2} g x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b e^{2} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} + \frac{5 b e^{2} i x^{3} \sqrt{- c^{2} x^{2} + 1}}{144 c^{3}} - \frac{3 b d^{2} i \operatorname{asin}{\left(c x \right)}}{32 c^{4}} - \frac{3 b d e h \operatorname{asin}{\left(c x \right)}}{16 c^{4}} - \frac{3 b e^{2} g \operatorname{asin}{\left(c x \right)}}{32 c^{4}} + \frac{16 b d e i \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} + \frac{8 b e^{2} h \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} + \frac{5 b e^{2} i x \sqrt{- c^{2} x^{2} + 1}}{96 c^{5}} - \frac{5 b e^{2} i \operatorname{asin}{\left(c x \right)}}{96 c^{6}} & \text{for}\: c \neq 0 \\a \left(d^{2} f x + \frac{d^{2} g x^{2}}{2} + \frac{d^{2} h x^{3}}{3} + \frac{d^{2} i x^{4}}{4} + d e f x^{2} + \frac{2 d e g x^{3}}{3} + \frac{d e h x^{4}}{2} + \frac{2 d e i x^{5}}{5} + \frac{e^{2} f x^{3}}{3} + \frac{e^{2} g x^{4}}{4} + \frac{e^{2} h x^{5}}{5} + \frac{e^{2} i x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d**2*f*x + a*d**2*g*x**2/2 + a*d**2*h*x**3/3 + a*d**2*i*x**4/4 + a*d*e*f*x**2 + 2*a*d*e*g*x**3/3 + a*d*e*h*x**4/2 + 2*a*d*e*i*x**5/5 + a*e**2*f*x**3/3 + a*e**2*g*x**4/4 + a*e**2*h*x**5/5 + a*e**2*i*x**6/6 + b*d**2*f*x*asin(c*x) + b*d**2*g*x**2*asin(c*x)/2 + b*d**2*h*x**3*asin(c*x)/3 + b*d**2*i*x**4*asin(c*x)/4 + b*d*e*f*x**2*asin(c*x) + 2*b*d*e*g*x**3*asin(c*x)/3 + b*d*e*h*x**4*asin(c*x)/2 + 2*b*d*e*i*x**5*asin(c*x)/5 + b*e**2*f*x**3*asin(c*x)/3 + b*e**2*g*x**4*asin(c*x)/4 + b*e**2*h*x**5*asin(c*x)/5 + b*e**2*i*x**6*asin(c*x)/6 + b*d**2*f*sqrt(-c**2*x**2 + 1)/c + b*d**2*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d**2*h*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*d**2*i*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*d*e*f*x*sqrt(-c**2*x**2 + 1)/(2*c) + 2*b*d*e*g*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*d*e*h*x**3*sqrt(-c**2*x**2 + 1)/(8*c) + 2*b*d*e*i*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + b*e**2*f*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*e**2*g*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*e**2*h*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + b*e**2*i*x**5*sqrt(-c**2*x**2 + 1)/(36*c) - b*d**2*g*asin(c*x)/(4*c**2) - b*d*e*f*asin(c*x)/(2*c**2) + 2*b*d**2*h*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*d**2*i*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*d*e*g*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*d*e*h*x*sqrt(-c**2*x**2 + 1)/(16*c**3) + 8*b*d*e*i*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) + 2*b*e**2*f*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*e**2*g*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*e**2*h*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) + 5*b*e**2*i*x**3*sqrt(-c**2*x**2 + 1)/(144*c**3) - 3*b*d**2*i*asin(c*x)/(32*c**4) - 3*b*d*e*h*asin(c*x)/(16*c**4) - 3*b*e**2*g*asin(c*x)/(32*c**4) + 16*b*d*e*i*sqrt(-c**2*x**2 + 1)/(75*c**5) + 8*b*e**2*h*sqrt(-c**2*x**2 + 1)/(75*c**5) + 5*b*e**2*i*x*sqrt(-c**2*x**2 + 1)/(96*c**5) - 5*b*e**2*i*asin(c*x)/(96*c**6), Ne(c, 0)), (a*(d**2*f*x + d**2*g*x**2/2 + d**2*h*x**3/3 + d**2*i*x**4/4 + d*e*f*x**2 + 2*d*e*g*x**3/3 + d*e*h*x**4/2 + 2*d*e*i*x**5/5 + e**2*f*x**3/3 + e**2*g*x**4/4 + e**2*h*x**5/5 + e**2*i*x**6/6), True))","A",0
108,1,658,0,3.355857," ","integrate((e*x+d)*(i*x**3+h*x**2+g*x+f)*(a+b*asin(c*x)),x)","\begin{cases} a d f x + \frac{a d g x^{2}}{2} + \frac{a d h x^{3}}{3} + \frac{a d i x^{4}}{4} + \frac{a e f x^{2}}{2} + \frac{a e g x^{3}}{3} + \frac{a e h x^{4}}{4} + \frac{a e i x^{5}}{5} + b d f x \operatorname{asin}{\left(c x \right)} + \frac{b d g x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b d h x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b d i x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b e f x^{2} \operatorname{asin}{\left(c x \right)}}{2} + \frac{b e g x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{b e h x^{4} \operatorname{asin}{\left(c x \right)}}{4} + \frac{b e i x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{b d f \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{b d g x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b d h x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b d i x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b e f x \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{b e g x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{b e h x^{3} \sqrt{- c^{2} x^{2} + 1}}{16 c} + \frac{b e i x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} - \frac{b d g \operatorname{asin}{\left(c x \right)}}{4 c^{2}} - \frac{b e f \operatorname{asin}{\left(c x \right)}}{4 c^{2}} + \frac{2 b d h \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b d i x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{2 b e g \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 b e h x \sqrt{- c^{2} x^{2} + 1}}{32 c^{3}} + \frac{4 b e i x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} - \frac{3 b d i \operatorname{asin}{\left(c x \right)}}{32 c^{4}} - \frac{3 b e h \operatorname{asin}{\left(c x \right)}}{32 c^{4}} + \frac{8 b e i \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} & \text{for}\: c \neq 0 \\a \left(d f x + \frac{d g x^{2}}{2} + \frac{d h x^{3}}{3} + \frac{d i x^{4}}{4} + \frac{e f x^{2}}{2} + \frac{e g x^{3}}{3} + \frac{e h x^{4}}{4} + \frac{e i x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*d*f*x + a*d*g*x**2/2 + a*d*h*x**3/3 + a*d*i*x**4/4 + a*e*f*x**2/2 + a*e*g*x**3/3 + a*e*h*x**4/4 + a*e*i*x**5/5 + b*d*f*x*asin(c*x) + b*d*g*x**2*asin(c*x)/2 + b*d*h*x**3*asin(c*x)/3 + b*d*i*x**4*asin(c*x)/4 + b*e*f*x**2*asin(c*x)/2 + b*e*g*x**3*asin(c*x)/3 + b*e*h*x**4*asin(c*x)/4 + b*e*i*x**5*asin(c*x)/5 + b*d*f*sqrt(-c**2*x**2 + 1)/c + b*d*g*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*d*h*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*d*i*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*e*f*x*sqrt(-c**2*x**2 + 1)/(4*c) + b*e*g*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + b*e*h*x**3*sqrt(-c**2*x**2 + 1)/(16*c) + b*e*i*x**4*sqrt(-c**2*x**2 + 1)/(25*c) - b*d*g*asin(c*x)/(4*c**2) - b*e*f*asin(c*x)/(4*c**2) + 2*b*d*h*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*d*i*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 2*b*e*g*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*b*e*h*x*sqrt(-c**2*x**2 + 1)/(32*c**3) + 4*b*e*i*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) - 3*b*d*i*asin(c*x)/(32*c**4) - 3*b*e*h*asin(c*x)/(32*c**4) + 8*b*e*i*sqrt(-c**2*x**2 + 1)/(75*c**5), Ne(c, 0)), (a*(d*f*x + d*g*x**2/2 + d*h*x**3/3 + d*i*x**4/4 + e*f*x**2/2 + e*g*x**3/3 + e*h*x**4/4 + e*i*x**5/5), True))","A",0
109,0,0,0,0.000000," ","integrate((i*x**3+h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2} + i x^{3}\right)}{d + e x}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2 + i*x**3)/(d + e*x), x)","F",0
110,0,0,0,0.000000," ","integrate((i*x**3+h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2} + i x^{3}\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2 + i*x**3)/(d + e*x)**2, x)","F",0
111,0,0,0,0.000000," ","integrate((i*x**3+h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2} + i x^{3}\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2 + i*x**3)/(d + e*x)**3, x)","F",0
112,0,0,0,0.000000," ","integrate((i*x**3+h*x**2+g*x+f)*(a+b*asin(c*x))/(e*x+d)**4,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right) \left(f + g x + h x^{2} + i x^{3}\right)}{\left(d + e x\right)^{4}}\, dx"," ",0,"Integral((a + b*asin(c*x))*(f + g*x + h*x**2 + i*x**3)/(d + e*x)**4, x)","F",0
113,0,0,0,0.000000," ","integrate((g*x+f)*(a+b*asin(c*x))**2/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(f + g*x)/(d + e*x)**3, x)","F",0
114,0,0,0,0.000000," ","integrate((g*x+f)**2*(a+b*asin(c*x))**2/(e*x+d)**3,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(f + g x\right)^{2}}{\left(d + e x\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(f + g*x)**2/(d + e*x)**3, x)","F",0
115,1,2992,0,17.689418," ","integrate((h*x+g)**3*(f*x**2+e*x+d)*(a+b*asin(c*x))**2,x)","\begin{cases} a^{2} d g^{3} x + \frac{3 a^{2} d g^{2} h x^{2}}{2} + a^{2} d g h^{2} x^{3} + \frac{a^{2} d h^{3} x^{4}}{4} + \frac{a^{2} e g^{3} x^{2}}{2} + a^{2} e g^{2} h x^{3} + \frac{3 a^{2} e g h^{2} x^{4}}{4} + \frac{a^{2} e h^{3} x^{5}}{5} + \frac{a^{2} f g^{3} x^{3}}{3} + \frac{3 a^{2} f g^{2} h x^{4}}{4} + \frac{3 a^{2} f g h^{2} x^{5}}{5} + \frac{a^{2} f h^{3} x^{6}}{6} + 2 a b d g^{3} x \operatorname{asin}{\left(c x \right)} + 3 a b d g^{2} h x^{2} \operatorname{asin}{\left(c x \right)} + 2 a b d g h^{2} x^{3} \operatorname{asin}{\left(c x \right)} + \frac{a b d h^{3} x^{4} \operatorname{asin}{\left(c x \right)}}{2} + a b e g^{3} x^{2} \operatorname{asin}{\left(c x \right)} + 2 a b e g^{2} h x^{3} \operatorname{asin}{\left(c x \right)} + \frac{3 a b e g h^{2} x^{4} \operatorname{asin}{\left(c x \right)}}{2} + \frac{2 a b e h^{3} x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{2 a b f g^{3} x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{3 a b f g^{2} h x^{4} \operatorname{asin}{\left(c x \right)}}{2} + \frac{6 a b f g h^{2} x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{a b f h^{3} x^{6} \operatorname{asin}{\left(c x \right)}}{3} + \frac{2 a b d g^{3} \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{3 a b d g^{2} h x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{2 a b d g h^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{a b d h^{3} x^{3} \sqrt{- c^{2} x^{2} + 1}}{8 c} + \frac{a b e g^{3} x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{2 a b e g^{2} h x^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c} + \frac{3 a b e g h^{2} x^{3} \sqrt{- c^{2} x^{2} + 1}}{8 c} + \frac{2 a b e h^{3} x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{2 a b f g^{3} x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{3 a b f g^{2} h x^{3} \sqrt{- c^{2} x^{2} + 1}}{8 c} + \frac{6 a b f g h^{2} x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} + \frac{a b f h^{3} x^{5} \sqrt{- c^{2} x^{2} + 1}}{18 c} - \frac{3 a b d g^{2} h \operatorname{asin}{\left(c x \right)}}{2 c^{2}} - \frac{a b e g^{3} \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + \frac{4 a b d g h^{2} \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{3 a b d h^{3} x \sqrt{- c^{2} x^{2} + 1}}{16 c^{3}} + \frac{4 a b e g^{2} h \sqrt{- c^{2} x^{2} + 1}}{3 c^{3}} + \frac{9 a b e g h^{2} x \sqrt{- c^{2} x^{2} + 1}}{16 c^{3}} + \frac{8 a b e h^{3} x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} + \frac{4 a b f g^{3} \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{9 a b f g^{2} h x \sqrt{- c^{2} x^{2} + 1}}{16 c^{3}} + \frac{8 a b f g h^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{25 c^{3}} + \frac{5 a b f h^{3} x^{3} \sqrt{- c^{2} x^{2} + 1}}{72 c^{3}} - \frac{3 a b d h^{3} \operatorname{asin}{\left(c x \right)}}{16 c^{4}} - \frac{9 a b e g h^{2} \operatorname{asin}{\left(c x \right)}}{16 c^{4}} - \frac{9 a b f g^{2} h \operatorname{asin}{\left(c x \right)}}{16 c^{4}} + \frac{16 a b e h^{3} \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} + \frac{16 a b f g h^{2} \sqrt{- c^{2} x^{2} + 1}}{25 c^{5}} + \frac{5 a b f h^{3} x \sqrt{- c^{2} x^{2} + 1}}{48 c^{5}} - \frac{5 a b f h^{3} \operatorname{asin}{\left(c x \right)}}{48 c^{6}} + b^{2} d g^{3} x \operatorname{asin}^{2}{\left(c x \right)} - 2 b^{2} d g^{3} x + \frac{3 b^{2} d g^{2} h x^{2} \operatorname{asin}^{2}{\left(c x \right)}}{2} - \frac{3 b^{2} d g^{2} h x^{2}}{4} + b^{2} d g h^{2} x^{3} \operatorname{asin}^{2}{\left(c x \right)} - \frac{2 b^{2} d g h^{2} x^{3}}{9} + \frac{b^{2} d h^{3} x^{4} \operatorname{asin}^{2}{\left(c x \right)}}{4} - \frac{b^{2} d h^{3} x^{4}}{32} + \frac{b^{2} e g^{3} x^{2} \operatorname{asin}^{2}{\left(c x \right)}}{2} - \frac{b^{2} e g^{3} x^{2}}{4} + b^{2} e g^{2} h x^{3} \operatorname{asin}^{2}{\left(c x \right)} - \frac{2 b^{2} e g^{2} h x^{3}}{9} + \frac{3 b^{2} e g h^{2} x^{4} \operatorname{asin}^{2}{\left(c x \right)}}{4} - \frac{3 b^{2} e g h^{2} x^{4}}{32} + \frac{b^{2} e h^{3} x^{5} \operatorname{asin}^{2}{\left(c x \right)}}{5} - \frac{2 b^{2} e h^{3} x^{5}}{125} + \frac{b^{2} f g^{3} x^{3} \operatorname{asin}^{2}{\left(c x \right)}}{3} - \frac{2 b^{2} f g^{3} x^{3}}{27} + \frac{3 b^{2} f g^{2} h x^{4} \operatorname{asin}^{2}{\left(c x \right)}}{4} - \frac{3 b^{2} f g^{2} h x^{4}}{32} + \frac{3 b^{2} f g h^{2} x^{5} \operatorname{asin}^{2}{\left(c x \right)}}{5} - \frac{6 b^{2} f g h^{2} x^{5}}{125} + \frac{b^{2} f h^{3} x^{6} \operatorname{asin}^{2}{\left(c x \right)}}{6} - \frac{b^{2} f h^{3} x^{6}}{108} + \frac{2 b^{2} d g^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} + \frac{3 b^{2} d g^{2} h x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{2 c} + \frac{2 b^{2} d g h^{2} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{3 c} + \frac{b^{2} d h^{3} x^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{8 c} + \frac{b^{2} e g^{3} x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{2 c} + \frac{2 b^{2} e g^{2} h x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{3 c} + \frac{3 b^{2} e g h^{2} x^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{8 c} + \frac{2 b^{2} e h^{3} x^{4} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{25 c} + \frac{2 b^{2} f g^{3} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c} + \frac{3 b^{2} f g^{2} h x^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{8 c} + \frac{6 b^{2} f g h^{2} x^{4} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{25 c} + \frac{b^{2} f h^{3} x^{5} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{18 c} - \frac{3 b^{2} d g^{2} h \operatorname{asin}^{2}{\left(c x \right)}}{4 c^{2}} - \frac{4 b^{2} d g h^{2} x}{3 c^{2}} - \frac{3 b^{2} d h^{3} x^{2}}{32 c^{2}} - \frac{b^{2} e g^{3} \operatorname{asin}^{2}{\left(c x \right)}}{4 c^{2}} - \frac{4 b^{2} e g^{2} h x}{3 c^{2}} - \frac{9 b^{2} e g h^{2} x^{2}}{32 c^{2}} - \frac{8 b^{2} e h^{3} x^{3}}{225 c^{2}} - \frac{4 b^{2} f g^{3} x}{9 c^{2}} - \frac{9 b^{2} f g^{2} h x^{2}}{32 c^{2}} - \frac{8 b^{2} f g h^{2} x^{3}}{75 c^{2}} - \frac{5 b^{2} f h^{3} x^{4}}{288 c^{2}} + \frac{4 b^{2} d g h^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{3 c^{3}} + \frac{3 b^{2} d h^{3} x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{16 c^{3}} + \frac{4 b^{2} e g^{2} h \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{3 c^{3}} + \frac{9 b^{2} e g h^{2} x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{16 c^{3}} + \frac{8 b^{2} e h^{3} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{75 c^{3}} + \frac{4 b^{2} f g^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c^{3}} + \frac{9 b^{2} f g^{2} h x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{16 c^{3}} + \frac{8 b^{2} f g h^{2} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{25 c^{3}} + \frac{5 b^{2} f h^{3} x^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{72 c^{3}} - \frac{3 b^{2} d h^{3} \operatorname{asin}^{2}{\left(c x \right)}}{32 c^{4}} - \frac{9 b^{2} e g h^{2} \operatorname{asin}^{2}{\left(c x \right)}}{32 c^{4}} - \frac{16 b^{2} e h^{3} x}{75 c^{4}} - \frac{9 b^{2} f g^{2} h \operatorname{asin}^{2}{\left(c x \right)}}{32 c^{4}} - \frac{16 b^{2} f g h^{2} x}{25 c^{4}} - \frac{5 b^{2} f h^{3} x^{2}}{96 c^{4}} + \frac{16 b^{2} e h^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{75 c^{5}} + \frac{16 b^{2} f g h^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{25 c^{5}} + \frac{5 b^{2} f h^{3} x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{48 c^{5}} - \frac{5 b^{2} f h^{3} \operatorname{asin}^{2}{\left(c x \right)}}{96 c^{6}} & \text{for}\: c \neq 0 \\a^{2} \left(d g^{3} x + \frac{3 d g^{2} h x^{2}}{2} + d g h^{2} x^{3} + \frac{d h^{3} x^{4}}{4} + \frac{e g^{3} x^{2}}{2} + e g^{2} h x^{3} + \frac{3 e g h^{2} x^{4}}{4} + \frac{e h^{3} x^{5}}{5} + \frac{f g^{3} x^{3}}{3} + \frac{3 f g^{2} h x^{4}}{4} + \frac{3 f g h^{2} x^{5}}{5} + \frac{f h^{3} x^{6}}{6}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*g**3*x + 3*a**2*d*g**2*h*x**2/2 + a**2*d*g*h**2*x**3 + a**2*d*h**3*x**4/4 + a**2*e*g**3*x**2/2 + a**2*e*g**2*h*x**3 + 3*a**2*e*g*h**2*x**4/4 + a**2*e*h**3*x**5/5 + a**2*f*g**3*x**3/3 + 3*a**2*f*g**2*h*x**4/4 + 3*a**2*f*g*h**2*x**5/5 + a**2*f*h**3*x**6/6 + 2*a*b*d*g**3*x*asin(c*x) + 3*a*b*d*g**2*h*x**2*asin(c*x) + 2*a*b*d*g*h**2*x**3*asin(c*x) + a*b*d*h**3*x**4*asin(c*x)/2 + a*b*e*g**3*x**2*asin(c*x) + 2*a*b*e*g**2*h*x**3*asin(c*x) + 3*a*b*e*g*h**2*x**4*asin(c*x)/2 + 2*a*b*e*h**3*x**5*asin(c*x)/5 + 2*a*b*f*g**3*x**3*asin(c*x)/3 + 3*a*b*f*g**2*h*x**4*asin(c*x)/2 + 6*a*b*f*g*h**2*x**5*asin(c*x)/5 + a*b*f*h**3*x**6*asin(c*x)/3 + 2*a*b*d*g**3*sqrt(-c**2*x**2 + 1)/c + 3*a*b*d*g**2*h*x*sqrt(-c**2*x**2 + 1)/(2*c) + 2*a*b*d*g*h**2*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + a*b*d*h**3*x**3*sqrt(-c**2*x**2 + 1)/(8*c) + a*b*e*g**3*x*sqrt(-c**2*x**2 + 1)/(2*c) + 2*a*b*e*g**2*h*x**2*sqrt(-c**2*x**2 + 1)/(3*c) + 3*a*b*e*g*h**2*x**3*sqrt(-c**2*x**2 + 1)/(8*c) + 2*a*b*e*h**3*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + 2*a*b*f*g**3*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + 3*a*b*f*g**2*h*x**3*sqrt(-c**2*x**2 + 1)/(8*c) + 6*a*b*f*g*h**2*x**4*sqrt(-c**2*x**2 + 1)/(25*c) + a*b*f*h**3*x**5*sqrt(-c**2*x**2 + 1)/(18*c) - 3*a*b*d*g**2*h*asin(c*x)/(2*c**2) - a*b*e*g**3*asin(c*x)/(2*c**2) + 4*a*b*d*g*h**2*sqrt(-c**2*x**2 + 1)/(3*c**3) + 3*a*b*d*h**3*x*sqrt(-c**2*x**2 + 1)/(16*c**3) + 4*a*b*e*g**2*h*sqrt(-c**2*x**2 + 1)/(3*c**3) + 9*a*b*e*g*h**2*x*sqrt(-c**2*x**2 + 1)/(16*c**3) + 8*a*b*e*h**3*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) + 4*a*b*f*g**3*sqrt(-c**2*x**2 + 1)/(9*c**3) + 9*a*b*f*g**2*h*x*sqrt(-c**2*x**2 + 1)/(16*c**3) + 8*a*b*f*g*h**2*x**2*sqrt(-c**2*x**2 + 1)/(25*c**3) + 5*a*b*f*h**3*x**3*sqrt(-c**2*x**2 + 1)/(72*c**3) - 3*a*b*d*h**3*asin(c*x)/(16*c**4) - 9*a*b*e*g*h**2*asin(c*x)/(16*c**4) - 9*a*b*f*g**2*h*asin(c*x)/(16*c**4) + 16*a*b*e*h**3*sqrt(-c**2*x**2 + 1)/(75*c**5) + 16*a*b*f*g*h**2*sqrt(-c**2*x**2 + 1)/(25*c**5) + 5*a*b*f*h**3*x*sqrt(-c**2*x**2 + 1)/(48*c**5) - 5*a*b*f*h**3*asin(c*x)/(48*c**6) + b**2*d*g**3*x*asin(c*x)**2 - 2*b**2*d*g**3*x + 3*b**2*d*g**2*h*x**2*asin(c*x)**2/2 - 3*b**2*d*g**2*h*x**2/4 + b**2*d*g*h**2*x**3*asin(c*x)**2 - 2*b**2*d*g*h**2*x**3/9 + b**2*d*h**3*x**4*asin(c*x)**2/4 - b**2*d*h**3*x**4/32 + b**2*e*g**3*x**2*asin(c*x)**2/2 - b**2*e*g**3*x**2/4 + b**2*e*g**2*h*x**3*asin(c*x)**2 - 2*b**2*e*g**2*h*x**3/9 + 3*b**2*e*g*h**2*x**4*asin(c*x)**2/4 - 3*b**2*e*g*h**2*x**4/32 + b**2*e*h**3*x**5*asin(c*x)**2/5 - 2*b**2*e*h**3*x**5/125 + b**2*f*g**3*x**3*asin(c*x)**2/3 - 2*b**2*f*g**3*x**3/27 + 3*b**2*f*g**2*h*x**4*asin(c*x)**2/4 - 3*b**2*f*g**2*h*x**4/32 + 3*b**2*f*g*h**2*x**5*asin(c*x)**2/5 - 6*b**2*f*g*h**2*x**5/125 + b**2*f*h**3*x**6*asin(c*x)**2/6 - b**2*f*h**3*x**6/108 + 2*b**2*d*g**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/c + 3*b**2*d*g**2*h*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(2*c) + 2*b**2*d*g*h**2*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(3*c) + b**2*d*h**3*x**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(8*c) + b**2*e*g**3*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(2*c) + 2*b**2*e*g**2*h*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(3*c) + 3*b**2*e*g*h**2*x**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(8*c) + 2*b**2*e*h**3*x**4*sqrt(-c**2*x**2 + 1)*asin(c*x)/(25*c) + 2*b**2*f*g**3*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c) + 3*b**2*f*g**2*h*x**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(8*c) + 6*b**2*f*g*h**2*x**4*sqrt(-c**2*x**2 + 1)*asin(c*x)/(25*c) + b**2*f*h**3*x**5*sqrt(-c**2*x**2 + 1)*asin(c*x)/(18*c) - 3*b**2*d*g**2*h*asin(c*x)**2/(4*c**2) - 4*b**2*d*g*h**2*x/(3*c**2) - 3*b**2*d*h**3*x**2/(32*c**2) - b**2*e*g**3*asin(c*x)**2/(4*c**2) - 4*b**2*e*g**2*h*x/(3*c**2) - 9*b**2*e*g*h**2*x**2/(32*c**2) - 8*b**2*e*h**3*x**3/(225*c**2) - 4*b**2*f*g**3*x/(9*c**2) - 9*b**2*f*g**2*h*x**2/(32*c**2) - 8*b**2*f*g*h**2*x**3/(75*c**2) - 5*b**2*f*h**3*x**4/(288*c**2) + 4*b**2*d*g*h**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(3*c**3) + 3*b**2*d*h**3*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(16*c**3) + 4*b**2*e*g**2*h*sqrt(-c**2*x**2 + 1)*asin(c*x)/(3*c**3) + 9*b**2*e*g*h**2*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(16*c**3) + 8*b**2*e*h**3*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(75*c**3) + 4*b**2*f*g**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c**3) + 9*b**2*f*g**2*h*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(16*c**3) + 8*b**2*f*g*h**2*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(25*c**3) + 5*b**2*f*h**3*x**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(72*c**3) - 3*b**2*d*h**3*asin(c*x)**2/(32*c**4) - 9*b**2*e*g*h**2*asin(c*x)**2/(32*c**4) - 16*b**2*e*h**3*x/(75*c**4) - 9*b**2*f*g**2*h*asin(c*x)**2/(32*c**4) - 16*b**2*f*g*h**2*x/(25*c**4) - 5*b**2*f*h**3*x**2/(96*c**4) + 16*b**2*e*h**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(75*c**5) + 16*b**2*f*g*h**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(25*c**5) + 5*b**2*f*h**3*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(48*c**5) - 5*b**2*f*h**3*asin(c*x)**2/(96*c**6), Ne(c, 0)), (a**2*(d*g**3*x + 3*d*g**2*h*x**2/2 + d*g*h**2*x**3 + d*h**3*x**4/4 + e*g**3*x**2/2 + e*g**2*h*x**3 + 3*e*g*h**2*x**4/4 + e*h**3*x**5/5 + f*g**3*x**3/3 + 3*f*g**2*h*x**4/4 + 3*f*g*h**2*x**5/5 + f*h**3*x**6/6), True))","A",0
116,1,1935,0,9.249102," ","integrate((h*x+g)**2*(f*x**2+e*x+d)*(a+b*asin(c*x))**2,x)","\begin{cases} a^{2} d g^{2} x + a^{2} d g h x^{2} + \frac{a^{2} d h^{2} x^{3}}{3} + \frac{a^{2} e g^{2} x^{2}}{2} + \frac{2 a^{2} e g h x^{3}}{3} + \frac{a^{2} e h^{2} x^{4}}{4} + \frac{a^{2} f g^{2} x^{3}}{3} + \frac{a^{2} f g h x^{4}}{2} + \frac{a^{2} f h^{2} x^{5}}{5} + 2 a b d g^{2} x \operatorname{asin}{\left(c x \right)} + 2 a b d g h x^{2} \operatorname{asin}{\left(c x \right)} + \frac{2 a b d h^{2} x^{3} \operatorname{asin}{\left(c x \right)}}{3} + a b e g^{2} x^{2} \operatorname{asin}{\left(c x \right)} + \frac{4 a b e g h x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{a b e h^{2} x^{4} \operatorname{asin}{\left(c x \right)}}{2} + \frac{2 a b f g^{2} x^{3} \operatorname{asin}{\left(c x \right)}}{3} + a b f g h x^{4} \operatorname{asin}{\left(c x \right)} + \frac{2 a b f h^{2} x^{5} \operatorname{asin}{\left(c x \right)}}{5} + \frac{2 a b d g^{2} \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{a b d g h x \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{2 a b d h^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{a b e g^{2} x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{4 a b e g h x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{a b e h^{2} x^{3} \sqrt{- c^{2} x^{2} + 1}}{8 c} + \frac{2 a b f g^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{a b f g h x^{3} \sqrt{- c^{2} x^{2} + 1}}{4 c} + \frac{2 a b f h^{2} x^{4} \sqrt{- c^{2} x^{2} + 1}}{25 c} - \frac{a b d g h \operatorname{asin}{\left(c x \right)}}{c^{2}} - \frac{a b e g^{2} \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + \frac{4 a b d h^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{8 a b e g h \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 a b e h^{2} x \sqrt{- c^{2} x^{2} + 1}}{16 c^{3}} + \frac{4 a b f g^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 a b f g h x \sqrt{- c^{2} x^{2} + 1}}{8 c^{3}} + \frac{8 a b f h^{2} x^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{3}} - \frac{3 a b e h^{2} \operatorname{asin}{\left(c x \right)}}{16 c^{4}} - \frac{3 a b f g h \operatorname{asin}{\left(c x \right)}}{8 c^{4}} + \frac{16 a b f h^{2} \sqrt{- c^{2} x^{2} + 1}}{75 c^{5}} + b^{2} d g^{2} x \operatorname{asin}^{2}{\left(c x \right)} - 2 b^{2} d g^{2} x + b^{2} d g h x^{2} \operatorname{asin}^{2}{\left(c x \right)} - \frac{b^{2} d g h x^{2}}{2} + \frac{b^{2} d h^{2} x^{3} \operatorname{asin}^{2}{\left(c x \right)}}{3} - \frac{2 b^{2} d h^{2} x^{3}}{27} + \frac{b^{2} e g^{2} x^{2} \operatorname{asin}^{2}{\left(c x \right)}}{2} - \frac{b^{2} e g^{2} x^{2}}{4} + \frac{2 b^{2} e g h x^{3} \operatorname{asin}^{2}{\left(c x \right)}}{3} - \frac{4 b^{2} e g h x^{3}}{27} + \frac{b^{2} e h^{2} x^{4} \operatorname{asin}^{2}{\left(c x \right)}}{4} - \frac{b^{2} e h^{2} x^{4}}{32} + \frac{b^{2} f g^{2} x^{3} \operatorname{asin}^{2}{\left(c x \right)}}{3} - \frac{2 b^{2} f g^{2} x^{3}}{27} + \frac{b^{2} f g h x^{4} \operatorname{asin}^{2}{\left(c x \right)}}{2} - \frac{b^{2} f g h x^{4}}{16} + \frac{b^{2} f h^{2} x^{5} \operatorname{asin}^{2}{\left(c x \right)}}{5} - \frac{2 b^{2} f h^{2} x^{5}}{125} + \frac{2 b^{2} d g^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} + \frac{b^{2} d g h x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} + \frac{2 b^{2} d h^{2} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c} + \frac{b^{2} e g^{2} x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{2 c} + \frac{4 b^{2} e g h x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c} + \frac{b^{2} e h^{2} x^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{8 c} + \frac{2 b^{2} f g^{2} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c} + \frac{b^{2} f g h x^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{4 c} + \frac{2 b^{2} f h^{2} x^{4} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{25 c} - \frac{b^{2} d g h \operatorname{asin}^{2}{\left(c x \right)}}{2 c^{2}} - \frac{4 b^{2} d h^{2} x}{9 c^{2}} - \frac{b^{2} e g^{2} \operatorname{asin}^{2}{\left(c x \right)}}{4 c^{2}} - \frac{8 b^{2} e g h x}{9 c^{2}} - \frac{3 b^{2} e h^{2} x^{2}}{32 c^{2}} - \frac{4 b^{2} f g^{2} x}{9 c^{2}} - \frac{3 b^{2} f g h x^{2}}{16 c^{2}} - \frac{8 b^{2} f h^{2} x^{3}}{225 c^{2}} + \frac{4 b^{2} d h^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c^{3}} + \frac{8 b^{2} e g h \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c^{3}} + \frac{3 b^{2} e h^{2} x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{16 c^{3}} + \frac{4 b^{2} f g^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c^{3}} + \frac{3 b^{2} f g h x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{8 c^{3}} + \frac{8 b^{2} f h^{2} x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{75 c^{3}} - \frac{3 b^{2} e h^{2} \operatorname{asin}^{2}{\left(c x \right)}}{32 c^{4}} - \frac{3 b^{2} f g h \operatorname{asin}^{2}{\left(c x \right)}}{16 c^{4}} - \frac{16 b^{2} f h^{2} x}{75 c^{4}} + \frac{16 b^{2} f h^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{75 c^{5}} & \text{for}\: c \neq 0 \\a^{2} \left(d g^{2} x + d g h x^{2} + \frac{d h^{2} x^{3}}{3} + \frac{e g^{2} x^{2}}{2} + \frac{2 e g h x^{3}}{3} + \frac{e h^{2} x^{4}}{4} + \frac{f g^{2} x^{3}}{3} + \frac{f g h x^{4}}{2} + \frac{f h^{2} x^{5}}{5}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*g**2*x + a**2*d*g*h*x**2 + a**2*d*h**2*x**3/3 + a**2*e*g**2*x**2/2 + 2*a**2*e*g*h*x**3/3 + a**2*e*h**2*x**4/4 + a**2*f*g**2*x**3/3 + a**2*f*g*h*x**4/2 + a**2*f*h**2*x**5/5 + 2*a*b*d*g**2*x*asin(c*x) + 2*a*b*d*g*h*x**2*asin(c*x) + 2*a*b*d*h**2*x**3*asin(c*x)/3 + a*b*e*g**2*x**2*asin(c*x) + 4*a*b*e*g*h*x**3*asin(c*x)/3 + a*b*e*h**2*x**4*asin(c*x)/2 + 2*a*b*f*g**2*x**3*asin(c*x)/3 + a*b*f*g*h*x**4*asin(c*x) + 2*a*b*f*h**2*x**5*asin(c*x)/5 + 2*a*b*d*g**2*sqrt(-c**2*x**2 + 1)/c + a*b*d*g*h*x*sqrt(-c**2*x**2 + 1)/c + 2*a*b*d*h**2*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + a*b*e*g**2*x*sqrt(-c**2*x**2 + 1)/(2*c) + 4*a*b*e*g*h*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + a*b*e*h**2*x**3*sqrt(-c**2*x**2 + 1)/(8*c) + 2*a*b*f*g**2*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + a*b*f*g*h*x**3*sqrt(-c**2*x**2 + 1)/(4*c) + 2*a*b*f*h**2*x**4*sqrt(-c**2*x**2 + 1)/(25*c) - a*b*d*g*h*asin(c*x)/c**2 - a*b*e*g**2*asin(c*x)/(2*c**2) + 4*a*b*d*h**2*sqrt(-c**2*x**2 + 1)/(9*c**3) + 8*a*b*e*g*h*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*a*b*e*h**2*x*sqrt(-c**2*x**2 + 1)/(16*c**3) + 4*a*b*f*g**2*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*a*b*f*g*h*x*sqrt(-c**2*x**2 + 1)/(8*c**3) + 8*a*b*f*h**2*x**2*sqrt(-c**2*x**2 + 1)/(75*c**3) - 3*a*b*e*h**2*asin(c*x)/(16*c**4) - 3*a*b*f*g*h*asin(c*x)/(8*c**4) + 16*a*b*f*h**2*sqrt(-c**2*x**2 + 1)/(75*c**5) + b**2*d*g**2*x*asin(c*x)**2 - 2*b**2*d*g**2*x + b**2*d*g*h*x**2*asin(c*x)**2 - b**2*d*g*h*x**2/2 + b**2*d*h**2*x**3*asin(c*x)**2/3 - 2*b**2*d*h**2*x**3/27 + b**2*e*g**2*x**2*asin(c*x)**2/2 - b**2*e*g**2*x**2/4 + 2*b**2*e*g*h*x**3*asin(c*x)**2/3 - 4*b**2*e*g*h*x**3/27 + b**2*e*h**2*x**4*asin(c*x)**2/4 - b**2*e*h**2*x**4/32 + b**2*f*g**2*x**3*asin(c*x)**2/3 - 2*b**2*f*g**2*x**3/27 + b**2*f*g*h*x**4*asin(c*x)**2/2 - b**2*f*g*h*x**4/16 + b**2*f*h**2*x**5*asin(c*x)**2/5 - 2*b**2*f*h**2*x**5/125 + 2*b**2*d*g**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/c + b**2*d*g*h*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/c + 2*b**2*d*h**2*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c) + b**2*e*g**2*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(2*c) + 4*b**2*e*g*h*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c) + b**2*e*h**2*x**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(8*c) + 2*b**2*f*g**2*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c) + b**2*f*g*h*x**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(4*c) + 2*b**2*f*h**2*x**4*sqrt(-c**2*x**2 + 1)*asin(c*x)/(25*c) - b**2*d*g*h*asin(c*x)**2/(2*c**2) - 4*b**2*d*h**2*x/(9*c**2) - b**2*e*g**2*asin(c*x)**2/(4*c**2) - 8*b**2*e*g*h*x/(9*c**2) - 3*b**2*e*h**2*x**2/(32*c**2) - 4*b**2*f*g**2*x/(9*c**2) - 3*b**2*f*g*h*x**2/(16*c**2) - 8*b**2*f*h**2*x**3/(225*c**2) + 4*b**2*d*h**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c**3) + 8*b**2*e*g*h*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c**3) + 3*b**2*e*h**2*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(16*c**3) + 4*b**2*f*g**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c**3) + 3*b**2*f*g*h*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(8*c**3) + 8*b**2*f*h**2*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(75*c**3) - 3*b**2*e*h**2*asin(c*x)**2/(32*c**4) - 3*b**2*f*g*h*asin(c*x)**2/(16*c**4) - 16*b**2*f*h**2*x/(75*c**4) + 16*b**2*f*h**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(75*c**5), Ne(c, 0)), (a**2*(d*g**2*x + d*g*h*x**2 + d*h**2*x**3/3 + e*g**2*x**2/2 + 2*e*g*h*x**3/3 + e*h**2*x**4/4 + f*g**2*x**3/3 + f*g*h*x**4/2 + f*h**2*x**5/5), True))","A",0
117,1,1059,0,4.429223," ","integrate((h*x+g)*(f*x**2+e*x+d)*(a+b*asin(c*x))**2,x)","\begin{cases} a^{2} d g x + \frac{a^{2} d h x^{2}}{2} + \frac{a^{2} e g x^{2}}{2} + \frac{a^{2} e h x^{3}}{3} + \frac{a^{2} f g x^{3}}{3} + \frac{a^{2} f h x^{4}}{4} + 2 a b d g x \operatorname{asin}{\left(c x \right)} + a b d h x^{2} \operatorname{asin}{\left(c x \right)} + a b e g x^{2} \operatorname{asin}{\left(c x \right)} + \frac{2 a b e h x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{2 a b f g x^{3} \operatorname{asin}{\left(c x \right)}}{3} + \frac{a b f h x^{4} \operatorname{asin}{\left(c x \right)}}{2} + \frac{2 a b d g \sqrt{- c^{2} x^{2} + 1}}{c} + \frac{a b d h x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{a b e g x \sqrt{- c^{2} x^{2} + 1}}{2 c} + \frac{2 a b e h x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{2 a b f g x^{2} \sqrt{- c^{2} x^{2} + 1}}{9 c} + \frac{a b f h x^{3} \sqrt{- c^{2} x^{2} + 1}}{8 c} - \frac{a b d h \operatorname{asin}{\left(c x \right)}}{2 c^{2}} - \frac{a b e g \operatorname{asin}{\left(c x \right)}}{2 c^{2}} + \frac{4 a b e h \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{4 a b f g \sqrt{- c^{2} x^{2} + 1}}{9 c^{3}} + \frac{3 a b f h x \sqrt{- c^{2} x^{2} + 1}}{16 c^{3}} - \frac{3 a b f h \operatorname{asin}{\left(c x \right)}}{16 c^{4}} + b^{2} d g x \operatorname{asin}^{2}{\left(c x \right)} - 2 b^{2} d g x + \frac{b^{2} d h x^{2} \operatorname{asin}^{2}{\left(c x \right)}}{2} - \frac{b^{2} d h x^{2}}{4} + \frac{b^{2} e g x^{2} \operatorname{asin}^{2}{\left(c x \right)}}{2} - \frac{b^{2} e g x^{2}}{4} + \frac{b^{2} e h x^{3} \operatorname{asin}^{2}{\left(c x \right)}}{3} - \frac{2 b^{2} e h x^{3}}{27} + \frac{b^{2} f g x^{3} \operatorname{asin}^{2}{\left(c x \right)}}{3} - \frac{2 b^{2} f g x^{3}}{27} + \frac{b^{2} f h x^{4} \operatorname{asin}^{2}{\left(c x \right)}}{4} - \frac{b^{2} f h x^{4}}{32} + \frac{2 b^{2} d g \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{c} + \frac{b^{2} d h x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{2 c} + \frac{b^{2} e g x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{2 c} + \frac{2 b^{2} e h x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c} + \frac{2 b^{2} f g x^{2} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c} + \frac{b^{2} f h x^{3} \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{8 c} - \frac{b^{2} d h \operatorname{asin}^{2}{\left(c x \right)}}{4 c^{2}} - \frac{b^{2} e g \operatorname{asin}^{2}{\left(c x \right)}}{4 c^{2}} - \frac{4 b^{2} e h x}{9 c^{2}} - \frac{4 b^{2} f g x}{9 c^{2}} - \frac{3 b^{2} f h x^{2}}{32 c^{2}} + \frac{4 b^{2} e h \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c^{3}} + \frac{4 b^{2} f g \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{9 c^{3}} + \frac{3 b^{2} f h x \sqrt{- c^{2} x^{2} + 1} \operatorname{asin}{\left(c x \right)}}{16 c^{3}} - \frac{3 b^{2} f h \operatorname{asin}^{2}{\left(c x \right)}}{32 c^{4}} & \text{for}\: c \neq 0 \\a^{2} \left(d g x + \frac{d h x^{2}}{2} + \frac{e g x^{2}}{2} + \frac{e h x^{3}}{3} + \frac{f g x^{3}}{3} + \frac{f h x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*d*g*x + a**2*d*h*x**2/2 + a**2*e*g*x**2/2 + a**2*e*h*x**3/3 + a**2*f*g*x**3/3 + a**2*f*h*x**4/4 + 2*a*b*d*g*x*asin(c*x) + a*b*d*h*x**2*asin(c*x) + a*b*e*g*x**2*asin(c*x) + 2*a*b*e*h*x**3*asin(c*x)/3 + 2*a*b*f*g*x**3*asin(c*x)/3 + a*b*f*h*x**4*asin(c*x)/2 + 2*a*b*d*g*sqrt(-c**2*x**2 + 1)/c + a*b*d*h*x*sqrt(-c**2*x**2 + 1)/(2*c) + a*b*e*g*x*sqrt(-c**2*x**2 + 1)/(2*c) + 2*a*b*e*h*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + 2*a*b*f*g*x**2*sqrt(-c**2*x**2 + 1)/(9*c) + a*b*f*h*x**3*sqrt(-c**2*x**2 + 1)/(8*c) - a*b*d*h*asin(c*x)/(2*c**2) - a*b*e*g*asin(c*x)/(2*c**2) + 4*a*b*e*h*sqrt(-c**2*x**2 + 1)/(9*c**3) + 4*a*b*f*g*sqrt(-c**2*x**2 + 1)/(9*c**3) + 3*a*b*f*h*x*sqrt(-c**2*x**2 + 1)/(16*c**3) - 3*a*b*f*h*asin(c*x)/(16*c**4) + b**2*d*g*x*asin(c*x)**2 - 2*b**2*d*g*x + b**2*d*h*x**2*asin(c*x)**2/2 - b**2*d*h*x**2/4 + b**2*e*g*x**2*asin(c*x)**2/2 - b**2*e*g*x**2/4 + b**2*e*h*x**3*asin(c*x)**2/3 - 2*b**2*e*h*x**3/27 + b**2*f*g*x**3*asin(c*x)**2/3 - 2*b**2*f*g*x**3/27 + b**2*f*h*x**4*asin(c*x)**2/4 - b**2*f*h*x**4/32 + 2*b**2*d*g*sqrt(-c**2*x**2 + 1)*asin(c*x)/c + b**2*d*h*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(2*c) + b**2*e*g*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(2*c) + 2*b**2*e*h*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c) + 2*b**2*f*g*x**2*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c) + b**2*f*h*x**3*sqrt(-c**2*x**2 + 1)*asin(c*x)/(8*c) - b**2*d*h*asin(c*x)**2/(4*c**2) - b**2*e*g*asin(c*x)**2/(4*c**2) - 4*b**2*e*h*x/(9*c**2) - 4*b**2*f*g*x/(9*c**2) - 3*b**2*f*h*x**2/(32*c**2) + 4*b**2*e*h*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c**3) + 4*b**2*f*g*sqrt(-c**2*x**2 + 1)*asin(c*x)/(9*c**3) + 3*b**2*f*h*x*sqrt(-c**2*x**2 + 1)*asin(c*x)/(16*c**3) - 3*b**2*f*h*asin(c*x)**2/(32*c**4), Ne(c, 0)), (a**2*(d*g*x + d*h*x**2/2 + e*g*x**2/2 + e*h*x**3/3 + f*g*x**3/3 + f*h*x**4/4), True))","A",0
118,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(a+b*asin(c*x))**2/(h*x+g),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(d + e x + f x^{2}\right)}{g + h x}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(d + e*x + f*x**2)/(g + h*x), x)","F",0
119,0,0,0,0.000000," ","integrate((f*x**2+e*x+d)*(a+b*asin(c*x))**2/(h*x+g)**2,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(d + e x + f x^{2}\right)}{\left(g + h x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(d + e*x + f*x**2)/(g + h*x)**2, x)","F",0
120,0,0,0,0.000000," ","integrate((e*h*x**2+2*d*h*x+e*f)*(a+b*asin(c*x))**2/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(2 d h x + e f + e h x^{2}\right)}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(2*d*h*x + e*f + e*h*x**2)/(d + e*x)**2, x)","F",0
121,0,0,0,0.000000," ","integrate((e*h*x**2+2*d*h*x+e*f)**2*(a+b*asin(c*x))**2/(e*x+d)**2,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c x \right)}\right)^{2} \left(2 d h x + e f + e h x^{2}\right)^{2}}{\left(d + e x\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c*x))**2*(2*d*h*x + e*f + e*h*x**2)**2/(d + e*x)**2, x)","F",0
122,1,255,0,1.327062," ","integrate(x**3*asin(b*x+a),x)","\begin{cases} - \frac{a^{4} \operatorname{asin}{\left(a + b x \right)}}{4 b^{4}} - \frac{25 a^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{48 b^{4}} + \frac{13 a^{2} x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{48 b^{3}} - \frac{3 a^{2} \operatorname{asin}{\left(a + b x \right)}}{4 b^{4}} - \frac{7 a x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{48 b^{2}} - \frac{55 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{96 b^{4}} + \frac{x^{4} \operatorname{asin}{\left(a + b x \right)}}{4} + \frac{x^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{16 b} + \frac{3 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{32 b^{3}} - \frac{3 \operatorname{asin}{\left(a + b x \right)}}{32 b^{4}} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{asin}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*asin(a + b*x)/(4*b**4) - 25*a**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(48*b**4) + 13*a**2*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(48*b**3) - 3*a**2*asin(a + b*x)/(4*b**4) - 7*a*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(48*b**2) - 55*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(96*b**4) + x**4*asin(a + b*x)/4 + x**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(16*b) + 3*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(32*b**3) - 3*asin(a + b*x)/(32*b**4), Ne(b, 0)), (x**4*asin(a)/4, True))","A",0
123,1,170,0,0.619387," ","integrate(x**2*asin(b*x+a),x)","\begin{cases} \frac{a^{3} \operatorname{asin}{\left(a + b x \right)}}{3 b^{3}} + \frac{11 a^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{18 b^{3}} - \frac{5 a x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{18 b^{2}} + \frac{a \operatorname{asin}{\left(a + b x \right)}}{2 b^{3}} + \frac{x^{3} \operatorname{asin}{\left(a + b x \right)}}{3} + \frac{x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{9 b} + \frac{2 \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{9 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \operatorname{asin}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*asin(a + b*x)/(3*b**3) + 11*a**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(18*b**3) - 5*a*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(18*b**2) + a*asin(a + b*x)/(2*b**3) + x**3*asin(a + b*x)/3 + x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(9*b) + 2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(9*b**3), Ne(b, 0)), (x**3*asin(a)/3, True))","A",0
124,1,104,0,0.285286," ","integrate(x*asin(b*x+a),x)","\begin{cases} - \frac{a^{2} \operatorname{asin}{\left(a + b x \right)}}{2 b^{2}} - \frac{3 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{4 b^{2}} + \frac{x^{2} \operatorname{asin}{\left(a + b x \right)}}{2} + \frac{x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{4 b} - \frac{\operatorname{asin}{\left(a + b x \right)}}{4 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \operatorname{asin}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*asin(a + b*x)/(2*b**2) - 3*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(4*b**2) + x**2*asin(a + b*x)/2 + x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(4*b) - asin(a + b*x)/(4*b**2), Ne(b, 0)), (x**2*asin(a)/2, True))","A",0
125,1,46,0,0.147208," ","integrate(asin(b*x+a),x)","\begin{cases} \frac{a \operatorname{asin}{\left(a + b x \right)}}{b} + x \operatorname{asin}{\left(a + b x \right)} + \frac{\sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{b} & \text{for}\: b \neq 0 \\x \operatorname{asin}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*asin(a + b*x)/b + x*asin(a + b*x) + sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/b, Ne(b, 0)), (x*asin(a), True))","A",0
126,0,0,0,0.000000," ","integrate(asin(b*x+a)/x,x)","\int \frac{\operatorname{asin}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(asin(a + b*x)/x, x)","F",0
127,0,0,0,0.000000," ","integrate(asin(b*x+a)/x**2,x)","\int \frac{\operatorname{asin}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(asin(a + b*x)/x**2, x)","F",0
128,0,0,0,0.000000," ","integrate(asin(b*x+a)/x**3,x)","\int \frac{\operatorname{asin}{\left(a + b x \right)}}{x^{3}}\, dx"," ",0,"Integral(asin(a + b*x)/x**3, x)","F",0
129,0,0,0,0.000000," ","integrate(asin(b*x+a)/x**4,x)","\int \frac{\operatorname{asin}{\left(a + b x \right)}}{x^{4}}\, dx"," ",0,"Integral(asin(a + b*x)/x**4, x)","F",0
130,0,0,0,0.000000," ","integrate(asin(b*x+a)/x**5,x)","\int \frac{\operatorname{asin}{\left(a + b x \right)}}{x^{5}}\, dx"," ",0,"Integral(asin(a + b*x)/x**5, x)","F",0
131,1,366,0,2.912842," ","integrate(x**3*asin(b*x+a)**2,x)","\begin{cases} - \frac{a^{4} \operatorname{asin}^{2}{\left(a + b x \right)}}{4 b^{4}} + \frac{25 a^{3} x}{24 b^{3}} - \frac{25 a^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{24 b^{4}} - \frac{13 a^{2} x^{2}}{48 b^{2}} + \frac{13 a^{2} x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{24 b^{3}} - \frac{3 a^{2} \operatorname{asin}^{2}{\left(a + b x \right)}}{4 b^{4}} + \frac{7 a x^{3}}{72 b} - \frac{7 a x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{24 b^{2}} + \frac{55 a x}{48 b^{3}} - \frac{55 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{48 b^{4}} + \frac{x^{4} \operatorname{asin}^{2}{\left(a + b x \right)}}{4} - \frac{x^{4}}{32} + \frac{x^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{8 b} - \frac{3 x^{2}}{32 b^{2}} + \frac{3 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{16 b^{3}} - \frac{3 \operatorname{asin}^{2}{\left(a + b x \right)}}{32 b^{4}} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{asin}^{2}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*asin(a + b*x)**2/(4*b**4) + 25*a**3*x/(24*b**3) - 25*a**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(24*b**4) - 13*a**2*x**2/(48*b**2) + 13*a**2*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(24*b**3) - 3*a**2*asin(a + b*x)**2/(4*b**4) + 7*a*x**3/(72*b) - 7*a*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(24*b**2) + 55*a*x/(48*b**3) - 55*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(48*b**4) + x**4*asin(a + b*x)**2/4 - x**4/32 + x**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(8*b) - 3*x**2/(32*b**2) + 3*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(16*b**3) - 3*asin(a + b*x)**2/(32*b**4), Ne(b, 0)), (x**4*asin(a)**2/4, True))","A",0
132,1,243,0,1.278257," ","integrate(x**2*asin(b*x+a)**2,x)","\begin{cases} \frac{a^{3} \operatorname{asin}^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{11 a^{2} x}{9 b^{2}} + \frac{11 a^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{9 b^{3}} + \frac{5 a x^{2}}{18 b} - \frac{5 a x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{9 b^{2}} + \frac{a \operatorname{asin}^{2}{\left(a + b x \right)}}{2 b^{3}} + \frac{x^{3} \operatorname{asin}^{2}{\left(a + b x \right)}}{3} - \frac{2 x^{3}}{27} + \frac{2 x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{9 b} - \frac{4 x}{9 b^{2}} + \frac{4 \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{9 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \operatorname{asin}^{2}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*asin(a + b*x)**2/(3*b**3) - 11*a**2*x/(9*b**2) + 11*a**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(9*b**3) + 5*a*x**2/(18*b) - 5*a*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(9*b**2) + a*asin(a + b*x)**2/(2*b**3) + x**3*asin(a + b*x)**2/3 - 2*x**3/27 + 2*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(9*b) - 4*x/(9*b**2) + 4*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(9*b**3), Ne(b, 0)), (x**3*asin(a)**2/3, True))","A",0
133,1,138,0,0.591916," ","integrate(x*asin(b*x+a)**2,x)","\begin{cases} - \frac{a^{2} \operatorname{asin}^{2}{\left(a + b x \right)}}{2 b^{2}} + \frac{3 a x}{2 b} - \frac{3 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{2 b^{2}} + \frac{x^{2} \operatorname{asin}^{2}{\left(a + b x \right)}}{2} - \frac{x^{2}}{4} + \frac{x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{2 b} - \frac{\operatorname{asin}^{2}{\left(a + b x \right)}}{4 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \operatorname{asin}^{2}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*asin(a + b*x)**2/(2*b**2) + 3*a*x/(2*b) - 3*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(2*b**2) + x**2*asin(a + b*x)**2/2 - x**2/4 + x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(2*b) - asin(a + b*x)**2/(4*b**2), Ne(b, 0)), (x**2*asin(a)**2/2, True))","A",0
134,1,63,0,0.241351," ","integrate(asin(b*x+a)**2,x)","\begin{cases} \frac{a \operatorname{asin}^{2}{\left(a + b x \right)}}{b} + x \operatorname{asin}^{2}{\left(a + b x \right)} - 2 x + \frac{2 \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \operatorname{asin}^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*asin(a + b*x)**2/b + x*asin(a + b*x)**2 - 2*x + 2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/b, Ne(b, 0)), (x*asin(a)**2, True))","A",0
135,0,0,0,0.000000," ","integrate(asin(b*x+a)**2/x,x)","\int \frac{\operatorname{asin}^{2}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(asin(a + b*x)**2/x, x)","F",0
136,0,0,0,0.000000," ","integrate(asin(b*x+a)**2/x**2,x)","\int \frac{\operatorname{asin}^{2}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(asin(a + b*x)**2/x**2, x)","F",0
137,0,0,0,0.000000," ","integrate(asin(b*x+a)**2/x**3,x)","\int \frac{\operatorname{asin}^{2}{\left(a + b x \right)}}{x^{3}}\, dx"," ",0,"Integral(asin(a + b*x)**2/x**3, x)","F",0
138,1,432,0,2.802250," ","integrate(x**2*asin(b*x+a)**3,x)","\begin{cases} \frac{a^{3} \operatorname{asin}^{3}{\left(a + b x \right)}}{3 b^{3}} - \frac{85 a^{3} \operatorname{asin}{\left(a + b x \right)}}{18 b^{3}} - \frac{11 a^{2} x \operatorname{asin}{\left(a + b x \right)}}{3 b^{2}} + \frac{11 a^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{6 b^{3}} - \frac{575 a^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{108 b^{3}} + \frac{5 a x^{2} \operatorname{asin}{\left(a + b x \right)}}{6 b} - \frac{5 a x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{6 b^{2}} + \frac{65 a x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{108 b^{2}} + \frac{a \operatorname{asin}^{3}{\left(a + b x \right)}}{2 b^{3}} - \frac{25 a \operatorname{asin}{\left(a + b x \right)}}{12 b^{3}} + \frac{x^{3} \operatorname{asin}^{3}{\left(a + b x \right)}}{3} - \frac{2 x^{3} \operatorname{asin}{\left(a + b x \right)}}{9} + \frac{x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{3 b} - \frac{2 x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{27 b} - \frac{4 x \operatorname{asin}{\left(a + b x \right)}}{3 b^{2}} + \frac{2 \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{3 b^{3}} - \frac{40 \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{27 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \operatorname{asin}^{3}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*asin(a + b*x)**3/(3*b**3) - 85*a**3*asin(a + b*x)/(18*b**3) - 11*a**2*x*asin(a + b*x)/(3*b**2) + 11*a**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/(6*b**3) - 575*a**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(108*b**3) + 5*a*x**2*asin(a + b*x)/(6*b) - 5*a*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/(6*b**2) + 65*a*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(108*b**2) + a*asin(a + b*x)**3/(2*b**3) - 25*a*asin(a + b*x)/(12*b**3) + x**3*asin(a + b*x)**3/3 - 2*x**3*asin(a + b*x)/9 + x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/(3*b) - 2*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(27*b) - 4*x*asin(a + b*x)/(3*b**2) + 2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/(3*b**3) - 40*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(27*b**3), Ne(b, 0)), (x**3*asin(a)**3/3, True))","A",0
139,1,248,0,1.198515," ","integrate(x*asin(b*x+a)**3,x)","\begin{cases} - \frac{a^{2} \operatorname{asin}^{3}{\left(a + b x \right)}}{2 b^{2}} + \frac{21 a^{2} \operatorname{asin}{\left(a + b x \right)}}{4 b^{2}} + \frac{9 a x \operatorname{asin}{\left(a + b x \right)}}{2 b} - \frac{9 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{4 b^{2}} + \frac{45 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{8 b^{2}} + \frac{x^{2} \operatorname{asin}^{3}{\left(a + b x \right)}}{2} - \frac{3 x^{2} \operatorname{asin}{\left(a + b x \right)}}{4} + \frac{3 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{4 b} - \frac{3 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{8 b} - \frac{\operatorname{asin}^{3}{\left(a + b x \right)}}{4 b^{2}} + \frac{3 \operatorname{asin}{\left(a + b x \right)}}{8 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \operatorname{asin}^{3}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*asin(a + b*x)**3/(2*b**2) + 21*a**2*asin(a + b*x)/(4*b**2) + 9*a*x*asin(a + b*x)/(2*b) - 9*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/(4*b**2) + 45*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(8*b**2) + x**2*asin(a + b*x)**3/2 - 3*x**2*asin(a + b*x)/4 + 3*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/(4*b) - 3*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(8*b) - asin(a + b*x)**3/(4*b**2) + 3*asin(a + b*x)/(8*b**2), Ne(b, 0)), (x**2*asin(a)**3/2, True))","A",0
140,1,109,0,0.512378," ","integrate(asin(b*x+a)**3,x)","\begin{cases} \frac{a \operatorname{asin}^{3}{\left(a + b x \right)}}{b} - \frac{6 a \operatorname{asin}{\left(a + b x \right)}}{b} + x \operatorname{asin}^{3}{\left(a + b x \right)} - 6 x \operatorname{asin}{\left(a + b x \right)} + \frac{3 \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{b} - \frac{6 \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{b} & \text{for}\: b \neq 0 \\x \operatorname{asin}^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*asin(a + b*x)**3/b - 6*a*asin(a + b*x)/b + x*asin(a + b*x)**3 - 6*x*asin(a + b*x) + 3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/b - 6*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/b, Ne(b, 0)), (x*asin(a)**3, True))","A",0
141,0,0,0,0.000000," ","integrate(asin(b*x+a)**3/x,x)","\int \frac{\operatorname{asin}^{3}{\left(a + b x \right)}}{x}\, dx"," ",0,"Integral(asin(a + b*x)**3/x, x)","F",0
142,0,0,0,0.000000," ","integrate(asin(b*x+a)**3/x**2,x)","\int \frac{\operatorname{asin}^{3}{\left(a + b x \right)}}{x^{2}}\, dx"," ",0,"Integral(asin(a + b*x)**3/x**2, x)","F",0
143,0,0,0,0.000000," ","integrate(x**2/asin(b*x+a),x)","\int \frac{x^{2}}{\operatorname{asin}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2/asin(a + b*x), x)","F",0
144,0,0,0,0.000000," ","integrate(x/asin(b*x+a),x)","\int \frac{x}{\operatorname{asin}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x/asin(a + b*x), x)","F",0
145,0,0,0,0.000000," ","integrate(1/asin(b*x+a),x)","\int \frac{1}{\operatorname{asin}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/asin(a + b*x), x)","F",0
146,0,0,0,0.000000," ","integrate(1/x/asin(b*x+a),x)","\int \frac{1}{x \operatorname{asin}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/(x*asin(a + b*x)), x)","F",0
147,0,0,0,0.000000," ","integrate(x**2/asin(b*x+a)**2,x)","\int \frac{x^{2}}{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2/asin(a + b*x)**2, x)","F",0
148,0,0,0,0.000000," ","integrate(x/asin(b*x+a)**2,x)","\int \frac{x}{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x/asin(a + b*x)**2, x)","F",0
149,0,0,0,0.000000," ","integrate(1/asin(b*x+a)**2,x)","\int \frac{1}{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(asin(a + b*x)**(-2), x)","F",0
150,0,0,0,0.000000," ","integrate(1/x/asin(b*x+a)**2,x)","\int \frac{1}{x \operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/(x*asin(a + b*x)**2), x)","F",0
151,0,0,0,0.000000," ","integrate(x**2/asin(b*x+a)**3,x)","\int \frac{x^{2}}{\operatorname{asin}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2/asin(a + b*x)**3, x)","F",0
152,0,0,0,0.000000," ","integrate(x/asin(b*x+a)**3,x)","\int \frac{x}{\operatorname{asin}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x/asin(a + b*x)**3, x)","F",0
153,0,0,0,0.000000," ","integrate(1/asin(b*x+a)**3,x)","\int \frac{1}{\operatorname{asin}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(asin(a + b*x)**(-3), x)","F",0
154,0,0,0,0.000000," ","integrate(1/x/asin(b*x+a)**3,x)","\int \frac{1}{x \operatorname{asin}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/(x*asin(a + b*x)**3), x)","F",0
155,0,0,0,0.000000," ","integrate(x**2*(a+b*asin(d*x+c))**(1/2),x)","\int x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx"," ",0,"Integral(x**2*sqrt(a + b*asin(c + d*x)), x)","F",0
156,0,0,0,0.000000," ","integrate(x*(a+b*asin(d*x+c))**(1/2),x)","\int x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx"," ",0,"Integral(x*sqrt(a + b*asin(c + d*x)), x)","F",0
157,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(1/2),x)","\int \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*asin(c + d*x)), x)","F",0
158,0,0,0,0.000000," ","integrate(x*(a+b*asin(d*x+c))**(3/2),x)","\int x \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(x*(a + b*asin(c + d*x))**(3/2), x)","F",0
159,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(3/2),x)","\int \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(3/2), x)","F",0
160,0,0,0,0.000000," ","integrate(x*(a+b*asin(d*x+c))**(5/2),x)","\int x \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral(x*(a + b*asin(c + d*x))**(5/2), x)","F",0
161,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(5/2),x)","\int \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(5/2), x)","F",0
162,-1,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,0,0,0,0.000000," ","integrate(x**2/(a+b*asin(d*x+c))**(1/2),x)","\int \frac{x^{2}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(x**2/sqrt(a + b*asin(c + d*x)), x)","F",0
164,0,0,0,0.000000," ","integrate(x/(a+b*asin(d*x+c))**(1/2),x)","\int \frac{x}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(x/sqrt(a + b*asin(c + d*x)), x)","F",0
165,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*asin(c + d*x)), x)","F",0
166,0,0,0,0.000000," ","integrate(x/(a+b*asin(d*x+c))**(3/2),x)","\int \frac{x}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(x/(a + b*asin(c + d*x))**(3/2), x)","F",0
167,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-3/2), x)","F",0
168,0,0,0,0.000000," ","integrate(x/(a+b*asin(d*x+c))**(5/2),x)","\int \frac{x}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(x/(a + b*asin(c + d*x))**(5/2), x)","F",0
169,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-5/2), x)","F",0
170,0,0,0,0.000000," ","integrate(x/(a+b*asin(d*x+c))**(7/2),x)","\int \frac{x}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(x/(a + b*asin(c + d*x))**(7/2), x)","F",0
171,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-7/2), x)","F",0
172,0,0,0,0.000000," ","integrate(x**m*(a+b*asin(d*x+c))**n,x)","\int x^{m} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral(x**m*(a + b*asin(c + d*x))**n, x)","F",0
173,0,0,0,0.000000," ","integrate(x**2*(a+b*asin(d*x+c))**n,x)","\int x^{2} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral(x**2*(a + b*asin(c + d*x))**n, x)","F",0
174,0,0,0,0.000000," ","integrate(x*(a+b*asin(d*x+c))**n,x)","\int x \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral(x*(a + b*asin(c + d*x))**n, x)","F",0
175,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**n,x)","\int \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**n, x)","F",0
176,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**n/x,x)","\int \frac{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{n}}{x}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**n/x, x)","F",0
177,1,527,0,3.139631," ","integrate((d*e*x+c*e)**4*(a+b*asin(d*x+c)),x)","\begin{cases} a c^{4} e^{4} x + 2 a c^{3} d e^{4} x^{2} + 2 a c^{2} d^{2} e^{4} x^{3} + a c d^{3} e^{4} x^{4} + \frac{a d^{4} e^{4} x^{5}}{5} + \frac{b c^{5} e^{4} \operatorname{asin}{\left(c + d x \right)}}{5 d} + b c^{4} e^{4} x \operatorname{asin}{\left(c + d x \right)} + \frac{b c^{4} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25 d} + 2 b c^{3} d e^{4} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{4 b c^{3} e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + 2 b c^{2} d^{2} e^{4} x^{3} \operatorname{asin}{\left(c + d x \right)} + \frac{6 b c^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{4 b c^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{75 d} + b c d^{3} e^{4} x^{4} \operatorname{asin}{\left(c + d x \right)} + \frac{4 b c d^{2} e^{4} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{8 b c e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{75} + \frac{b d^{4} e^{4} x^{5} \operatorname{asin}{\left(c + d x \right)}}{5} + \frac{b d^{3} e^{4} x^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{4 b d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{75} + \frac{8 b e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{75 d} & \text{for}\: d \neq 0 \\c^{4} e^{4} x \left(a + b \operatorname{asin}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**4*e**4*x + 2*a*c**3*d*e**4*x**2 + 2*a*c**2*d**2*e**4*x**3 + a*c*d**3*e**4*x**4 + a*d**4*e**4*x**5/5 + b*c**5*e**4*asin(c + d*x)/(5*d) + b*c**4*e**4*x*asin(c + d*x) + b*c**4*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(25*d) + 2*b*c**3*d*e**4*x**2*asin(c + d*x) + 4*b*c**3*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 2*b*c**2*d**2*e**4*x**3*asin(c + d*x) + 6*b*c**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 4*b*c**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(75*d) + b*c*d**3*e**4*x**4*asin(c + d*x) + 4*b*c*d**2*e**4*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 8*b*c*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/75 + b*d**4*e**4*x**5*asin(c + d*x)/5 + b*d**3*e**4*x**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 4*b*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/75 + 8*b*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(75*d), Ne(d, 0)), (c**4*e**4*x*(a + b*asin(c)), True))","A",0
178,1,394,0,1.577416," ","integrate((d*e*x+c*e)**3*(a+b*asin(d*x+c)),x)","\begin{cases} a c^{3} e^{3} x + \frac{3 a c^{2} d e^{3} x^{2}}{2} + a c d^{2} e^{3} x^{3} + \frac{a d^{3} e^{3} x^{4}}{4} + \frac{b c^{4} e^{3} \operatorname{asin}{\left(c + d x \right)}}{4 d} + b c^{3} e^{3} x \operatorname{asin}{\left(c + d x \right)} + \frac{b c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16 d} + \frac{3 b c^{2} d e^{3} x^{2} \operatorname{asin}{\left(c + d x \right)}}{2} + \frac{3 b c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16} + b c d^{2} e^{3} x^{3} \operatorname{asin}{\left(c + d x \right)} + \frac{3 b c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16} + \frac{3 b c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{32 d} + \frac{b d^{3} e^{3} x^{4} \operatorname{asin}{\left(c + d x \right)}}{4} + \frac{b d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16} + \frac{3 b e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{32} - \frac{3 b e^{3} \operatorname{asin}{\left(c + d x \right)}}{32 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{asin}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**3*e**3*x + 3*a*c**2*d*e**3*x**2/2 + a*c*d**2*e**3*x**3 + a*d**3*e**3*x**4/4 + b*c**4*e**3*asin(c + d*x)/(4*d) + b*c**3*e**3*x*asin(c + d*x) + b*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(16*d) + 3*b*c**2*d*e**3*x**2*asin(c + d*x)/2 + 3*b*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/16 + b*c*d**2*e**3*x**3*asin(c + d*x) + 3*b*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/16 + 3*b*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(32*d) + b*d**3*e**3*x**4*asin(c + d*x)/4 + b*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/16 + 3*b*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/32 - 3*b*e**3*asin(c + d*x)/(32*d), Ne(d, 0)), (c**3*e**3*x*(a + b*asin(c)), True))","A",0
179,1,258,0,0.724001," ","integrate((d*e*x+c*e)**2*(a+b*asin(d*x+c)),x)","\begin{cases} a c^{2} e^{2} x + a c d e^{2} x^{2} + \frac{a d^{2} e^{2} x^{3}}{3} + \frac{b c^{3} e^{2} \operatorname{asin}{\left(c + d x \right)}}{3 d} + b c^{2} e^{2} x \operatorname{asin}{\left(c + d x \right)} + \frac{b c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9 d} + b c d e^{2} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{2 b c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9} + \frac{b d^{2} e^{2} x^{3} \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{b d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9} + \frac{2 b e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{asin}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c**2*e**2*x + a*c*d*e**2*x**2 + a*d**2*e**2*x**3/3 + b*c**3*e**2*asin(c + d*x)/(3*d) + b*c**2*e**2*x*asin(c + d*x) + b*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(9*d) + b*c*d*e**2*x**2*asin(c + d*x) + 2*b*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/9 + b*d**2*e**2*x**3*asin(c + d*x)/3 + b*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/9 + 2*b*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(9*d), Ne(d, 0)), (c**2*e**2*x*(a + b*asin(c)), True))","A",0
180,1,148,0,0.312833," ","integrate((d*e*x+c*e)*(a+b*asin(d*x+c)),x)","\begin{cases} a c e x + \frac{a d e x^{2}}{2} + \frac{b c^{2} e \operatorname{asin}{\left(c + d x \right)}}{2 d} + b c e x \operatorname{asin}{\left(c + d x \right)} + \frac{b c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{4 d} + \frac{b d e x^{2} \operatorname{asin}{\left(c + d x \right)}}{2} + \frac{b e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{4} - \frac{b e \operatorname{asin}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{asin}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*e*x + a*d*e*x**2/2 + b*c**2*e*asin(c + d*x)/(2*d) + b*c*e*x*asin(c + d*x) + b*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(4*d) + b*d*e*x**2*asin(c + d*x)/2 + b*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/4 - b*e*asin(c + d*x)/(4*d), Ne(d, 0)), (c*e*x*(a + b*asin(c)), True))","A",0
181,1,51,0,0.148315," ","integrate(a+b*asin(d*x+c),x)","a x + b \left(\begin{cases} \frac{c \operatorname{asin}{\left(c + d x \right)}}{d} + x \operatorname{asin}{\left(c + d x \right)} + \frac{\sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} & \text{for}\: d \neq 0 \\x \operatorname{asin}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((c*asin(c + d*x)/d + x*asin(c + d*x) + sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d, Ne(d, 0)), (x*asin(c), True))","A",0
182,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e),x)","\frac{\int \frac{a}{c + d x}\, dx + \int \frac{b \operatorname{asin}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a/(c + d*x), x) + Integral(b*asin(c + d*x)/(c + d*x), x))/e","F",0
183,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**2,x)","\frac{\int \frac{a}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{b \operatorname{asin}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx}{e^{2}}"," ",0,"(Integral(a/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(b*asin(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
184,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**3,x)","\frac{\int \frac{a}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{b \operatorname{asin}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx}{e^{3}}"," ",0,"(Integral(a/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(b*asin(c + d*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))/e**3","F",0
185,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**4,x)","\frac{\int \frac{a}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{b \operatorname{asin}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}}"," ",0,"(Integral(a/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(b*asin(c + d*x)/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x))/e**4","F",0
186,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**5,x)","\frac{\int \frac{a}{c^{5} + 5 c^{4} d x + 10 c^{3} d^{2} x^{2} + 10 c^{2} d^{3} x^{3} + 5 c d^{4} x^{4} + d^{5} x^{5}}\, dx + \int \frac{b \operatorname{asin}{\left(c + d x \right)}}{c^{5} + 5 c^{4} d x + 10 c^{3} d^{2} x^{2} + 10 c^{2} d^{3} x^{3} + 5 c d^{4} x^{4} + d^{5} x^{5}}\, dx}{e^{5}}"," ",0,"(Integral(a/(c**5 + 5*c**4*d*x + 10*c**3*d**2*x**2 + 10*c**2*d**3*x**3 + 5*c*d**4*x**4 + d**5*x**5), x) + Integral(b*asin(c + d*x)/(c**5 + 5*c**4*d*x + 10*c**3*d**2*x**2 + 10*c**2*d**3*x**3 + 5*c*d**4*x**4 + d**5*x**5), x))/e**5","F",0
187,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**6,x)","\frac{\int \frac{a}{c^{6} + 6 c^{5} d x + 15 c^{4} d^{2} x^{2} + 20 c^{3} d^{3} x^{3} + 15 c^{2} d^{4} x^{4} + 6 c d^{5} x^{5} + d^{6} x^{6}}\, dx + \int \frac{b \operatorname{asin}{\left(c + d x \right)}}{c^{6} + 6 c^{5} d x + 15 c^{4} d^{2} x^{2} + 20 c^{3} d^{3} x^{3} + 15 c^{2} d^{4} x^{4} + 6 c d^{5} x^{5} + d^{6} x^{6}}\, dx}{e^{6}}"," ",0,"(Integral(a/(c**6 + 6*c**5*d*x + 15*c**4*d**2*x**2 + 20*c**3*d**3*x**3 + 15*c**2*d**4*x**4 + 6*c*d**5*x**5 + d**6*x**6), x) + Integral(b*asin(c + d*x)/(c**6 + 6*c**5*d*x + 15*c**4*d**2*x**2 + 20*c**3*d**3*x**3 + 15*c**2*d**4*x**4 + 6*c*d**5*x**5 + d**6*x**6), x))/e**6","F",0
188,1,1268,0,6.662287," ","integrate((d*e*x+c*e)**4*(a+b*asin(d*x+c))**2,x)","\begin{cases} a^{2} c^{4} e^{4} x + 2 a^{2} c^{3} d e^{4} x^{2} + 2 a^{2} c^{2} d^{2} e^{4} x^{3} + a^{2} c d^{3} e^{4} x^{4} + \frac{a^{2} d^{4} e^{4} x^{5}}{5} + \frac{2 a b c^{5} e^{4} \operatorname{asin}{\left(c + d x \right)}}{5 d} + 2 a b c^{4} e^{4} x \operatorname{asin}{\left(c + d x \right)} + \frac{2 a b c^{4} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25 d} + 4 a b c^{3} d e^{4} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{8 a b c^{3} e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + 4 a b c^{2} d^{2} e^{4} x^{3} \operatorname{asin}{\left(c + d x \right)} + \frac{12 a b c^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{8 a b c^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{75 d} + 2 a b c d^{3} e^{4} x^{4} \operatorname{asin}{\left(c + d x \right)} + \frac{8 a b c d^{2} e^{4} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{16 a b c e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{75} + \frac{2 a b d^{4} e^{4} x^{5} \operatorname{asin}{\left(c + d x \right)}}{5} + \frac{2 a b d^{3} e^{4} x^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{8 a b d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{75} + \frac{16 a b e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{75 d} + \frac{b^{2} c^{5} e^{4} \operatorname{asin}^{2}{\left(c + d x \right)}}{5 d} + b^{2} c^{4} e^{4} x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{2 b^{2} c^{4} e^{4} x}{25} + \frac{2 b^{2} c^{4} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25 d} + 2 b^{2} c^{3} d e^{4} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{4 b^{2} c^{3} d e^{4} x^{2}}{25} + \frac{8 b^{2} c^{3} e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} + 2 b^{2} c^{2} d^{2} e^{4} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{4 b^{2} c^{2} d^{2} e^{4} x^{3}}{25} + \frac{12 b^{2} c^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} - \frac{8 b^{2} c^{2} e^{4} x}{75} + \frac{8 b^{2} c^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{75 d} + b^{2} c d^{3} e^{4} x^{4} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{2 b^{2} c d^{3} e^{4} x^{4}}{25} + \frac{8 b^{2} c d^{2} e^{4} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} - \frac{8 b^{2} c d e^{4} x^{2}}{75} + \frac{16 b^{2} c e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{75} + \frac{b^{2} d^{4} e^{4} x^{5} \operatorname{asin}^{2}{\left(c + d x \right)}}{5} - \frac{2 b^{2} d^{4} e^{4} x^{5}}{125} + \frac{2 b^{2} d^{3} e^{4} x^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} - \frac{8 b^{2} d^{2} e^{4} x^{3}}{225} + \frac{8 b^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{75} - \frac{16 b^{2} e^{4} x}{75} + \frac{16 b^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{75 d} & \text{for}\: d \neq 0 \\c^{4} e^{4} x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**4*e**4*x + 2*a**2*c**3*d*e**4*x**2 + 2*a**2*c**2*d**2*e**4*x**3 + a**2*c*d**3*e**4*x**4 + a**2*d**4*e**4*x**5/5 + 2*a*b*c**5*e**4*asin(c + d*x)/(5*d) + 2*a*b*c**4*e**4*x*asin(c + d*x) + 2*a*b*c**4*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(25*d) + 4*a*b*c**3*d*e**4*x**2*asin(c + d*x) + 8*a*b*c**3*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 4*a*b*c**2*d**2*e**4*x**3*asin(c + d*x) + 12*a*b*c**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 8*a*b*c**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(75*d) + 2*a*b*c*d**3*e**4*x**4*asin(c + d*x) + 8*a*b*c*d**2*e**4*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 16*a*b*c*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/75 + 2*a*b*d**4*e**4*x**5*asin(c + d*x)/5 + 2*a*b*d**3*e**4*x**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 8*a*b*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/75 + 16*a*b*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(75*d) + b**2*c**5*e**4*asin(c + d*x)**2/(5*d) + b**2*c**4*e**4*x*asin(c + d*x)**2 - 2*b**2*c**4*e**4*x/25 + 2*b**2*c**4*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(25*d) + 2*b**2*c**3*d*e**4*x**2*asin(c + d*x)**2 - 4*b**2*c**3*d*e**4*x**2/25 + 8*b**2*c**3*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 + 2*b**2*c**2*d**2*e**4*x**3*asin(c + d*x)**2 - 4*b**2*c**2*d**2*e**4*x**3/25 + 12*b**2*c**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 - 8*b**2*c**2*e**4*x/75 + 8*b**2*c**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(75*d) + b**2*c*d**3*e**4*x**4*asin(c + d*x)**2 - 2*b**2*c*d**3*e**4*x**4/25 + 8*b**2*c*d**2*e**4*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 - 8*b**2*c*d*e**4*x**2/75 + 16*b**2*c*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/75 + b**2*d**4*e**4*x**5*asin(c + d*x)**2/5 - 2*b**2*d**4*e**4*x**5/125 + 2*b**2*d**3*e**4*x**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 - 8*b**2*d**2*e**4*x**3/225 + 8*b**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/75 - 16*b**2*e**4*x/75 + 16*b**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(75*d), Ne(d, 0)), (c**4*e**4*x*(a + b*asin(c))**2, True))","A",0
189,1,916,0,4.166544," ","integrate((d*e*x+c*e)**3*(a+b*asin(d*x+c))**2,x)","\begin{cases} a^{2} c^{3} e^{3} x + \frac{3 a^{2} c^{2} d e^{3} x^{2}}{2} + a^{2} c d^{2} e^{3} x^{3} + \frac{a^{2} d^{3} e^{3} x^{4}}{4} + \frac{a b c^{4} e^{3} \operatorname{asin}{\left(c + d x \right)}}{2 d} + 2 a b c^{3} e^{3} x \operatorname{asin}{\left(c + d x \right)} + \frac{a b c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{8 d} + 3 a b c^{2} d e^{3} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{3 a b c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{8} + 2 a b c d^{2} e^{3} x^{3} \operatorname{asin}{\left(c + d x \right)} + \frac{3 a b c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{8} + \frac{3 a b c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16 d} + \frac{a b d^{3} e^{3} x^{4} \operatorname{asin}{\left(c + d x \right)}}{2} + \frac{a b d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{8} + \frac{3 a b e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16} - \frac{3 a b e^{3} \operatorname{asin}{\left(c + d x \right)}}{16 d} + \frac{b^{2} c^{4} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{4 d} + b^{2} c^{3} e^{3} x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{b^{2} c^{3} e^{3} x}{8} + \frac{b^{2} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8 d} + \frac{3 b^{2} c^{2} d e^{3} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{2} - \frac{3 b^{2} c^{2} d e^{3} x^{2}}{16} + \frac{3 b^{2} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8} + b^{2} c d^{2} e^{3} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{b^{2} c d^{2} e^{3} x^{3}}{8} + \frac{3 b^{2} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8} - \frac{3 b^{2} c e^{3} x}{16} + \frac{3 b^{2} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{16 d} + \frac{b^{2} d^{3} e^{3} x^{4} \operatorname{asin}^{2}{\left(c + d x \right)}}{4} - \frac{b^{2} d^{3} e^{3} x^{4}}{32} + \frac{b^{2} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8} - \frac{3 b^{2} d e^{3} x^{2}}{32} + \frac{3 b^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{16} - \frac{3 b^{2} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{32 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**3*e**3*x + 3*a**2*c**2*d*e**3*x**2/2 + a**2*c*d**2*e**3*x**3 + a**2*d**3*e**3*x**4/4 + a*b*c**4*e**3*asin(c + d*x)/(2*d) + 2*a*b*c**3*e**3*x*asin(c + d*x) + a*b*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(8*d) + 3*a*b*c**2*d*e**3*x**2*asin(c + d*x) + 3*a*b*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/8 + 2*a*b*c*d**2*e**3*x**3*asin(c + d*x) + 3*a*b*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/8 + 3*a*b*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(16*d) + a*b*d**3*e**3*x**4*asin(c + d*x)/2 + a*b*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/8 + 3*a*b*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/16 - 3*a*b*e**3*asin(c + d*x)/(16*d) + b**2*c**4*e**3*asin(c + d*x)**2/(4*d) + b**2*c**3*e**3*x*asin(c + d*x)**2 - b**2*c**3*e**3*x/8 + b**2*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(8*d) + 3*b**2*c**2*d*e**3*x**2*asin(c + d*x)**2/2 - 3*b**2*c**2*d*e**3*x**2/16 + 3*b**2*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/8 + b**2*c*d**2*e**3*x**3*asin(c + d*x)**2 - b**2*c*d**2*e**3*x**3/8 + 3*b**2*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/8 - 3*b**2*c*e**3*x/16 + 3*b**2*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(16*d) + b**2*d**3*e**3*x**4*asin(c + d*x)**2/4 - b**2*d**3*e**3*x**4/32 + b**2*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/8 - 3*b**2*d*e**3*x**2/32 + 3*b**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/16 - 3*b**2*e**3*asin(c + d*x)**2/(32*d), Ne(d, 0)), (c**3*e**3*x*(a + b*asin(c))**2, True))","A",0
190,1,610,0,1.776651," ","integrate((d*e*x+c*e)**2*(a+b*asin(d*x+c))**2,x)","\begin{cases} a^{2} c^{2} e^{2} x + a^{2} c d e^{2} x^{2} + \frac{a^{2} d^{2} e^{2} x^{3}}{3} + \frac{2 a b c^{3} e^{2} \operatorname{asin}{\left(c + d x \right)}}{3 d} + 2 a b c^{2} e^{2} x \operatorname{asin}{\left(c + d x \right)} + \frac{2 a b c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9 d} + 2 a b c d e^{2} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{4 a b c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9} + \frac{2 a b d^{2} e^{2} x^{3} \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{2 a b d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9} + \frac{4 a b e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9 d} + \frac{b^{2} c^{3} e^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{3 d} + b^{2} c^{2} e^{2} x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{2 b^{2} c^{2} e^{2} x}{9} + \frac{2 b^{2} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{9 d} + b^{2} c d e^{2} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{2 b^{2} c d e^{2} x^{2}}{9} + \frac{4 b^{2} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{9} + \frac{b^{2} d^{2} e^{2} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{3} - \frac{2 b^{2} d^{2} e^{2} x^{3}}{27} + \frac{2 b^{2} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{9} - \frac{4 b^{2} e^{2} x}{9} + \frac{4 b^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{9 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c**2*e**2*x + a**2*c*d*e**2*x**2 + a**2*d**2*e**2*x**3/3 + 2*a*b*c**3*e**2*asin(c + d*x)/(3*d) + 2*a*b*c**2*e**2*x*asin(c + d*x) + 2*a*b*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(9*d) + 2*a*b*c*d*e**2*x**2*asin(c + d*x) + 4*a*b*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/9 + 2*a*b*d**2*e**2*x**3*asin(c + d*x)/3 + 2*a*b*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/9 + 4*a*b*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(9*d) + b**2*c**3*e**2*asin(c + d*x)**2/(3*d) + b**2*c**2*e**2*x*asin(c + d*x)**2 - 2*b**2*c**2*e**2*x/9 + 2*b**2*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(9*d) + b**2*c*d*e**2*x**2*asin(c + d*x)**2 - 2*b**2*c*d*e**2*x**2/9 + 4*b**2*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/9 + b**2*d**2*e**2*x**3*asin(c + d*x)**2/3 - 2*b**2*d**2*e**2*x**3/27 + 2*b**2*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/9 - 4*b**2*e**2*x/9 + 4*b**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(9*d), Ne(d, 0)), (c**2*e**2*x*(a + b*asin(c))**2, True))","A",0
191,1,335,0,0.817019," ","integrate((d*e*x+c*e)*(a+b*asin(d*x+c))**2,x)","\begin{cases} a^{2} c e x + \frac{a^{2} d e x^{2}}{2} + \frac{a b c^{2} e \operatorname{asin}{\left(c + d x \right)}}{d} + 2 a b c e x \operatorname{asin}{\left(c + d x \right)} + \frac{a b c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{2 d} + a b d e x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{a b e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{2} - \frac{a b e \operatorname{asin}{\left(c + d x \right)}}{2 d} + \frac{b^{2} c^{2} e \operatorname{asin}^{2}{\left(c + d x \right)}}{2 d} + b^{2} c e x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{b^{2} c e x}{2} + \frac{b^{2} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{2 d} + \frac{b^{2} d e x^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{2} - \frac{b^{2} d e x^{2}}{4} + \frac{b^{2} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{2} - \frac{b^{2} e \operatorname{asin}^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*c*e*x + a**2*d*e*x**2/2 + a*b*c**2*e*asin(c + d*x)/d + 2*a*b*c*e*x*asin(c + d*x) + a*b*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(2*d) + a*b*d*e*x**2*asin(c + d*x) + a*b*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/2 - a*b*e*asin(c + d*x)/(2*d) + b**2*c**2*e*asin(c + d*x)**2/(2*d) + b**2*c*e*x*asin(c + d*x)**2 - b**2*c*e*x/2 + b**2*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(2*d) + b**2*d*e*x**2*asin(c + d*x)**2/2 - b**2*d*e*x**2/4 + b**2*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/2 - b**2*e*asin(c + d*x)**2/(4*d), Ne(d, 0)), (c*e*x*(a + b*asin(c))**2, True))","A",0
192,1,143,0,0.305921," ","integrate((a+b*asin(d*x+c))**2,x)","\begin{cases} a^{2} x + \frac{2 a b c \operatorname{asin}{\left(c + d x \right)}}{d} + 2 a b x \operatorname{asin}{\left(c + d x \right)} + \frac{2 a b \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} + \frac{b^{2} c \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + b^{2} x \operatorname{asin}^{2}{\left(c + d x \right)} - 2 b^{2} x + \frac{2 b^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*c*asin(c + d*x)/d + 2*a*b*x*asin(c + d*x) + 2*a*b*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d + b**2*c*asin(c + d*x)**2/d + b**2*x*asin(c + d*x)**2 - 2*b**2*x + 2*b**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/d, Ne(d, 0)), (x*(a + b*asin(c))**2, True))","A",0
193,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e),x)","\frac{\int \frac{a^{2}}{c + d x}\, dx + \int \frac{b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{2 a b \operatorname{asin}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**2/(c + d*x), x) + Integral(b**2*asin(c + d*x)**2/(c + d*x), x) + Integral(2*a*b*asin(c + d*x)/(c + d*x), x))/e","F",0
194,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e)**2,x)","\frac{\int \frac{a^{2}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{2 a b \operatorname{asin}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx}{e^{2}}"," ",0,"(Integral(a**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(b**2*asin(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(2*a*b*asin(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
195,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e)**3,x)","\frac{\int \frac{a^{2}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{2 a b \operatorname{asin}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx}{e^{3}}"," ",0,"(Integral(a**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(b**2*asin(c + d*x)**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(2*a*b*asin(c + d*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))/e**3","F",0
196,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e)**4,x)","\frac{\int \frac{a^{2}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{2 a b \operatorname{asin}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}}"," ",0,"(Integral(a**2/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(b**2*asin(c + d*x)**2/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(2*a*b*asin(c + d*x)/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x))/e**4","F",0
197,1,2518,0,14.995512," ","integrate((d*e*x+c*e)**4*(a+b*asin(d*x+c))**3,x)","\begin{cases} a^{3} c^{4} e^{4} x + 2 a^{3} c^{3} d e^{4} x^{2} + 2 a^{3} c^{2} d^{2} e^{4} x^{3} + a^{3} c d^{3} e^{4} x^{4} + \frac{a^{3} d^{4} e^{4} x^{5}}{5} + \frac{3 a^{2} b c^{5} e^{4} \operatorname{asin}{\left(c + d x \right)}}{5 d} + 3 a^{2} b c^{4} e^{4} x \operatorname{asin}{\left(c + d x \right)} + \frac{3 a^{2} b c^{4} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25 d} + 6 a^{2} b c^{3} d e^{4} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{12 a^{2} b c^{3} e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + 6 a^{2} b c^{2} d^{2} e^{4} x^{3} \operatorname{asin}{\left(c + d x \right)} + \frac{18 a^{2} b c^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{4 a^{2} b c^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25 d} + 3 a^{2} b c d^{3} e^{4} x^{4} \operatorname{asin}{\left(c + d x \right)} + \frac{12 a^{2} b c d^{2} e^{4} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{8 a^{2} b c e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{3 a^{2} b d^{4} e^{4} x^{5} \operatorname{asin}{\left(c + d x \right)}}{5} + \frac{3 a^{2} b d^{3} e^{4} x^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{4 a^{2} b d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25} + \frac{8 a^{2} b e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{25 d} + \frac{3 a b^{2} c^{5} e^{4} \operatorname{asin}^{2}{\left(c + d x \right)}}{5 d} + 3 a b^{2} c^{4} e^{4} x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{6 a b^{2} c^{4} e^{4} x}{25} + \frac{6 a b^{2} c^{4} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25 d} + 6 a b^{2} c^{3} d e^{4} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{12 a b^{2} c^{3} d e^{4} x^{2}}{25} + \frac{24 a b^{2} c^{3} e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} + 6 a b^{2} c^{2} d^{2} e^{4} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{12 a b^{2} c^{2} d^{2} e^{4} x^{3}}{25} + \frac{36 a b^{2} c^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} - \frac{8 a b^{2} c^{2} e^{4} x}{25} + \frac{8 a b^{2} c^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25 d} + 3 a b^{2} c d^{3} e^{4} x^{4} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{6 a b^{2} c d^{3} e^{4} x^{4}}{25} + \frac{24 a b^{2} c d^{2} e^{4} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} - \frac{8 a b^{2} c d e^{4} x^{2}}{25} + \frac{16 a b^{2} c e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} + \frac{3 a b^{2} d^{4} e^{4} x^{5} \operatorname{asin}^{2}{\left(c + d x \right)}}{5} - \frac{6 a b^{2} d^{4} e^{4} x^{5}}{125} + \frac{6 a b^{2} d^{3} e^{4} x^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} - \frac{8 a b^{2} d^{2} e^{4} x^{3}}{75} + \frac{8 a b^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25} - \frac{16 a b^{2} e^{4} x}{25} + \frac{16 a b^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{25 d} + \frac{b^{3} c^{5} e^{4} \operatorname{asin}^{3}{\left(c + d x \right)}}{5 d} - \frac{6 b^{3} c^{5} e^{4} \operatorname{asin}{\left(c + d x \right)}}{125 d} + b^{3} c^{4} e^{4} x \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{6 b^{3} c^{4} e^{4} x \operatorname{asin}{\left(c + d x \right)}}{25} + \frac{3 b^{3} c^{4} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25 d} - \frac{6 b^{3} c^{4} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{625 d} + 2 b^{3} c^{3} d e^{4} x^{2} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{12 b^{3} c^{3} d e^{4} x^{2} \operatorname{asin}{\left(c + d x \right)}}{25} + \frac{12 b^{3} c^{3} e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25} - \frac{24 b^{3} c^{3} e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{625} - \frac{8 b^{3} c^{3} e^{4} \operatorname{asin}{\left(c + d x \right)}}{75 d} + 2 b^{3} c^{2} d^{2} e^{4} x^{3} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{12 b^{3} c^{2} d^{2} e^{4} x^{3} \operatorname{asin}{\left(c + d x \right)}}{25} + \frac{18 b^{3} c^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25} - \frac{36 b^{3} c^{2} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{625} - \frac{8 b^{3} c^{2} e^{4} x \operatorname{asin}{\left(c + d x \right)}}{25} + \frac{4 b^{3} c^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25 d} - \frac{272 b^{3} c^{2} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{5625 d} + b^{3} c d^{3} e^{4} x^{4} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{6 b^{3} c d^{3} e^{4} x^{4} \operatorname{asin}{\left(c + d x \right)}}{25} + \frac{12 b^{3} c d^{2} e^{4} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25} - \frac{24 b^{3} c d^{2} e^{4} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{625} - \frac{8 b^{3} c d e^{4} x^{2} \operatorname{asin}{\left(c + d x \right)}}{25} + \frac{8 b^{3} c e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25} - \frac{544 b^{3} c e^{4} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{5625} - \frac{16 b^{3} c e^{4} \operatorname{asin}{\left(c + d x \right)}}{25 d} + \frac{b^{3} d^{4} e^{4} x^{5} \operatorname{asin}^{3}{\left(c + d x \right)}}{5} - \frac{6 b^{3} d^{4} e^{4} x^{5} \operatorname{asin}{\left(c + d x \right)}}{125} + \frac{3 b^{3} d^{3} e^{4} x^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25} - \frac{6 b^{3} d^{3} e^{4} x^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{625} - \frac{8 b^{3} d^{2} e^{4} x^{3} \operatorname{asin}{\left(c + d x \right)}}{75} + \frac{4 b^{3} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25} - \frac{272 b^{3} d e^{4} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{5625} - \frac{16 b^{3} e^{4} x \operatorname{asin}{\left(c + d x \right)}}{25} + \frac{8 b^{3} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{25 d} - \frac{4144 b^{3} e^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{5625 d} & \text{for}\: d \neq 0 \\c^{4} e^{4} x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**4*e**4*x + 2*a**3*c**3*d*e**4*x**2 + 2*a**3*c**2*d**2*e**4*x**3 + a**3*c*d**3*e**4*x**4 + a**3*d**4*e**4*x**5/5 + 3*a**2*b*c**5*e**4*asin(c + d*x)/(5*d) + 3*a**2*b*c**4*e**4*x*asin(c + d*x) + 3*a**2*b*c**4*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(25*d) + 6*a**2*b*c**3*d*e**4*x**2*asin(c + d*x) + 12*a**2*b*c**3*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 6*a**2*b*c**2*d**2*e**4*x**3*asin(c + d*x) + 18*a**2*b*c**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 4*a**2*b*c**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(25*d) + 3*a**2*b*c*d**3*e**4*x**4*asin(c + d*x) + 12*a**2*b*c*d**2*e**4*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 8*a**2*b*c*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 3*a**2*b*d**4*e**4*x**5*asin(c + d*x)/5 + 3*a**2*b*d**3*e**4*x**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 4*a**2*b*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/25 + 8*a**2*b*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(25*d) + 3*a*b**2*c**5*e**4*asin(c + d*x)**2/(5*d) + 3*a*b**2*c**4*e**4*x*asin(c + d*x)**2 - 6*a*b**2*c**4*e**4*x/25 + 6*a*b**2*c**4*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(25*d) + 6*a*b**2*c**3*d*e**4*x**2*asin(c + d*x)**2 - 12*a*b**2*c**3*d*e**4*x**2/25 + 24*a*b**2*c**3*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 + 6*a*b**2*c**2*d**2*e**4*x**3*asin(c + d*x)**2 - 12*a*b**2*c**2*d**2*e**4*x**3/25 + 36*a*b**2*c**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 - 8*a*b**2*c**2*e**4*x/25 + 8*a*b**2*c**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(25*d) + 3*a*b**2*c*d**3*e**4*x**4*asin(c + d*x)**2 - 6*a*b**2*c*d**3*e**4*x**4/25 + 24*a*b**2*c*d**2*e**4*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 - 8*a*b**2*c*d*e**4*x**2/25 + 16*a*b**2*c*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 + 3*a*b**2*d**4*e**4*x**5*asin(c + d*x)**2/5 - 6*a*b**2*d**4*e**4*x**5/125 + 6*a*b**2*d**3*e**4*x**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 - 8*a*b**2*d**2*e**4*x**3/75 + 8*a*b**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/25 - 16*a*b**2*e**4*x/25 + 16*a*b**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(25*d) + b**3*c**5*e**4*asin(c + d*x)**3/(5*d) - 6*b**3*c**5*e**4*asin(c + d*x)/(125*d) + b**3*c**4*e**4*x*asin(c + d*x)**3 - 6*b**3*c**4*e**4*x*asin(c + d*x)/25 + 3*b**3*c**4*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(25*d) - 6*b**3*c**4*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(625*d) + 2*b**3*c**3*d*e**4*x**2*asin(c + d*x)**3 - 12*b**3*c**3*d*e**4*x**2*asin(c + d*x)/25 + 12*b**3*c**3*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/25 - 24*b**3*c**3*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/625 - 8*b**3*c**3*e**4*asin(c + d*x)/(75*d) + 2*b**3*c**2*d**2*e**4*x**3*asin(c + d*x)**3 - 12*b**3*c**2*d**2*e**4*x**3*asin(c + d*x)/25 + 18*b**3*c**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/25 - 36*b**3*c**2*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/625 - 8*b**3*c**2*e**4*x*asin(c + d*x)/25 + 4*b**3*c**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(25*d) - 272*b**3*c**2*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(5625*d) + b**3*c*d**3*e**4*x**4*asin(c + d*x)**3 - 6*b**3*c*d**3*e**4*x**4*asin(c + d*x)/25 + 12*b**3*c*d**2*e**4*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/25 - 24*b**3*c*d**2*e**4*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/625 - 8*b**3*c*d*e**4*x**2*asin(c + d*x)/25 + 8*b**3*c*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/25 - 544*b**3*c*e**4*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/5625 - 16*b**3*c*e**4*asin(c + d*x)/(25*d) + b**3*d**4*e**4*x**5*asin(c + d*x)**3/5 - 6*b**3*d**4*e**4*x**5*asin(c + d*x)/125 + 3*b**3*d**3*e**4*x**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/25 - 6*b**3*d**3*e**4*x**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/625 - 8*b**3*d**2*e**4*x**3*asin(c + d*x)/75 + 4*b**3*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/25 - 272*b**3*d*e**4*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/5625 - 16*b**3*e**4*x*asin(c + d*x)/25 + 8*b**3*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(25*d) - 4144*b**3*e**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(5625*d), Ne(d, 0)), (c**4*e**4*x*(a + b*asin(c))**3, True))","A",0
198,1,1828,0,9.217027," ","integrate((d*e*x+c*e)**3*(a+b*asin(d*x+c))**3,x)","\begin{cases} a^{3} c^{3} e^{3} x + \frac{3 a^{3} c^{2} d e^{3} x^{2}}{2} + a^{3} c d^{2} e^{3} x^{3} + \frac{a^{3} d^{3} e^{3} x^{4}}{4} + \frac{3 a^{2} b c^{4} e^{3} \operatorname{asin}{\left(c + d x \right)}}{4 d} + 3 a^{2} b c^{3} e^{3} x \operatorname{asin}{\left(c + d x \right)} + \frac{3 a^{2} b c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16 d} + \frac{9 a^{2} b c^{2} d e^{3} x^{2} \operatorname{asin}{\left(c + d x \right)}}{2} + \frac{9 a^{2} b c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16} + 3 a^{2} b c d^{2} e^{3} x^{3} \operatorname{asin}{\left(c + d x \right)} + \frac{9 a^{2} b c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16} + \frac{9 a^{2} b c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{32 d} + \frac{3 a^{2} b d^{3} e^{3} x^{4} \operatorname{asin}{\left(c + d x \right)}}{4} + \frac{3 a^{2} b d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{16} + \frac{9 a^{2} b e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{32} - \frac{9 a^{2} b e^{3} \operatorname{asin}{\left(c + d x \right)}}{32 d} + \frac{3 a b^{2} c^{4} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{4 d} + 3 a b^{2} c^{3} e^{3} x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{3 a b^{2} c^{3} e^{3} x}{8} + \frac{3 a b^{2} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8 d} + \frac{9 a b^{2} c^{2} d e^{3} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{2} - \frac{9 a b^{2} c^{2} d e^{3} x^{2}}{16} + \frac{9 a b^{2} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8} + 3 a b^{2} c d^{2} e^{3} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{3 a b^{2} c d^{2} e^{3} x^{3}}{8} + \frac{9 a b^{2} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8} - \frac{9 a b^{2} c e^{3} x}{16} + \frac{9 a b^{2} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{16 d} + \frac{3 a b^{2} d^{3} e^{3} x^{4} \operatorname{asin}^{2}{\left(c + d x \right)}}{4} - \frac{3 a b^{2} d^{3} e^{3} x^{4}}{32} + \frac{3 a b^{2} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8} - \frac{9 a b^{2} d e^{3} x^{2}}{32} + \frac{9 a b^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{16} - \frac{9 a b^{2} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{32 d} + \frac{b^{3} c^{4} e^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{4 d} - \frac{3 b^{3} c^{4} e^{3} \operatorname{asin}{\left(c + d x \right)}}{32 d} + b^{3} c^{3} e^{3} x \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{3 b^{3} c^{3} e^{3} x \operatorname{asin}{\left(c + d x \right)}}{8} + \frac{3 b^{3} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{16 d} - \frac{3 b^{3} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{128 d} + \frac{3 b^{3} c^{2} d e^{3} x^{2} \operatorname{asin}^{3}{\left(c + d x \right)}}{2} - \frac{9 b^{3} c^{2} d e^{3} x^{2} \operatorname{asin}{\left(c + d x \right)}}{16} + \frac{9 b^{3} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{16} - \frac{9 b^{3} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{128} - \frac{9 b^{3} c^{2} e^{3} \operatorname{asin}{\left(c + d x \right)}}{32 d} + b^{3} c d^{2} e^{3} x^{3} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{3 b^{3} c d^{2} e^{3} x^{3} \operatorname{asin}{\left(c + d x \right)}}{8} + \frac{9 b^{3} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{16} - \frac{9 b^{3} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{128} - \frac{9 b^{3} c e^{3} x \operatorname{asin}{\left(c + d x \right)}}{16} + \frac{9 b^{3} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{32 d} - \frac{45 b^{3} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{256 d} + \frac{b^{3} d^{3} e^{3} x^{4} \operatorname{asin}^{3}{\left(c + d x \right)}}{4} - \frac{3 b^{3} d^{3} e^{3} x^{4} \operatorname{asin}{\left(c + d x \right)}}{32} + \frac{3 b^{3} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{16} - \frac{3 b^{3} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{128} - \frac{9 b^{3} d e^{3} x^{2} \operatorname{asin}{\left(c + d x \right)}}{32} + \frac{9 b^{3} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{32} - \frac{45 b^{3} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{256} - \frac{3 b^{3} e^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{32 d} + \frac{45 b^{3} e^{3} \operatorname{asin}{\left(c + d x \right)}}{256 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**3*e**3*x + 3*a**3*c**2*d*e**3*x**2/2 + a**3*c*d**2*e**3*x**3 + a**3*d**3*e**3*x**4/4 + 3*a**2*b*c**4*e**3*asin(c + d*x)/(4*d) + 3*a**2*b*c**3*e**3*x*asin(c + d*x) + 3*a**2*b*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(16*d) + 9*a**2*b*c**2*d*e**3*x**2*asin(c + d*x)/2 + 9*a**2*b*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/16 + 3*a**2*b*c*d**2*e**3*x**3*asin(c + d*x) + 9*a**2*b*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/16 + 9*a**2*b*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(32*d) + 3*a**2*b*d**3*e**3*x**4*asin(c + d*x)/4 + 3*a**2*b*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/16 + 9*a**2*b*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/32 - 9*a**2*b*e**3*asin(c + d*x)/(32*d) + 3*a*b**2*c**4*e**3*asin(c + d*x)**2/(4*d) + 3*a*b**2*c**3*e**3*x*asin(c + d*x)**2 - 3*a*b**2*c**3*e**3*x/8 + 3*a*b**2*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(8*d) + 9*a*b**2*c**2*d*e**3*x**2*asin(c + d*x)**2/2 - 9*a*b**2*c**2*d*e**3*x**2/16 + 9*a*b**2*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/8 + 3*a*b**2*c*d**2*e**3*x**3*asin(c + d*x)**2 - 3*a*b**2*c*d**2*e**3*x**3/8 + 9*a*b**2*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/8 - 9*a*b**2*c*e**3*x/16 + 9*a*b**2*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(16*d) + 3*a*b**2*d**3*e**3*x**4*asin(c + d*x)**2/4 - 3*a*b**2*d**3*e**3*x**4/32 + 3*a*b**2*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/8 - 9*a*b**2*d*e**3*x**2/32 + 9*a*b**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/16 - 9*a*b**2*e**3*asin(c + d*x)**2/(32*d) + b**3*c**4*e**3*asin(c + d*x)**3/(4*d) - 3*b**3*c**4*e**3*asin(c + d*x)/(32*d) + b**3*c**3*e**3*x*asin(c + d*x)**3 - 3*b**3*c**3*e**3*x*asin(c + d*x)/8 + 3*b**3*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(16*d) - 3*b**3*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(128*d) + 3*b**3*c**2*d*e**3*x**2*asin(c + d*x)**3/2 - 9*b**3*c**2*d*e**3*x**2*asin(c + d*x)/16 + 9*b**3*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/16 - 9*b**3*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/128 - 9*b**3*c**2*e**3*asin(c + d*x)/(32*d) + b**3*c*d**2*e**3*x**3*asin(c + d*x)**3 - 3*b**3*c*d**2*e**3*x**3*asin(c + d*x)/8 + 9*b**3*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/16 - 9*b**3*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/128 - 9*b**3*c*e**3*x*asin(c + d*x)/16 + 9*b**3*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(32*d) - 45*b**3*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(256*d) + b**3*d**3*e**3*x**4*asin(c + d*x)**3/4 - 3*b**3*d**3*e**3*x**4*asin(c + d*x)/32 + 3*b**3*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/16 - 3*b**3*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/128 - 9*b**3*d*e**3*x**2*asin(c + d*x)/32 + 9*b**3*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/32 - 45*b**3*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/256 - 3*b**3*e**3*asin(c + d*x)**3/(32*d) + 45*b**3*e**3*asin(c + d*x)/(256*d), Ne(d, 0)), (c**3*e**3*x*(a + b*asin(c))**3, True))","A",0
199,1,1173,0,4.610351," ","integrate((d*e*x+c*e)**2*(a+b*asin(d*x+c))**3,x)","\begin{cases} a^{3} c^{2} e^{2} x + a^{3} c d e^{2} x^{2} + \frac{a^{3} d^{2} e^{2} x^{3}}{3} + \frac{a^{2} b c^{3} e^{2} \operatorname{asin}{\left(c + d x \right)}}{d} + 3 a^{2} b c^{2} e^{2} x \operatorname{asin}{\left(c + d x \right)} + \frac{a^{2} b c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{3 d} + 3 a^{2} b c d e^{2} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{2 a^{2} b c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{3} + a^{2} b d^{2} e^{2} x^{3} \operatorname{asin}{\left(c + d x \right)} + \frac{a^{2} b d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{3} + \frac{2 a^{2} b e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{3 d} + \frac{a b^{2} c^{3} e^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + 3 a b^{2} c^{2} e^{2} x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{2 a b^{2} c^{2} e^{2} x}{3} + \frac{2 a b^{2} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{3 d} + 3 a b^{2} c d e^{2} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{2 a b^{2} c d e^{2} x^{2}}{3} + \frac{4 a b^{2} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{3} + a b^{2} d^{2} e^{2} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{2 a b^{2} d^{2} e^{2} x^{3}}{9} + \frac{2 a b^{2} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{3} - \frac{4 a b^{2} e^{2} x}{3} + \frac{4 a b^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{3 d} + \frac{b^{3} c^{3} e^{2} \operatorname{asin}^{3}{\left(c + d x \right)}}{3 d} - \frac{2 b^{3} c^{3} e^{2} \operatorname{asin}{\left(c + d x \right)}}{9 d} + b^{3} c^{2} e^{2} x \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{2 b^{3} c^{2} e^{2} x \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{b^{3} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{3 d} - \frac{2 b^{3} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{27 d} + b^{3} c d e^{2} x^{2} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{2 b^{3} c d e^{2} x^{2} \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{2 b^{3} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{3} - \frac{4 b^{3} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{27} - \frac{4 b^{3} c e^{2} \operatorname{asin}{\left(c + d x \right)}}{3 d} + \frac{b^{3} d^{2} e^{2} x^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{3} - \frac{2 b^{3} d^{2} e^{2} x^{3} \operatorname{asin}{\left(c + d x \right)}}{9} + \frac{b^{3} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{3} - \frac{2 b^{3} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{27} - \frac{4 b^{3} e^{2} x \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{2 b^{3} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{3 d} - \frac{40 b^{3} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{27 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c**2*e**2*x + a**3*c*d*e**2*x**2 + a**3*d**2*e**2*x**3/3 + a**2*b*c**3*e**2*asin(c + d*x)/d + 3*a**2*b*c**2*e**2*x*asin(c + d*x) + a**2*b*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(3*d) + 3*a**2*b*c*d*e**2*x**2*asin(c + d*x) + 2*a**2*b*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/3 + a**2*b*d**2*e**2*x**3*asin(c + d*x) + a**2*b*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/3 + 2*a**2*b*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(3*d) + a*b**2*c**3*e**2*asin(c + d*x)**2/d + 3*a*b**2*c**2*e**2*x*asin(c + d*x)**2 - 2*a*b**2*c**2*e**2*x/3 + 2*a*b**2*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(3*d) + 3*a*b**2*c*d*e**2*x**2*asin(c + d*x)**2 - 2*a*b**2*c*d*e**2*x**2/3 + 4*a*b**2*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/3 + a*b**2*d**2*e**2*x**3*asin(c + d*x)**2 - 2*a*b**2*d**2*e**2*x**3/9 + 2*a*b**2*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/3 - 4*a*b**2*e**2*x/3 + 4*a*b**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(3*d) + b**3*c**3*e**2*asin(c + d*x)**3/(3*d) - 2*b**3*c**3*e**2*asin(c + d*x)/(9*d) + b**3*c**2*e**2*x*asin(c + d*x)**3 - 2*b**3*c**2*e**2*x*asin(c + d*x)/3 + b**3*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(3*d) - 2*b**3*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(27*d) + b**3*c*d*e**2*x**2*asin(c + d*x)**3 - 2*b**3*c*d*e**2*x**2*asin(c + d*x)/3 + 2*b**3*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/3 - 4*b**3*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/27 - 4*b**3*c*e**2*asin(c + d*x)/(3*d) + b**3*d**2*e**2*x**3*asin(c + d*x)**3/3 - 2*b**3*d**2*e**2*x**3*asin(c + d*x)/9 + b**3*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/3 - 2*b**3*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/27 - 4*b**3*e**2*x*asin(c + d*x)/3 + 2*b**3*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(3*d) - 40*b**3*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(27*d), Ne(d, 0)), (c**2*e**2*x*(a + b*asin(c))**3, True))","A",0
200,1,685,0,1.955112," ","integrate((d*e*x+c*e)*(a+b*asin(d*x+c))**3,x)","\begin{cases} a^{3} c e x + \frac{a^{3} d e x^{2}}{2} + \frac{3 a^{2} b c^{2} e \operatorname{asin}{\left(c + d x \right)}}{2 d} + 3 a^{2} b c e x \operatorname{asin}{\left(c + d x \right)} + \frac{3 a^{2} b c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{4 d} + \frac{3 a^{2} b d e x^{2} \operatorname{asin}{\left(c + d x \right)}}{2} + \frac{3 a^{2} b e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{4} - \frac{3 a^{2} b e \operatorname{asin}{\left(c + d x \right)}}{4 d} + \frac{3 a b^{2} c^{2} e \operatorname{asin}^{2}{\left(c + d x \right)}}{2 d} + 3 a b^{2} c e x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{3 a b^{2} c e x}{2} + \frac{3 a b^{2} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{2 d} + \frac{3 a b^{2} d e x^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{2} - \frac{3 a b^{2} d e x^{2}}{4} + \frac{3 a b^{2} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{2} - \frac{3 a b^{2} e \operatorname{asin}^{2}{\left(c + d x \right)}}{4 d} + \frac{b^{3} c^{2} e \operatorname{asin}^{3}{\left(c + d x \right)}}{2 d} - \frac{3 b^{3} c^{2} e \operatorname{asin}{\left(c + d x \right)}}{4 d} + b^{3} c e x \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{3 b^{3} c e x \operatorname{asin}{\left(c + d x \right)}}{2} + \frac{3 b^{3} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{4 d} - \frac{3 b^{3} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{8 d} + \frac{b^{3} d e x^{2} \operatorname{asin}^{3}{\left(c + d x \right)}}{2} - \frac{3 b^{3} d e x^{2} \operatorname{asin}{\left(c + d x \right)}}{4} + \frac{3 b^{3} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{4} - \frac{3 b^{3} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{8} - \frac{b^{3} e \operatorname{asin}^{3}{\left(c + d x \right)}}{4 d} + \frac{3 b^{3} e \operatorname{asin}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*c*e*x + a**3*d*e*x**2/2 + 3*a**2*b*c**2*e*asin(c + d*x)/(2*d) + 3*a**2*b*c*e*x*asin(c + d*x) + 3*a**2*b*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(4*d) + 3*a**2*b*d*e*x**2*asin(c + d*x)/2 + 3*a**2*b*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/4 - 3*a**2*b*e*asin(c + d*x)/(4*d) + 3*a*b**2*c**2*e*asin(c + d*x)**2/(2*d) + 3*a*b**2*c*e*x*asin(c + d*x)**2 - 3*a*b**2*c*e*x/2 + 3*a*b**2*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(2*d) + 3*a*b**2*d*e*x**2*asin(c + d*x)**2/2 - 3*a*b**2*d*e*x**2/4 + 3*a*b**2*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/2 - 3*a*b**2*e*asin(c + d*x)**2/(4*d) + b**3*c**2*e*asin(c + d*x)**3/(2*d) - 3*b**3*c**2*e*asin(c + d*x)/(4*d) + b**3*c*e*x*asin(c + d*x)**3 - 3*b**3*c*e*x*asin(c + d*x)/2 + 3*b**3*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(4*d) - 3*b**3*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(8*d) + b**3*d*e*x**2*asin(c + d*x)**3/2 - 3*b**3*d*e*x**2*asin(c + d*x)/4 + 3*b**3*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/4 - 3*b**3*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/8 - b**3*e*asin(c + d*x)**3/(4*d) + 3*b**3*e*asin(c + d*x)/(8*d), Ne(d, 0)), (c*e*x*(a + b*asin(c))**3, True))","A",0
201,1,282,0,0.736699," ","integrate((a+b*asin(d*x+c))**3,x)","\begin{cases} a^{3} x + \frac{3 a^{2} b c \operatorname{asin}{\left(c + d x \right)}}{d} + 3 a^{2} b x \operatorname{asin}{\left(c + d x \right)} + \frac{3 a^{2} b \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} + \frac{3 a b^{2} c \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + 3 a b^{2} x \operatorname{asin}^{2}{\left(c + d x \right)} - 6 a b^{2} x + \frac{6 a b^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{d} + \frac{b^{3} c \operatorname{asin}^{3}{\left(c + d x \right)}}{d} - \frac{6 b^{3} c \operatorname{asin}{\left(c + d x \right)}}{d} + b^{3} x \operatorname{asin}^{3}{\left(c + d x \right)} - 6 b^{3} x \operatorname{asin}{\left(c + d x \right)} + \frac{3 b^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{d} - \frac{6 b^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 3*a**2*b*c*asin(c + d*x)/d + 3*a**2*b*x*asin(c + d*x) + 3*a**2*b*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d + 3*a*b**2*c*asin(c + d*x)**2/d + 3*a*b**2*x*asin(c + d*x)**2 - 6*a*b**2*x + 6*a*b**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/d + b**3*c*asin(c + d*x)**3/d - 6*b**3*c*asin(c + d*x)/d + b**3*x*asin(c + d*x)**3 - 6*b**3*x*asin(c + d*x) + 3*b**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/d - 6*b**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d, Ne(d, 0)), (x*(a + b*asin(c))**3, True))","A",0
202,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**3/(d*e*x+c*e),x)","\frac{\int \frac{a^{3}}{c + d x}\, dx + \int \frac{b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{3 a^{2} b \operatorname{asin}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**3/(c + d*x), x) + Integral(b**3*asin(c + d*x)**3/(c + d*x), x) + Integral(3*a*b**2*asin(c + d*x)**2/(c + d*x), x) + Integral(3*a**2*b*asin(c + d*x)/(c + d*x), x))/e","F",0
203,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**3/(d*e*x+c*e)**2,x)","\frac{\int \frac{a^{3}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{3 a^{2} b \operatorname{asin}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx}{e^{2}}"," ",0,"(Integral(a**3/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(b**3*asin(c + d*x)**3/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(3*a*b**2*asin(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(3*a**2*b*asin(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
204,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**3/(d*e*x+c*e)**3,x)","\frac{\int \frac{a^{3}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{3 a^{2} b \operatorname{asin}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx}{e^{3}}"," ",0,"(Integral(a**3/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(b**3*asin(c + d*x)**3/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(3*a*b**2*asin(c + d*x)**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(3*a**2*b*asin(c + d*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))/e**3","F",0
205,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**3/(d*e*x+c*e)**4,x)","\frac{\int \frac{a^{3}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{3 a^{2} b \operatorname{asin}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}}"," ",0,"(Integral(a**3/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(b**3*asin(c + d*x)**3/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(3*a*b**2*asin(c + d*x)**2/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(3*a**2*b*asin(c + d*x)/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x))/e**4","F",0
206,1,2876,0,18.603295," ","integrate((d*e*x+c*e)**3*(a+b*asin(d*x+c))**4,x)","\begin{cases} a^{4} c^{3} e^{3} x + \frac{3 a^{4} c^{2} d e^{3} x^{2}}{2} + a^{4} c d^{2} e^{3} x^{3} + \frac{a^{4} d^{3} e^{3} x^{4}}{4} + \frac{a^{3} b c^{4} e^{3} \operatorname{asin}{\left(c + d x \right)}}{d} + 4 a^{3} b c^{3} e^{3} x \operatorname{asin}{\left(c + d x \right)} + \frac{a^{3} b c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{4 d} + 6 a^{3} b c^{2} d e^{3} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{3 a^{3} b c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{4} + 4 a^{3} b c d^{2} e^{3} x^{3} \operatorname{asin}{\left(c + d x \right)} + \frac{3 a^{3} b c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{4} + \frac{3 a^{3} b c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{8 d} + a^{3} b d^{3} e^{3} x^{4} \operatorname{asin}{\left(c + d x \right)} + \frac{a^{3} b d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{4} + \frac{3 a^{3} b e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{8} - \frac{3 a^{3} b e^{3} \operatorname{asin}{\left(c + d x \right)}}{8 d} + \frac{3 a^{2} b^{2} c^{4} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{2 d} + 6 a^{2} b^{2} c^{3} e^{3} x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{3 a^{2} b^{2} c^{3} e^{3} x}{4} + \frac{3 a^{2} b^{2} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{4 d} + 9 a^{2} b^{2} c^{2} d e^{3} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{9 a^{2} b^{2} c^{2} d e^{3} x^{2}}{8} + \frac{9 a^{2} b^{2} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{4} + 6 a^{2} b^{2} c d^{2} e^{3} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{3 a^{2} b^{2} c d^{2} e^{3} x^{3}}{4} + \frac{9 a^{2} b^{2} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{4} - \frac{9 a^{2} b^{2} c e^{3} x}{8} + \frac{9 a^{2} b^{2} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8 d} + \frac{3 a^{2} b^{2} d^{3} e^{3} x^{4} \operatorname{asin}^{2}{\left(c + d x \right)}}{2} - \frac{3 a^{2} b^{2} d^{3} e^{3} x^{4}}{16} + \frac{3 a^{2} b^{2} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{4} - \frac{9 a^{2} b^{2} d e^{3} x^{2}}{16} + \frac{9 a^{2} b^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{8} - \frac{9 a^{2} b^{2} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{16 d} + \frac{a b^{3} c^{4} e^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{d} - \frac{3 a b^{3} c^{4} e^{3} \operatorname{asin}{\left(c + d x \right)}}{8 d} + 4 a b^{3} c^{3} e^{3} x \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{3 a b^{3} c^{3} e^{3} x \operatorname{asin}{\left(c + d x \right)}}{2} + \frac{3 a b^{3} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{4 d} - \frac{3 a b^{3} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{32 d} + 6 a b^{3} c^{2} d e^{3} x^{2} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{9 a b^{3} c^{2} d e^{3} x^{2} \operatorname{asin}{\left(c + d x \right)}}{4} + \frac{9 a b^{3} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{4} - \frac{9 a b^{3} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{32} - \frac{9 a b^{3} c^{2} e^{3} \operatorname{asin}{\left(c + d x \right)}}{8 d} + 4 a b^{3} c d^{2} e^{3} x^{3} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{3 a b^{3} c d^{2} e^{3} x^{3} \operatorname{asin}{\left(c + d x \right)}}{2} + \frac{9 a b^{3} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{4} - \frac{9 a b^{3} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{32} - \frac{9 a b^{3} c e^{3} x \operatorname{asin}{\left(c + d x \right)}}{4} + \frac{9 a b^{3} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{8 d} - \frac{45 a b^{3} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{64 d} + a b^{3} d^{3} e^{3} x^{4} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{3 a b^{3} d^{3} e^{3} x^{4} \operatorname{asin}{\left(c + d x \right)}}{8} + \frac{3 a b^{3} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{4} - \frac{3 a b^{3} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{32} - \frac{9 a b^{3} d e^{3} x^{2} \operatorname{asin}{\left(c + d x \right)}}{8} + \frac{9 a b^{3} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{8} - \frac{45 a b^{3} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{64} - \frac{3 a b^{3} e^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{8 d} + \frac{45 a b^{3} e^{3} \operatorname{asin}{\left(c + d x \right)}}{64 d} + \frac{b^{4} c^{4} e^{3} \operatorname{asin}^{4}{\left(c + d x \right)}}{4 d} - \frac{3 b^{4} c^{4} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{16 d} + b^{4} c^{3} e^{3} x \operatorname{asin}^{4}{\left(c + d x \right)} - \frac{3 b^{4} c^{3} e^{3} x \operatorname{asin}^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{4} c^{3} e^{3} x}{32} + \frac{b^{4} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{4 d} - \frac{3 b^{4} c^{3} e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{32 d} + \frac{3 b^{4} c^{2} d e^{3} x^{2} \operatorname{asin}^{4}{\left(c + d x \right)}}{2} - \frac{9 b^{4} c^{2} d e^{3} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{8} + \frac{9 b^{4} c^{2} d e^{3} x^{2}}{64} + \frac{3 b^{4} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{4} - \frac{9 b^{4} c^{2} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{32} - \frac{9 b^{4} c^{2} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{16 d} + b^{4} c d^{2} e^{3} x^{3} \operatorname{asin}^{4}{\left(c + d x \right)} - \frac{3 b^{4} c d^{2} e^{3} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{4} c d^{2} e^{3} x^{3}}{32} + \frac{3 b^{4} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{4} - \frac{9 b^{4} c d e^{3} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{32} - \frac{9 b^{4} c e^{3} x \operatorname{asin}^{2}{\left(c + d x \right)}}{8} + \frac{45 b^{4} c e^{3} x}{64} + \frac{3 b^{4} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{8 d} - \frac{45 b^{4} c e^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{64 d} + \frac{b^{4} d^{3} e^{3} x^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}{4} - \frac{3 b^{4} d^{3} e^{3} x^{4} \operatorname{asin}^{2}{\left(c + d x \right)}}{16} + \frac{3 b^{4} d^{3} e^{3} x^{4}}{128} + \frac{b^{4} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{4} - \frac{3 b^{4} d^{2} e^{3} x^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{32} - \frac{9 b^{4} d e^{3} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{16} + \frac{45 b^{4} d e^{3} x^{2}}{128} + \frac{3 b^{4} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{8} - \frac{45 b^{4} e^{3} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{64} - \frac{3 b^{4} e^{3} \operatorname{asin}^{4}{\left(c + d x \right)}}{32 d} + \frac{45 b^{4} e^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\c^{3} e^{3} x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**3*e**3*x + 3*a**4*c**2*d*e**3*x**2/2 + a**4*c*d**2*e**3*x**3 + a**4*d**3*e**3*x**4/4 + a**3*b*c**4*e**3*asin(c + d*x)/d + 4*a**3*b*c**3*e**3*x*asin(c + d*x) + a**3*b*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(4*d) + 6*a**3*b*c**2*d*e**3*x**2*asin(c + d*x) + 3*a**3*b*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/4 + 4*a**3*b*c*d**2*e**3*x**3*asin(c + d*x) + 3*a**3*b*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/4 + 3*a**3*b*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(8*d) + a**3*b*d**3*e**3*x**4*asin(c + d*x) + a**3*b*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/4 + 3*a**3*b*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/8 - 3*a**3*b*e**3*asin(c + d*x)/(8*d) + 3*a**2*b**2*c**4*e**3*asin(c + d*x)**2/(2*d) + 6*a**2*b**2*c**3*e**3*x*asin(c + d*x)**2 - 3*a**2*b**2*c**3*e**3*x/4 + 3*a**2*b**2*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(4*d) + 9*a**2*b**2*c**2*d*e**3*x**2*asin(c + d*x)**2 - 9*a**2*b**2*c**2*d*e**3*x**2/8 + 9*a**2*b**2*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/4 + 6*a**2*b**2*c*d**2*e**3*x**3*asin(c + d*x)**2 - 3*a**2*b**2*c*d**2*e**3*x**3/4 + 9*a**2*b**2*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/4 - 9*a**2*b**2*c*e**3*x/8 + 9*a**2*b**2*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(8*d) + 3*a**2*b**2*d**3*e**3*x**4*asin(c + d*x)**2/2 - 3*a**2*b**2*d**3*e**3*x**4/16 + 3*a**2*b**2*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/4 - 9*a**2*b**2*d*e**3*x**2/16 + 9*a**2*b**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/8 - 9*a**2*b**2*e**3*asin(c + d*x)**2/(16*d) + a*b**3*c**4*e**3*asin(c + d*x)**3/d - 3*a*b**3*c**4*e**3*asin(c + d*x)/(8*d) + 4*a*b**3*c**3*e**3*x*asin(c + d*x)**3 - 3*a*b**3*c**3*e**3*x*asin(c + d*x)/2 + 3*a*b**3*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(4*d) - 3*a*b**3*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(32*d) + 6*a*b**3*c**2*d*e**3*x**2*asin(c + d*x)**3 - 9*a*b**3*c**2*d*e**3*x**2*asin(c + d*x)/4 + 9*a*b**3*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/4 - 9*a*b**3*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/32 - 9*a*b**3*c**2*e**3*asin(c + d*x)/(8*d) + 4*a*b**3*c*d**2*e**3*x**3*asin(c + d*x)**3 - 3*a*b**3*c*d**2*e**3*x**3*asin(c + d*x)/2 + 9*a*b**3*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/4 - 9*a*b**3*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/32 - 9*a*b**3*c*e**3*x*asin(c + d*x)/4 + 9*a*b**3*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(8*d) - 45*a*b**3*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(64*d) + a*b**3*d**3*e**3*x**4*asin(c + d*x)**3 - 3*a*b**3*d**3*e**3*x**4*asin(c + d*x)/8 + 3*a*b**3*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/4 - 3*a*b**3*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/32 - 9*a*b**3*d*e**3*x**2*asin(c + d*x)/8 + 9*a*b**3*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/8 - 45*a*b**3*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/64 - 3*a*b**3*e**3*asin(c + d*x)**3/(8*d) + 45*a*b**3*e**3*asin(c + d*x)/(64*d) + b**4*c**4*e**3*asin(c + d*x)**4/(4*d) - 3*b**4*c**4*e**3*asin(c + d*x)**2/(16*d) + b**4*c**3*e**3*x*asin(c + d*x)**4 - 3*b**4*c**3*e**3*x*asin(c + d*x)**2/4 + 3*b**4*c**3*e**3*x/32 + b**4*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/(4*d) - 3*b**4*c**3*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(32*d) + 3*b**4*c**2*d*e**3*x**2*asin(c + d*x)**4/2 - 9*b**4*c**2*d*e**3*x**2*asin(c + d*x)**2/8 + 9*b**4*c**2*d*e**3*x**2/64 + 3*b**4*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/4 - 9*b**4*c**2*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/32 - 9*b**4*c**2*e**3*asin(c + d*x)**2/(16*d) + b**4*c*d**2*e**3*x**3*asin(c + d*x)**4 - 3*b**4*c*d**2*e**3*x**3*asin(c + d*x)**2/4 + 3*b**4*c*d**2*e**3*x**3/32 + 3*b**4*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/4 - 9*b**4*c*d*e**3*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/32 - 9*b**4*c*e**3*x*asin(c + d*x)**2/8 + 45*b**4*c*e**3*x/64 + 3*b**4*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/(8*d) - 45*b**4*c*e**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(64*d) + b**4*d**3*e**3*x**4*asin(c + d*x)**4/4 - 3*b**4*d**3*e**3*x**4*asin(c + d*x)**2/16 + 3*b**4*d**3*e**3*x**4/128 + b**4*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/4 - 3*b**4*d**2*e**3*x**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/32 - 9*b**4*d*e**3*x**2*asin(c + d*x)**2/16 + 45*b**4*d*e**3*x**2/128 + 3*b**4*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/8 - 45*b**4*e**3*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/64 - 3*b**4*e**3*asin(c + d*x)**4/(32*d) + 45*b**4*e**3*asin(c + d*x)**2/(128*d), Ne(d, 0)), (c**3*e**3*x*(a + b*asin(c))**4, True))","A",0
207,1,1889,0,8.779057," ","integrate((d*e*x+c*e)**2*(a+b*asin(d*x+c))**4,x)","\begin{cases} a^{4} c^{2} e^{2} x + a^{4} c d e^{2} x^{2} + \frac{a^{4} d^{2} e^{2} x^{3}}{3} + \frac{4 a^{3} b c^{3} e^{2} \operatorname{asin}{\left(c + d x \right)}}{3 d} + 4 a^{3} b c^{2} e^{2} x \operatorname{asin}{\left(c + d x \right)} + \frac{4 a^{3} b c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9 d} + 4 a^{3} b c d e^{2} x^{2} \operatorname{asin}{\left(c + d x \right)} + \frac{8 a^{3} b c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9} + \frac{4 a^{3} b d^{2} e^{2} x^{3} \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{4 a^{3} b d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9} + \frac{8 a^{3} b e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{9 d} + \frac{2 a^{2} b^{2} c^{3} e^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} c^{2} e^{2} x \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{4 a^{2} b^{2} c^{2} e^{2} x}{3} + \frac{4 a^{2} b^{2} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{3 d} + 6 a^{2} b^{2} c d e^{2} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{4 a^{2} b^{2} c d e^{2} x^{2}}{3} + \frac{8 a^{2} b^{2} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{3} + 2 a^{2} b^{2} d^{2} e^{2} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{4 a^{2} b^{2} d^{2} e^{2} x^{3}}{9} + \frac{4 a^{2} b^{2} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{3} - \frac{8 a^{2} b^{2} e^{2} x}{3} + \frac{8 a^{2} b^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} c^{3} e^{2} \operatorname{asin}^{3}{\left(c + d x \right)}}{3 d} - \frac{8 a b^{3} c^{3} e^{2} \operatorname{asin}{\left(c + d x \right)}}{9 d} + 4 a b^{3} c^{2} e^{2} x \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{8 a b^{3} c^{2} e^{2} x \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{4 a b^{3} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{3 d} - \frac{8 a b^{3} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{27 d} + 4 a b^{3} c d e^{2} x^{2} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{8 a b^{3} c d e^{2} x^{2} \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{8 a b^{3} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{3} - \frac{16 a b^{3} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{27} - \frac{16 a b^{3} c e^{2} \operatorname{asin}{\left(c + d x \right)}}{3 d} + \frac{4 a b^{3} d^{2} e^{2} x^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{3} - \frac{8 a b^{3} d^{2} e^{2} x^{3} \operatorname{asin}{\left(c + d x \right)}}{9} + \frac{4 a b^{3} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{3} - \frac{8 a b^{3} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{27} - \frac{16 a b^{3} e^{2} x \operatorname{asin}{\left(c + d x \right)}}{3} + \frac{8 a b^{3} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{3 d} - \frac{160 a b^{3} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{27 d} + \frac{b^{4} c^{3} e^{2} \operatorname{asin}^{4}{\left(c + d x \right)}}{3 d} - \frac{4 b^{4} c^{3} e^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{9 d} + b^{4} c^{2} e^{2} x \operatorname{asin}^{4}{\left(c + d x \right)} - \frac{4 b^{4} c^{2} e^{2} x \operatorname{asin}^{2}{\left(c + d x \right)}}{3} + \frac{8 b^{4} c^{2} e^{2} x}{27} + \frac{4 b^{4} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{9 d} - \frac{8 b^{4} c^{2} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{27 d} + b^{4} c d e^{2} x^{2} \operatorname{asin}^{4}{\left(c + d x \right)} - \frac{4 b^{4} c d e^{2} x^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{3} + \frac{8 b^{4} c d e^{2} x^{2}}{27} + \frac{8 b^{4} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{9} - \frac{16 b^{4} c e^{2} x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{27} - \frac{8 b^{4} c e^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{3 d} + \frac{b^{4} d^{2} e^{2} x^{3} \operatorname{asin}^{4}{\left(c + d x \right)}}{3} - \frac{4 b^{4} d^{2} e^{2} x^{3} \operatorname{asin}^{2}{\left(c + d x \right)}}{9} + \frac{8 b^{4} d^{2} e^{2} x^{3}}{81} + \frac{4 b^{4} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{9} - \frac{8 b^{4} d e^{2} x^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{27} - \frac{8 b^{4} e^{2} x \operatorname{asin}^{2}{\left(c + d x \right)}}{3} + \frac{160 b^{4} e^{2} x}{27} + \frac{8 b^{4} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{9 d} - \frac{160 b^{4} e^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{27 d} & \text{for}\: d \neq 0 \\c^{2} e^{2} x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c**2*e**2*x + a**4*c*d*e**2*x**2 + a**4*d**2*e**2*x**3/3 + 4*a**3*b*c**3*e**2*asin(c + d*x)/(3*d) + 4*a**3*b*c**2*e**2*x*asin(c + d*x) + 4*a**3*b*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(9*d) + 4*a**3*b*c*d*e**2*x**2*asin(c + d*x) + 8*a**3*b*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/9 + 4*a**3*b*d**2*e**2*x**3*asin(c + d*x)/3 + 4*a**3*b*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/9 + 8*a**3*b*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(9*d) + 2*a**2*b**2*c**3*e**2*asin(c + d*x)**2/d + 6*a**2*b**2*c**2*e**2*x*asin(c + d*x)**2 - 4*a**2*b**2*c**2*e**2*x/3 + 4*a**2*b**2*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(3*d) + 6*a**2*b**2*c*d*e**2*x**2*asin(c + d*x)**2 - 4*a**2*b**2*c*d*e**2*x**2/3 + 8*a**2*b**2*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/3 + 2*a**2*b**2*d**2*e**2*x**3*asin(c + d*x)**2 - 4*a**2*b**2*d**2*e**2*x**3/9 + 4*a**2*b**2*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/3 - 8*a**2*b**2*e**2*x/3 + 8*a**2*b**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(3*d) + 4*a*b**3*c**3*e**2*asin(c + d*x)**3/(3*d) - 8*a*b**3*c**3*e**2*asin(c + d*x)/(9*d) + 4*a*b**3*c**2*e**2*x*asin(c + d*x)**3 - 8*a*b**3*c**2*e**2*x*asin(c + d*x)/3 + 4*a*b**3*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(3*d) - 8*a*b**3*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(27*d) + 4*a*b**3*c*d*e**2*x**2*asin(c + d*x)**3 - 8*a*b**3*c*d*e**2*x**2*asin(c + d*x)/3 + 8*a*b**3*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/3 - 16*a*b**3*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/27 - 16*a*b**3*c*e**2*asin(c + d*x)/(3*d) + 4*a*b**3*d**2*e**2*x**3*asin(c + d*x)**3/3 - 8*a*b**3*d**2*e**2*x**3*asin(c + d*x)/9 + 4*a*b**3*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/3 - 8*a*b**3*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/27 - 16*a*b**3*e**2*x*asin(c + d*x)/3 + 8*a*b**3*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/(3*d) - 160*a*b**3*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(27*d) + b**4*c**3*e**2*asin(c + d*x)**4/(3*d) - 4*b**4*c**3*e**2*asin(c + d*x)**2/(9*d) + b**4*c**2*e**2*x*asin(c + d*x)**4 - 4*b**4*c**2*e**2*x*asin(c + d*x)**2/3 + 8*b**4*c**2*e**2*x/27 + 4*b**4*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/(9*d) - 8*b**4*c**2*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(27*d) + b**4*c*d*e**2*x**2*asin(c + d*x)**4 - 4*b**4*c*d*e**2*x**2*asin(c + d*x)**2/3 + 8*b**4*c*d*e**2*x**2/27 + 8*b**4*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/9 - 16*b**4*c*e**2*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/27 - 8*b**4*c*e**2*asin(c + d*x)**2/(3*d) + b**4*d**2*e**2*x**3*asin(c + d*x)**4/3 - 4*b**4*d**2*e**2*x**3*asin(c + d*x)**2/9 + 8*b**4*d**2*e**2*x**3/81 + 4*b**4*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/9 - 8*b**4*d*e**2*x**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/27 - 8*b**4*e**2*x*asin(c + d*x)**2/3 + 160*b**4*e**2*x/27 + 8*b**4*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/(9*d) - 160*b**4*e**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(27*d), Ne(d, 0)), (c**2*e**2*x*(a + b*asin(c))**4, True))","A",0
208,1,1027,0,4.356225," ","integrate((d*e*x+c*e)*(a+b*asin(d*x+c))**4,x)","\begin{cases} a^{4} c e x + \frac{a^{4} d e x^{2}}{2} + \frac{2 a^{3} b c^{2} e \operatorname{asin}{\left(c + d x \right)}}{d} + 4 a^{3} b c e x \operatorname{asin}{\left(c + d x \right)} + \frac{a^{3} b c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} + 2 a^{3} b d e x^{2} \operatorname{asin}{\left(c + d x \right)} + a^{3} b e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} - \frac{a^{3} b e \operatorname{asin}{\left(c + d x \right)}}{d} + \frac{3 a^{2} b^{2} c^{2} e \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} c e x \operatorname{asin}^{2}{\left(c + d x \right)} - 3 a^{2} b^{2} c e x + \frac{3 a^{2} b^{2} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{d} + 3 a^{2} b^{2} d e x^{2} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{3 a^{2} b^{2} d e x^{2}}{2} + 3 a^{2} b^{2} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)} - \frac{3 a^{2} b^{2} e \operatorname{asin}^{2}{\left(c + d x \right)}}{2 d} + \frac{2 a b^{3} c^{2} e \operatorname{asin}^{3}{\left(c + d x \right)}}{d} - \frac{3 a b^{3} c^{2} e \operatorname{asin}{\left(c + d x \right)}}{d} + 4 a b^{3} c e x \operatorname{asin}^{3}{\left(c + d x \right)} - 6 a b^{3} c e x \operatorname{asin}{\left(c + d x \right)} + \frac{3 a b^{3} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{d} - \frac{3 a b^{3} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{2 d} + 2 a b^{3} d e x^{2} \operatorname{asin}^{3}{\left(c + d x \right)} - 3 a b^{3} d e x^{2} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{3} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)} - \frac{3 a b^{3} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{2} - \frac{a b^{3} e \operatorname{asin}^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{3} e \operatorname{asin}{\left(c + d x \right)}}{2 d} + \frac{b^{4} c^{2} e \operatorname{asin}^{4}{\left(c + d x \right)}}{2 d} - \frac{3 b^{4} c^{2} e \operatorname{asin}^{2}{\left(c + d x \right)}}{2 d} + b^{4} c e x \operatorname{asin}^{4}{\left(c + d x \right)} - 3 b^{4} c e x \operatorname{asin}^{2}{\left(c + d x \right)} + \frac{3 b^{4} c e x}{2} + \frac{b^{4} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{d} - \frac{3 b^{4} c e \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{2 d} + \frac{b^{4} d e x^{2} \operatorname{asin}^{4}{\left(c + d x \right)}}{2} - \frac{3 b^{4} d e x^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{2} + \frac{3 b^{4} d e x^{2}}{4} + b^{4} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)} - \frac{3 b^{4} e x \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{2} - \frac{b^{4} e \operatorname{asin}^{4}{\left(c + d x \right)}}{4 d} + \frac{3 b^{4} e \operatorname{asin}^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\c e x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*c*e*x + a**4*d*e*x**2/2 + 2*a**3*b*c**2*e*asin(c + d*x)/d + 4*a**3*b*c*e*x*asin(c + d*x) + a**3*b*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d + 2*a**3*b*d*e*x**2*asin(c + d*x) + a**3*b*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1) - a**3*b*e*asin(c + d*x)/d + 3*a**2*b**2*c**2*e*asin(c + d*x)**2/d + 6*a**2*b**2*c*e*x*asin(c + d*x)**2 - 3*a**2*b**2*c*e*x + 3*a**2*b**2*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/d + 3*a**2*b**2*d*e*x**2*asin(c + d*x)**2 - 3*a**2*b**2*d*e*x**2/2 + 3*a**2*b**2*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x) - 3*a**2*b**2*e*asin(c + d*x)**2/(2*d) + 2*a*b**3*c**2*e*asin(c + d*x)**3/d - 3*a*b**3*c**2*e*asin(c + d*x)/d + 4*a*b**3*c*e*x*asin(c + d*x)**3 - 6*a*b**3*c*e*x*asin(c + d*x) + 3*a*b**3*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/d - 3*a*b**3*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/(2*d) + 2*a*b**3*d*e*x**2*asin(c + d*x)**3 - 3*a*b**3*d*e*x**2*asin(c + d*x) + 3*a*b**3*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2 - 3*a*b**3*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/2 - a*b**3*e*asin(c + d*x)**3/d + 3*a*b**3*e*asin(c + d*x)/(2*d) + b**4*c**2*e*asin(c + d*x)**4/(2*d) - 3*b**4*c**2*e*asin(c + d*x)**2/(2*d) + b**4*c*e*x*asin(c + d*x)**4 - 3*b**4*c*e*x*asin(c + d*x)**2 + 3*b**4*c*e*x/2 + b**4*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/d - 3*b**4*c*e*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/(2*d) + b**4*d*e*x**2*asin(c + d*x)**4/2 - 3*b**4*d*e*x**2*asin(c + d*x)**2/2 + 3*b**4*d*e*x**2/4 + b**4*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3 - 3*b**4*e*x*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/2 - b**4*e*asin(c + d*x)**4/(4*d) + 3*b**4*e*asin(c + d*x)**2/(4*d), Ne(d, 0)), (c*e*x*(a + b*asin(c))**4, True))","A",0
209,1,444,0,1.539052," ","integrate((a+b*asin(d*x+c))**4,x)","\begin{cases} a^{4} x + \frac{4 a^{3} b c \operatorname{asin}{\left(c + d x \right)}}{d} + 4 a^{3} b x \operatorname{asin}{\left(c + d x \right)} + \frac{4 a^{3} b \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} + \frac{6 a^{2} b^{2} c \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + 6 a^{2} b^{2} x \operatorname{asin}^{2}{\left(c + d x \right)} - 12 a^{2} b^{2} x + \frac{12 a^{2} b^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{d} + \frac{4 a b^{3} c \operatorname{asin}^{3}{\left(c + d x \right)}}{d} - \frac{24 a b^{3} c \operatorname{asin}{\left(c + d x \right)}}{d} + 4 a b^{3} x \operatorname{asin}^{3}{\left(c + d x \right)} - 24 a b^{3} x \operatorname{asin}{\left(c + d x \right)} + \frac{12 a b^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{d} - \frac{24 a b^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} + \frac{b^{4} c \operatorname{asin}^{4}{\left(c + d x \right)}}{d} - \frac{12 b^{4} c \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + b^{4} x \operatorname{asin}^{4}{\left(c + d x \right)} - 12 b^{4} x \operatorname{asin}^{2}{\left(c + d x \right)} + 24 b^{4} x + \frac{4 b^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{d} - \frac{24 b^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 4*a**3*b*c*asin(c + d*x)/d + 4*a**3*b*x*asin(c + d*x) + 4*a**3*b*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d + 6*a**2*b**2*c*asin(c + d*x)**2/d + 6*a**2*b**2*x*asin(c + d*x)**2 - 12*a**2*b**2*x + 12*a**2*b**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/d + 4*a*b**3*c*asin(c + d*x)**3/d - 24*a*b**3*c*asin(c + d*x)/d + 4*a*b**3*x*asin(c + d*x)**3 - 24*a*b**3*x*asin(c + d*x) + 12*a*b**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/d - 24*a*b**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d + b**4*c*asin(c + d*x)**4/d - 12*b**4*c*asin(c + d*x)**2/d + b**4*x*asin(c + d*x)**4 - 12*b**4*x*asin(c + d*x)**2 + 24*b**4*x + 4*b**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/d - 24*b**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/d, Ne(d, 0)), (x*(a + b*asin(c))**4, True))","A",0
210,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**4/(d*e*x+c*e),x)","\frac{\int \frac{a^{4}}{c + d x}\, dx + \int \frac{b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{4 a^{3} b \operatorname{asin}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**4/(c + d*x), x) + Integral(b**4*asin(c + d*x)**4/(c + d*x), x) + Integral(4*a*b**3*asin(c + d*x)**3/(c + d*x), x) + Integral(6*a**2*b**2*asin(c + d*x)**2/(c + d*x), x) + Integral(4*a**3*b*asin(c + d*x)/(c + d*x), x))/e","F",0
211,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**4/(d*e*x+c*e)**2,x)","\frac{\int \frac{a^{4}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx + \int \frac{4 a^{3} b \operatorname{asin}{\left(c + d x \right)}}{c^{2} + 2 c d x + d^{2} x^{2}}\, dx}{e^{2}}"," ",0,"(Integral(a**4/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(b**4*asin(c + d*x)**4/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(4*a*b**3*asin(c + d*x)**3/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(6*a**2*b**2*asin(c + d*x)**2/(c**2 + 2*c*d*x + d**2*x**2), x) + Integral(4*a**3*b*asin(c + d*x)/(c**2 + 2*c*d*x + d**2*x**2), x))/e**2","F",0
212,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**4/(d*e*x+c*e)**3,x)","\frac{\int \frac{a^{4}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx + \int \frac{4 a^{3} b \operatorname{asin}{\left(c + d x \right)}}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}\, dx}{e^{3}}"," ",0,"(Integral(a**4/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(b**4*asin(c + d*x)**4/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(4*a*b**3*asin(c + d*x)**3/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(6*a**2*b**2*asin(c + d*x)**2/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x) + Integral(4*a**3*b*asin(c + d*x)/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3), x))/e**3","F",0
213,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**4/(d*e*x+c*e)**4,x)","\frac{\int \frac{a^{4}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx + \int \frac{4 a^{3} b \operatorname{asin}{\left(c + d x \right)}}{c^{4} + 4 c^{3} d x + 6 c^{2} d^{2} x^{2} + 4 c d^{3} x^{3} + d^{4} x^{4}}\, dx}{e^{4}}"," ",0,"(Integral(a**4/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(b**4*asin(c + d*x)**4/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(4*a*b**3*asin(c + d*x)**3/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(6*a**2*b**2*asin(c + d*x)**2/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x) + Integral(4*a**3*b*asin(c + d*x)/(c**4 + 4*c**3*d*x + 6*c**2*d**2*x**2 + 4*c*d**3*x**3 + d**4*x**4), x))/e**4","F",0
214,1,663,0,3.499082," ","integrate((a+b*asin(d*x+c))**5,x)","\begin{cases} a^{5} x + \frac{5 a^{4} b c \operatorname{asin}{\left(c + d x \right)}}{d} + 5 a^{4} b x \operatorname{asin}{\left(c + d x \right)} + \frac{5 a^{4} b \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} + \frac{10 a^{3} b^{2} c \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + 10 a^{3} b^{2} x \operatorname{asin}^{2}{\left(c + d x \right)} - 20 a^{3} b^{2} x + \frac{20 a^{3} b^{2} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{d} + \frac{10 a^{2} b^{3} c \operatorname{asin}^{3}{\left(c + d x \right)}}{d} - \frac{60 a^{2} b^{3} c \operatorname{asin}{\left(c + d x \right)}}{d} + 10 a^{2} b^{3} x \operatorname{asin}^{3}{\left(c + d x \right)} - 60 a^{2} b^{3} x \operatorname{asin}{\left(c + d x \right)} + \frac{30 a^{2} b^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{d} - \frac{60 a^{2} b^{3} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} + \frac{5 a b^{4} c \operatorname{asin}^{4}{\left(c + d x \right)}}{d} - \frac{60 a b^{4} c \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + 5 a b^{4} x \operatorname{asin}^{4}{\left(c + d x \right)} - 60 a b^{4} x \operatorname{asin}^{2}{\left(c + d x \right)} + 120 a b^{4} x + \frac{20 a b^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(c + d x \right)}}{d} - \frac{120 a b^{4} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}{\left(c + d x \right)}}{d} + \frac{b^{5} c \operatorname{asin}^{5}{\left(c + d x \right)}}{d} - \frac{20 b^{5} c \operatorname{asin}^{3}{\left(c + d x \right)}}{d} + \frac{120 b^{5} c \operatorname{asin}{\left(c + d x \right)}}{d} + b^{5} x \operatorname{asin}^{5}{\left(c + d x \right)} - 20 b^{5} x \operatorname{asin}^{3}{\left(c + d x \right)} + 120 b^{5} x \operatorname{asin}{\left(c + d x \right)} + \frac{5 b^{5} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{4}{\left(c + d x \right)}}{d} - \frac{60 b^{5} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(c + d x \right)}}{d} + \frac{120 b^{5} \sqrt{- c^{2} - 2 c d x - d^{2} x^{2} + 1}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \operatorname{asin}{\left(c \right)}\right)^{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*x + 5*a**4*b*c*asin(c + d*x)/d + 5*a**4*b*x*asin(c + d*x) + 5*a**4*b*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d + 10*a**3*b**2*c*asin(c + d*x)**2/d + 10*a**3*b**2*x*asin(c + d*x)**2 - 20*a**3*b**2*x + 20*a**3*b**2*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/d + 10*a**2*b**3*c*asin(c + d*x)**3/d - 60*a**2*b**3*c*asin(c + d*x)/d + 10*a**2*b**3*x*asin(c + d*x)**3 - 60*a**2*b**3*x*asin(c + d*x) + 30*a**2*b**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/d - 60*a**2*b**3*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d + 5*a*b**4*c*asin(c + d*x)**4/d - 60*a*b**4*c*asin(c + d*x)**2/d + 5*a*b**4*x*asin(c + d*x)**4 - 60*a*b**4*x*asin(c + d*x)**2 + 120*a*b**4*x + 20*a*b**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**3/d - 120*a*b**4*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)/d + b**5*c*asin(c + d*x)**5/d - 20*b**5*c*asin(c + d*x)**3/d + 120*b**5*c*asin(c + d*x)/d + b**5*x*asin(c + d*x)**5 - 20*b**5*x*asin(c + d*x)**3 + 120*b**5*x*asin(c + d*x) + 5*b**5*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**4/d - 60*b**5*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)*asin(c + d*x)**2/d + 120*b**5*sqrt(-c**2 - 2*c*d*x - d**2*x**2 + 1)/d, Ne(d, 0)), (x*(a + b*asin(c))**5, True))","A",0
215,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asin(d*x+c)),x)","e^{4} \left(\int \frac{c^{4}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a + b*asin(c + d*x)), x) + Integral(d**4*x**4/(a + b*asin(c + d*x)), x) + Integral(4*c*d**3*x**3/(a + b*asin(c + d*x)), x) + Integral(6*c**2*d**2*x**2/(a + b*asin(c + d*x)), x) + Integral(4*c**3*d*x/(a + b*asin(c + d*x)), x))","F",0
216,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asin(d*x+c)),x)","e^{3} \left(\int \frac{c^{3}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a + b*asin(c + d*x)), x) + Integral(d**3*x**3/(a + b*asin(c + d*x)), x) + Integral(3*c*d**2*x**2/(a + b*asin(c + d*x)), x) + Integral(3*c**2*d*x/(a + b*asin(c + d*x)), x))","F",0
217,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asin(d*x+c)),x)","e^{2} \left(\int \frac{c^{2}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a + b*asin(c + d*x)), x) + Integral(d**2*x**2/(a + b*asin(c + d*x)), x) + Integral(2*c*d*x/(a + b*asin(c + d*x)), x))","F",0
218,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asin(d*x+c)),x)","e \left(\int \frac{c}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a + b*asin(c + d*x)), x) + Integral(d*x/(a + b*asin(c + d*x)), x))","F",0
219,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c)),x)","\int \frac{1}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(a + b*asin(c + d*x)), x)","F",0
220,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asin(d*x+c)),x)","\frac{\int \frac{1}{a c + a d x + b c \operatorname{asin}{\left(c + d x \right)} + b d x \operatorname{asin}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a*c + a*d*x + b*c*asin(c + d*x) + b*d*x*asin(c + d*x)), x)/e","F",0
221,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asin(d*x+c))**2,x)","e^{4} \left(\int \frac{c^{4}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(d**4*x**4/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(4*c*d**3*x**3/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(6*c**2*d**2*x**2/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(4*c**3*d*x/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x))","F",0
222,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asin(d*x+c))**2,x)","e^{3} \left(\int \frac{c^{3}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(d**3*x**3/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(3*c*d**2*x**2/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(3*c**2*d*x/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x))","F",0
223,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asin(d*x+c))**2,x)","e^{2} \left(\int \frac{c^{2}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(d**2*x**2/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(2*c*d*x/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x))","F",0
224,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asin(d*x+c))**2,x)","e \left(\int \frac{c}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{2} + 2 a b \operatorname{asin}{\left(c + d x \right)} + b^{2} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x) + Integral(d*x/(a**2 + 2*a*b*asin(c + d*x) + b**2*asin(c + d*x)**2), x))","F",0
225,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**2,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-2), x)","F",0
226,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asin(d*x+c))**2,x)","\frac{\int \frac{1}{a^{2} c + a^{2} d x + 2 a b c \operatorname{asin}{\left(c + d x \right)} + 2 a b d x \operatorname{asin}{\left(c + d x \right)} + b^{2} c \operatorname{asin}^{2}{\left(c + d x \right)} + b^{2} d x \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**2*c + a**2*d*x + 2*a*b*c*asin(c + d*x) + 2*a*b*d*x*asin(c + d*x) + b**2*c*asin(c + d*x)**2 + b**2*d*x*asin(c + d*x)**2), x)/e","F",0
227,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asin(d*x+c))**3,x)","e^{4} \left(\int \frac{c^{4}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(d**4*x**4/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(4*c*d**3*x**3/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(6*c**2*d**2*x**2/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(4*c**3*d*x/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x))","F",0
228,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asin(d*x+c))**3,x)","e^{3} \left(\int \frac{c^{3}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(d**3*x**3/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(3*c*d**2*x**2/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(3*c**2*d*x/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x))","F",0
229,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asin(d*x+c))**3,x)","e^{2} \left(\int \frac{c^{2}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(d**2*x**2/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(2*c*d*x/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x))","F",0
230,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asin(d*x+c))**3,x)","e \left(\int \frac{c}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{3} + 3 a^{2} b \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x) + Integral(d*x/(a**3 + 3*a**2*b*asin(c + d*x) + 3*a*b**2*asin(c + d*x)**2 + b**3*asin(c + d*x)**3), x))","F",0
231,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**3,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-3), x)","F",0
232,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asin(d*x+c))**3,x)","\frac{\int \frac{1}{a^{3} c + a^{3} d x + 3 a^{2} b c \operatorname{asin}{\left(c + d x \right)} + 3 a^{2} b d x \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} c \operatorname{asin}^{2}{\left(c + d x \right)} + 3 a b^{2} d x \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} c \operatorname{asin}^{3}{\left(c + d x \right)} + b^{3} d x \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**3*c + a**3*d*x + 3*a**2*b*c*asin(c + d*x) + 3*a**2*b*d*x*asin(c + d*x) + 3*a*b**2*c*asin(c + d*x)**2 + 3*a*b**2*d*x*asin(c + d*x)**2 + b**3*c*asin(c + d*x)**3 + b**3*d*x*asin(c + d*x)**3), x)/e","F",0
233,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asin(d*x+c))**4,x)","e^{4} \left(\int \frac{c^{4}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(d**4*x**4/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(4*c*d**3*x**3/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(6*c**2*d**2*x**2/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(4*c**3*d*x/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x))","F",0
234,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asin(d*x+c))**4,x)","e^{3} \left(\int \frac{c^{3}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(d**3*x**3/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(3*c*d**2*x**2/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(3*c**2*d*x/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x))","F",0
235,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asin(d*x+c))**4,x)","e^{2} \left(\int \frac{c^{2}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(d**2*x**2/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(2*c*d*x/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x))","F",0
236,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asin(d*x+c))**4,x)","e \left(\int \frac{c}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{4} + 4 a^{3} b \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x) + Integral(d*x/(a**4 + 4*a**3*b*asin(c + d*x) + 6*a**2*b**2*asin(c + d*x)**2 + 4*a*b**3*asin(c + d*x)**3 + b**4*asin(c + d*x)**4), x))","F",0
237,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**4,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-4), x)","F",0
238,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asin(d*x+c))**4,x)","\frac{\int \frac{1}{a^{4} c + a^{4} d x + 4 a^{3} b c \operatorname{asin}{\left(c + d x \right)} + 4 a^{3} b d x \operatorname{asin}{\left(c + d x \right)} + 6 a^{2} b^{2} c \operatorname{asin}^{2}{\left(c + d x \right)} + 6 a^{2} b^{2} d x \operatorname{asin}^{2}{\left(c + d x \right)} + 4 a b^{3} c \operatorname{asin}^{3}{\left(c + d x \right)} + 4 a b^{3} d x \operatorname{asin}^{3}{\left(c + d x \right)} + b^{4} c \operatorname{asin}^{4}{\left(c + d x \right)} + b^{4} d x \operatorname{asin}^{4}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**4*c + a**4*d*x + 4*a**3*b*c*asin(c + d*x) + 4*a**3*b*d*x*asin(c + d*x) + 6*a**2*b**2*c*asin(c + d*x)**2 + 6*a**2*b**2*d*x*asin(c + d*x)**2 + 4*a*b**3*c*asin(c + d*x)**3 + 4*a*b**3*d*x*asin(c + d*x)**3 + b**4*c*asin(c + d*x)**4 + b**4*d*x*asin(c + d*x)**4), x)/e","F",0
239,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**5,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{5}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-5), x)","F",0
240,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*asin(d*x+c))**(1/2),x)","e^{3} \left(\int c^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int d^{3} x^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int 3 c d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int 3 c^{2} d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3*sqrt(a + b*asin(c + d*x)), x) + Integral(d**3*x**3*sqrt(a + b*asin(c + d*x)), x) + Integral(3*c*d**2*x**2*sqrt(a + b*asin(c + d*x)), x) + Integral(3*c**2*d*x*sqrt(a + b*asin(c + d*x)), x))","F",0
241,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*asin(d*x+c))**(1/2),x)","e^{2} \left(\int c^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int 2 c d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2*sqrt(a + b*asin(c + d*x)), x) + Integral(d**2*x**2*sqrt(a + b*asin(c + d*x)), x) + Integral(2*c*d*x*sqrt(a + b*asin(c + d*x)), x))","F",0
242,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*asin(d*x+c))**(1/2),x)","e \left(\int c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c*sqrt(a + b*asin(c + d*x)), x) + Integral(d*x*sqrt(a + b*asin(c + d*x)), x))","F",0
243,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(1/2),x)","\int \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*asin(c + d*x)), x)","F",0
244,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(1/2)/(d*e*x+c*e),x)","\frac{\int \frac{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}{c + d x}\, dx}{e}"," ",0,"Integral(sqrt(a + b*asin(c + d*x))/(c + d*x), x)/e","F",0
245,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*asin(d*x+c))**(3/2),x)","e^{3} \left(\int a c^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int a d^{3} x^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int b c^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int 3 a c d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int 3 a c^{2} d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int b d^{3} x^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int 3 b c d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int 3 b c^{2} d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx\right)"," ",0,"e**3*(Integral(a*c**3*sqrt(a + b*asin(c + d*x)), x) + Integral(a*d**3*x**3*sqrt(a + b*asin(c + d*x)), x) + Integral(b*c**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(3*a*c*d**2*x**2*sqrt(a + b*asin(c + d*x)), x) + Integral(3*a*c**2*d*x*sqrt(a + b*asin(c + d*x)), x) + Integral(b*d**3*x**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(3*b*c*d**2*x**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(3*b*c**2*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x))","F",0
246,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*asin(d*x+c))**(3/2),x)","e^{2} \left(\int a c^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int a d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int b c^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int 2 a c d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int b d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int 2 b c d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx\right)"," ",0,"e**2*(Integral(a*c**2*sqrt(a + b*asin(c + d*x)), x) + Integral(a*d**2*x**2*sqrt(a + b*asin(c + d*x)), x) + Integral(b*c**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(2*a*c*d*x*sqrt(a + b*asin(c + d*x)), x) + Integral(b*d**2*x**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(2*b*c*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x))","F",0
247,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*asin(d*x+c))**(3/2),x)","e \left(\int a c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int a d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int b c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int b d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx\right)"," ",0,"e*(Integral(a*c*sqrt(a + b*asin(c + d*x)), x) + Integral(a*d*x*sqrt(a + b*asin(c + d*x)), x) + Integral(b*c*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(b*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x))","F",0
248,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(3/2),x)","\int \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(3/2), x)","F",0
249,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(3/2)/(d*e*x+c*e),x)","\frac{\int \frac{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}{c + d x}\, dx + \int \frac{b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a*sqrt(a + b*asin(c + d*x))/(c + d*x), x) + Integral(b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)/(c + d*x), x))/e","F",0
250,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**3*(a+b*asin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*asin(d*x+c))**(5/2),x)","e^{2} \left(\int a^{2} c^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int a^{2} d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int b^{2} c^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}\, dx + \int 2 a b c^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int 2 a^{2} c d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int b^{2} d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}\, dx + \int 2 a b d^{2} x^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int 2 b^{2} c d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}\, dx + \int 4 a b c d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx\right)"," ",0,"e**2*(Integral(a**2*c**2*sqrt(a + b*asin(c + d*x)), x) + Integral(a**2*d**2*x**2*sqrt(a + b*asin(c + d*x)), x) + Integral(b**2*c**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2, x) + Integral(2*a*b*c**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(2*a**2*c*d*x*sqrt(a + b*asin(c + d*x)), x) + Integral(b**2*d**2*x**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2, x) + Integral(2*a*b*d**2*x**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(2*b**2*c*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2, x) + Integral(4*a*b*c*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x))","F",0
252,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*asin(d*x+c))**(5/2),x)","e \left(\int a^{2} c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int a^{2} d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx + \int b^{2} c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}\, dx + \int 2 a b c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx + \int b^{2} d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}\, dx + \int 2 a b d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}\, dx\right)"," ",0,"e*(Integral(a**2*c*sqrt(a + b*asin(c + d*x)), x) + Integral(a**2*d*x*sqrt(a + b*asin(c + d*x)), x) + Integral(b**2*c*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2, x) + Integral(2*a*b*c*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x) + Integral(b**2*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2, x) + Integral(2*a*b*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x), x))","F",0
253,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(5/2),x)","\int \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(5/2), x)","F",0
254,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(5/2)/(d*e*x+c*e),x)","\frac{\int \frac{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}{c + d x}\, dx + \int \frac{b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}{c + d x}\, dx + \int \frac{2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}{c + d x}\, dx}{e}"," ",0,"(Integral(a**2*sqrt(a + b*asin(c + d*x))/(c + d*x), x) + Integral(b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2/(c + d*x), x) + Integral(2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)/(c + d*x), x))/e","F",0
255,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**2*(a+b*asin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*asin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**(7/2)/(d*e*x+c*e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asin(d*x+c))**(1/2),x)","e^{4} \left(\int \frac{c^{4}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{d^{4} x^{4}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{4 c d^{3} x^{3}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{4 c^{3} d x}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**4*(Integral(c**4/sqrt(a + b*asin(c + d*x)), x) + Integral(d**4*x**4/sqrt(a + b*asin(c + d*x)), x) + Integral(4*c*d**3*x**3/sqrt(a + b*asin(c + d*x)), x) + Integral(6*c**2*d**2*x**2/sqrt(a + b*asin(c + d*x)), x) + Integral(4*c**3*d*x/sqrt(a + b*asin(c + d*x)), x))","F",0
260,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asin(d*x+c))**(1/2),x)","e^{3} \left(\int \frac{c^{3}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{d^{3} x^{3}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{3 c d^{2} x^{2}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{3 c^{2} d x}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**3*(Integral(c**3/sqrt(a + b*asin(c + d*x)), x) + Integral(d**3*x**3/sqrt(a + b*asin(c + d*x)), x) + Integral(3*c*d**2*x**2/sqrt(a + b*asin(c + d*x)), x) + Integral(3*c**2*d*x/sqrt(a + b*asin(c + d*x)), x))","F",0
261,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asin(d*x+c))**(1/2),x)","e^{2} \left(\int \frac{c^{2}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{d^{2} x^{2}}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{2 c d x}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e**2*(Integral(c**2/sqrt(a + b*asin(c + d*x)), x) + Integral(d**2*x**2/sqrt(a + b*asin(c + d*x)), x) + Integral(2*c*d*x/sqrt(a + b*asin(c + d*x)), x))","F",0
262,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asin(d*x+c))**(1/2),x)","e \left(\int \frac{c}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx + \int \frac{d x}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx\right)"," ",0,"e*(Integral(c/sqrt(a + b*asin(c + d*x)), x) + Integral(d*x/sqrt(a + b*asin(c + d*x)), x))","F",0
263,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*asin(c + d*x)), x)","F",0
264,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asin(d*x+c))**(1/2),x)","\frac{\int \frac{1}{c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}}}\, dx}{e}"," ",0,"Integral(1/(c*sqrt(a + b*asin(c + d*x)) + d*x*sqrt(a + b*asin(c + d*x))), x)/e","F",0
265,0,0,0,0.000000," ","integrate((d*e*x+c*e)**4/(a+b*asin(d*x+c))**(3/2),x)","e^{4} \left(\int \frac{c^{4}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{d^{4} x^{4}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{4 c d^{3} x^{3}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{6 c^{2} d^{2} x^{2}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{4 c^{3} d x}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**4*(Integral(c**4/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(d**4*x**4/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(4*c*d**3*x**3/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(6*c**2*d**2*x**2/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(4*c**3*d*x/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x))","F",0
266,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asin(d*x+c))**(3/2),x)","e^{3} \left(\int \frac{c^{3}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(d**3*x**3/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(3*c*d**2*x**2/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(3*c**2*d*x/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x))","F",0
267,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asin(d*x+c))**(3/2),x)","e^{2} \left(\int \frac{c^{2}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(d**2*x**2/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(2*c*d*x/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x))","F",0
268,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asin(d*x+c))**(3/2),x)","e \left(\int \frac{c}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x) + Integral(d*x/(a*sqrt(a + b*asin(c + d*x)) + b*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x))","F",0
269,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-3/2), x)","F",0
270,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asin(d*x+c))**(3/2),x)","\frac{\int \frac{1}{a c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + a d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + b c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a*c*sqrt(a + b*asin(c + d*x)) + a*d*x*sqrt(a + b*asin(c + d*x)) + b*c*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x)), x)/e","F",0
271,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asin(d*x+c))**(5/2),x)","e^{3} \left(\int \frac{c^{3}}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x) + Integral(d**3*x**3/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x) + Integral(3*c*d**2*x**2/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x) + Integral(3*c**2*d*x/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x))","F",0
272,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asin(d*x+c))**(5/2),x)","e^{2} \left(\int \frac{c^{2}}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x) + Integral(d**2*x**2/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x) + Integral(2*c*d*x/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x))","F",0
273,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asin(d*x+c))**(5/2),x)","e \left(\int \frac{c}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x) + Integral(d*x/(a**2*sqrt(a + b*asin(c + d*x)) + 2*a*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x))","F",0
274,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-5/2), x)","F",0
275,0,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asin(d*x+c))**(5/2),x)","\frac{\int \frac{1}{a^{2} c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + a^{2} d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 2 a b c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 2 a b d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + b^{2} c \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{2} d x \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)}}\, dx}{e}"," ",0,"Integral(1/(a**2*c*sqrt(a + b*asin(c + d*x)) + a**2*d*x*sqrt(a + b*asin(c + d*x)) + 2*a*b*c*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 2*a*b*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + b**2*c*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**2*d*x*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2), x)/e","F",0
276,0,0,0,0.000000," ","integrate((d*e*x+c*e)**3/(a+b*asin(d*x+c))**(7/2),x)","e^{3} \left(\int \frac{c^{3}}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{3} x^{3}}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c d^{2} x^{2}}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{3 c^{2} d x}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**3*(Integral(c**3/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x) + Integral(d**3*x**3/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x) + Integral(3*c*d**2*x**2/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x) + Integral(3*c**2*d*x/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x))","F",0
277,0,0,0,0.000000," ","integrate((d*e*x+c*e)**2/(a+b*asin(d*x+c))**(7/2),x)","e^{2} \left(\int \frac{c^{2}}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d^{2} x^{2}}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{2 c d x}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e**2*(Integral(c**2/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x) + Integral(d**2*x**2/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x) + Integral(2*c*d*x/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x))","F",0
278,0,0,0,0.000000," ","integrate((d*e*x+c*e)/(a+b*asin(d*x+c))**(7/2),x)","e \left(\int \frac{c}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx + \int \frac{d x}{a^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} + 3 a^{2} b \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}{\left(c + d x \right)} + 3 a b^{2} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{2}{\left(c + d x \right)} + b^{3} \sqrt{a + b \operatorname{asin}{\left(c + d x \right)}} \operatorname{asin}^{3}{\left(c + d x \right)}}\, dx\right)"," ",0,"e*(Integral(c/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x) + Integral(d*x/(a**3*sqrt(a + b*asin(c + d*x)) + 3*a**2*b*sqrt(a + b*asin(c + d*x))*asin(c + d*x) + 3*a*b**2*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**2 + b**3*sqrt(a + b*asin(c + d*x))*asin(c + d*x)**3), x))","F",0
279,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x+c))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**(-7/2), x)","F",0
280,-1,0,0,0.000000," ","integrate(1/(d*e*x+c*e)/(a+b*asin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)*(a+b*asin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,1,163,0,133.129699," ","integrate((d*e*x+c*e)**(5/2)*(a+b*asin(d*x+c)),x)","a c^{2} e^{2} \left(\begin{cases} x \sqrt{c e} & \text{for}\: d = 0 \\0 & \text{for}\: e = 0 \\\frac{2 \left(c e + d e x\right)^{\frac{3}{2}}}{3 d e} & \text{otherwise} \end{cases}\right) - \frac{2 a c^{2} e \left(c e + d e x\right)^{\frac{3}{2}}}{3 d} + \frac{2 a \left(c e + d e x\right)^{\frac{7}{2}}}{7 d e} + \frac{2 b \left(c e + d e x\right)^{\frac{7}{2}} \operatorname{asin}{\left(c + d x \right)}}{7 d e} - \frac{b \left(c e + d e x\right)^{\frac{9}{2}} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {\frac{\left(c e + d e x\right)^{2} e^{2 i \pi}}{e^{2}}} \right)}}{7 d e^{2} \Gamma\left(\frac{13}{4}\right)}"," ",0,"a*c**2*e**2*Piecewise((x*sqrt(c*e), Eq(d, 0)), (0, Eq(e, 0)), (2*(c*e + d*e*x)**(3/2)/(3*d*e), True)) - 2*a*c**2*e*(c*e + d*e*x)**(3/2)/(3*d) + 2*a*(c*e + d*e*x)**(7/2)/(7*d*e) + 2*b*(c*e + d*e*x)**(7/2)*asin(c + d*x)/(7*d*e) - b*(c*e + d*e*x)**(9/2)*gamma(9/4)*hyper((1/2, 9/4), (13/4,), (c*e + d*e*x)**2*exp_polar(2*I*pi)/e**2)/(7*d*e**2*gamma(13/4))","A",0
283,1,156,0,19.215892," ","integrate((d*e*x+c*e)**(3/2)*(a+b*asin(d*x+c)),x)","a c e \left(\begin{cases} x \sqrt{c e} & \text{for}\: d = 0 \\0 & \text{for}\: e = 0 \\\frac{2 \left(c e + d e x\right)^{\frac{3}{2}}}{3 d e} & \text{otherwise} \end{cases}\right) - \frac{2 a c \left(c e + d e x\right)^{\frac{3}{2}}}{3 d} + \frac{2 a \left(c e + d e x\right)^{\frac{5}{2}}}{5 d e} + \frac{2 b \left(c e + d e x\right)^{\frac{5}{2}} \operatorname{asin}{\left(c + d x \right)}}{5 d e} - \frac{b \left(c e + d e x\right)^{\frac{7}{2}} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {\frac{\left(c e + d e x\right)^{2} e^{2 i \pi}}{e^{2}}} \right)}}{5 d e^{2} \Gamma\left(\frac{11}{4}\right)}"," ",0,"a*c*e*Piecewise((x*sqrt(c*e), Eq(d, 0)), (0, Eq(e, 0)), (2*(c*e + d*e*x)**(3/2)/(3*d*e), True)) - 2*a*c*(c*e + d*e*x)**(3/2)/(3*d) + 2*a*(c*e + d*e*x)**(5/2)/(5*d*e) + 2*b*(c*e + d*e*x)**(5/2)*asin(c + d*x)/(5*d*e) - b*(c*e + d*e*x)**(7/2)*gamma(7/4)*hyper((1/2, 7/4), (11/4,), (c*e + d*e*x)**2*exp_polar(2*I*pi)/e**2)/(5*d*e**2*gamma(11/4))","A",0
284,1,104,0,2.402849," ","integrate((d*e*x+c*e)**(1/2)*(a+b*asin(d*x+c)),x)","\frac{2 a \left(c e + d e x\right)^{\frac{3}{2}}}{3 d e} + \frac{2 b \left(c e + d e x\right)^{\frac{3}{2}} \operatorname{asin}{\left(c + d x \right)}}{3 d e} - \frac{b \left(c e + d e x\right)^{\frac{5}{2}} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {\frac{\left(c e + d e x\right)^{2} e^{2 i \pi}}{e^{2}}} \right)}}{3 d e^{2} \Gamma\left(\frac{9}{4}\right)}"," ",0,"2*a*(c*e + d*e*x)**(3/2)/(3*d*e) + 2*b*(c*e + d*e*x)**(3/2)*asin(c + d*x)/(3*d*e) - b*(c*e + d*e*x)**(5/2)*gamma(5/4)*hyper((1/2, 5/4), (9/4,), (c*e + d*e*x)**2*exp_polar(2*I*pi)/e**2)/(3*d*e**2*gamma(9/4))","A",0
285,-2,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
286,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**(3/2),x)","\int \frac{a + b \operatorname{asin}{\left(c + d x \right)}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))/(e*(c + d*x))**(3/2), x)","F",0
287,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**(5/2),x)","\int \frac{a + b \operatorname{asin}{\left(c + d x \right)}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))/(e*(c + d*x))**(5/2), x)","F",0
288,-1,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate((a+b*asin(d*x+c))/(d*e*x+c*e)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(7/2)*(a+b*asin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((d*e*x+c*e)**(5/2)*(a+b*asin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(3/2)*(a+b*asin(d*x+c))**2,x)","\int \left(e \left(c + d x\right)\right)^{\frac{3}{2}} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((e*(c + d*x))**(3/2)*(a + b*asin(c + d*x))**2, x)","F",0
294,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(1/2)*(a+b*asin(d*x+c))**2,x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*asin(c + d*x))**2, x)","F",0
295,-2,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
296,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{2}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**2/(e*(c + d*x))**(3/2), x)","F",0
297,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{2}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**2/(e*(c + d*x))**(5/2), x)","F",0
298,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e)**(7/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{2}}{\left(e \left(c + d x\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**2/(e*(c + d*x))**(7/2), x)","F",0
299,-1,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**2/(d*e*x+c*e)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(1/2)*(a+b*asin(d*x+c))**3,x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*asin(c + d*x))**3, x)","F",0
301,-2,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**3/(d*e*x+c*e)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
302,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**3/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{3}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**3/(e*(c + d*x))**(3/2), x)","F",0
303,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**3/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{3}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**3/(e*(c + d*x))**(5/2), x)","F",0
304,0,0,0,0.000000," ","integrate((d*e*x+c*e)**(1/2)*(a+b*asin(d*x+c))**4,x)","\int \sqrt{e \left(c + d x\right)} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{4}\, dx"," ",0,"Integral(sqrt(e*(c + d*x))*(a + b*asin(c + d*x))**4, x)","F",0
305,-2,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**4/(d*e*x+c*e)**(1/2),x)","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError","F(-2)",0
306,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**4/(d*e*x+c*e)**(3/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{4}}{\left(e \left(c + d x\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**4/(e*(c + d*x))**(3/2), x)","F",0
307,0,0,0,0.000000," ","integrate((a+b*asin(d*x+c))**4/(d*e*x+c*e)**(5/2),x)","\int \frac{\left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{4}}{\left(e \left(c + d x\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(c + d*x))**4/(e*(c + d*x))**(5/2), x)","F",0
308,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*asin(d*x+c))**4,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{4}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*asin(c + d*x))**4, x)","F",0
309,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*asin(d*x+c))**3,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*asin(c + d*x))**3, x)","F",0
310,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*asin(d*x+c))**2,x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*asin(c + d*x))**2, x)","F",0
311,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m*(a+b*asin(d*x+c)),x)","\int \left(e \left(c + d x\right)\right)^{m} \left(a + b \operatorname{asin}{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((e*(c + d*x))**m*(a + b*asin(c + d*x)), x)","F",0
312,0,0,0,0.000000," ","integrate((d*e*x+c*e)**m/(a+b*asin(d*x+c)),x)","\int \frac{\left(e \left(c + d x\right)\right)^{m}}{a + b \operatorname{asin}{\left(c + d x \right)}}\, dx"," ",0,"Integral((e*(c + d*x))**m/(a + b*asin(c + d*x)), x)","F",0
313,0,0,0,0.000000," ","integrate(asin(b*x+a)**3*(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\int \sqrt{- \left(a + b x - 1\right) \left(a + b x + 1\right)} \operatorname{asin}^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(-(a + b*x - 1)*(a + b*x + 1))*asin(a + b*x)**3, x)","F",0
314,0,0,0,0.000000," ","integrate(asin(b*x+a)**2*(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\int \sqrt{- \left(a + b x - 1\right) \left(a + b x + 1\right)} \operatorname{asin}^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(-(a + b*x - 1)*(a + b*x + 1))*asin(a + b*x)**2, x)","F",0
315,0,0,0,0.000000," ","integrate(asin(b*x+a)*(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\int \sqrt{- \left(a + b x - 1\right) \left(a + b x + 1\right)} \operatorname{asin}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(-(a + b*x - 1)*(a + b*x + 1))*asin(a + b*x), x)","F",0
316,0,0,0,0.000000," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(1/2)/asin(b*x+a),x)","\int \frac{\sqrt{- \left(a + b x - 1\right) \left(a + b x + 1\right)}}{\operatorname{asin}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(-(a + b*x - 1)*(a + b*x + 1))/asin(a + b*x), x)","F",0
317,0,0,0,0.000000," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(1/2)/asin(b*x+a)**2,x)","\int \frac{\sqrt{- \left(a + b x - 1\right) \left(a + b x + 1\right)}}{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(-(a + b*x - 1)*(a + b*x + 1))/asin(a + b*x)**2, x)","F",0
318,0,0,0,0.000000," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(1/2)/asin(b*x+a)**3,x)","\int \frac{\sqrt{- \left(a + b x - 1\right) \left(a + b x + 1\right)}}{\operatorname{asin}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(-(a + b*x - 1)*(a + b*x + 1))/asin(a + b*x)**3, x)","F",0
319,0,0,0,0.000000," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(1/2)/asin(b*x+a)**4,x)","\int \frac{\sqrt{- \left(a + b x - 1\right) \left(a + b x + 1\right)}}{\operatorname{asin}^{4}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(-(a + b*x - 1)*(a + b*x + 1))/asin(a + b*x)**4, x)","F",0
320,1,694,0,13.199884," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(3/2)*asin(b*x+a)**3,x)","\begin{cases} \frac{3 a^{4} \operatorname{asin}^{2}{\left(a + b x \right)}}{16 b} + \frac{3 a^{3} x \operatorname{asin}^{2}{\left(a + b x \right)}}{4} - \frac{3 a^{3} x}{32} - \frac{a^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(a + b x \right)}}{4 b} + \frac{3 a^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{32 b} + \frac{9 a^{2} b x^{2} \operatorname{asin}^{2}{\left(a + b x \right)}}{8} - \frac{9 a^{2} b x^{2}}{64} - \frac{3 a^{2} x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(a + b x \right)}}{4} + \frac{9 a^{2} x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{32} - \frac{15 a^{2} \operatorname{asin}^{2}{\left(a + b x \right)}}{16 b} + \frac{3 a b^{2} x^{3} \operatorname{asin}^{2}{\left(a + b x \right)}}{4} - \frac{3 a b^{2} x^{3}}{32} - \frac{3 a b x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(a + b x \right)}}{4} + \frac{9 a b x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{32} - \frac{15 a x \operatorname{asin}^{2}{\left(a + b x \right)}}{8} + \frac{51 a x}{64} + \frac{5 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(a + b x \right)}}{8 b} - \frac{51 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{64 b} + \frac{3 b^{3} x^{4} \operatorname{asin}^{2}{\left(a + b x \right)}}{16} - \frac{3 b^{3} x^{4}}{128} - \frac{b^{2} x^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(a + b x \right)}}{4} + \frac{3 b^{2} x^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{32} - \frac{15 b x^{2} \operatorname{asin}^{2}{\left(a + b x \right)}}{16} + \frac{51 b x^{2}}{128} + \frac{5 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{3}{\left(a + b x \right)}}{8} - \frac{51 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{64} + \frac{3 \operatorname{asin}^{4}{\left(a + b x \right)}}{32 b} + \frac{51 \operatorname{asin}^{2}{\left(a + b x \right)}}{128 b} & \text{for}\: b \neq 0 \\x \left(1 - a^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*asin(a + b*x)**2/(16*b) + 3*a**3*x*asin(a + b*x)**2/4 - 3*a**3*x/32 - a**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**3/(4*b) + 3*a**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(32*b) + 9*a**2*b*x**2*asin(a + b*x)**2/8 - 9*a**2*b*x**2/64 - 3*a**2*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**3/4 + 9*a**2*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/32 - 15*a**2*asin(a + b*x)**2/(16*b) + 3*a*b**2*x**3*asin(a + b*x)**2/4 - 3*a*b**2*x**3/32 - 3*a*b*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**3/4 + 9*a*b*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/32 - 15*a*x*asin(a + b*x)**2/8 + 51*a*x/64 + 5*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**3/(8*b) - 51*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(64*b) + 3*b**3*x**4*asin(a + b*x)**2/16 - 3*b**3*x**4/128 - b**2*x**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**3/4 + 3*b**2*x**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/32 - 15*b*x**2*asin(a + b*x)**2/16 + 51*b*x**2/128 + 5*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**3/8 - 51*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/64 + 3*asin(a + b*x)**4/(32*b) + 51*asin(a + b*x)**2/(128*b), Ne(b, 0)), (x*(1 - a**2)**(3/2)*asin(a)**3, True))","A",0
321,1,568,0,8.423156," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(3/2)*asin(b*x+a)**2,x)","\begin{cases} \frac{a^{4} \operatorname{asin}{\left(a + b x \right)}}{8 b} + \frac{a^{3} x \operatorname{asin}{\left(a + b x \right)}}{2} - \frac{a^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{4 b} + \frac{a^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{32 b} + \frac{3 a^{2} b x^{2} \operatorname{asin}{\left(a + b x \right)}}{4} - \frac{3 a^{2} x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{4} + \frac{3 a^{2} x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{32} - \frac{5 a^{2} \operatorname{asin}{\left(a + b x \right)}}{8 b} + \frac{a b^{2} x^{3} \operatorname{asin}{\left(a + b x \right)}}{2} - \frac{3 a b x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{4} + \frac{3 a b x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{32} - \frac{5 a x \operatorname{asin}{\left(a + b x \right)}}{4} + \frac{5 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{8 b} - \frac{17 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{64 b} + \frac{b^{3} x^{4} \operatorname{asin}{\left(a + b x \right)}}{8} - \frac{b^{2} x^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{4} + \frac{b^{2} x^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{32} - \frac{5 b x^{2} \operatorname{asin}{\left(a + b x \right)}}{8} + \frac{5 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}^{2}{\left(a + b x \right)}}{8} - \frac{17 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1}}{64} + \frac{\operatorname{asin}^{3}{\left(a + b x \right)}}{8 b} + \frac{17 \operatorname{asin}{\left(a + b x \right)}}{64 b} & \text{for}\: b \neq 0 \\x \left(1 - a^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*asin(a + b*x)/(8*b) + a**3*x*asin(a + b*x)/2 - a**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/(4*b) + a**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(32*b) + 3*a**2*b*x**2*asin(a + b*x)/4 - 3*a**2*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/4 + 3*a**2*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/32 - 5*a**2*asin(a + b*x)/(8*b) + a*b**2*x**3*asin(a + b*x)/2 - 3*a*b*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/4 + 3*a*b*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/32 - 5*a*x*asin(a + b*x)/4 + 5*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/(8*b) - 17*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/(64*b) + b**3*x**4*asin(a + b*x)/8 - b**2*x**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/4 + b**2*x**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/32 - 5*b*x**2*asin(a + b*x)/8 + 5*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)**2/8 - 17*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)/64 + asin(a + b*x)**3/(8*b) + 17*asin(a + b*x)/(64*b), Ne(b, 0)), (x*(1 - a**2)**(3/2)*asin(a)**2, True))","A",0
322,1,298,0,4.331577," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(3/2)*asin(b*x+a),x)","\begin{cases} \frac{a^{3} x}{4} - \frac{a^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{4 b} + \frac{3 a^{2} b x^{2}}{8} - \frac{3 a^{2} x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{4} + \frac{a b^{2} x^{3}}{4} - \frac{3 a b x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{4} - \frac{5 a x}{8} + \frac{5 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{8 b} + \frac{b^{3} x^{4}}{16} - \frac{b^{2} x^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{4} - \frac{5 b x^{2}}{16} + \frac{5 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} \operatorname{asin}{\left(a + b x \right)}}{8} + \frac{3 \operatorname{asin}^{2}{\left(a + b x \right)}}{16 b} & \text{for}\: b \neq 0 \\x \left(1 - a^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x/4 - a**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(4*b) + 3*a**2*b*x**2/8 - 3*a**2*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/4 + a*b**2*x**3/4 - 3*a*b*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/4 - 5*a*x/8 + 5*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/(8*b) + b**3*x**4/16 - b**2*x**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/4 - 5*b*x**2/16 + 5*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*asin(a + b*x)/8 + 3*asin(a + b*x)**2/(16*b), Ne(b, 0)), (x*(1 - a**2)**(3/2)*asin(a), True))","A",0
323,0,0,0,0.000000," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(3/2)/asin(b*x+a),x)","\int \frac{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}}}{\operatorname{asin}{\left(a + b x \right)}}\, dx"," ",0,"Integral((-(a + b*x - 1)*(a + b*x + 1))**(3/2)/asin(a + b*x), x)","F",0
324,0,0,0,0.000000," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(3/2)/asin(b*x+a)**2,x)","\int \frac{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}}}{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral((-(a + b*x - 1)*(a + b*x + 1))**(3/2)/asin(a + b*x)**2, x)","F",0
325,0,0,0,0.000000," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(3/2)/asin(b*x+a)**3,x)","\int \frac{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}}}{\operatorname{asin}^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral((-(a + b*x - 1)*(a + b*x + 1))**(3/2)/asin(a + b*x)**3, x)","F",0
326,0,0,0,0.000000," ","integrate((-b**2*x**2-2*a*b*x-a**2+1)**(3/2)/asin(b*x+a)**4,x)","\int \frac{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}}}{\operatorname{asin}^{4}{\left(a + b x \right)}}\, dx"," ",0,"Integral((-(a + b*x - 1)*(a + b*x + 1))**(3/2)/asin(a + b*x)**4, x)","F",0
327,1,60,0,1.195593," ","integrate(asin(b*x+a)**n/(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\begin{cases} \frac{x}{\sqrt{1 - a^{2}} \operatorname{asin}{\left(a \right)}} & \text{for}\: b = 0 \wedge n = -1 \\\frac{x \operatorname{asin}^{n}{\left(a \right)}}{\sqrt{1 - a^{2}}} & \text{for}\: b = 0 \\\frac{\log{\left(\operatorname{asin}{\left(a + b x \right)} \right)}}{b} & \text{for}\: n = -1 \\\frac{\operatorname{asin}{\left(a + b x \right)} \operatorname{asin}^{n}{\left(a + b x \right)}}{b n + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/(sqrt(1 - a**2)*asin(a)), Eq(b, 0) & Eq(n, -1)), (x*asin(a)**n/sqrt(1 - a**2), Eq(b, 0)), (log(asin(a + b*x))/b, Eq(n, -1)), (asin(a + b*x)*asin(a + b*x)**n/(b*n + b), True))","A",0
328,1,26,0,0.745079," ","integrate(asin(b*x+a)**2/(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asin}^{3}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\\frac{x \operatorname{asin}^{2}{\left(a \right)}}{\sqrt{1 - a^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((asin(a + b*x)**3/(3*b), Ne(b, 0)), (x*asin(a)**2/sqrt(1 - a**2), True))","A",0
329,1,24,0,0.651614," ","integrate(asin(b*x+a)/(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\begin{cases} \frac{\operatorname{asin}^{2}{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\\frac{x \operatorname{asin}{\left(a \right)}}{\sqrt{1 - a^{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((asin(a + b*x)**2/(2*b), Ne(b, 0)), (x*asin(a)/sqrt(1 - a**2), True))","A",0
330,1,22,0,0.889675," ","integrate(1/asin(b*x+a)/(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\begin{cases} \frac{\log{\left(\operatorname{asin}{\left(a + b x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt{1 - a^{2}} \operatorname{asin}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(asin(a + b*x))/b, Ne(b, 0)), (x/(sqrt(1 - a**2)*asin(a)), True))","A",0
331,1,26,0,1.291515," ","integrate(1/asin(b*x+a)**2/(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\begin{cases} - \frac{1}{b \operatorname{asin}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt{1 - a^{2}} \operatorname{asin}^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(b*asin(a + b*x)), Ne(b, 0)), (x/(sqrt(1 - a**2)*asin(a)**2), True))","A",0
332,1,29,0,1.730998," ","integrate(1/asin(b*x+a)**3/(-b**2*x**2-2*a*b*x-a**2+1)**(1/2),x)","\begin{cases} - \frac{1}{2 b \operatorname{asin}^{2}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x}{\sqrt{1 - a^{2}} \operatorname{asin}^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(2*b*asin(a + b*x)**2), Ne(b, 0)), (x/(sqrt(1 - a**2)*asin(a)**3), True))","A",0
333,0,0,0,0.000000," ","integrate(asin(b*x+a)**3/(-b**2*x**2-2*a*b*x-a**2+1)**(3/2),x)","\int \frac{\operatorname{asin}^{3}{\left(a + b x \right)}}{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asin(a + b*x)**3/(-(a + b*x - 1)*(a + b*x + 1))**(3/2), x)","F",0
334,0,0,0,0.000000," ","integrate(asin(b*x+a)**2/(-b**2*x**2-2*a*b*x-a**2+1)**(3/2),x)","\int \frac{\operatorname{asin}^{2}{\left(a + b x \right)}}{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asin(a + b*x)**2/(-(a + b*x - 1)*(a + b*x + 1))**(3/2), x)","F",0
335,0,0,0,0.000000," ","integrate(asin(b*x+a)/(-b**2*x**2-2*a*b*x-a**2+1)**(3/2),x)","\int \frac{\operatorname{asin}{\left(a + b x \right)}}{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(asin(a + b*x)/(-(a + b*x - 1)*(a + b*x + 1))**(3/2), x)","F",0
336,0,0,0,0.000000," ","integrate(1/(-b**2*x**2-2*a*b*x-a**2+1)**(3/2)/asin(b*x+a),x)","\int \frac{1}{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}} \operatorname{asin}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/((-(a + b*x - 1)*(a + b*x + 1))**(3/2)*asin(a + b*x)), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(-b**2*x**2-2*a*b*x-a**2+1)**(3/2)/asin(b*x+a)**2,x)","\int \frac{1}{\left(- \left(a + b x - 1\right) \left(a + b x + 1\right)\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(1/((-(a + b*x - 1)*(a + b*x + 1))**(3/2)*asin(a + b*x)**2), x)","F",0
338,0,0,0,0.000000," ","integrate(asin(b*x+a)/(c-c*(b*x+a)**2)**(1/2),x)","\int \frac{\operatorname{asin}{\left(a + b x \right)}}{\sqrt{- c \left(a + b x - 1\right) \left(a + b x + 1\right)}}\, dx"," ",0,"Integral(asin(a + b*x)/sqrt(-c*(a + b*x - 1)*(a + b*x + 1)), x)","F",0
339,0,0,0,0.000000," ","integrate(asin(b*x+a)/((-a**2+1)*c-2*a*b*c*x-c*x**2*b**2)**(1/2),x)","\int \frac{\operatorname{asin}{\left(a + b x \right)}}{\sqrt{- c \left(a + b x - 1\right) \left(a + b x + 1\right)}}\, dx"," ",0,"Integral(asin(a + b*x)/sqrt(-c*(a + b*x - 1)*(a + b*x + 1)), x)","F",0
340,1,90,0,18.773783," ","integrate(x**9*(a+b*asin(c*x**2)),x)","\begin{cases} \frac{a x^{10}}{10} + \frac{b x^{10} \operatorname{asin}{\left(c x^{2} \right)}}{10} + \frac{b x^{8} \sqrt{- c^{2} x^{4} + 1}}{50 c} + \frac{2 b x^{4} \sqrt{- c^{2} x^{4} + 1}}{75 c^{3}} + \frac{4 b \sqrt{- c^{2} x^{4} + 1}}{75 c^{5}} & \text{for}\: c \neq 0 \\\frac{a x^{10}}{10} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**10/10 + b*x**10*asin(c*x**2)/10 + b*x**8*sqrt(-c**2*x**4 + 1)/(50*c) + 2*b*x**4*sqrt(-c**2*x**4 + 1)/(75*c**3) + 4*b*sqrt(-c**2*x**4 + 1)/(75*c**5), Ne(c, 0)), (a*x**10/10, True))","A",0
341,1,85,0,7.620820," ","integrate(x**7*(a+b*asin(c*x**2)),x)","\begin{cases} \frac{a x^{8}}{8} + \frac{b x^{8} \operatorname{asin}{\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 \operatorname{asin}{\left(c x^{2} \right)}}{64 c^{4}} & \text{for}\: c \neq 0 \\\frac{a x^{8}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**8/8 + b*x**8*asin(c*x**2)/8 + b*x**6*sqrt(-c**2*x**4 + 1)/(32*c) + 3*b*x**2*sqrt(-c**2*x**4 + 1)/(64*c**3) - 3*b*asin(c*x**2)/(64*c**4), Ne(c, 0)), (a*x**8/8, True))","A",0
342,1,65,0,2.523545," ","integrate(x**5*(a+b*asin(c*x**2)),x)","\begin{cases} \frac{a x^{6}}{6} + \frac{b x^{6} \operatorname{asin}{\left(c x^{2} \right)}}{6} + \frac{b x^{4} \sqrt{- c^{2} x^{4} + 1}}{18 c} + \frac{b \sqrt{- c^{2} x^{4} + 1}}{9 c^{3}} & \text{for}\: c \neq 0 \\\frac{a x^{6}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**6/6 + b*x**6*asin(c*x**2)/6 + b*x**4*sqrt(-c**2*x**4 + 1)/(18*c) + b*sqrt(-c**2*x**4 + 1)/(9*c**3), Ne(c, 0)), (a*x**6/6, True))","A",0
343,1,60,0,0.778352," ","integrate(x**3*(a+b*asin(c*x**2)),x)","\begin{cases} \frac{a x^{4}}{4} + \frac{b x^{4} \operatorname{asin}{\left(c x^{2} \right)}}{4} + \frac{b x^{2} \sqrt{- c^{2} x^{4} + 1}}{8 c} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{8 c^{2}} & \text{for}\: c \neq 0 \\\frac{a x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**4/4 + b*x**4*asin(c*x**2)/4 + b*x**2*sqrt(-c**2*x**4 + 1)/(8*c) - b*asin(c*x**2)/(8*c**2), Ne(c, 0)), (a*x**4/4, True))","A",0
344,1,42,0,0.194219," ","integrate(x*(a+b*asin(c*x**2)),x)","\begin{cases} \frac{a x^{2}}{2} + \frac{b x^{2} \operatorname{asin}{\left(c x^{2} \right)}}{2} + \frac{b \sqrt{- c^{2} x^{4} + 1}}{2 c} & \text{for}\: c \neq 0 \\\frac{a x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**2/2 + b*x**2*asin(c*x**2)/2 + b*sqrt(-c**2*x**4 + 1)/(2*c), Ne(c, 0)), (a*x**2/2, True))","A",0
345,0,0,0,0.000000," ","integrate((a+b*asin(c*x**2))/x,x)","\int \frac{a + b \operatorname{asin}{\left(c x^{2} \right)}}{x}\, dx"," ",0,"Integral((a + b*asin(c*x**2))/x, x)","F",0
346,1,54,0,1.738908," ","integrate((a+b*asin(c*x**2))/x**3,x)","- \frac{a}{2 x^{2}} + b c \left(\begin{cases} - \frac{\operatorname{acosh}{\left(\frac{1}{c x^{2}} \right)}}{2} & \text{for}\: \frac{1}{\left|{c^{2} x^{4}}\right|} > 1 \\\frac{i \operatorname{asin}{\left(\frac{1}{c x^{2}} \right)}}{2} & \text{otherwise} \end{cases}\right) - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{2 x^{2}}"," ",0,"-a/(2*x**2) + b*c*Piecewise((-acosh(1/(c*x**2))/2, 1/Abs(c**2*x**4) > 1), (I*asin(1/(c*x**2))/2, True)) - b*asin(c*x**2)/(2*x**2)","A",0
347,1,70,0,1.699238," ","integrate((a+b*asin(c*x**2))/x**5,x)","- \frac{a}{4 x^{4}} + \frac{b c \left(\begin{cases} - \frac{i \sqrt{c^{2} x^{4} - 1}}{2 x^{2}} & \text{for}\: \left|{c^{2} x^{4}}\right| > 1 \\- \frac{\sqrt{- c^{2} x^{4} + 1}}{2 x^{2}} & \text{otherwise} \end{cases}\right)}{2} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{4 x^{4}}"," ",0,"-a/(4*x**4) + b*c*Piecewise((-I*sqrt(c**2*x**4 - 1)/(2*x**2), Abs(c**2*x**4) > 1), (-sqrt(-c**2*x**4 + 1)/(2*x**2), True))/2 - b*asin(c*x**2)/(4*x**4)","A",0
348,1,128,0,3.345130," ","integrate((a+b*asin(c*x**2))/x**7,x)","- \frac{a}{6 x^{6}} + \frac{b c \left(\begin{cases} - \frac{c^{2} \operatorname{acosh}{\left(\frac{1}{c x^{2}} \right)}}{4} - \frac{c \sqrt{-1 + \frac{1}{c^{2} x^{4}}}}{4 x^{2}} & \text{for}\: \frac{1}{\left|{c^{2} x^{4}}\right|} > 1 \\\frac{i c^{2} \operatorname{asin}{\left(\frac{1}{c x^{2}} \right)}}{4} - \frac{i c}{4 x^{2} \sqrt{1 - \frac{1}{c^{2} x^{4}}}} + \frac{i}{4 c x^{6} \sqrt{1 - \frac{1}{c^{2} x^{4}}}} & \text{otherwise} \end{cases}\right)}{3} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{6 x^{6}}"," ",0,"-a/(6*x**6) + b*c*Piecewise((-c**2*acosh(1/(c*x**2))/4 - c*sqrt(-1 + 1/(c**2*x**4))/(4*x**2), 1/Abs(c**2*x**4) > 1), (I*c**2*asin(1/(c*x**2))/4 - I*c/(4*x**2*sqrt(1 - 1/(c**2*x**4))) + I/(4*c*x**6*sqrt(1 - 1/(c**2*x**4))), True))/3 - b*asin(c*x**2)/(6*x**6)","A",0
349,1,112,0,3.674017," ","integrate((a+b*asin(c*x**2))/x**9,x)","- \frac{a}{8 x^{8}} + \frac{b c \left(\begin{cases} - \frac{i c^{2} \sqrt{c^{2} x^{4} - 1}}{3 x^{2}} - \frac{i \sqrt{c^{2} x^{4} - 1}}{6 x^{6}} & \text{for}\: \left|{c^{2} x^{4}}\right| > 1 \\- \frac{c^{2} \sqrt{- c^{2} x^{4} + 1}}{3 x^{2}} - \frac{\sqrt{- c^{2} x^{4} + 1}}{6 x^{6}} & \text{otherwise} \end{cases}\right)}{4} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{8 x^{8}}"," ",0,"-a/(8*x**8) + b*c*Piecewise((-I*c**2*sqrt(c**2*x**4 - 1)/(3*x**2) - I*sqrt(c**2*x**4 - 1)/(6*x**6), Abs(c**2*x**4) > 1), (-c**2*sqrt(-c**2*x**4 + 1)/(3*x**2) - sqrt(-c**2*x**4 + 1)/(6*x**6), True))/4 - b*asin(c*x**2)/(8*x**8)","A",0
350,1,201,0,7.579168," ","integrate((a+b*asin(c*x**2))/x**11,x)","- \frac{a}{10 x^{10}} + \frac{b c \left(\begin{cases} - \frac{3 c^{4} \operatorname{acosh}{\left(\frac{1}{c x^{2}} \right)}}{16} + \frac{3 c^{3}}{16 x^{2} \sqrt{-1 + \frac{1}{c^{2} x^{4}}}} - \frac{c}{16 x^{6} \sqrt{-1 + \frac{1}{c^{2} x^{4}}}} - \frac{1}{8 c x^{10} \sqrt{-1 + \frac{1}{c^{2} x^{4}}}} & \text{for}\: \frac{1}{\left|{c^{2} x^{4}}\right|} > 1 \\\frac{3 i c^{4} \operatorname{asin}{\left(\frac{1}{c x^{2}} \right)}}{16} - \frac{3 i c^{3}}{16 x^{2} \sqrt{1 - \frac{1}{c^{2} x^{4}}}} + \frac{i c}{16 x^{6} \sqrt{1 - \frac{1}{c^{2} x^{4}}}} + \frac{i}{8 c x^{10} \sqrt{1 - \frac{1}{c^{2} x^{4}}}} & \text{otherwise} \end{cases}\right)}{5} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{10 x^{10}}"," ",0,"-a/(10*x**10) + b*c*Piecewise((-3*c**4*acosh(1/(c*x**2))/16 + 3*c**3/(16*x**2*sqrt(-1 + 1/(c**2*x**4))) - c/(16*x**6*sqrt(-1 + 1/(c**2*x**4))) - 1/(8*c*x**10*sqrt(-1 + 1/(c**2*x**4))), 1/Abs(c**2*x**4) > 1), (3*I*c**4*asin(1/(c*x**2))/16 - 3*I*c**3/(16*x**2*sqrt(1 - 1/(c**2*x**4))) + I*c/(16*x**6*sqrt(1 - 1/(c**2*x**4))) + I/(8*c*x**10*sqrt(1 - 1/(c**2*x**4))), True))/5 - b*asin(c*x**2)/(10*x**10)","A",0
351,1,170,0,8.812848," ","integrate((a+b*asin(c*x**2))/x**13,x)","- \frac{a}{12 x^{12}} + \frac{b c \left(\begin{cases} - \frac{4 c^{5} \sqrt{-1 + \frac{1}{c^{2} x^{4}}}}{15} - \frac{2 c^{3} \sqrt{-1 + \frac{1}{c^{2} x^{4}}}}{15 x^{4}} - \frac{c \sqrt{-1 + \frac{1}{c^{2} x^{4}}}}{10 x^{8}} & \text{for}\: \frac{1}{\left|{c^{2} x^{4}}\right|} > 1 \\- \frac{4 i c^{5} \sqrt{1 - \frac{1}{c^{2} x^{4}}}}{15} - \frac{2 i c^{3} \sqrt{1 - \frac{1}{c^{2} x^{4}}}}{15 x^{4}} - \frac{i c \sqrt{1 - \frac{1}{c^{2} x^{4}}}}{10 x^{8}} & \text{otherwise} \end{cases}\right)}{6} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{12 x^{12}}"," ",0,"-a/(12*x**12) + b*c*Piecewise((-4*c**5*sqrt(-1 + 1/(c**2*x**4))/15 - 2*c**3*sqrt(-1 + 1/(c**2*x**4))/(15*x**4) - c*sqrt(-1 + 1/(c**2*x**4))/(10*x**8), 1/Abs(c**2*x**4) > 1), (-4*I*c**5*sqrt(1 - 1/(c**2*x**4))/15 - 2*I*c**3*sqrt(1 - 1/(c**2*x**4))/(15*x**4) - I*c*sqrt(1 - 1/(c**2*x**4))/(10*x**8), True))/6 - b*asin(c*x**2)/(12*x**12)","A",0
352,1,58,0,2.651809," ","integrate(x**6*(a+b*asin(c*x**2)),x)","\frac{a x^{7}}{7} - \frac{b c x^{9} \Gamma\left(\frac{9}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{9}{4} \\ \frac{13}{4} \end{matrix}\middle| {c^{2} x^{4} e^{2 i \pi}} \right)}}{14 \Gamma\left(\frac{13}{4}\right)} + \frac{b x^{7} \operatorname{asin}{\left(c x^{2} \right)}}{7}"," ",0,"a*x**7/7 - b*c*x**9*gamma(9/4)*hyper((1/2, 9/4), (13/4,), c**2*x**4*exp_polar(2*I*pi))/(14*gamma(13/4)) + b*x**7*asin(c*x**2)/7","A",0
353,1,58,0,2.089089," ","integrate(x**4*(a+b*asin(c*x**2)),x)","\frac{a x^{5}}{5} - \frac{b c x^{7} \Gamma\left(\frac{7}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{4} \\ \frac{11}{4} \end{matrix}\middle| {c^{2} x^{4} e^{2 i \pi}} \right)}}{10 \Gamma\left(\frac{11}{4}\right)} + \frac{b x^{5} \operatorname{asin}{\left(c x^{2} \right)}}{5}"," ",0,"a*x**5/5 - b*c*x**7*gamma(7/4)*hyper((1/2, 7/4), (11/4,), c**2*x**4*exp_polar(2*I*pi))/(10*gamma(11/4)) + b*x**5*asin(c*x**2)/5","A",0
354,1,58,0,1.775317," ","integrate(x**2*(a+b*asin(c*x**2)),x)","\frac{a x^{3}}{3} - \frac{b c x^{5} \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{5}{4} \\ \frac{9}{4} \end{matrix}\middle| {c^{2} x^{4} e^{2 i \pi}} \right)}}{6 \Gamma\left(\frac{9}{4}\right)} + \frac{b x^{3} \operatorname{asin}{\left(c x^{2} \right)}}{3}"," ",0,"a*x**3/3 - b*c*x**5*gamma(5/4)*hyper((1/2, 5/4), (9/4,), c**2*x**4*exp_polar(2*I*pi))/(6*gamma(9/4)) + b*x**3*asin(c*x**2)/3","A",0
355,1,49,0,1.002792," ","integrate(a+b*asin(c*x**2),x)","a x + b \left(- \frac{c x^{3} \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{3}{4} \\ \frac{7}{4} \end{matrix}\middle| {c^{2} x^{4} e^{2 i \pi}} \right)}}{2 \Gamma\left(\frac{7}{4}\right)} + x \operatorname{asin}{\left(c x^{2} \right)}\right)"," ",0,"a*x + b*(-c*x**3*gamma(3/4)*hyper((1/2, 3/4), (7/4,), c**2*x**4*exp_polar(2*I*pi))/(2*gamma(7/4)) + x*asin(c*x**2))","A",0
356,1,49,0,1.322166," ","integrate((a+b*asin(c*x**2))/x**2,x)","- \frac{a}{x} + \frac{b c x \Gamma\left(\frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{4}, \frac{1}{2} \\ \frac{5}{4} \end{matrix}\middle| {c^{2} x^{4} e^{2 i \pi}} \right)}}{2 \Gamma\left(\frac{5}{4}\right)} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{x}"," ",0,"-a/x + b*c*x*gamma(1/4)*hyper((1/4, 1/2), (5/4,), c**2*x**4*exp_polar(2*I*pi))/(2*gamma(5/4)) - b*asin(c*x**2)/x","A",0
357,1,60,0,1.656405," ","integrate((a+b*asin(c*x**2))/x**4,x)","- \frac{a}{3 x^{3}} + \frac{b c \Gamma\left(- \frac{1}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{1}{4}, \frac{1}{2} \\ \frac{3}{4} \end{matrix}\middle| {c^{2} x^{4} e^{2 i \pi}} \right)}}{6 x \Gamma\left(\frac{3}{4}\right)} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{3 x^{3}}"," ",0,"-a/(3*x**3) + b*c*gamma(-1/4)*hyper((-1/4, 1/2), (3/4,), c**2*x**4*exp_polar(2*I*pi))/(6*x*gamma(3/4)) - b*asin(c*x**2)/(3*x**3)","A",0
358,1,61,0,2.105663," ","integrate((a+b*asin(c*x**2))/x**6,x)","- \frac{a}{5 x^{5}} + \frac{b c \Gamma\left(- \frac{3}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{3}{4}, \frac{1}{2} \\ \frac{1}{4} \end{matrix}\middle| {c^{2} x^{4} e^{2 i \pi}} \right)}}{10 x^{3} \Gamma\left(\frac{1}{4}\right)} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{5 x^{5}}"," ",0,"-a/(5*x**5) + b*c*gamma(-3/4)*hyper((-3/4, 1/2), (1/4,), c**2*x**4*exp_polar(2*I*pi))/(10*x**3*gamma(1/4)) - b*asin(c*x**2)/(5*x**5)","A",0
359,1,65,0,3.080633," ","integrate((a+b*asin(c*x**2))/x**8,x)","- \frac{a}{7 x^{7}} + \frac{b c \Gamma\left(- \frac{5}{4}\right) {{}_{2}F_{1}\left(\begin{matrix} - \frac{5}{4}, \frac{1}{2} \\ - \frac{1}{4} \end{matrix}\middle| {c^{2} x^{4} e^{2 i \pi}} \right)}}{14 x^{5} \Gamma\left(- \frac{1}{4}\right)} - \frac{b \operatorname{asin}{\left(c x^{2} \right)}}{7 x^{7}}"," ",0,"-a/(7*x**7) + b*c*gamma(-5/4)*hyper((-5/4, 1/2), (-1/4,), c**2*x**4*exp_polar(2*I*pi))/(14*x**5*gamma(-1/4)) - b*asin(c*x**2)/(7*x**7)","A",0
360,0,0,0,0.000000," ","integrate(asin(a*x**5)/x,x)","\int \frac{\operatorname{asin}{\left(a x^{5} \right)}}{x}\, dx"," ",0,"Integral(asin(a*x**5)/x, x)","F",0
361,1,73,0,7.979248," ","integrate(x**2*asin(x**(1/2)),x)","\frac{x^{3} \operatorname{asin}{\left(\sqrt{x} \right)}}{3} - \frac{\begin{cases} \frac{x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}}{6} + \frac{3 \sqrt{x} \left(1 - 2 x\right) \sqrt{1 - x}}{16} - \frac{\sqrt{x} \sqrt{1 - x}}{2} + \frac{5 \operatorname{asin}{\left(\sqrt{x} \right)}}{16} & \text{for}\: x \geq 0 \wedge x < 1 \end{cases}}{3}"," ",0,"x**3*asin(sqrt(x))/3 - Piecewise((x**(3/2)*(1 - x)**(3/2)/6 + 3*sqrt(x)*(1 - 2*x)*sqrt(1 - x)/16 - sqrt(x)*sqrt(1 - x)/2 + 5*asin(sqrt(x))/16, (x >= 0) & (x < 1)))/3","A",0
362,1,58,0,3.833420," ","integrate(x*asin(x**(1/2)),x)","\frac{x^{2} \operatorname{asin}{\left(\sqrt{x} \right)}}{2} - \frac{\begin{cases} \frac{\sqrt{x} \left(1 - 2 x\right) \sqrt{1 - x}}{8} - \frac{\sqrt{x} \sqrt{1 - x}}{2} + \frac{3 \operatorname{asin}{\left(\sqrt{x} \right)}}{8} & \text{for}\: x \geq 0 \wedge x < 1 \end{cases}}{2}"," ",0,"x**2*asin(sqrt(x))/2 - Piecewise((sqrt(x)*(1 - 2*x)*sqrt(1 - x)/8 - sqrt(x)*sqrt(1 - x)/2 + 3*asin(sqrt(x))/8, (x >= 0) & (x < 1)))/2","A",0
363,1,29,0,0.250620," ","integrate(asin(x**(1/2)),x)","\frac{\sqrt{x} \sqrt{1 - x}}{2} + x \operatorname{asin}{\left(\sqrt{x} \right)} - \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{2}"," ",0,"sqrt(x)*sqrt(1 - x)/2 + x*asin(sqrt(x)) - asin(sqrt(x))/2","A",0
364,0,0,0,0.000000," ","integrate(asin(x**(1/2))/x,x)","\int \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x}\, dx"," ",0,"Integral(asin(sqrt(x))/x, x)","F",0
365,1,42,0,3.100449," ","integrate(asin(x**(1/2))/x**2,x)","\frac{\begin{cases} - \frac{2 i \sqrt{x - 1}}{\sqrt{x}} & \text{for}\: \left|{x}\right| > 1 \\- \frac{2 \sqrt{1 - x}}{\sqrt{x}} & \text{otherwise} \end{cases}}{2} - \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x}"," ",0,"Piecewise((-2*I*sqrt(x - 1)/sqrt(x), Abs(x) > 1), (-2*sqrt(1 - x)/sqrt(x), True))/2 - asin(sqrt(x))/x","C",0
366,1,42,0,7.131191," ","integrate(asin(x**(1/2))/x**3,x)","\frac{\begin{cases} - \frac{\sqrt{1 - x}}{\sqrt{x}} - \frac{\left(1 - x\right)^{\frac{3}{2}}}{3 x^{\frac{3}{2}}} & \text{for}\: x \geq 0 \wedge x < 1 \end{cases}}{2} - \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{2 x^{2}}"," ",0,"Piecewise((-sqrt(1 - x)/sqrt(x) - (1 - x)**(3/2)/(3*x**(3/2)), (x >= 0) & (x < 1)))/2 - asin(sqrt(x))/(2*x**2)","A",0
367,1,58,0,15.686106," ","integrate(asin(x**(1/2))/x**4,x)","\frac{\begin{cases} - \frac{\sqrt{1 - x}}{\sqrt{x}} - \frac{2 \left(1 - x\right)^{\frac{3}{2}}}{3 x^{\frac{3}{2}}} - \frac{\left(1 - x\right)^{\frac{5}{2}}}{5 x^{\frac{5}{2}}} & \text{for}\: x \geq 0 \wedge x < 1 \end{cases}}{3} - \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{3 x^{3}}"," ",0,"Piecewise((-sqrt(1 - x)/sqrt(x) - 2*(1 - x)**(3/2)/(3*x**(3/2)) - (1 - x)**(5/2)/(5*x**(5/2)), (x >= 0) & (x < 1)))/3 - asin(sqrt(x))/(3*x**3)","A",0
368,1,70,0,36.276515," ","integrate(asin(x**(1/2))/x**5,x)","\frac{\begin{cases} - \frac{\sqrt{1 - x}}{\sqrt{x}} - \frac{\left(1 - x\right)^{\frac{3}{2}}}{x^{\frac{3}{2}}} - \frac{3 \left(1 - x\right)^{\frac{5}{2}}}{5 x^{\frac{5}{2}}} - \frac{\left(1 - x\right)^{\frac{7}{2}}}{7 x^{\frac{7}{2}}} & \text{for}\: x \geq 0 \wedge x < 1 \end{cases}}{4} - \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{4 x^{4}}"," ",0,"Piecewise((-sqrt(1 - x)/sqrt(x) - (1 - x)**(3/2)/x**(3/2) - 3*(1 - x)**(5/2)/(5*x**(5/2)) - (1 - x)**(7/2)/(7*x**(7/2)), (x >= 0) & (x < 1)))/4 - asin(sqrt(x))/(4*x**4)","A",0
369,1,175,0,5.260229," ","integrate(x**4*(a+b*asin(c/x)),x)","\frac{a x^{5}}{5} + \frac{b c \left(\begin{cases} \frac{3 c^{4} \operatorname{acosh}{\left(\frac{x}{c} \right)}}{8} - \frac{3 c^{3} x}{8 \sqrt{-1 + \frac{x^{2}}{c^{2}}}} + \frac{c x^{3}}{8 \sqrt{-1 + \frac{x^{2}}{c^{2}}}} + \frac{x^{5}}{4 c \sqrt{-1 + \frac{x^{2}}{c^{2}}}} & \text{for}\: \left|{\frac{x^{2}}{c^{2}}}\right| > 1 \\- \frac{3 i c^{4} \operatorname{asin}{\left(\frac{x}{c} \right)}}{8} + \frac{3 i c^{3} x}{8 \sqrt{1 - \frac{x^{2}}{c^{2}}}} - \frac{i c x^{3}}{8 \sqrt{1 - \frac{x^{2}}{c^{2}}}} - \frac{i x^{5}}{4 c \sqrt{1 - \frac{x^{2}}{c^{2}}}} & \text{otherwise} \end{cases}\right)}{5} + \frac{b x^{5} \operatorname{asin}{\left(\frac{c}{x} \right)}}{5}"," ",0,"a*x**5/5 + b*c*Piecewise((3*c**4*acosh(x/c)/8 - 3*c**3*x/(8*sqrt(-1 + x**2/c**2)) + c*x**3/(8*sqrt(-1 + x**2/c**2)) + x**5/(4*c*sqrt(-1 + x**2/c**2)), Abs(x**2/c**2) > 1), (-3*I*c**4*asin(x/c)/8 + 3*I*c**3*x/(8*sqrt(1 - x**2/c**2)) - I*c*x**3/(8*sqrt(1 - x**2/c**2)) - I*x**5/(4*c*sqrt(1 - x**2/c**2)), True))/5 + b*x**5*asin(c/x)/5","A",0
370,1,107,0,2.689390," ","integrate(x**3*(a+b*asin(c/x)),x)","\frac{a x^{4}}{4} + \frac{b c \left(\begin{cases} \frac{2 c^{3} \sqrt{-1 + \frac{x^{2}}{c^{2}}}}{3} + \frac{c x^{2} \sqrt{-1 + \frac{x^{2}}{c^{2}}}}{3} & \text{for}\: \left|{\frac{x^{2}}{c^{2}}}\right| > 1 \\\frac{2 i c^{3} \sqrt{1 - \frac{x^{2}}{c^{2}}}}{3} + \frac{i c x^{2} \sqrt{1 - \frac{x^{2}}{c^{2}}}}{3} & \text{otherwise} \end{cases}\right)}{4} + \frac{b x^{4} \operatorname{asin}{\left(\frac{c}{x} \right)}}{4}"," ",0,"a*x**4/4 + b*c*Piecewise((2*c**3*sqrt(-1 + x**2/c**2)/3 + c*x**2*sqrt(-1 + x**2/c**2)/3, Abs(x**2/c**2) > 1), (2*I*c**3*sqrt(1 - x**2/c**2)/3 + I*c*x**2*sqrt(1 - x**2/c**2)/3, True))/4 + b*x**4*asin(c/x)/4","A",0
371,1,107,0,3.177167," ","integrate(x**2*(a+b*asin(c/x)),x)","\frac{a x^{3}}{3} + \frac{b c \left(\begin{cases} \frac{c^{2} \operatorname{acosh}{\left(\frac{x}{c} \right)}}{2} + \frac{c x \sqrt{-1 + \frac{x^{2}}{c^{2}}}}{2} & \text{for}\: \left|{\frac{x^{2}}{c^{2}}}\right| > 1 \\- \frac{i c^{2} \operatorname{asin}{\left(\frac{x}{c} \right)}}{2} + \frac{i c x}{2 \sqrt{1 - \frac{x^{2}}{c^{2}}}} - \frac{i x^{3}}{2 c \sqrt{1 - \frac{x^{2}}{c^{2}}}} & \text{otherwise} \end{cases}\right)}{3} + \frac{b x^{3} \operatorname{asin}{\left(\frac{c}{x} \right)}}{3}"," ",0,"a*x**3/3 + b*c*Piecewise((c**2*acosh(x/c)/2 + c*x*sqrt(-1 + x**2/c**2)/2, Abs(x**2/c**2) > 1), (-I*c**2*asin(x/c)/2 + I*c*x/(2*sqrt(1 - x**2/c**2)) - I*x**3/(2*c*sqrt(1 - x**2/c**2)), True))/3 + b*x**3*asin(c/x)/3","A",0
372,1,58,0,1.931778," ","integrate(x*(a+b*asin(c/x)),x)","\frac{a x^{2}}{2} + \frac{b c \left(\begin{cases} c \sqrt{-1 + \frac{x^{2}}{c^{2}}} & \text{for}\: \left|{\frac{x^{2}}{c^{2}}}\right| > 1 \\i c \sqrt{1 - \frac{x^{2}}{c^{2}}} & \text{otherwise} \end{cases}\right)}{2} + \frac{b x^{2} \operatorname{asin}{\left(\frac{c}{x} \right)}}{2}"," ",0,"a*x**2/2 + b*c*Piecewise((c*sqrt(-1 + x**2/c**2), Abs(x**2/c**2) > 1), (I*c*sqrt(1 - x**2/c**2), True))/2 + b*x**2*asin(c/x)/2","A",0
373,1,32,0,1.703466," ","integrate(a+b*asin(c/x),x)","a x + b \left(c \left(\begin{cases} \operatorname{acosh}{\left(\frac{x}{c} \right)} & \text{for}\: \left|{\frac{x^{2}}{c^{2}}}\right| > 1 \\- i \operatorname{asin}{\left(\frac{x}{c} \right)} & \text{otherwise} \end{cases}\right) + x \operatorname{asin}{\left(\frac{c}{x} \right)}\right)"," ",0,"a*x + b*(c*Piecewise((acosh(x/c), Abs(x**2/c**2) > 1), (-I*asin(x/c), True)) + x*asin(c/x))","A",0
374,0,0,0,0.000000," ","integrate((a+b*asin(c/x))/x,x)","\int \frac{a + b \operatorname{asin}{\left(\frac{c}{x} \right)}}{x}\, dx"," ",0,"Integral((a + b*asin(c/x))/x, x)","F",0
375,1,32,0,1.754152," ","integrate((a+b*asin(c/x))/x**2,x)","\begin{cases} - \frac{a}{x} - \frac{b \operatorname{asin}{\left(\frac{c}{x} \right)}}{x} - \frac{b \sqrt{- \frac{c^{2}}{x^{2}} + 1}}{c} & \text{for}\: c \neq 0 \\- \frac{a}{x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a/x - b*asin(c/x)/x - b*sqrt(-c**2/x**2 + 1)/c, Ne(c, 0)), (-a/x, True))","A",0
376,1,112,0,3.040808," ","integrate((a+b*asin(c/x))/x**3,x)","- \frac{a}{2 x^{2}} - \frac{b c \left(\begin{cases} \frac{i \sqrt{\frac{c^{2}}{x^{2}} - 1}}{2 c^{2} x} + \frac{i \operatorname{acosh}{\left(\frac{c}{x} \right)}}{2 c^{3}} & \text{for}\: \left|{\frac{c^{2}}{x^{2}}}\right| > 1 \\- \frac{1}{2 x^{3} \sqrt{- \frac{c^{2}}{x^{2}} + 1}} + \frac{1}{2 c^{2} x \sqrt{- \frac{c^{2}}{x^{2}} + 1}} - \frac{\operatorname{asin}{\left(\frac{c}{x} \right)}}{2 c^{3}} & \text{otherwise} \end{cases}\right)}{2} - \frac{b \operatorname{asin}{\left(\frac{c}{x} \right)}}{2 x^{2}}"," ",0,"-a/(2*x**2) - b*c*Piecewise((I*sqrt(c**2/x**2 - 1)/(2*c**2*x) + I*acosh(c/x)/(2*c**3), Abs(c**2/x**2) > 1), (-1/(2*x**3*sqrt(-c**2/x**2 + 1)) + 1/(2*c**2*x*sqrt(-c**2/x**2 + 1)) - asin(c/x)/(2*c**3), True))/2 - b*asin(c/x)/(2*x**2)","A",0
377,1,112,0,2.809757," ","integrate((a+b*asin(c/x))/x**4,x)","- \frac{a}{3 x^{3}} - \frac{b c \left(\begin{cases} \frac{\sqrt{-1 + \frac{x^{2}}{c^{2}}}}{3 c x^{3}} + \frac{2 \sqrt{-1 + \frac{x^{2}}{c^{2}}}}{3 c^{3} x} & \text{for}\: \left|{\frac{x^{2}}{c^{2}}}\right| > 1 \\\frac{i \sqrt{1 - \frac{x^{2}}{c^{2}}}}{3 c x^{3}} + \frac{2 i \sqrt{1 - \frac{x^{2}}{c^{2}}}}{3 c^{3} x} & \text{otherwise} \end{cases}\right)}{3} - \frac{b \operatorname{asin}{\left(\frac{c}{x} \right)}}{3 x^{3}}"," ",0,"-a/(3*x**3) - b*c*Piecewise((sqrt(-1 + x**2/c**2)/(3*c*x**3) + 2*sqrt(-1 + x**2/c**2)/(3*c**3*x), Abs(x**2/c**2) > 1), (I*sqrt(1 - x**2/c**2)/(3*c*x**3) + 2*I*sqrt(1 - x**2/c**2)/(3*c**3*x), True))/3 - b*asin(c/x)/(3*x**3)","A",0
378,1,180,0,5.063419," ","integrate((a+b*asin(c/x))/x**5,x)","- \frac{a}{4 x^{4}} - \frac{b c \left(\begin{cases} \frac{i}{4 x^{5} \sqrt{\frac{c^{2}}{x^{2}} - 1}} + \frac{i}{8 c^{2} x^{3} \sqrt{\frac{c^{2}}{x^{2}} - 1}} - \frac{3 i}{8 c^{4} x \sqrt{\frac{c^{2}}{x^{2}} - 1}} + \frac{3 i \operatorname{acosh}{\left(\frac{c}{x} \right)}}{8 c^{5}} & \text{for}\: \left|{\frac{c^{2}}{x^{2}}}\right| > 1 \\- \frac{1}{4 x^{5} \sqrt{- \frac{c^{2}}{x^{2}} + 1}} - \frac{1}{8 c^{2} x^{3} \sqrt{- \frac{c^{2}}{x^{2}} + 1}} + \frac{3}{8 c^{4} x \sqrt{- \frac{c^{2}}{x^{2}} + 1}} - \frac{3 \operatorname{asin}{\left(\frac{c}{x} \right)}}{8 c^{5}} & \text{otherwise} \end{cases}\right)}{4} - \frac{b \operatorname{asin}{\left(\frac{c}{x} \right)}}{4 x^{4}}"," ",0,"-a/(4*x**4) - b*c*Piecewise((I/(4*x**5*sqrt(c**2/x**2 - 1)) + I/(8*c**2*x**3*sqrt(c**2/x**2 - 1)) - 3*I/(8*c**4*x*sqrt(c**2/x**2 - 1)) + 3*I*acosh(c/x)/(8*c**5), Abs(c**2/x**2) > 1), (-1/(4*x**5*sqrt(-c**2/x**2 + 1)) - 1/(8*c**2*x**3*sqrt(-c**2/x**2 + 1)) + 3/(8*c**4*x*sqrt(-c**2/x**2 + 1)) - 3*asin(c/x)/(8*c**5), True))/4 - b*asin(c/x)/(4*x**4)","A",0
379,0,0,0,0.000000," ","integrate(x**m*(a+b*asin(c*x**n)),x)","\int x^{m} \left(a + b \operatorname{asin}{\left(c x^{n} \right)}\right)\, dx"," ",0,"Integral(x**m*(a + b*asin(c*x**n)), x)","F",0
380,1,66,0,6.827221," ","integrate(x**2*(a+b*asin(c*x**n)),x)","\frac{a x^{3}}{3} + \frac{b x^{3} \operatorname{asin}{\left(c x^{n} \right)}}{3} + \frac{i b x^{3} \Gamma\left(\frac{3}{2 n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - \frac{3}{2 n} \\ 1 - \frac{3}{2 n} \end{matrix}\middle| {\frac{x^{- 2 n}}{c^{2}}} \right)}}{6 \Gamma\left(1 + \frac{3}{2 n}\right)}"," ",0,"a*x**3/3 + b*x**3*asin(c*x**n)/3 + I*b*x**3*gamma(3/(2*n))*hyper((1/2, -3/(2*n)), (1 - 3/(2*n),), x**(-2*n)/c**2)/(6*gamma(1 + 3/(2*n)))","C",0
381,1,60,0,3.710521," ","integrate(x*(a+b*asin(c*x**n)),x)","\frac{a x^{2}}{2} + \frac{b x^{2} \operatorname{asin}{\left(c x^{n} \right)}}{2} + \frac{i b x^{2} \Gamma\left(\frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - \frac{1}{n} \\ 1 - \frac{1}{n} \end{matrix}\middle| {\frac{x^{- 2 n}}{c^{2}}} \right)}}{4 \Gamma\left(1 + \frac{1}{n}\right)}"," ",0,"a*x**2/2 + b*x**2*asin(c*x**n)/2 + I*b*x**2*gamma(1/n)*hyper((1/2, -1/n), (1 - 1/n,), x**(-2*n)/c**2)/(4*gamma(1 + 1/n))","C",0
382,1,56,0,2.179934," ","integrate(a+b*asin(c*x**n),x)","a x + b \left(x \operatorname{asin}{\left(c x^{n} \right)} + \frac{i x \Gamma\left(\frac{1}{2 n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - \frac{1}{2 n} \\ 1 - \frac{1}{2 n} \end{matrix}\middle| {\frac{x^{- 2 n}}{c^{2}}} \right)}}{2 \Gamma\left(1 + \frac{1}{2 n}\right)}\right)"," ",0,"a*x + b*(x*asin(c*x**n) + I*x*gamma(1/(2*n))*hyper((1/2, -1/(2*n)), (1 - 1/(2*n),), x**(-2*n)/c**2)/(2*gamma(1 + 1/(2*n))))","C",0
383,0,0,0,0.000000," ","integrate((a+b*asin(c*x**n))/x,x)","\int \frac{a + b \operatorname{asin}{\left(c x^{n} \right)}}{x}\, dx"," ",0,"Integral((a + b*asin(c*x**n))/x, x)","F",0
384,1,60,0,3.906960," ","integrate((a+b*asin(c*x**n))/x**2,x)","- \frac{a}{x} - \frac{b \operatorname{asin}{\left(c x^{n} \right)}}{x} - \frac{i b \Gamma\left(- \frac{1}{2 n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{1}{2 n} \\ 1 + \frac{1}{2 n} \end{matrix}\middle| {\frac{x^{- 2 n}}{c^{2}}} \right)}}{2 x \Gamma\left(1 - \frac{1}{2 n}\right)}"," ",0,"-a/x - b*asin(c*x**n)/x - I*b*gamma(-1/(2*n))*hyper((1/2, 1/(2*n)), (1 + 1/(2*n),), x**(-2*n)/c**2)/(2*x*gamma(1 - 1/(2*n)))","C",0
385,1,61,0,7.603610," ","integrate((a+b*asin(c*x**n))/x**3,x)","- \frac{a}{2 x^{2}} - \frac{b \operatorname{asin}{\left(c x^{n} \right)}}{2 x^{2}} - \frac{i b \Gamma\left(- \frac{1}{n}\right) {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{1}{n} \\ 1 + \frac{1}{n} \end{matrix}\middle| {\frac{x^{- 2 n}}{c^{2}}} \right)}}{4 x^{2} \Gamma\left(1 - \frac{1}{n}\right)}"," ",0,"-a/(2*x**2) - b*asin(c*x**n)/(2*x**2) - I*b*gamma(-1/n)*hyper((1/2, 1/n), (1 + 1/n,), x**(-2*n)/c**2)/(4*x**2*gamma(1 - 1/n))","C",0
386,1,204,0,3.054083," ","integrate(x**5*(a+b*asin(d*x**2+c)),x)","\begin{cases} \frac{a x^{6}}{6} + \frac{b c^{3} \operatorname{asin}{\left(c + d x^{2} \right)}}{6 d^{3}} + \frac{11 b c^{2} \sqrt{- c^{2} - 2 c d x^{2} - d^{2} x^{4} + 1}}{36 d^{3}} - \frac{5 b c x^{2} \sqrt{- c^{2} - 2 c d x^{2} - d^{2} x^{4} + 1}}{36 d^{2}} + \frac{b c \operatorname{asin}{\left(c + d x^{2} \right)}}{4 d^{3}} + \frac{b x^{6} \operatorname{asin}{\left(c + d x^{2} \right)}}{6} + \frac{b x^{4} \sqrt{- c^{2} - 2 c d x^{2} - d^{2} x^{4} + 1}}{18 d} + \frac{b \sqrt{- c^{2} - 2 c d x^{2} - d^{2} x^{4} + 1}}{9 d^{3}} & \text{for}\: d \neq 0 \\\frac{x^{6} \left(a + b \operatorname{asin}{\left(c \right)}\right)}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**6/6 + b*c**3*asin(c + d*x**2)/(6*d**3) + 11*b*c**2*sqrt(-c**2 - 2*c*d*x**2 - d**2*x**4 + 1)/(36*d**3) - 5*b*c*x**2*sqrt(-c**2 - 2*c*d*x**2 - d**2*x**4 + 1)/(36*d**2) + b*c*asin(c + d*x**2)/(4*d**3) + b*x**6*asin(c + d*x**2)/6 + b*x**4*sqrt(-c**2 - 2*c*d*x**2 - d**2*x**4 + 1)/(18*d) + b*sqrt(-c**2 - 2*c*d*x**2 - d**2*x**4 + 1)/(9*d**3), Ne(d, 0)), (x**6*(a + b*asin(c))/6, True))","A",0
387,1,133,0,0.912898," ","integrate(x**3*(a+b*asin(d*x**2+c)),x)","\begin{cases} \frac{a x^{4}}{4} - \frac{b c^{2} \operatorname{asin}{\left(c + d x^{2} \right)}}{4 d^{2}} - \frac{3 b c \sqrt{- c^{2} - 2 c d x^{2} - d^{2} x^{4} + 1}}{8 d^{2}} + \frac{b x^{4} \operatorname{asin}{\left(c + d x^{2} \right)}}{4} + \frac{b x^{2} \sqrt{- c^{2} - 2 c d x^{2} - d^{2} x^{4} + 1}}{8 d} - \frac{b \operatorname{asin}{\left(c + d x^{2} \right)}}{8 d^{2}} & \text{for}\: d \neq 0 \\\frac{x^{4} \left(a + b \operatorname{asin}{\left(c \right)}\right)}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**4/4 - b*c**2*asin(c + d*x**2)/(4*d**2) - 3*b*c*sqrt(-c**2 - 2*c*d*x**2 - d**2*x**4 + 1)/(8*d**2) + b*x**4*asin(c + d*x**2)/4 + b*x**2*sqrt(-c**2 - 2*c*d*x**2 - d**2*x**4 + 1)/(8*d) - b*asin(c + d*x**2)/(8*d**2), Ne(d, 0)), (x**4*(a + b*asin(c))/4, True))","A",0
388,1,76,0,0.254139," ","integrate(x*(a+b*asin(d*x**2+c)),x)","\begin{cases} \frac{a x^{2}}{2} + \frac{b c \operatorname{asin}{\left(c + d x^{2} \right)}}{2 d} + \frac{b x^{2} \operatorname{asin}{\left(c + d x^{2} \right)}}{2} + \frac{b \sqrt{- c^{2} - 2 c d x^{2} - d^{2} x^{4} + 1}}{2 d} & \text{for}\: d \neq 0 \\\frac{x^{2} \left(a + b \operatorname{asin}{\left(c \right)}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x**2/2 + b*c*asin(c + d*x**2)/(2*d) + b*x**2*asin(c + d*x**2)/2 + b*sqrt(-c**2 - 2*c*d*x**2 - d**2*x**4 + 1)/(2*d), Ne(d, 0)), (x**2*(a + b*asin(c))/2, True))","A",0
389,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+c))/x,x)","\int \frac{a + b \operatorname{asin}{\left(c + d x^{2} \right)}}{x}\, dx"," ",0,"Integral((a + b*asin(c + d*x**2))/x, x)","F",0
390,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+c))/x**3,x)","\int \frac{a + b \operatorname{asin}{\left(c + d x^{2} \right)}}{x^{3}}\, dx"," ",0,"Integral((a + b*asin(c + d*x**2))/x**3, x)","F",0
391,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+c))/x**5,x)","\int \frac{a + b \operatorname{asin}{\left(c + d x^{2} \right)}}{x^{5}}\, dx"," ",0,"Integral((a + b*asin(c + d*x**2))/x**5, x)","F",0
392,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+c))/x**7,x)","\int \frac{a + b \operatorname{asin}{\left(c + d x^{2} \right)}}{x^{7}}\, dx"," ",0,"Integral((a + b*asin(c + d*x**2))/x**7, x)","F",0
393,0,0,0,0.000000," ","integrate(x**4*(a+b*asin(d*x**2+c)),x)","\int x^{4} \left(a + b \operatorname{asin}{\left(c + d x^{2} \right)}\right)\, dx"," ",0,"Integral(x**4*(a + b*asin(c + d*x**2)), x)","F",0
394,0,0,0,0.000000," ","integrate(x**2*(a+b*asin(d*x**2+c)),x)","\int x^{2} \left(a + b \operatorname{asin}{\left(c + d x^{2} \right)}\right)\, dx"," ",0,"Integral(x**2*(a + b*asin(c + d*x**2)), x)","F",0
395,0,0,0,0.000000," ","integrate(a+b*asin(d*x**2+c),x)","\int \left(a + b \operatorname{asin}{\left(c + d x^{2} \right)}\right)\, dx"," ",0,"Integral(a + b*asin(c + d*x**2), x)","F",0
396,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+c))/x**2,x)","\int \frac{a + b \operatorname{asin}{\left(c + d x^{2} \right)}}{x^{2}}\, dx"," ",0,"Integral((a + b*asin(c + d*x**2))/x**2, x)","F",0
397,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+c))/x**4,x)","\int \frac{a + b \operatorname{asin}{\left(c + d x^{2} \right)}}{x^{4}}\, dx"," ",0,"Integral((a + b*asin(c + d*x**2))/x**4, x)","F",0
398,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+c))/x**6,x)","\int \frac{a + b \operatorname{asin}{\left(c + d x^{2} \right)}}{x^{6}}\, dx"," ",0,"Integral((a + b*asin(c + d*x**2))/x**6, x)","F",0
399,1,61,0,0.753224," ","integrate(x**3*asin(b*x**4+a),x)","\begin{cases} \frac{a \operatorname{asin}{\left(a + b x^{4} \right)}}{4 b} + \frac{x^{4} \operatorname{asin}{\left(a + b x^{4} \right)}}{4} + \frac{\sqrt{- a^{2} - 2 a b x^{4} - b^{2} x^{8} + 1}}{4 b} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{asin}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*asin(a + b*x**4)/(4*b) + x**4*asin(a + b*x**4)/4 + sqrt(-a**2 - 2*a*b*x**4 - b**2*x**8 + 1)/(4*b), Ne(b, 0)), (x**4*asin(a)/4, True))","A",0
400,1,76,0,54.604238," ","integrate(x**(-1+n)*asin(a+b*x**n),x)","\begin{cases} \log{\left(x \right)} \operatorname{asin}{\left(a \right)} & \text{for}\: b = 0 \wedge n = 0 \\\log{\left(x \right)} \operatorname{asin}{\left(a + b \right)} & \text{for}\: n = 0 \\\frac{x^{n} \operatorname{asin}{\left(a \right)}}{n} & \text{for}\: b = 0 \\\frac{a \operatorname{asin}{\left(a + b x^{n} \right)}}{b n} + \frac{x^{n} \operatorname{asin}{\left(a + b x^{n} \right)}}{n} + \frac{\sqrt{- a^{2} - 2 a b x^{n} - b^{2} x^{2 n} + 1}}{b n} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(x)*asin(a), Eq(b, 0) & Eq(n, 0)), (log(x)*asin(a + b), Eq(n, 0)), (x**n*asin(a)/n, Eq(b, 0)), (a*asin(a + b*x**n)/(b*n) + x**n*asin(a + b*x**n)/n + sqrt(-a**2 - 2*a*b*x**n - b**2*x**(2*n) + 1)/(b*n), True))","A",0
401,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+1))**4,x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{4}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**4, x)","F",0
402,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+1))**3,x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**3, x)","F",0
403,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+1))**2,x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**2, x)","F",0
404,0,0,0,0.000000," ","integrate(a+b*asin(d*x**2+1),x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)\, dx"," ",0,"Integral(a + b*asin(d*x**2 + 1), x)","F",0
405,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2+1)),x)","\int \frac{1}{a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}}\, dx"," ",0,"Integral(1/(a + b*asin(d*x**2 + 1)), x)","F",0
406,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2+1))**2,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**(-2), x)","F",0
407,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2+1))**3,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**(-3), x)","F",0
408,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2-1))**4,x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{4}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**4, x)","F",0
409,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2-1))**3,x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**3, x)","F",0
410,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2-1))**2,x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**2, x)","F",0
411,0,0,0,0.000000," ","integrate(a+b*asin(d*x**2-1),x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)\, dx"," ",0,"Integral(a + b*asin(d*x**2 - 1), x)","F",0
412,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2-1)),x)","\int \frac{1}{a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}}\, dx"," ",0,"Integral(1/(a + b*asin(d*x**2 - 1)), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2-1))**2,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**(-2), x)","F",0
414,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2-1))**3,x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**(-3), x)","F",0
415,0,0,0,0.000000," ","integrate(asin(x**2+1)**2,x)","\int \operatorname{asin}^{2}{\left(x^{2} + 1 \right)}\, dx"," ",0,"Integral(asin(x**2 + 1)**2, x)","F",0
416,0,0,0,0.000000," ","integrate(asin(x**2-1)**2,x)","\int \operatorname{asin}^{2}{\left(x^{2} - 1 \right)}\, dx"," ",0,"Integral(asin(x**2 - 1)**2, x)","F",0
417,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+1))**(5/2),x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**(5/2), x)","F",0
418,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+1))**(3/2),x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**(3/2), x)","F",0
419,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2+1))**(1/2),x)","\int \sqrt{a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}}\, dx"," ",0,"Integral(sqrt(a + b*asin(d*x**2 + 1)), x)","F",0
420,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2+1))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*asin(d*x**2 + 1)), x)","F",0
421,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2+1))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**(-3/2), x)","F",0
422,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2+1))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**(-5/2), x)","F",0
423,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2+1))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} + 1 \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 + 1))**(-7/2), x)","F",0
424,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2-1))**(5/2),x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**(5/2), x)","F",0
425,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2-1))**(3/2),x)","\int \left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**(3/2), x)","F",0
426,0,0,0,0.000000," ","integrate((a+b*asin(d*x**2-1))**(1/2),x)","\int \sqrt{a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}}\, dx"," ",0,"Integral(sqrt(a + b*asin(d*x**2 - 1)), x)","F",0
427,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2-1))**(1/2),x)","\int \frac{1}{\sqrt{a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*asin(d*x**2 - 1)), x)","F",0
428,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2-1))**(3/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**(-3/2), x)","F",0
429,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2-1))**(5/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**(-5/2), x)","F",0
430,0,0,0,0.000000," ","integrate(1/(a+b*asin(d*x**2-1))**(7/2),x)","\int \frac{1}{\left(a + b \operatorname{asin}{\left(d x^{2} - 1 \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*asin(d*x**2 - 1))**(-7/2), x)","F",0
431,-1,0,0,0.000000," ","integrate((a+b*asin((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**n/(-c**2*x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate((a+b*asin((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**3/(-c**2*x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((a+b*asin((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**2/(-c**2*x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,-1,0,0,0.000000," ","integrate((a+b*asin((-c*x+1)**(1/2)/(c*x+1)**(1/2)))/(-c**2*x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate(1/(-c**2*x**2+1)/(a+b*asin((-c*x+1)**(1/2)/(c*x+1)**(1/2))),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate(1/(-c**2*x**2+1)/(a+b*asin((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,1,17,0,0.595404," ","integrate(exp(x)*asin(exp(x)),x)","\sqrt{1 - e^{2 x}} + e^{x} \operatorname{asin}{\left(e^{x} \right)}"," ",0,"sqrt(1 - exp(2*x)) + exp(x)*asin(exp(x))","A",0
438,0,0,0,0.000000," ","integrate(asin(c*exp(b*x+a)),x)","\int \operatorname{asin}{\left(c e^{a + b x} \right)}\, dx"," ",0,"Integral(asin(c*exp(a + b*x)), x)","F",0
439,1,100,0,2.927569," ","integrate(exp(asin(a*x))*x**3,x)","\begin{cases} \frac{4 x^{4} e^{\operatorname{asin}{\left(a x \right)}}}{17} + \frac{x^{3} \sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{17 a} - \frac{3 x^{2} e^{\operatorname{asin}{\left(a x \right)}}}{85 a^{2}} + \frac{6 x \sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{85 a^{3}} - \frac{6 e^{\operatorname{asin}{\left(a x \right)}}}{85 a^{4}} & \text{for}\: a \neq 0 \\\frac{x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*x**4*exp(asin(a*x))/17 + x**3*sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/(17*a) - 3*x**2*exp(asin(a*x))/(85*a**2) + 6*x*sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/(85*a**3) - 6*exp(asin(a*x))/(85*a**4), Ne(a, 0)), (x**4/4, True))","A",0
440,1,80,0,1.123178," ","integrate(exp(asin(a*x))*x**2,x)","\begin{cases} \frac{3 x^{3} e^{\operatorname{asin}{\left(a x \right)}}}{10} + \frac{x^{2} \sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{10 a} - \frac{x e^{\operatorname{asin}{\left(a x \right)}}}{10 a^{2}} + \frac{\sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{10 a^{3}} & \text{for}\: a \neq 0 \\\frac{x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x**3*exp(asin(a*x))/10 + x**2*sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/(10*a) - x*exp(asin(a*x))/(10*a**2) + sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/(10*a**3), Ne(a, 0)), (x**3/3, True))","A",0
441,1,53,0,0.393909," ","integrate(exp(asin(a*x))*x,x)","\begin{cases} \frac{2 x^{2} e^{\operatorname{asin}{\left(a x \right)}}}{5} + \frac{x \sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{5 a} - \frac{e^{\operatorname{asin}{\left(a x \right)}}}{5 a^{2}} & \text{for}\: a \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x**2*exp(asin(a*x))/5 + x*sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/(5*a) - exp(asin(a*x))/(5*a**2), Ne(a, 0)), (x**2/2, True))","A",0
442,1,32,0,0.163394," ","integrate(exp(asin(a*x)),x)","\begin{cases} \frac{x e^{\operatorname{asin}{\left(a x \right)}}}{2} + \frac{\sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{2 a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*exp(asin(a*x))/2 + sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/(2*a), Ne(a, 0)), (x, True))","A",0
443,0,0,0,0.000000," ","integrate(exp(asin(a*x))/x,x)","\int \frac{e^{\operatorname{asin}{\left(a x \right)}}}{x}\, dx"," ",0,"Integral(exp(asin(a*x))/x, x)","F",0
444,0,0,0,0.000000," ","integrate(exp(asin(a*x))/x**2,x)","\int \frac{e^{\operatorname{asin}{\left(a x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(asin(a*x))/x**2, x)","F",0
445,0,0,0,0.000000," ","integrate(exp(asin(a*x)**2)*x**3,x)","\int x^{3} e^{\operatorname{asin}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**3*exp(asin(a*x)**2), x)","F",0
446,0,0,0,0.000000," ","integrate(exp(asin(a*x)**2)*x**2,x)","\int x^{2} e^{\operatorname{asin}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x**2*exp(asin(a*x)**2), x)","F",0
447,0,0,0,0.000000," ","integrate(exp(asin(a*x)**2)*x,x)","\int x e^{\operatorname{asin}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(x*exp(asin(a*x)**2), x)","F",0
448,0,0,0,0.000000," ","integrate(exp(asin(a*x)**2),x)","\int e^{\operatorname{asin}^{2}{\left(a x \right)}}\, dx"," ",0,"Integral(exp(asin(a*x)**2), x)","F",0
449,0,0,0,0.000000," ","integrate(exp(asin(a*x)**2)/x,x)","\int \frac{e^{\operatorname{asin}^{2}{\left(a x \right)}}}{x}\, dx"," ",0,"Integral(exp(asin(a*x)**2)/x, x)","F",0
450,0,0,0,0.000000," ","integrate(exp(asin(a*x)**2)/x**2,x)","\int \frac{e^{\operatorname{asin}^{2}{\left(a x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(asin(a*x)**2)/x**2, x)","F",0
451,1,416,0,3.805551," ","integrate(exp(asin(b*x+a))*x**3,x)","\begin{cases} \frac{3 a^{4} e^{\operatorname{asin}{\left(a + b x \right)}}}{85 b^{4}} + \frac{12 a^{3} x e^{\operatorname{asin}{\left(a + b x \right)}}}{85 b^{3}} - \frac{12 a^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{85 b^{4}} - \frac{3 a^{2} x^{2} e^{\operatorname{asin}{\left(a + b x \right)}}}{34 b^{2}} + \frac{3 a^{2} x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{17 b^{3}} - \frac{57 a^{2} e^{\operatorname{asin}{\left(a + b x \right)}}}{170 b^{4}} + \frac{7 a x^{3} e^{\operatorname{asin}{\left(a + b x \right)}}}{170 b} - \frac{21 a x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{170 b^{2}} + \frac{39 a x e^{\operatorname{asin}{\left(a + b x \right)}}}{170 b^{3}} - \frac{39 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{170 b^{4}} + \frac{4 x^{4} e^{\operatorname{asin}{\left(a + b x \right)}}}{17} + \frac{x^{3} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{17 b} - \frac{3 x^{2} e^{\operatorname{asin}{\left(a + b x \right)}}}{85 b^{2}} + \frac{6 x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{85 b^{3}} - \frac{6 e^{\operatorname{asin}{\left(a + b x \right)}}}{85 b^{4}} & \text{for}\: b \neq 0 \\\frac{x^{4} e^{\operatorname{asin}{\left(a \right)}}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*exp(asin(a + b*x))/(85*b**4) + 12*a**3*x*exp(asin(a + b*x))/(85*b**3) - 12*a**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(85*b**4) - 3*a**2*x**2*exp(asin(a + b*x))/(34*b**2) + 3*a**2*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(17*b**3) - 57*a**2*exp(asin(a + b*x))/(170*b**4) + 7*a*x**3*exp(asin(a + b*x))/(170*b) - 21*a*x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(170*b**2) + 39*a*x*exp(asin(a + b*x))/(170*b**3) - 39*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(170*b**4) + 4*x**4*exp(asin(a + b*x))/17 + x**3*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(17*b) - 3*x**2*exp(asin(a + b*x))/(85*b**2) + 6*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(85*b**3) - 6*exp(asin(a + b*x))/(85*b**4), Ne(b, 0)), (x**4*exp(asin(a))/4, True))","A",0
452,1,243,0,1.527932," ","integrate(exp(asin(b*x+a))*x**2,x)","\begin{cases} - \frac{a^{2} x e^{\operatorname{asin}{\left(a + b x \right)}}}{5 b^{2}} + \frac{a^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{5 b^{3}} + \frac{a x^{2} e^{\operatorname{asin}{\left(a + b x \right)}}}{10 b} - \frac{a x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{5 b^{2}} + \frac{3 a e^{\operatorname{asin}{\left(a + b x \right)}}}{10 b^{3}} + \frac{3 x^{3} e^{\operatorname{asin}{\left(a + b x \right)}}}{10} + \frac{x^{2} \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{10 b} - \frac{x e^{\operatorname{asin}{\left(a + b x \right)}}}{10 b^{2}} + \frac{\sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{10 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} e^{\operatorname{asin}{\left(a \right)}}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x*exp(asin(a + b*x))/(5*b**2) + a**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(5*b**3) + a*x**2*exp(asin(a + b*x))/(10*b) - a*x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(5*b**2) + 3*a*exp(asin(a + b*x))/(10*b**3) + 3*x**3*exp(asin(a + b*x))/10 + x**2*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(10*b) - x*exp(asin(a + b*x))/(10*b**2) + sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(10*b**3), Ne(b, 0)), (x**3*exp(asin(a))/3, True))","A",0
453,1,146,0,0.504686," ","integrate(exp(asin(b*x+a))*x,x)","\begin{cases} - \frac{a^{2} e^{\operatorname{asin}{\left(a + b x \right)}}}{10 b^{2}} + \frac{3 a x e^{\operatorname{asin}{\left(a + b x \right)}}}{10 b} - \frac{3 a \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{10 b^{2}} + \frac{2 x^{2} e^{\operatorname{asin}{\left(a + b x \right)}}}{5} + \frac{x \sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{5 b} - \frac{e^{\operatorname{asin}{\left(a + b x \right)}}}{5 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} e^{\operatorname{asin}{\left(a \right)}}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*exp(asin(a + b*x))/(10*b**2) + 3*a*x*exp(asin(a + b*x))/(10*b) - 3*a*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(10*b**2) + 2*x**2*exp(asin(a + b*x))/5 + x*sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(5*b) - exp(asin(a + b*x))/(5*b**2), Ne(b, 0)), (x**2*exp(asin(a))/2, True))","A",0
454,1,65,0,0.198988," ","integrate(exp(asin(b*x+a)),x)","\begin{cases} \frac{a e^{\operatorname{asin}{\left(a + b x \right)}}}{2 b} + \frac{x e^{\operatorname{asin}{\left(a + b x \right)}}}{2} + \frac{\sqrt{- a^{2} - 2 a b x - b^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a + b x \right)}}}{2 b} & \text{for}\: b \neq 0 \\x e^{\operatorname{asin}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*exp(asin(a + b*x))/(2*b) + x*exp(asin(a + b*x))/2 + sqrt(-a**2 - 2*a*b*x - b**2*x**2 + 1)*exp(asin(a + b*x))/(2*b), Ne(b, 0)), (x*exp(asin(a)), True))","A",0
455,0,0,0,0.000000," ","integrate(exp(asin(b*x+a))/x,x)","\int \frac{e^{\operatorname{asin}{\left(a + b x \right)}}}{x}\, dx"," ",0,"Integral(exp(asin(a + b*x))/x, x)","F",0
456,0,0,0,0.000000," ","integrate(exp(asin(b*x+a))/x**2,x)","\int \frac{e^{\operatorname{asin}{\left(a + b x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(asin(a + b*x))/x**2, x)","F",0
457,0,0,0,0.000000," ","integrate(exp(asin(b*x+a)**2)*x**3,x)","\int x^{3} e^{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**3*exp(asin(a + b*x)**2), x)","F",0
458,0,0,0,0.000000," ","integrate(exp(asin(b*x+a)**2)*x**2,x)","\int x^{2} e^{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x**2*exp(asin(a + b*x)**2), x)","F",0
459,0,0,0,0.000000," ","integrate(exp(asin(b*x+a)**2)*x,x)","\int x e^{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(x*exp(asin(a + b*x)**2), x)","F",0
460,0,0,0,0.000000," ","integrate(exp(asin(b*x+a)**2),x)","\int e^{\operatorname{asin}^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(exp(asin(a + b*x)**2), x)","F",0
461,0,0,0,0.000000," ","integrate(exp(asin(b*x+a)**2)/x,x)","\int \frac{e^{\operatorname{asin}^{2}{\left(a + b x \right)}}}{x}\, dx"," ",0,"Integral(exp(asin(a + b*x)**2)/x, x)","F",0
462,0,0,0,0.000000," ","integrate(exp(asin(b*x+a)**2)/x**2,x)","\int \frac{e^{\operatorname{asin}^{2}{\left(a + b x \right)}}}{x^{2}}\, dx"," ",0,"Integral(exp(asin(a + b*x)**2)/x**2, x)","F",0
463,-1,0,0,0.000000," ","integrate(exp(asin(a*x))*(-a**2*x**2+1)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,1,95,0,15.840199," ","integrate(exp(asin(a*x))*(-a**2*x**2+1)**(3/2),x)","\begin{cases} \frac{a^{3} x^{4} e^{\operatorname{asin}{\left(a x \right)}}}{17} - \frac{4 a^{2} x^{3} \sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{17} - \frac{22 a x^{2} e^{\operatorname{asin}{\left(a x \right)}}}{85} + \frac{44 x \sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{85} + \frac{41 e^{\operatorname{asin}{\left(a x \right)}}}{85 a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x**4*exp(asin(a*x))/17 - 4*a**2*x**3*sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/17 - 22*a*x**2*exp(asin(a*x))/85 + 44*x*sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/85 + 41*exp(asin(a*x))/(85*a), Ne(a, 0)), (x, True))","A",0
465,1,49,0,0.378557," ","integrate(exp(asin(a*x))*(-a**2*x**2+1)**(1/2),x)","\begin{cases} - \frac{a x^{2} e^{\operatorname{asin}{\left(a x \right)}}}{5} + \frac{2 x \sqrt{- a^{2} x^{2} + 1} e^{\operatorname{asin}{\left(a x \right)}}}{5} + \frac{3 e^{\operatorname{asin}{\left(a x \right)}}}{5 a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*x**2*exp(asin(a*x))/5 + 2*x*sqrt(-a**2*x**2 + 1)*exp(asin(a*x))/5 + 3*exp(asin(a*x))/(5*a), Ne(a, 0)), (x, True))","A",0
466,1,8,0,0.352876," ","integrate(exp(asin(a*x))/(-a**2*x**2+1)**(1/2),x)","\begin{cases} \frac{e^{\operatorname{asin}{\left(a x \right)}}}{a} & \text{for}\: a \neq 0 \\x & \text{otherwise} \end{cases}"," ",0,"Piecewise((exp(asin(a*x))/a, Ne(a, 0)), (x, True))","A",0
467,0,0,0,0.000000," ","integrate(exp(asin(a*x))/(-a**2*x**2+1)**(3/2),x)","\int \frac{e^{\operatorname{asin}{\left(a x \right)}}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(exp(asin(a*x))/(-(a*x - 1)*(a*x + 1))**(3/2), x)","F",0
468,0,0,0,0.000000," ","integrate(exp(asin(a*x))/(-a**2*x**2+1)**(5/2),x)","\int \frac{e^{\operatorname{asin}{\left(a x \right)}}}{\left(- \left(a x - 1\right) \left(a x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(exp(asin(a*x))/(-(a*x - 1)*(a*x + 1))**(5/2), x)","F",0
469,0,0,0,0.000000," ","integrate(asin(c/(b*x+a)),x)","\int \operatorname{asin}{\left(\frac{c}{a + b x} \right)}\, dx"," ",0,"Integral(asin(c/(a + b*x)), x)","F",0
470,0,0,0,0.000000," ","integrate(x/asin(sin(x)),x)","\int \frac{x}{\operatorname{asin}{\left(\sin{\left(x \right)} \right)}}\, dx"," ",0,"Integral(x/asin(sin(x)), x)","F",0
471,0,0,0,0.000000," ","integrate(asin((b*x**2+1)**(1/2))**n/(b*x**2+1)**(1/2),x)","\begin{cases} \frac{2 x}{\pi} & \text{for}\: b = 0 \wedge n = -1 \\x \left(\frac{\pi}{2}\right)^{n} & \text{for}\: b = 0 \\\int \frac{1}{\sqrt{b x^{2} + 1} \operatorname{asin}{\left(\sqrt{b x^{2} + 1} \right)}}\, dx & \text{for}\: n = -1 \\\frac{i \sqrt{b} \sqrt{x^{2}} \operatorname{asin}{\left(\sqrt{b x^{2} + 1} \right)} \operatorname{asin}^{n}{\left(\sqrt{b x^{2} + 1} \right)}}{b n x + b x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*x/pi, Eq(b, 0) & Eq(n, -1)), (x*(pi/2)**n, Eq(b, 0)), (Integral(1/(sqrt(b*x**2 + 1)*asin(sqrt(b*x**2 + 1))), x), Eq(n, -1)), (I*sqrt(b)*sqrt(x**2)*asin(sqrt(b*x**2 + 1))*asin(sqrt(b*x**2 + 1))**n/(b*n*x + b*x), True))","F",0
472,0,0,0,0.000000," ","integrate(1/asin((b*x**2+1)**(1/2))/(b*x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{b x^{2} + 1} \operatorname{asin}{\left(\sqrt{b x^{2} + 1} \right)}}\, dx"," ",0,"Integral(1/(sqrt(b*x**2 + 1)*asin(sqrt(b*x**2 + 1))), x)","F",0
473,1,12,0,0.173904," ","integrate(x/(-x**2+1)+1/asin(x)/(-x**2+1)**(1/2),x)","- \frac{\log{\left(x^{2} - 1 \right)}}{2} + \log{\left(\operatorname{asin}{\left(x \right)} \right)}"," ",0,"-log(x**2 - 1)/2 + log(asin(x))","A",0
474,1,14,0,4.367282," ","integrate((x*asin(x)+(-x**2+1)**(1/2))/(asin(x)-x**2*asin(x)),x)","- \frac{\log{\left(2 x^{2} - 2 \right)}}{2} + \log{\left(\operatorname{asin}{\left(x \right)} \right)}"," ",0,"-log(2*x**2 - 2)/2 + log(asin(x))","A",0
